University of Nevada, Reno
ATOM DYNAMICS OF AMORPHOUS MATERIALS BY X-RAY PHOTON CORRELATION SPECTROSCOPY (XPCS) & NEUTRON SPECTROSCOPY
A Dissertation Submitted in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy in Materials Science and Engineering
By
Suchismita Sarker
Dr. Dhanesh Chandra, Dissertation Advisor
August 2017
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ABSTRACT
The mitigation of greenhouse gas emissions on the environment led to the development of non-polluting hydrogen fuel cell use in automobiles. Syngas produced from coal gasification is converted to H2 and CO2 gasses by the water shift reaction. Metallic membranes are used to separate H2 from CO2 and other gasses obtained from the water shift reaction of coal-derived syngas. Commercial crystalline Pd-Ag membranes are widely used for this purpose; however, Pd is an expensive strategic metal. Thus, inexpensive Ni-
Nb-Zr alloys are studied. The permeation property of amorphous membranes are known, however, the mechanism of permeation and the nature of the local atomic order of the amorphous membranes was not fully understood.
In this study, atom dynamics studied by synchrotron x-ray photon correlation spectroscopy
(XPCS) showed the movement of heavier elements such as Ni, Nb, and Zr, at room temperature and 373K. The addition of hydrogen significantly accentuates the motion of atoms as the hydrogen occupies the tetrahedral sites within the icosahedra leading to expansion and short-range diffusion, and no long-range diffusion is observed estimated to be ~10-22 m2/s. Vacuum removal of hydrogen from these membranes showed a contraction of the icosahedra and approached to its original position. This suggests that the process reversible due to the pressure gradient. The XPCS results did not reveal the specific position of hydrogen atoms in the icosahedra; hydrogen goes into the tetrahedral sites of
Zr4 and distorted Nb4 sites as determined by neutron vibrational spectroscopy. Total neutron scattering and DFT-MD simulation determine the short-range order of up to 1.8 nm and the nearest neighbor bond distances. Determination of cluster formation was first ii attempted by using small neutron scattering, but it did not have appropriate “Q” range.
Thus atom probe tomography (APT) was attempted. This APT study revealed Nb-rich and
Zr-rich clusters embedded in Ni-rich matrix, whose compositions are reported. DFT-MD simulation reveals interconnected icosahedra in the metal matrix. The atom dynamics
(NVS and XPCS), atom probe tomography, total neutron scattering studies are discussed which have implication in the mechanisms of hydrogen permeation in amorphous metallic membranes.
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To my loving husband & family
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Acknowledgement
I hereby would like to express my gratitude to those people who supported me on the way to the completion of this Ph.D. work, which is a truly life-changing experience for me. First and foremost, I would like to thank my advisor, Prof. Dhanesh Chandra, for his inspiring advice and ideas throughout my research work. Ever since, Dr. Chandra has supported me not only by providing a research assistantship, but also constant encouragement. Thanks to him, I had the opportunity to work with several national laboratories. It would not have been possible for me to complete this thesis without his support. I would also like to thank
Dr. Yanyao Jiang, Dr. Bin Li, Dr. Wen-Ming Chien, and Dr. Jaak Daemen as my advisory committee members for sparing their precious time and suggestions towards finalizing dissertation. I will be forever thankful to Dr. Beatrice Ruta, at European
Synchrotron Radiation Facility for her guidance in x-ray photon correlation spectroscopy work and Dr. Terrence J. Udovic for his immense support for neutron work. I am also indebted to Dr. Maddury Somayazulu, Dr. Dieter Isheim and Dr. Graham King for high pressure, atom tomography and neutron work. I would also like to thank Dr. Qi An and S. I. Morozov for DFT-MD simulation work. I would like to give my special thanks to my friends Madhura for giving me a pleasant and memorable time at school.
Finally, I want to express thanks to my parents, in-laws and family. Their unconditional love and support has been all these years throughout my study, specially, my best friend and husband Unmagna for always believing in me and encouraging me. I would not have made it this far without him. His love and limitless emotional support helped me make my way to success. v
TABLE OF CONTENTS
ABSTRACT ...... i Acknowledgement ...... iv List of Table ...... vii List of Figure...... viii 1 Introduction ...... 1 1.1 Organization of the Thesis ...... 4 1.2 Amorphous material for Hydrogen permeability ...... 6 1.3 Development of Ni-based membranes for Hydrogen permeation ...... 7 1.4 Metallic glasses ...... 10 1.5 Glass transition ...... 11 2 Dynamical X-ray Studies of Disordered Materials: X-ray Photon Correlation Spectroscopy (XPCS) ...... 18 2.1 Synchrotron Technique ...... 23 2.2 Theory of XPCS ...... 30 2.3 Historical Perspective of XPCS ...... 37 2.4 Experimental Details ...... 48 2.5 Results and Discussions ...... 49 2.5.1 XPCS Results ...... 49 2.5.2 Extended X-ray Absorption Spectroscopy Results ...... 62 3 Neutron Characterization Studies of Disordered Materials ...... 68 3.1 Introduction to Neutron scattering studies ...... 68 3.2 Inelastic neutron scattering Studies ...... 76 3.3 Neutron Vibrational Spectroscopy ...... 79 3.3.1 Theory ...... 79 3.3.2 Experimental Details ...... 99 3.3.3 NVS Result and Discussions ...... 103 3.4 Neutron Total Scattering experiment (HIPD) ...... 131 3.4.1 Theory of Total Neutron Scattering ...... 131 3.4.2 Result and Discussions ...... 134 vi
3.5 Small angle neutron scattering (SANS) ...... 137 3.5.1 Brief Theory ...... 138 3.5.2 Result and Discussions ...... 143 4 Atom Probe Tomography ...... 145 4.1 Introduction: ...... 145 4.2 Theory ...... 148 4.3 Experimental details ...... 152 4.3.1 Sample preparation by Focused Ion Beam ...... 152 4.3.2 Local Electrode Atom Probe (LEAP) ...... 154 4.4 Results and Discussions ...... 156 5 High-Pressure Studies on Disordered Materials: Diamond Anvil Cell (DAC) ...... 173 5.1 Introduction ...... 173 5.2 Diamond Anvil Cell and Raman Spectroscopy...... 173 5.3 Experimental Details ...... 177 5.4 Result and Discussions ...... 179 6 Summary & Future Study ...... 187 7 References ...... 192
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List of Table
Table 3.1. Neutron properties ...... 69 Table 3.2. Comparison of cross section (barns) for 1 Å neutrons ...... 78 Table 3.3. Advantages and Disadvantages of Neutron vibrational spectra ...... 78 Table 3.4. Different types of inelastic neutron vibrational spectroscopy ...... 90 Table 3.5. NVS spectrum range ...... 93 Table 3.6. Energy range of different zirconium phases ...... 112 Table 3.7. Comparison of optical vibrational peaks ...... 129 Table 3.8. Interatomic distance between atoms ...... 137 Table 4.1 Periodic Table of isotopes for mass spectroscopy ...... 158 Table 4.2. Composition of clusters in amorphous materials ...... 165 Table 4.3. Different composition of icosahedra………………………………………..166
Table 5.1. Roton and vibron peak ...... 180
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List of Figure
Figure 1.1 Coal gasification based energy conversion ...... 2 Figure 1.2 Hydrogen separation using amorphous membrane taken from ...... 8 Figure 1.3 Hydrogen permeability values for Ni-based amorphous alloy ...... 9 Figure 1.4 Glass Transition ...... 12 Figure 1.5 Density auto-correlation function ...... 15 Figure 1.6 Potential energy landscape ...... 17 Figure 2.1 Comparison of dynamic techniques ...... 19 Figure 2.2 Spakle formation...... 21 Figure 2.3 Schematic diagram of Synchrotron X-ray source ...... 23 Figure 2.4 Longitudinal coherence length ...... 25 Figure 2.5 Transverse coherence length ...... 26 Figure 2.6 Beamline ID10 set up at ESRF ...... 29 Figure 2.7 First measurement of Two-time correlation function ...... 41
Figure 2.8 Dynamic behavior of the Mg65Cu25Y10 ...... 44 Figure 2.9 Comparison of relaxation time and viscosity of metallic glass ...... 46 Figure 2.10 Comparison of dynamic and stationary aging with volume ...... 47
Figure 2.11 Hydrogen permeability of (Ni0.6Nb0.4)100-xZrx (x = 0, 30 at. %) alloys...... 49
Figure 2.12 Structural measurement on Ni60Nb40 by CCD camera ...... 50
Figure 2.13 (a) Intensity correlation function of Ni60Nb40 at 373 K under vacuum and (b)
1 bar H2 ...... 51
Figure 2.14 Reversible Intensity correlation function of Ni60Nb40...... 53 Figure 2.15 Evolution of the structural relaxation time during hydrogenation and
dehydrogenation in Ni60Nb4 ...... 53
Figure 2.16 Normalized auto correlation function for Ni60Nb40 ...... 55 Figure 2.17 Two-time correlation function at 273 and 373 K vacuum and hydrogen ..... 58 Figure 2.18. Intensity correlation function at room temperature and 373K on vacuum and hydrogen ...... 59 ix
Figure 2.19. Relaxation vs annealing time both in vacuum and hydrogenated condition ...... 60 Figure 2.20 Hydrogenation and dehydrogenation of Icosahedra structure...... 61 Figure 2.21 Nb K edge and Zr K edge k3-weighted EXAFS oscillations ...... 63 Figure 2.22 Zr K edge and Nb K edge k3-weighted EXAFS oscillations vacuum and Hydrogenated condition at 300oC ...... 64 Figure 2.23 Zr K edge and Nb K edge k3-weighted EXAFS oscillations vacuum and hydrogenated condition at 400oC ...... 66 Figure 2.24 Zr K edge k3-weighted EXAFS oscillations in vacuum and hydrogenated condition at room temperature in vacuum and hydrogen ...... 66 Figure 2.25 Nb K edge k3-weighted EXAFS oscillations in hydrogenated condition and at room temperature in vacuum and hydrogen ...... 67 Figure 3.1 Neutrons beam, x rays, and electrons interact with material...... 70 Figure 3.2 Generation of neutron ...... 73 Figure 3.3 Schematic diagram of Transmission measurement ...... 74 Figure 3.4 Schematic diagram of diffractometer ...... 74 Figure 3.5 Schematic diagram of quasi/inelastic scattering ...... 75 Figure 3.6 Schematic diagram of neutron spin echo ...... 76 Figure 3.7 Inelastic neutron scattering spectrum ...... 77 Figure 3.8 Neutron beam single scattering ...... 80 Figure 3.9 Potential of hydrogen in disordered system ...... 84 Figure 3.10 Potential trace for hydrogen in amorphous material ...... 85 Figure 3.11 Potential/position curves and corresponding distribution of site energies for hydrogen in sigle crystal and amorphous material ...... 86 Figure 3.12 Transverse optical and transverse acoustical waves ...... 88 Figure 3.13 The principle of Filter-analyzer neutron instrument...... 90 Figure 3.14 Schematic diagram of Filter Analyzer Neutron Spectroscopy instrument ... 91 Figure 3.15 Filters and detector of FANS instrument ...... 95 Figure 3.16 Q-range and estimated flux at sample position ...... 96 Figure 3.17 Upgraded of Filter Analyzer Neutron Spectroscopy instrument ...... 97 x
Figure 3.18 Comparison of total cross section of beryllium and graphite crystal ...... 99 Figure 3.19 Aluminium sample holder pan ...... 100 Figure 3.20 Filter-Analyzer Neutron Spectrometer (FANS) at NCNR ...... 101 Figure 3.21 Sample holder and Closed circle Refrigerator ...... 102
Figure 3.22 Sieverts results of Pd and ternary alloy (Ni0.6Nb0.4)80Zr20 ...... 103
Figure 3.23 Pressure-composition isotherms of (Ni0.6Nb0.4)100-xZrx (x=0-50 at %) ...... 104
Figure 3.24 NVS data for amorphous alloys and Crystalline ZrH2...... 107
Figure 3.25 NVS data of amorphous (Ni0.60Nb0.40)80Zr20Hy (y= 0.015-0.55) ...... 114 Figure 3.26 Compasion of NVS data with crystalline ε NbHx and ZrNiHx ...... 118 Figure 3.27 Schematic diagram of Radial Distribution Function ...... 131
Figure 3.28 Pair distribution function of (Ni0.60Nb0.40)70Zr30...... 134 Figure 3.29. DMT-MD simulation for Radial Distribution Function (RDF)...... 140 Figure 3.30. Schematic diagram of Small angle neutron scattering ...... 140 Figure 3.31. Principle of small angle neutron scattering ...... 141 Figure 3.32 Sample holder for SANS experiment ...... 142 Figure 3.33 Small angle neutron scattering data of all the amorphous and crystallized
(Ni0.6Nb0.4)80Zr20 (x=0-20) ...... 144 Figure 4.1 The detection range vs resolvable features of microscope ...... 146 Figure 4.2 History of development of Local electrode atom tomography ...... 147 Figure 4.3 Schematic diagram of Local electrode atom probe (LEAP)...... 148 Figure 4.4 Schematic diagram of delay-line detector ...... 149 Figure 4.5 Electron field evaporation escape mechanism...... 150 Figure 4.6. Focused Ion Beam apparatus (FIB) at Northwestern University ...... 152 Figure 4.7 Sample preparation inside Focused Ion Beam apparatus (FIB) ...... 153 Figure 4.8 LEAP (local electrode atom probe) instrument...... 155 Figure 4.9 Mass spectra data of amorphous sample by APT ...... 157 Figure 4.10 Schematic diagram of Field line and detector ...... 160
Figure 4.11. Atom probe 3D reconstruction of a portion of the (Ni0.60Nb0.40)70Zr30) .... 161
Figure 4.12 Dtailed Atom probe 3D reconstruction of a portion of the (Ni0.60Nb0.40)70Zr30 ...... 162 xi
Figure 4.13 APT 3D-construction and proximity diagram on Ni42Nb28Zr30 alloy ...... 163 Figure 4.14 Results of cluster formation in Ni-Nb-Zr by APT ...... 166 Figure 4.15 DFT-MD calculation………………………………………………………167 Figure 4.16 Bright field TEM image of bulk metallic NI-Nb-Zr glass and the composition ...... 171 Figure 5.1 Diamond Anvil cell ...... 174 Figure 5.2 Schematic diagram of Raman scattering ...... 176 Figure 5.3 Diamond anvil cell and sample setup ...... 178 Figure 5.4 In-situ Raman spectroscopy for high pressure using diamond anvil cell at Carnegie Institute of Washington...... 178
Figure 5.5 Raman spectra of (Ni0.6Nb0.4)70Zr30 and Ni60Nb40 with H2 loading at different pressures ...... 179 Figure 5.6 Roton and Vibron peaks of hydrogen in binary alloy ...... 180 Figure 5.7 Raman results from the mechanically milled and FIB samples...... 181 Figure 5.8 Schematic of the Diamond Anvil Cell setup with the hydrogen diffusion. .. 182 Figure 5.9 Schematic representation of DAC experimental set up with Kbr ...... 183 Figure 5.10 Schematic representation of DAC experimental set up with water ...... 184 Figure 5.11 Raman spectra of the ribbon sample with hydrogen and water ...... 185 Figure 5.12 Synchrotron x-ray diffraction ...... 186 Figure 6.1 Result summary of the dissertation...... 187
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Chapter 1 Introduction Contents
1.1 Organization of the Thesis……………………………………………………..4 1.2 Amorphous material for Hydrogen permeability…………………………...….6 1.3 Development of Ni-based membranes for Hydrogen permeation……...... 7 1.4 Metallic Glasses ……...……………………………………………………...10 1.5 Glass Transition ...……………………………………………………………11
1 Introduction
The demand for hydrogen is increasing due to new developments in the use of fuel cells in automobiles and other vehicular applications; for example, recently, Toyota car company has made commitments to use hydrogen fuel cells for their automobiles and to bring hydrogen economy a reality in the twenty-first century of having nearly pollution free vehicles [1]. Hydrogen produced at a lower price is essential on a sustainable basis.
Countries like USA, Australia, and others have substantial coal reserves that can last for hundreds of years and potentially supply coal at a very inexpensive cost for use to produce hydrogen by coal gasification. Around ~37 percent, electric power generate by fossil fuel power plants. Significant advances have been made in coal gasification technologies [2-7] for producing hydrogen and clean electricity generation. The bulk of global H2 production i.e. ~ 95 percent of the hydrogen used in the United States still originated from the conversion of hydrocarbon fuels such as coal, crude oil, natural gas and biomass. The co- 2
production of CO2 necessitates a H2/CO2 separation process to deliver H2 of the desired purity to downstream processes [1].
In this coal gasification technology, carbon-based feedstock such as coal, petroleum, coke, and biomass, etc. have been gasified by a partial oxidation process in the presence of steam and oxygen at higher temperature ~1200oC and moderate pressure [8]. In this process, the oil, phenol and other hydrocarbon gasses are converted to produce mainly CH4 gas and use
the water-shift reaction to produce "syngas." Syngas is primarily combination of H2 and
CO2 [8-12]. The coal gasification system is shown in the Figure 1.1. The role of the
Figure 1.1 Coal gasification based energy conversion [8] membrane is to separate H2 from CO2 and other entrained gasses and obtain ultra-pure hydrogen. Pressure swing adsorption (PSA) is a reliable, established technique for this 3 separation, however, it is less than ideal from an efficiency and size perspective. Alloy membranes offer the advantage of compact size and continuous separation but are currently limited to small-scale, niche applications. For example, crystalline Pd and Pd-Ag (100 –
200 m thickness) membranes have been employed for several decades to obtain ultrapure
H2 [3-9]. However, there are some restrictions to use thin (30-~50 m) amorphous membranes for separation of H2 in coal gasification system, as dynamic changes take place continuously in the solid membranes. These membranes are also potential for hydride formation under certain operating conditions, and can lead to eventual failure of the membranes by increasing brittleness. The greatest barrier to further deployment of Pd membrane technology is the high price of Pd metal, in recent times the cost of Pd has risen from USD 160 oz-1 in April 2003 to USD 697 oz-1 in September 2015. This cost is driving the development of less-expensive alternative membrane materials. Steward’s review of hydrogen permeability [11] showed several metals have equivalent or greater permeability than Pd. Furthermore, many of these metals, such as Ni, Co, Nb, and Zr cost in the range of USD 1-3 oz-1, making them of great interest as potential Pd-alternatives.
In particular, amorphous alloys formed from a combination of Ni and one or more early transition metals (ETMs) show a promising candidate for coal-gasification technology
[12]. These alloy membranes are developed directly from the molten state by melt spinning, in which the molten alloy is rapidly solidified on the surface of a rolling copper wheel, cooling rates as fast as 106 K s-1 can be achieved by this method. The ribbon thickness is typically 20 to 60 m, and 25 mm wide. One of the main barriers to the use of amorphous membranes is that long-term elevated temperature causes crystallization. In general, atomic density of amorphous alloy is lower than its crystalline form. Amorphous materials 4 propensity towards crystalline state causes an increase in atomic density. These leads toward a reduction in hydrogen diffusion pathways and eventually decrease hydrogen permeation. These crystallizations often cause brittleness in the ribbon. Thus, it is required to understand the fundamental properties.
1.1 Organization of the Thesis
Nickel based amorphous alloy membranes have permeability comparable to the Pd-based crystalline membranes, which is commercially used to separate hydrogen in coal gasification system. To commercialize, the Ni-based alloy membranes, it is essential to understand atomic level dynamic behavior of these glassy alloy. Due to lack of long-range order, x-ray diffraction technique of these amorphous materials gives a broad hump in the
XRD pattern and the atomic structure. The motion of atoms with respect to time information, is not obtained from XRD laboratory methods. To understand the dynamic behavior of metallic glasses, one requires extremely high-intensity x-ray coherent source.
The European Synchrotron Radiation Facility (ESRF), Grenoble, France has one such high brilliance coherent x-ray source that allows obtaining information of weak “Laue” type spots. XPCS reveals information on the time necessary for atomic movement with temperature as well as hydrogen atmosphere and sheds light on the macroscopic properties membranes. The XPCS is a technique, which reveals slow dynamics of an “out-of- equilibrium” system. The binary Ni60Nb40 and ternary (Ni.60Nb0.40)70Zr30 amorphous ribbon is fabricated by a melt-spinning method to understand the atom dynamics, which is expected to reveal the enhanced permeation of hydrogen in the ternary alloys because of the Zr additions. The atom dynamics is determined at different temperatures by the XPCS 5 system which give structural relaxation time (), well below glass transition temperature
(푇푔). These experiments are performed at much lower than the glass transition temperature, which usually considered as a frozen state. We obtain local atomic diffusion/motion of atoms via x-ray scattering that yield spots in the reciprocal space called
“speckles” to give the spatial position of the atoms at a certain period. We also obtain relaxation time () and aging effects by periodically tracking the location of these speckles and applying the KWW function. To understand the effect of solubilizing hydrogen atoms and dehydrogenation in the membranes on the atom dynamics and relaxation times is determined. These reveals the knowledge about the atoms relaxation and back to their initial positions after withdrawing hydrogen from the membrane by vacuum. These kind of experiments are not yet performed on the metallic glass with hydrogen or any other gaseous atmosphere to the best of our knowledge.
Although synchrotron x-ray reveals the heavier atom dynamics of Ni, Nb, and Zr, this technique is not applicable in the smaller atom such as hydrogen. To understand hydrogen vibrational density of states Neutron Vibrational Spectroscopy (NVS) is performed at NIST center for neutron research. We obtain the position of hydrogen inside the lattice of ZrH2,
Ni60Nb40 and ternary (Ni0.6Nb0.4)100-xZrx (x=10, 20, 30) amorphous alloys. Neutron Total scattering (HIPD) is performed to obtain nearest neighboring distance at Los Alamos
National Library (LANSCE). We obtain short-range order and nearest neighbour distance by this method. Next, small angle neutron scattering (SANS) is performed to observe local cluster arrangement at NIST. However, SANS does not reveal significant information; thus
Atom Probe Tomography (APT) is performed at Northwestern University (NUCAPT).
Atom Probe Tomography results showed significant cluster formation within the 6 amorphous matrix. To understand permeation behavior high-pressure diamond anvil cell is used in Raman Spectroscopy measurement. Altogether, these studies showed the atom dynamics with and without hydrogen, local atomic structure of the amorphous ribbon and cluster formation is determined in the membranes.
1.2 Amorphous Material for Hydrogen permeability
In 1960, Klement et al. [13] was prepared first amorphous AuSi alloy at the California
Institute of Technology. These membranes are fabricated by melt spinning methods. In the late 1980s, the pioneering work of Inoue [14] by discovering glass forming ability and formation of bulk metallic glasses (BMG) in La-Al-Ni and La-Al-Cu by casting in copper molds at relatively slow cooling rates less than 100 K s-1 opens a new area for the scientific community. Inoue [14] also established important parameters for the formation of BMG in which three or more components are needed with atomic size ratio greater than 12%, and a negative heat of mixing. The selection of compositions for metallic glass formation can be driven by thermodynamic arguments [15] and metallic glasses with various compositions have been produced. The thin amorphous alloys are used in electrical, magnetic and membranes for hydrogen separation applications, whereas, the bulk metallic glass alloys are used for structural applications.
Several notable reviews on separation of H2 from CO2 by various membrane technologies have published. Ceramic ion transport membranes, inorganic microporous membranes, and alloy membranes, both crystalline and amorphous possible to use for coal gasification system. In 2006, Phair and Donelson [16] reviewed developments in non-palladium alloy membranes and Phair and Badwal [17] reviewed materials for separation of membranes 7
for hydrogen and oxygen production, H2 and CO2 separation, and power generation. In the same year, Dolan et al. [12] published a comprehensive review such as such as affecting diffusion rates, the influence of hydrogen on thermal stability site symmetry and energies on hydrogen-selective amorphous membranes. They also discussed significant issues of these amorphous membranes during long-term sustainability at elevated temperatures.
1.3 Development of Ni-based membranes for Hydrogen permeation
Currently, crystalline Pd/Pd-Ag membranes are widely used for separation of hydrogen from other mixed gasses in coal-gasification purpose, but Pd is a strategic metal and needs replacement by inexpensive metals in the service. The very first experiment is performed on hydrogen permeation of Ni-based early transition materials (Ni-ETM) by Steward’s
[11] making led the scientific community to explore cheaper materials for membranes. In
1981. Spit et al. [18] and Aoki et al. [19] both explored hydrogen absorption properties of
Ni-based amorphous alloys. In the 1990s, several researchers were developed different hydrogen separation membranes such as Pd, Ni-based and other alloys [20–23]. In 2000, the revolutionary work on permeation through the Ni-based amorphous alloys Ni64Zr36 was first performed by Hara et al. [25]. He reported to produced melt spun ribbons and found high purity hydrogen permeation rates of 1.9 × 10−9 mol m-1 s-1 Pa-0.5. In 2005, Yamaura et al. [26] performed permeation experiment of binary Ni-based amorphous alloys
(Ni0.6Nb0.4)100-xZrx (x=0, 10, 20, 30, 50) amorphous ribbons and observed permeation of binary alloy is lower than ternary alloy and increasing in Zr content causes higher permeability and lower thermal stability.
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Hydrogen permeability
Hydrogen permeability through a membrane is occurred by the following three steps: (i) the dissociation of gaseous hydrogen molecules into hydrogen atoms on the surface of the one side of the membrane; (ii) the diffusion of hydrogen atoms through the membrane and
(iii) the recombination of hydrogen atoms on the surface of the permeate side of the membrane shown in Figure 1.2. Therefore, hydrogen permeability of the membrane can be calculated by the following equation
퐽. 푥 푃퐻 = √푝1−√푝2 where 퐽 is the flux of a given membrane varies with the difference in the square roots of the pressure at the high-pressure surface 푝1and the low-pressure surface 푝2 and 푥 is the thickness of the membrane [12].
Figure 1.2 Schematic representation of hydrogen separation using amorphous membrane taken from [26] 9
Amorphous alloy membranes, Ni, Nb, Zr and others, have a lower atomic density as compared to the crystalline counterparts, and are relatively stable at high temperatures, for example at 673K [27]. They also have high solubility and less prone to embrittlement in the presence of hydrogen [27]. The permeability of Pd and Pd-alloys with Ni-based alloys showed that the binary alloys such as Ni60Nb40, Ni60Nb30Ta10 had low permeability as compared to those of the ternary alloys, but the mechanism was not clear [27]. Indeed, the hydrogen solubility of Ni-Nb binary is enhanced with Zr; however, diffusional aspects also control the permeability; the mechanisms on a microscopic basis were not clear. The Ni–
Figure 1.3 Summary of reported hydrogen permeability values for Ni-based amorphous alloy membranes and selected Pd-based alloys as reference materials [S. Sarker et al. 27] 14] 10
Nb–Zr alloy system studied from the perspective of hydrogen separation as well as electrical properties. The addition of Nb to Ni–Zr alloys brings the beneficial effects of increased crystallization temperature and fracture strength [27] and reduced susceptibility to hydrogen embrittlement. A summary plot of hydrogen permeation through Ni–Nb–Zr alloys, with alloying elements such as Ta, Co, Hf, and others, is shown in Figure 1.3; selected crystalline Pd-based alloys are included as a reference. Certainly, the reason behind the permeability of crystalline Pd ordered structure is different from the behavior of any disordered system like Ni60Nb40 or (Ni.60Nb.40)100-xZrx (x=10, 20, 30). Therefore, it is important to understand the hydrogen effect on these short-range order structures in atomic level.
1.4 Metallic glasses
The molten metal is undercooled uniformly, and rapidly enough atoms do not have enough time or energy to rearrange for crystal nucleation. The liquid reaches the glass transition temperature and solidifies as a metallic glass. Since then metallic glasses (MGs) are the focus in the international metals community [28] due to its lack of long-range order and the absence of traditional defects such as dislocations and grain boundaries. MGs have many interesting mechanical, physical and chemical properties help the field of materials science and engineering [29]. The significant research advances were made in understanding the nature of membranes in Japan, particularly at the Tohuku University and
AIST. The amorphous membranes are fabricated by melt spinning methods, with critical cooling rates higher than 106 K.s-1. Amorphous Technologies International with Caltech’s 11 was the first company to produce amorphous metal alloys in viable bulk form, and they produce sports and luxury goods, electronics, medical, and defense products. The first application of metallic glass was golf club head. However, we will concentrate our study on the permeation behavior of amorphous alloys membrane, which could be used as non- expensive membrane separator for coal gasification.
One of the main barriers to the use of amorphous membranes is their propensity to crystallize during long-term operation at elevated temperatures, a process that increases atomic density and leads to a reduction in hydrogen diffusion pathways. In addition, crystallization often induces brittleness in the ribbon, limiting as a consequence the operating conditions. To overcome such problems, we need to understand atom behavior below glass transition temperature, the effect of hydrogen on the atomic level. Therefore, it is essential to comprehend basic property of glasses; next section is a discussion about general glass property.
1.5 Glass transition
Two types of phenomena either crystallization or verification take place if the liquid is cooled below its melting point. The liquid volume or enthalpy behaviors on temperature at constant pressure shown in Figure 1.4. For crystalline material, with decreasing temperature below melting point (푇푚), melt permits kinetics for nucleation and growth of the molecule which causes the sudden decrease in the volume (enthalpy). However, if the cooling rate is sufficiently fast below the melting temperature (푇푚) to avoid crystallization, the molecule will not get enough time to rearrange themselves, a metastable state is obtained, but no abrupt change will occur in the volume of enthalpy, eventually with 12 decease temperature, the structure become frozen and form glass. In general, the glass transition is defined as around 2(푇푚)/3.
Another definition of glass transition temperature is that the density of the liquid become 1013
Poise [30, 31]. However, the transition from liquid to glassy Figure 1.4 Schematic diagram of temperature dependence volume at constant pressure. Tm is state is a range of temperature; it is melting point, Tg(a) is the glass transition of fast often defined as fictive temperature cooled glass and Tg (b) is the slow cooled glass. τ and
(푇푓) which is the specific η represents the relaxation time and viscosity in temperature obtained from crystal, supercooled liquid region and glassy state. Adapted from ref. [30] intersection of extrapolation of liquid and glass curve. Therefore, at the fictive temperature (푇푓) same atomic configuration is observed in glass and liquid state. As in the Figure 1.4 showed during fast cooled glass
(a) generate larger free volume and lower density than slowly cooled glass (b). However, it is interesting to observe that the reheated sample path does not follow the same cooled path as before. After reheat material i.e. anneal the disordered system to a temperature within the transformation range and below the original fictive temperature (푇푓), the sample readjust to the structure to a more stable configuration for the new temperature and free volume decreases and density increases. The glasses are prone to change its configuration towards more stable the state, this process is called “physical aging” and it may have much 13 longer time scale than the experimental time, so the system view as frozen from macroscopic timescale. The time necessary for these slowly rearrangement of structure and volume shrinkage phenomena to more stable configurational state is called “structural relaxation time, τ” and the density is proportional to structural relaxation [30].
In glass thermodynamics properties such as density, compressibility, and specific heat is temperature dependent and structural properties by like static structure factor, and radial distribution functions are slightly temperature dependent. However, dynamic properties of the glass such as viscosity, structural relaxation time and diffusion constant are strongly temperature dependent. It is interesting that with decreasing temperature if thermodynamics and structural properties change two-three order magnitude then dynamic property changes drastically. These dramatic changes in the dynamic properties do not follow Arrhenius behavior; means that activation energy causes simple breaking the bonds and enhance movement of the atoms do not usually happen in the system. These unique dynamic heterogeneous properties of glasses generate a lot of interest among scientists from past few decades. Physical aging in glasses is commonly studied by the temporal evolution of the system with a parameter such as a temperature and the pressure. Although many theories have been developed the heterogeneous property of the glasses yet till not well understood; some of them discussed below.
Mode coupling theory (MCT) [32, 33] and Potential energy landscape (PEL) [34] two advanced theories are discussed in this section which some extended described the heterogeneous behavior of glass. The dynamic property can be characterized by measuring the time-dependent evolution of density correlator function, which is simply a fluctuation of density at the time t in mode coupling theory. The density auto-correlation function with 14 time scale shown in Figure 1.5. In Figure 1.5 (a) density-density correlation function shown for liquid and these is extended to the supercooled liquid phases towards glass transition temperature Figure 1.5 (b). In Figure 1.5 (i) showed liquid region when the molecule is freely diffuse and causes the decay of the density correlation function. In Figure 1.5 (b), density correlation function with time showed that there is the vibration of atoms at the very short time, the decay is related to free motion and collision of the atoms. In the density correlator plot, there is the first step; secondary relaxation also called β-relaxation followed by long plateau before terminal decay completely to zero known as structural relaxation or
α-relaxation. The β-relaxation is comparatively insensitive closer to the glass transition temperature, whereas α-relaxation slows down significantly as it is closer to glass transition. To explain these phenomena physically, glass former composed of small groups of particles trapped inside the “cage” formed by their neighboring atoms. 훽-relaxation is rotational or liberation vibration of particle within their local cages and rearrangement of structure within the cage; these can be explained by simple power law. The density-density correlation spectroscopy showed at time independent intermediate time a plateau where the particle still temporally trapped in the cage and rattle around causes “cage-effect”. The particle is always try to escape from the cage and reasonable probability of the particle escape from the cage give rise to terminal decal and it is described by Kohlrausch-Willium-
Watts function. German physicist Friedrich Kohlrausch in 1863 described the mechanical creep in glassy fibers [35] and several years later the stretched exponential was reintroduced by Graham Williams and David C. Watts in 1970 to characterize dielectric relaxation rates in polymers [36] and these function described as Kohlrausch-Willium-
Watts function (KWW). These functions is used to describe time dependent non- 15 exponential heterogeneous dynamics of liquid at low temperature which means at any given time there are region in supercooled liquid where the particles relax faster than the average region particles. According to Tanaka’s model [35], in glass there exist two levels of dynamic structural heterogeneity i.e. “locally favored structures and their clusters” which is β-relaxation and “metastable solid-like islands” represents as α-relaxation [38].
Two types of β relaxation shown in Figure 1.5; fast β-relaxation is associated with local structural rearrangements shown Figure 1.5 (ii) and slow β-relaxation with the linkage of (a) (b)
(i) (ii) (iii (iv (v) ) )
Figure 1.5 Density auto-correlation function with respect to time (a) in liquid, (b) in glass forming system, (i) Liquid region, (ii) The fast β relaxation is associated with local structural rearrangements, (ii) the slow b relaxation with the linkage of local structural rearrangement (iii) the α relaxation with the percolation of the local relaxations through the glass ‘matrix’ (v) Tanaka’s model for relaxation process Adapted from ref [ 32, 35,
38] 16 local structural rearrangements shown in Figure 1.5 (iii). α-relaxation with the local relaxations through the glass ‘matrix’ shown in the Figure 1.5 (iv); the red and blue spheres represent mobile and less mobile atoms respectively. This α-relaxation mode is associated with dynamics of creation and annihilation of metastable islands below Tm. The total process is depicted in Figure 1.5 (v) by Tanaka. The appearance and disappearance of this metastable α-relaxation mode still not understood properly. Mode coupling theory does not define thermodynamic relationship and dynamic behavior. In order to understand the relationship between them another approach is discussed below.
The relaxation behaviors of supercooled liquid and glass transition discussed by Goldstein in 1969 [34]. He proposed, the evolution of N-particle by 3N configurational coordinates is characterized by (3N+1) dimensional potential energy surface which means each different configuration of the system described by a point in the space and dynamic is assumed the motion of this point over the potential energy landscape. Schematic illustration of potential energy landscape is shown in Figure 1.6. It showed that the depth distribution of basin, element transition state, and deep minima of the potential energy landscape. When the temperature of the glass is lower than glass transition temperature i.e. the configurational state of glass is seen to belong mostly to one of the deep minima in this surface, or mostly to one inherent structure. For an ordered crystal at 0 K, the state belongs to only one minimum. Local minima of the potential energy landscape give most stable configuration as shown in Figure 1.6 absolute minima described as crystal and local minima of different depth cause metastable region which is always higher than crystal.
These local minima are determined by the rate of cooling of the liquid. The higher is the cooling rate, the less depth of the local minima. According to this theory, β-relaxation 17 described as the vibration of particles around the local minima and jump across the different barrier of the potential energy surface causes α-relaxation shown in Figure 1.6.
Therefore, it shows that the glassy state appears to have been trapped in a deep α-relaxation minimum, but liquid- like (re-orientational) configurational changes involving all molecules still occur in the state of Figure 1.6 Schematic representation of potential energy this deep minimum. landscape with configurational coordinates. Adapted from Thus, α-relaxation mode ref [30] or metastable solid like island, the coherence length of motion cannot be measured by static scattering methods like X-ray and neutron scattering and can be observed only by dynamic techniques. Therefore, we performed XPCS measurement to know the relaxation time, and we will be able to figure out dynamic heterogeneity in the system. In the next chapter, we will discuss x-ray photon correlation spectroscopy. 18
Chapter 2 Dynamical X-ray Studies of Disordered Materials: X-ray Photon Correlation Spectroscopy (XPCS)
Contents 2.1 The Synchrotron technique ……………………………………………….…23 2.2. Theory of XPCS ………………………………………………………...... 30 2.3 Historical Perspective of Development of XPCS ……….…………………. 37 2.4 Experimental Details…………………………………………………………48 2.5 Result and Discussion ……………………………………………………… 49 2.5.1 XPCS Results …………………………………………………………49 2.5.2 Complimentary XAFS Results .………………………………………61
2 Dynamical X-ray Studies of Disordered Materials: X-ray Photon Correlation Spectroscopy (XPCS)
Introduction Direct nanoscale dynamics measurement like x-ray photon correlation spectroscopy plays an important tool to achieve in-depth knowledge of the glassy material property. Many materials are produced by the non-equilibrium process often trapped in the out-of- equilibrium state. Therefore, understanding this out-of-equilibrium property is very challenging for modern condensed matter physics. In general, neutrons or x-rays are used for direct measurement of structure in a scattering experiment. The intensity in scattering measurements is proportional to the Fourier transform of a density-density correlation function. The relaxation dynamics of disorder system have been studied earlier by both visible light as well as a neutron. However, the neutron study on dynamic property only performed at higher frequency typically 1014 Hz to 1018 Hz and scattering vector (푞) is 19 usually accessible in 0.02 and 10 Å−1 range [39, 40]. XPCS bridges the gap of inelastic neutron spectroscopy in the frequency range. For studying dynamics of soft matter system at lower frequency region, X-ray photon correlation spectroscopy (XPCS) technique have been used. Conceptually, X-ray photon correlation spectroscopy (XPCS) is a relatively new method and is similar to the dynamic light scattering (DLS). The main advantages with respect to dynamic light scattering are the higher scattering wave vectors and less affected by multiple scattering [41]. In the time domain, x-ray provides short wavelength, high penetration power, surface sensitivity and element specificity. Photon correlation spectroscopy which is also called dynamic light scattering performed at much lower frequency (<106s-1), however, coherent visible light from a laser source λ~
500 nm or 5000 Å, Photon
Correlation Spectroscopy
(PCS) or Dynamic Light
Scattering (DLS) and coherent light from a synchrotron source λ~ 1Å. Figure 2.1 X-ray Photon Correlation Spectroscopy
The x-ray photo correlation (XPCS) technique covered region shown in Frequency– Scattering vector. Other techniques covered region shown spectroscopy capable of in the figure too where PCS-Photon Correlation performing probe to the Spectroscopy, INS-Inelastic Neutron Scattering, IXS- dynamic properties of the Inelastic X-ray Scattering, IXS-Inelastic X-ray Scattering, NFS- Nuclear Forward Scattering [36] material at low frequency i.e. 20
106 to 10−2s-1 and scattering vector range from 10−3 Å−1 to several Å−1 [40], thus, it is appropriate for measuring glassy state of amorphous ribbon. The lower limit of scattering wave-vector in XPCS is determine by Fraunhofer diffraction of the main beam which
−3 −1 present case is 푞푚푖푛=10 Å . X-ray photon correlation spectroscopy, which allows measuring the translational dynamics for time scales up to thousands of seconds and on the atomic length scales. The scattering vector and frequency diagram shown in the Figure 2.1.
Therefore, in order to perform XPCS required high intensity coherent x-ray source and the basic principle of this technique is discussed below.
If the coherent light is scattered from a disordered system, it gives rise to a random diffraction or ‘‘speckle’’ pattern [42] which is related to the exact spatial arrangement of the scatters in the disordered system. The laser is a coherent light source, which shows a graininess, speckles, and the pattern is produced whenever randomly distributed regions of material introduce a different phase shift into the scattering coherent light or arrangement of regions evolved with time [42]. The coherent light, the coherent sum of scattering from a random array of domains results speckle pattern modulating the diffuse peak. Each spot is arising by the independent diffraction from a small region. The equilibrium dynamics information is not accessible in an ordinary scattering experiment with incoherent light as the fine-scale speckle features are not resolved, and only the changes in the ensemble- average structure of the sample can be determined.
Like any other scattering techniques, the image of the spatial structure of the system is not directly observed, but length scales are resolved as Fourier wavevector components in reciprocal space. If the atomic arrangement changes with time, the observed speckle pattern will also change; therefore, by observing the intensity fluctuations in the speckle pattern, 21 the characteristic times of fluctuations in the system as a function of wavevector can be determined [43]. The angular extent of each spackle is comparable with Fraunhofer diffraction. Figure 2.2 is the taken from the Friso van der Veen and Franz Pfeiffer [44] for discussing the speckle pattern arise from coherent illumination. Suppose, we consider a
Bragg diffraction from a highly ordered sample Si simply reproduced the Fraunhofer diffraction pattern which shows spackle width in collimating pinhole is λ/L where λ change in largest path difference and L is beam diameter. Incoherent and coherent illumination both causes Fraunhofer diffraction pattern in a detector from a disordered medium, where the object size or the illuminated area is an average distance of the particle is 푑, wavelength is λ. For coherent scattering is fully coherent is transverse medium. The incoherent
Figure 2.2 X-ray diffraction from disordered samples where the object sixe is a and particle distance is d. Continuous diffraction ring appeared by incoherent scattering and speckle diffraction ring appeared due to coherent scattering [44] 22 scattering give rise to continuous diffraction ring. Therefore, incoherent pattern depends
휆 on , where the maximum intensity found. Due to coherent volume the diffraction pattern 푑
휆 exhibits much smaller feature of the disordered medium as it depends on . As we know 푎 the average particle size distribution is much smaller than the coherence volume as (푑 <<
푎) , therefore the diffraction feature will be much smaller in the coherent illumination
휆 휆 휆 ( ≫ ), so this angular width are speckles which arises due to interference between 푑 푎 푎 wave scattered from the particles [44]. In Bragg’s peak perspective, an incoherent experiment, the peak is isotopically broadened. However, coherent experiment like XPCS, speckle structure are appeared. The intensity of fully coherent scattering follows an exponential law. Therefore, with respect to time if any speckle changed then all the interference will be affected. Thus, XPCS measurement is time dependent corrections in diffraction intensity and it is related to the temporal evolution of electron density fluctuation. XPCS uses the partial coherence properties of x-rays. Each speckles are related to the positions of the atoms in that moment. As the system is out of equilibrium (such as glass), the atoms move and therefore the speckles will change with time. Therefore, temporal evolution of the intensity of the speckles or diffracted beam represents the atoms movement. In order get coherent x-ray source with very high brilliance in XPCS measurement, we need synchrotron x-ray source. In the next section, synchrotron x-ray source, set up for the XPCS measurement and achieving coherent x-ray source, theory of the XPCS and history of XPCS are discussed in details. 23
2.1 Synchrotron Technique
Rontgen discovered x-ray in 1895. Almost after ninety years later, synchrotron discovered in the mid-1970s. In a synchrotron, a bunch of charged particles like electron and positron accelerated in a closed magnetic field orbit at relativistic velocity and produced electromagnetic radiation. At ESRF, electron brunch is extracted from a solid cathode by a laser beam [45]. A synchrotron consists of storage ring, booster synchrotron, Linac, undulator and different magnets in the storage ring. The energy of the source like ESRF,
APS and Spring 8 around the range 6-8 GeV range
[46]. The storage ring is around 844 meters in circumference where the particles are accelerated at very low pressure. The electrons are accelerated along the direction Figure 2.3 Schematic diagram of Synchrotron X-ray perpendicular to their source taken from Als-Nielon’s book [48] velocity due to Lorentz’ law, which makes them, travel along the particular curved path. These bunch of electron with 120 MeV energy then focused and accelerated by electron ratio frequency gun, and it is directed towards 1.6 km long superconducting linear accelerator and LINAC bring the electron energy near 20 GeV produced from an electron gun. After that the electrons are 24 ejected to a booster synchrotron is pre-accelerator and around 300-meter-long where before sending to the storage ring. Large bending magnets helped to circulate charged particles around the orbits, and it makes broad spectrum to an intense electromagnetic radiation. The insertion device like undulator and wigglers are situated in the straight section of the storage ring. In wiggler, the amplitude of oscillation is larger which leads to enhancement in the intensity of observed radiation. The undulator source size of ESRF storage ring is
926 µm (H) and 23 µm (V) [47]. Undulator helped to produce small amplitude acceleration from single electron, which helps to produce coherent addition in each oscillation. Another important part is undulator which is a magnetic array create an alternative force and oscillate the particles to the undulating trajectory. This radiation then passes through a monochromator, focusing devices on achieving desirable property of the radiation and directed towards the beam-line before experimental use. A third generation synchrotron facility shown in Figure 2.3 adapted from Als-Nielon’s book [48].
Coherent X-ray Source
XPCS is the time dependent intensity fluctuation, which means the wave-fronts must be highly correlated in space and time. The independent and spontaneous electrons, which are coming towards beamline is not coherent illumination as it has a finite source size and bandwidth. The third generation synchrotron source have high brilliance and small source size which causes the possibility of obtaining coherent x-ray beam. This temporal and special coherence property of the synchrotron source can be described by longitudinal and transverse coherence length.
25
(a) Longitudinal coherence length (흃풍) Longitudinal coherence length measures energy distribution of photon. The temporal fluctuation takes in the account by this coherence length. Due to lack of monochromatism and not well-defined propagation direction of the x-ray source, the scattering process is slightly different than an ideal plane wave. However, it is also important to remember that monochromatizing reduces intensity. Suppose, two plane waves propagate from a single source in the same direction having a wavelength and +Δ shown in Figure 2.4 (orange
1 and blue color) and the first wave oscillate N times and second wave oscillate (푁 − ) 2 times over the same distance before it is out of phase, 휉l distance, then longitudinal coherence length will be 휉 = 푙 Figure 2.4 Schematic representation of longitudinal
1 푁 = (푁 − ) ( + Δ). coherence length [48] 2
2 훥 Solving the equation for longitudinal coherence length we get 휉 ≈ , so bandwidth 푙 2훥 play an important role for longitudinal coherence length. At ESRF, due to Si (111)
훥 monochromator the bandwidth is ≈ 14 × 10−4 and = 1 Å , so longitudinal coherence length is about 0.7 µm [40]. In XPCS measurement, sample should be illuminated coherently at the scattering angle 2휃, where sample thinness (t) and sample width (a) takes into consideration. The coherent illumination is only possible when longitudinal coherence length scale must be equal or greater than maximum path length difference (PLD) [40].
2 휉푙 ≥ 푃퐿퐷 ≈ 2푙 푠푖푛 (휃) + 푎 푠푖푛 (2휃) 26
As the incoming and scattered wave vector 퐾0 and 퐾푖 is equal in coherent scattering the momentum transfer is q. So, the limiting value of maximum wavevector transfer will be
4휋 푞 = 푆푖푛휃 , so maximum allowable wave transfer for longitudinal coherence 푚푎푥 휆 푚푎푥 length 0.7 µm will be 2 Å -1 [40]. This longitudinal coherence length can be achieved by collimating aperture of the beam.
(b) Transverse coherence length (ξt)
Transverse coherence length can describe a spatial coherence of the beam, and it is the related finite size of the source (w). As shown in Figure 2.5, the distance between the source and the sample is R, and the angle between them is 훥휃. 휉t distance the wave from two end of the source is out of phase and it can be described as
휉 ≈ , due to small value 푡 2 tan 훥휃
푤 of 훥휃 , as 휉 ≈ , as 훥휃 = , So 푡 2훥휃 2푅 transverse coherence length can be
푅 written as 휉 ≈ . Assuming a 푡 푤 Figure 2.5 Schematic representation of transverse rectangular source with horizontal coherence length [48] and vertical 푤ℎ and 푤푣 then
ℎ 푅 corresponding transverse coherent length in horizontal and vertical will be 휉푡 ≈ 푤ℎ
ℎ 푅 and 휉푣 ≈ . In ESRF, ID10 the distance between the source and sample is about, 푅 = 45 푤푣 m and wavelength 휆 = 1 Å and from asymmetric source size 928 µm (h) and 34 µm (v),
ℎ 푣 the transverse length become 휉푡 ≈ 3 µm and 휉푡 ≈ 98 µm. This transverse coherence length will be controlled by slit. 27
This longitudinal coherence length and transverse coherence length are related to a calculating number of photons in the coherence volume. The photon flux transmitted
ℎ 푣 through the coherent area from the distance R if the solid angle is 훥훺 = 휉푡 휉푡 from coherent
훥 훥 area퐴 = 푤 푤 , bandwidth , so the flux will be 퐹 = 퐵퐴 훥훺 . B is brilliance defined 푠 ℎ 푣 푠 as number of photon per unit time generated per unit source are per unit solid angle and per 0.1 % fractional bandwidth. Putting all the values to the above equation flux or the
훥 coherent intensity can be written as 퐹 = 퐵휆2 . In third generation x-ray source brilliance,
퐵 ≈ 1020푝ℎ/푚푟푎푑2푚푚2푠, so the coherent intensity or the flux carried by photon with wavelength = 1.5 Å with an 푆푖 (111) monochromator is estimated around 퐹~1011 푝ℎ/
푝ℎ 푠, however, the coherent experiment like XPCS is performed at ~1011 [44]. Number of 푠 photon 푁푝 in coherence volume can be derived from the photon flux and longitudinal coherence length. The longitudinal coherence length 휉푙 divided by the speed of light c give
퐵 display the value of coherence time (휏 ). So, 푁 = 퐹. 휏 = 퐵휆3 . Therefore, high brilliance 푐 푝 푐 푐 and longer wavelength is required to get large number of photon in coherence volume.
XPCS measurement set up
X-ray photon correlation Spectroscopy experiment was performed at ID10, a part of
TROIKA beamline of the European Synchrotron Radiation Facility (ESRF) at Grenoble by a coherent source of x-ray. A schematic representation of detailed ID10 beamline shown in Figure 2.6. The radiation of the beam energy is 8 퐾푒푉 having wavelength of 1.584 Å used here. The flux produced about 1011ph. s−1 at 200 푚퐴 current in storage ring. An 28 asymmetric undulator source having transverse horizontal (928 µm) and vertical (23 µm) coherence length is situated about 44.2 meters away from Si (111) perfect crystal
Δ −4 monochromator where the bandwidth ≈ 10 with a longitudinal coherence length ξl≈
1µm. The harmonic content is reduced by using a second piezoelectric mirror. It is placed
0.8 m downstream of 푆푖(111) monochromator. The collimated aperture is placed 0.5 m upstream of the sample to correlate the transverse coherent length with sample [44]. As shown in the Figure 2.6, guard slit is placed ~0.1 m away from the sample in order to suppress Fraunhofer fringe from the first pin hole. The partial coherent beam that can be achieved form this set up 4 (H) × 20(V)µm2. Charge coupled device (CCD) camera has been placed 2 m away from the sample. It helps to collect the signal continuously from different speckles. For XPCS experiment at ESRF an Ikon-M CCD camera from Andor
Technology is placed [40]. The back-illuminated deep depleted sensor has been under direct detection conditions.
For slow dynamics, correlation functions calculated by software for each pixel and then averaged over the pixel [45]. Statistical accuracy is increased by the pixel averaging. The total duration of the experiment possible to reduce by a factor equal to the number of coherence areas sampled. The Autocorrelation functions were calculated by taking an average over the rings of pixels centered about the transmitted beam position, where q=4πSinθ/λ , θ is the scattering angle, and λ is the wavelength in the medium [45]. Speckles corresponding to the exact magnitude of the scattering wave vector |q| but different azimuthal orientation. The computational load is huge as it required to calculate in real time autocorrelation functions averaged over both pixels and time [45]. For high resolution intensity measurement, direct illumination CCDs (DI-CCD) have a sufficient detection 29 quantum efficiency (DQE) have used with an energy range of 0.1–12 keV. These CCDs are made of silicon wafers. In XPCS experiment, two main CCD's are used for detecting quantum efficiency (DOE) energy. In ‘deep-depletion’ CCD (DD-CCD) and ‘back- illuminated’ BI-CCDs, charge depleted in different types of length scale. In DD-CCD, the charges are spread over a distance smaller than the pixel size, i.e. the order of 20 mm and in BI-CCDs, the wafer is thinned to about 50 mm. Generally, x-rays are detected at the surface due to absorption of it on opposite side detectors. As CCD cells saturate at about
200000 electrons, i.e. 100 photons per pixel at 8 푘푒푉 [45]. For dynamical studies, the frequency of the sample from the CCD is an essential parameter; limits the minimum
Figure 2.6 ID10 beamline set up at ESRF, adapted from Grűbel [45] sampling time Δt. High-quality CCDs have a only 1 MHz slow frequency, which lower the electronic noise to less than 10 electrons [45]. Small part a of CCD chip is used to record images continuously and other part of the chip transferred the image as a fast frame.
Raw image is getting by subtracting dark noise from each CCD frame. A digital auto correlator ALV500/E used to record time autocorrelation function in XPCS experiment. 30
2.2 Theory of XPCS
The relaxation time and viscosity of a glass forming liquid increase rapidly when liquid cooled very rapidly from high temperature to low temperature. XPCS relies on the fact that a particular arrangement of atoms in a sample produces a characteristic "speckle" pattern or diffraction pattern when it scatters a coherent beam of X-rays [42]. If the arrangement of atoms changes, the speckle pattern changes observed by coherent x-ray.
Studying these changes in speckle pattern as a function of time, one can obtain information at the atomic dynamics at various wave vector transfer (i.e. at different length scales).The speckles pattern can be reordered by a 2D detector and from the analysis of the temporal evolution of the speckles one can get information on dynamics and thus on time averaged temporal intensity autocorrelation function which is related to the intermediate scattering function through the Siegert relation.
XPCS studies are two-time intensity fluctuation spectroscopy in a non-equilibrium system.
It is a two-time correlation as it is the time difference between any measurements at any origin of time [49]. Therefore, we can figure out the dynamic property of any disordered system like metallic glass by this function.
To understand two-time correlation function first, we have to understand auto-correlation function. Quantitative analysis of scattering intensity with respect to time which is collected [40, 50] were analyzed to determine standard intensity auto-correlation 푔2(q, t)
〈퐼(푞,푡 )퐼(푞,푡+훥푡)〉 푔 (푞, 훥푡) = (2.1) 2 〈퐼(푞)〉2 31
Where 퐼(푞, 푡 ) and 퐼(푞, 푡 + 훥푡) are the intensity measured at same wave vector 푞 at the time 푡 and (푡 + 훥푡). At very large decay time suppose 푡 approaches towards ∞,
Then
〈퐼(푞)〉2 lim 푔2(푞, 훥푡) = = 1, 푡→∞ 〈퐼(푞)〉2
2 Where lim〈퐼(푞, 푡 )퐼(푞, 푡 + 훥푡)〉 = 〈퐼(푞)〉 푡→∞
But at very small decay time when t approaches towards 0,
〈퐼2(푞)〉 lim 푔2(푞, 훥푡) = = 1 + 퐵(푞) , 푡→0 〈퐼(푞)〉2
2 Where lim〈퐼(푞, 푡 )퐼(푞, 푡 + 훥푡)〉 = 〈퐼 (푞)〉 푡→0
퐵(푞) is set up dependent parameter, which can be measured by speckle pattern contrast.
Experimentally it is measured by taking snapshot of dynamics in disordered system at different waiting time interval. These speckle pattern contrast also describe as
coherence volume 퐵(푞) = 푆푐푎푡푡푒푟푖푛푔 푣표푙푢푚푒
For partial coherent x-ray beam the speckle pattern contrast 퐵(푞) is always in between 0 to 1. Siegert relate this intensity auto-correlation 푔2 (푞, 푡) and intermediate scattering function 푓(푞, 푡) by the following equation [51],
2 푔2(푞, 푡) = 1 + 퐵(푞)|푓(푞, 푡)| (2.2)
This intermediate scattering function is one of the most important functions of glass forming liquid as it is describing diffusional motion. We know in any glass-forming liquid diffusion become abnormal when approach towards glass transition temperature. If the fluctuation time of particle is larger than the observable time, then i.e. for time is equal to zero then, equation (2.2) become 32
푔2(푞, 푡) = 1 + 퐵(푞)
If measuring time is significantly larger than fluctuation time then, then the auto-correlation function is time dependent.
Two types of relaxation occur near glass transition temperature in amorphous liquid – β- relaxation followed by α-relaxation. In β-relaxation, the decay time is much faster and in
α-relaxation, the relaxation time increases drastically liquid become frozen and glass formed. In general terms, we can have described earlier that α -relaxation as the localized motion of molecules within the energy barrier to its neighboring cage and β -relaxation is the structural rearrangement of the atoms within the “cage.” These structural rearrangement i.e. α-relaxation is non-exponential decay and it is described by famous, “Kohlrausch-
Williams-Watts (KWW)” function. Intermediate scattering function, 푓(푞, 푡) can usually described by KWW function by the following equation:
푡 훽 푓(푞, 푡) =푓 exp [− ( ) ] (2.3) 푞 휏
Here, 휏 is structural relaxation time, 푓푞 nonergodicity plateau before final decay and it is associated to structural relaxation, and 훽 described as the distribution of relaxation times.
Generally, the different relaxation times present in glassy materials lead to a stretching of the correlation functions and an exponent β < 1 (which here is referred to as “stretched behavior”) i.e. β is stretch exponent factor which describes deviation from exponential behavior. Normally the exponent of β value in between 0.5 to 1. In this type of KWW correlation 훽 = 1 means single exponential decay and when it is decreases towards 0.5 decay takes place over larger and larger time intervals [40]. However, 훽 > 1 i.e. described as compressed behavior and attributed to the relaxation of internal stresses [50]. The above- 33 mentioned intermediate scattering function 푓(푞, 푡) could also be described as dynamic structure factor and static structure factor i.e.
Dynamic structure factor ,S(q⃗⃗ ,t) Intermediate scattering function, 푓(푞, 푡) = Static structure factor,S(q⃗⃗ ,0)
The intermediate scattering function gives us the information about mean interparticle distance over a length scale 2휋/푞. We can get static structure factor and as well as dynamic structure factor. The static structure factor and dynamic structure factor describe as the following equation below
푆(푞, 푡) = ∫ 푆(푞, 푡)푑푡 (2.4)
1 An 푆(푞, 푡) = ∑푁 ∑푁 〈푏 (푞 )푏 (푞 )exp [푖푞 [푟 (0) − 푟 (푡)]]〉 (2.5) 푁[푏2(푞⃗ )] 푛=1 푚=1 푛 푚 푛 푚
In equation (2.5), N denoted as number of scatterers, 푟푛(푡) describe as the time 푡 the position of 푛푡ℎ scatterer and 푏2(푞 ) is the square of the scattering amplitude averaged over the size distribution of the scatterers N, and angular brackets represents ensemble averages over the scattering volume.
With standard x-ray diffraction is scattering of the incoherent x-ray beam and the results is an average of all the possible atomic configuration in the system and from that we get a random arrangement of the domains measure the average structure factor. Structure factor is scattered intensity that would be measured in a diffraction experiment with a real crystal.
A coherent incident beam requires with third generation synchrotron sources to measure the nearly accurate structure factor S(Q). It has become feasible to produce a sufficiently intense coherent x-ray beam to perform such nearly accurate measurements dynamically.
Putting the value intermediate scattering function, 푓(푞, 푡) from Kohlrausch-Williams-
Watts (KWW) to Siegert equation (2.2) we get, 34
2 푡 훽 푔 (푞, 푡) = 1 + 퐵(푞) |푓 exp [− ( ) ]| (2.6) 2 푞 휏
It can also be written as
2 푡 훽 푔 (푞, 푡) = 1 + 퐵(푞)푓 2 |exp [− ( ) ]| (2.7) 2 푞 휏 i.e.
2 푡 훽 푔 (푞, 푡) = 1 + 푐(푞, 푡) |exp [− ( ) ]| (2.8) 2 휏
2 Where, 푐(푞, 푡) = 퐵(푞)푓푞
These equations can describe the intensity correlation function experimentally done by x- ray photon correlation spectroscopy. These 퐵(푞) is also depect the intermediate time plate height before final decay to the α-relaxation. Surprising, we found that it is not only slightly depend on temperature but also the hydrogen gas on the system.
The difference between equilibrium and the non-equilibrium system is that here the time difference originates from measurement and origin of time measurement does not plan role, so it is one-time correlation function. However, in the non-equilibrium system, both the measurement time and origin of the time comes into picture results it is two –time correlation function as the dynamics evolve in the non-equilibrium system with time. For this reason, two-time correlation faction discussed below.
The two-time intensity correlation function (TTCF) is the correlation of scattered intensity
퐼 at time 푡1 and 푡2 so can present the TTCF as
〈퐼(푞,푡 1)퐼(푞,푡2)〉푝 퐺 (푞, 푡1, 푡2) = (2.9) 〈퐼(푞,푡 1)〉푝〈퐼(푞,푡2)〉푝 35
The 푝 represents here average of all the pixels of CCD having wave vector 푞. So the equation (2.1) auto correlation can be written as
푔2(푞, 푡) = 〈퐺 (푞, 푡1, 푡푑)〉푑 (2.10)
In the above equation 푡푑 represent as fixed delay time, 푡푑 = 푡1 − 푡2 and it is also taken average of the fixed delay time. However, it is important to notice that very often the glass dynamics is very slow even for an out of equilibrium system in experimental time scale and evolves very slow which looks stationary even the system is out of equilibrium.
Therefore, single dynamic heterogeneity will not be detected by averaging 푔2(푞, 푡) [52].
This value is directly measured by connecting point detector and digital auto correlator device. The point detector is used due to high quantum efficiency and smaller dead time.
Direct online access to the wide range correlator time for a single 푞 value can be achieved by these ways [50, 53].
However, performing such a huge averaging over all the pixel of the CCD camera is a very hard task, therefore, we measure the two-time correlation function in a different way, which is event correlation technique. The auto-correlation measurement can be done by establishing the relation with event correlation. The event correlator 푒(푡, 푝) and 푒′(푡 +
훥푡, 푝) is the correlation from number of photon detected in a pixel p at the time 푡 and 푡 +
훥푡 of in CCD [54].
′ 〈∑ 푒 (푡+훥푡,푝)〉푡 푔2(푞, 훥푡) = 2 (2.11) 〈푒̅̅(̅̅푡̅,̅푝̅̅) 〉푡
Where 푒′(푡 + 훥푡, 푝) is 1 when a same set of pixel event appeared at the both time 푡 and
푡 + 훥푡 and other than that the event counts as 0. 푒̅̅(̅푡̅̅,̅푝̅̅) is the total number of photon 36 captured by entire CCD camera at the time 푡. As we can easily understand that large number of event does not contribute to the correlation function calculation so these calculations become faster.
The relaxation time and diffusion of the particle are related as mentioned earlier. If the particle undergoes Brownian motion which is continuous motion and showed intermittent or temporal heterogonous dynamics, can be described by intensity fluctuation. In this case, the position of the particles is independent due to lack of interaction and the dynamic structure factor is 1 in equation (2.5). For translational diffusion of the Stokes-Einstein equation,
푘푇 퐷 = 푎푝푝 (2.12) 6휋휂푅ℎ
푎푝푝 where 푘 is Boltzmann constant, 푇 is the temperature, 휂 is the viscosity and 푅ℎ radius of
푎푝푝 the diffusion particles. The concentration goes towards zero, 푅ℎ gives exact hydrodynamic radius of the diffusing particle. Brownian motion of particle at the beginning
2 of the time 푡 is 푟⃗⃗⃗푛 (0) and after certain time 푟⃗⃗⃗푛 (t) then the mean value is 〈[푟⃗⃗⃗푛 (0) − 푟⃗⃗⃗푛 (t)] 〉=
6Dt where 퐷 free particle diffusion coefficient. So the dynamic structure factor and the
Stoke-Einstein equation can be written as
1 푆(푞, 푡) = ∑푁 〈푏 2(푞 )exp [−퐷푞2푡]〉 (2.13) 푁[푏2(푞⃗ )] 푛=1 푛
So, calculating the these
2 푆(푞, 푡) = 1 − [−퐷0푞 푡]+… (2.14) where the diffusion coefficient averaged over the distribution of particle 〈퐷0〉 =
푁 2 ∑푛=1 푏푛 (푞 )퐷. Therefore, the equation (14) will be equal to the intermediate scattering
2 factor,푆(푞, 푡) = 푒푥푝[−퐷0푞 푡] = 푓(푞, 푡) = 1 + 푓푞exp[−2훤푡] where 훤 is relaxation 37 rate 훤 = 푞2퐷. The relaxation time inversely proportional to relaxation rate. Therefore, the relaxation rate 훤 determined from correlation graph and plotted as a function of 푞2. The linear relationship was observed which confirms the diffusive nature of the process. This behavior is expected the diffusion of the aggregate and the diffusion coefficient is determined. There experiment proved that the relaxation rate were proportional to 푞2 and inversely proportional to viscosity. However, sometimes relaxation time varies inversely with wave vector (휏~푞−1 ) i.e. relaxation rate is proportional to wavevector (훤~푞). These indicated an undisturbed motion of particles in one direction similar to a ballistic flight, which is called “hyper diffusion”. These motions are observed when relaxation time is very high large than Brownian motion relaxation time indicates very slow diffusion.
Therefore, the intensity auto-correlation function can be expressed with diffusion constant from equation (2.2) and (2.14)
2 푔2(푞, 푡) = 1 + 퐵(푞)[−2퐷0푞 푡] (2.15)
XPCS study can measured diffusion coefficients ranging from 10−4 cm2/sec down to
10−19 cm2/sec, earlier due to lack of appropriate technique these range of diffusion coefficient has not been studied [55].
2.3 Historical Perspective of XPCS
In 1991, Sutton et al. [42] observed a speckle pattern of a single crystal of the binary alloy
Cu3Au that are randomly arranged antiphase domains by using coherent X-rays. These experiments were performed at the beamline X25 at NSLS in Brookhaven National
Laboratory. These very first experiment laser drill holes 50-100-micron thick platinum sheets were used. In February 1995, the first XPCS experiments demonstrating the 38 feasibility of observing the motions of microstructures in gold colloidal was performed by
Chu et al. [56] in the same laboratory. Soon after that, in the same year March, Brauer et al. [57] performed experiment on single crystal binary alloy Fe3Al at equilibrium which has order- disorder transition occurred at critical temperature near 824K. Their experiment showed that below critical temperature the system is static, however, above the critical temperature the system fluctuates over time. The intensity fluctuation occurred almost
30% relative amplitude. The scattered intensity averaged near the superlattice peak with the temperature varies above the critical temperature. However, the scattering intensity, which is point-to-point deviation, is consistent below the critical temperature where random arrangement of long-range order domain is observed. This transition of order to disorder system give an idea that in disorder system the intensity fluctuation evolves over time. After few months Dierker et al. [58] published a paper on XPCS studying on gold colloids dispersed in viscous liquid glycerol at Brookhaven National Synchrotron Light
Source. They found that the XPCS worked at very low frequency material and dynamics of opaque material can observed directly by this method. They observe deviation from q2 as the relaxation rate depends on transitional as well as rotational diffusion. About a year a half later, Albrecht et al. [39] studied diffusive dynamics in optically opaque colloidal palladium in glycerol using coherent x-ray beam at ESRF and here is very first digital autocorrelator ALV5000/E was used. The earlier experiment of XPCS had been at limited time range 1 to 103 sec, however, the experiment Albrecht et al. [39] performed measure correlation function covering the time 10-4 to 102 seconds and dynamics covered range
1.5 × 10−3 to 6.5 × 10−3 Å -1. To get the relation of wave-vector and particle size, they performed static structure factor at higher wave-vector by SAXS. The scattering vector 39 described the scattering intensity by a distribution of spherical particle with different radii.
The form factor at high wave vector describe give the average radius. At smaller wave- vector the structure factor S(q) goes high and it no longer describe the average radius rather it was indicated existence of aggregates whose internal structure is reflected by such lower wave-vector values. In this S(q) and q range, it gave fractal structure of the aggregates, however, the exact size of the aggregates cannot be determined from static structure factor.
Thus, the time correlation function appears. They performed the experiment at lower wave- vector covering almost six decades of time. The correlation function of the incident beam proving absence of any correlated noise introduced in the detector of incident beam. Here, the relaxation rate Γ determined from correlation graph and plotted as a function of q2. The linear relationship observed which confirms the diffusive nature of the process. This behavior expected the diffusion of the aggregate and the diffusion coefficient is determined. There experiment proved that the relaxation rate were proportional to q2 and inversely proportional to viscosity. Soon after that Mochrie et al. [59] studied, the system polymer micelle liquids composed of spherical and wormlike particles and showed that in equilibrium dynamics due to variation of wave-vector have significant effect on particles within the time range from one to several hundred seconds. Due to correlation of micelles the peak rise and give the static structure factor, the system become mobile above 360K and to obverse the changes in the system within the time scale, they performed dynamics study at temperature 293K and 393K. The area detector collect 500 images and average them at different wave-vector range. The small wave-vectors gave stronger scattering
(pink, violet and blue) and large wave-vector display different scattering appearance
(green, yellow and red) depending upon the intensity. The grain like speckle appeared and 40 at 293K expected to be frozen. However, at higher temperature the micelles are mobile and their motion cause the instantaneous fluctuation of speckle with the experimental time scale and resulting the smoother appearance of the time averaged intensity. They also showed that wave-vector dependence viscosity as earlier suggested by Albrecht et al. [39]. In 2000,
Riese et al. [41] performed x-ray photon correlation spectroscopy and dynamic light scattering studied in order to compare the results of dynamics behavior of dense colloidal suspension. According to their study, the results from x-ray were more accurate due to absence of multiple scattering in dense system. The limitation of DLS is multiple scattering of light cases difficulties for the measurement of wave-vector. Another limitation is that accessible scattering vector is much higher so that the dynamic length scale lower than 200 nm is not accessible. X-ray we can measure faster dynamics in opaque or dense medium.
The intensity auto-correlation function measure for shorter timescale and longer time scale.
The oscillation is dominant at shorter time scale and the correlation function was observing higher time greater than 0.3 microseconds. In order to know the only sample intensity fluctuation, they measured reference incoming beam and correlation function at higher time shown in the bigger image (b) where the time was more than 100 microseconds. So there they measure auto correlation function and after as well as intermediate scattering function. At comparatively larger wave-vector range the intermediate scattering function match with dynamic light scattering. However, when the wave-vector was lower the intermediate scattering function changed significantly. The XPCS, the intermediate 41 scattering factor f(q, t) followed exponential function and light scattering follow non- exponential. The non-exponential function arises due to multiple scattering, heterodyne detection etc. The relaxation time significantly different in DLS and XPCS as both of them is wave-vector dependent. Therefore, the diffusion calculation, which is inversely proportional to relaxation rate, is affected by wave-vector as well as the technique. In the same year (2000), Geissler et al. [60] compared liquid and teixotropic samples by XPCS measurement. In 2001, speckle structure observed by Letoublon et al. [61]. In 2003, M.
Sutton et al. [49] is the first person who compared Intensity fluctuation spectroscopy of equilibrium and non- Equilibrium Dynamics Out of Equilibrium equilibrium system Dynamics and named the intensity fluctuation spectroscopy to x-ray photon correlation spectroscopy shown Figure 2.7 Two-time correlation function by XPCS measurement (Left) equilibrium dynamics (Right) out-of- equilibrium in Figure 2.7. As a dynamics, taken from Sutton 2003 [45] description of equilibrium system, gold colloids in polystyrene experiment taken into consideration. The gold particle in homogeneous material leads to a peak in SAXS, size, and particle shape distribution we get from the curve. The area detector shows at a particular temperature; the system has a diffusion constant such that the time constant for range of wave vector. In this isotopic system, the time constant fluctuation depends only one wave-vector but not the direction of it. In the homogenous system, the motion of particle possible to described by 42
Brownian motion, which causes intensity fluctuation. The complete homogenous system can be representing as two-time auto correlation function averaging over time as well as wave vector. It is important to remember in homogeneous equilibrium system is that the measurement time is constant as a function of wave vector. In non-equilibrium system, sodium borosilicate glass and unmixing of AlLi used to measure IFS. The area detector in non-equilibrium system measure many speckle intensities at the same time is help with statistics; also help to decompose the time evolution of scattering into an averaging and fluctuating component. The time evolution is clearly observing in AlLi system where sample is quenched from 475oC above its miscibility gap to room temperature and we increase annealing temperature as result the with time evolution of the particle size destitution over time clearly visible in the plot. The two-time correlation at fixed wave vector shows dynamic behavior, which is different from homogeneous equilibrium in two– time correlation plot and the non-equilibrium system evolve over time. The structure rearranges themselves and causes decrease in free energy of the system. After that, lot of experiment had been performed on order –disordered system and polymer. However, very recently direct evolution of intermediate scattering function measured comparably more complex system like amorphous material in glassy state by XPCS. In 2005, Ludwig et al.
[62] and Fluerasu et al. [63] in different experiment showed that speckles in the high intensity region had fluctuation time comparable to the aging time. In 2006, XPCS were performed on colloidal glass [64]. In 2007, XPCS were performed individually by Trappe et al. [65] and Fluerasu et al. [66] in gels. Trappe et al. [65] showed wave-vector dependence behavior of the gel. Fluerasu et al. [66] showed that the intermediate scattering functions change during the process from stretched to compressed exponential decays in 43 gels. In 2007, Grűbel et al. [45] studied detailed description of XPCS and used it as a standard tool for slow dynamics measurement in condensed matter. After two years, XPCS were studied in emulsions [67]. The first person reported the atomic length scale measurement was Leitner et al. [68] in 2009 and organic glass former behavior in 2010 in
[69]. In 2011, Czakkel & Madsen, [70] and Guo et al. [71] performed XPCS experiment in gels. Guo et al. [71] showed hyperdiffusive dynamics displays a time dependence similar to aging in polymer glasses. In 2011, Muller et al. [72] studied equilibrium and non- equilibrium dynamics in metallic alloys by X-ray photon correlation spectroscopy. They showed slow aging dynamics and avalanches in a Gold-Cadmium alloy by X-Ray Photon
Correlation Spectroscopy.
For many years, hard-condensed matters interatomic distances have not been studied due to insufficient flux. Not enough experimental data available below glass transition temperature i.e. in the glassy state due to lack of investigating tools [73-76]. The behavior of metallic glass is very different from network forming glass. Ruta et al. [77] studied sodium silicate network forming glass and found stretch exponential behavior. This networking forming glasses does not have physical aging property. Thus, the metallic glass requires a more intense source.
One of the very first experiment to understand dynamic evolution with a time below glass transition temperature that had been performed on metallic glass was Mg65Cu25Y10 both in the glassy state and the supercooled liquid phase by B. Ruta [78, 79] in 2013 and 2014.
The physical quantity that captures the slowing down particle motion is the time present as structural relaxation time, which is proportional to viscosity and represents the time required for shear relaxation. The structural relaxation is measured by an intermediate 44
scattering function which gives the information
about the evolution of atomic dynamics at an
interparticle distance and the function measured
Well Below 푻품 as density fluctuation on a length scale ~2π/q
where q is ~2.56 Å-1 shown in Figure 2.8.
According to their experimental study, the Below 푻품 Near supercooled region metallic glass behavior deviates from Arrhenius
plot. Although it is yet unknown the real reason
of non-diffusive nature of the material. The
Approaching Melting Temp. earlier study indicated that atomic dynamics has
been associated with begin of crystallization
Figure 2.8 Dynamic behavior of the process and relaxation of internal energy stored Mg65Cu25Y10 in glassy and with in the amorphous material when it is supercooled liquid state. (a) at 358K fast aging occurred, (b) Equilibrium quenched very fast. The exponential shape of
dynamics at 408 K and (c) KWW intermediate scattering factor in different in function fitting curve both glassy and super cooled states.
Temperature dependent structural relaxation time were observed. In Figure 2.9 showed that in liquid state relaxation time matched with macroscopic observation of viscosity data indicated as triangle. The function is stretch exponential shape (shown as full circle) observed in glassy state when the as quenched sample was heated very slowly and it is much different than the exponential function which observed in super cooled liquid state
(shown as star symbol). The measurements were taken at different thermal history i.e. is partially annealed at high temperature in glassy state and cooled back to the lower 45 temperature. The plot showed that the relaxation time decrease at the temperature increases and near 400oC and increased with that temperature. This type of behavior were observed due to slow heating associated with density change in the material close to Tg. If the sample is heated up high temperature without giving long time to rearrangement of the structure, then this step was not observed. Compressed exponential function was observed in glassy state and stretched exponential function in super cooled liquid state as mentioned in Figure
2.8. In the glassy state, the dynamics is not frozen, the relaxation time is very slow and compressed behavior were observed (β~1.5). As the sample far from glass transition and completely non-equilibrium system it had lot of internal energy stored and they structure rearrange themselves. The atom dynamics behave differently if the thermal history is different such as the sample was partially annealed and cooled down the temperature causes achieving equilibrium was much easier. The exponential function is still compressed, however, value β~1.15 much lower. It is interesting to find that after sometime the system become equilibrate and the annealing time does not have any effect on material. If the sample is examined the super cooled liquid state, the exponent become stretched (β~0.88) and it was not depending on the aging or thermal history of the material. Another experiment of X-ray photon correlation spectroscopy was performed by same group at
Zirconium based metallic glass to compare the behavior of atomic dynamics with the 46
structural glass Mg65Cu25Y10. The relaxation time, which represents the time necessary for the system to rearrange the structure towards more stable stage, is very large with waiting time [80]. In Zr-based metallic glass, the structural relaxation required ~ 103 Figure 2.9 Temperature dependence of the – 104 sec whereas the usual believe is structural relaxation time obtained from the that atom dynamics is frozen. However, analysis of the XPCS data following two it is interesting that like the previous different thermal paths (circles and stars). The arrows indicate the followed thermal paths, metallic glass the relaxation time slows while the dotted-dashed line is just a guide for down very rapidly and it is compressed the eye indicating the macroscopic behavior of the glass were observed. equilibrium liquid dada (empty triangles) [80]
The value is β~1.8 (β is decay of density fluctuation) which is higher than the Mg65Cu25Y10 and reason atomic mobility of
Zr-based glass is more than the Mg-based glass which means the internal stress is higher in Zr-based glass. This two separate experiment also depict that the atomic motion is ballistic rather than diffusion. Like any other experiment in metallic glass it is not possible to observe wave –vector dependence behavior as third generation synchrotron x-ray does not have such high intensity.
In 2015, a La-based metallic glasses dynamic study on as-cast and annealed sample had been reported by Wang et al. [81]. They showed fast and slow secondary relaxation process in addition to primary relaxation across temperature ~200 – 400 K. Recently in 2016, 47
Nogales and Fluerasu reported a detailed study of polymer dynamics by XPCS [82]. In
2016, Giordano and Ruta [83] very first who reported structural arrangement responsible for atomic dynamics in metallic glasses during physical again. To understand physical aging of metallic glass both dynamic and structural studies were performed by XPCS and
XRD. Usually, slight structural changes observed by high-resolution synchrotron XRD causes dramatic dynamic changes and XPCS experiment can reveal that. The decay of intensity correlation function describe by their new finding shown in the Figure 2.10.
Therefore, at the initial state of the glass particles are shown in the sample volume in the blue circle, and due to temporal evolution, the particles start to change its position shown by green circle (Figure 2.10 (a)). When g2(t) − 1 is zero indicated the intensity of that atom was not any more correlated on the experimental time scale, implying that the system is able to rearrange its structure indicating that they have moved of a distance equal to 2π/Q on the probed spatial length scale of few Å.
Their study as revealed that the fast aging shown in the Figure 2.10 (b) is dynamical aging, which causes density change in the sample volume, Figure 2.10 (a) Schematic representation of Intensity auto increases the relaxation correlation function with time of XPCS incorporated with particle movement in sample volume. (b) Dynamic ageing time during annealing of cause volume change with time, (b) Volume change become constant at stationary dynamics adapted from [83] the metallic glass. 48
However, when density inhomogeneity or the free volume completely annihilated which particles are constant to that volume give rise to the situation Figure 2.10 (c), stationary dynamics. These particles can still move and changes glass configuration towards medium range order. Form dynamic standpoint the relaxation time become constant.
Therefore, X-ray photon correlation study can reveal (i) the dynamic structure factor of liquids on length scale down to the interatomic spacing, including colloidal systems, liquid crystals, polymers and metallic glass. (ii) Solid alloy phase transitions and nucleation and growth studies, and order-disorder transition. (iii) Surface dynamics study on single crystal surfaces, and pattern formation dynamics accompanying surface chemical reactions, including during in-situ crystal growth (iv) internal conformational dynamics of polymer molecules and (v) dynamics of short range density fluctuations at the glass transition and even at a lower temperature.
2.4 Experimental Details
Fabrication of Ribbons for XPCS experiment
The amorphous alloy ingots (Ni.60Nb0.40)70Zr30 is fabricated by arc melting process. The Ni,
Nb and Zr alloys annealed and fractured in several large grains. Then these grains loaded into a boron nitride sample holder (with a small slit at the bottom). An induction coil in the melt spinner is used to melt the alloy at ~1600oC. Then, the melt is released on a fast rotating Cu-Be alloy lined drum (which is water-cooled) cooling rate is 106 K.s-1. The width of ~1′ and ~3-4 feet long and (30-60 m) thick amorphous ribbons are prepared. By further polishing of this ribbon, ~25-27 m thickness is achieved for the XPCS experiments (for enhanced transmission of the x-ray beam). For the purpose of hydrogen dissociation, 49
usually, a thin film of Pd is deposited. Hara et al. [24] showed that amorphous Ni64Zr36 contains sufficient Ni to enable hydrogen permeation without the need for an additional catalytic overlayer of Pd. Further examination by Spit et al. [18] and Adibhatla et al. [84] found Ni segregation on the surface of the alloy that promoted this catalytic activity. Thus, we plan to use ribbons without Pd coating.
2.5 Results and Discussions
2.5.1 XPCS Results
XPCS experiment performed on binary Ni60Nb40 and ternary (Ni0.6Nb0.4)70Zr30 amorphous ribbons. There are several issues concerning the hydrogen solubility in the binary and ternary Ni-based amorphous alloys. Therefore, we need to explore both systems at dynamic level. We found that the permeability of the binary alloys is very low as compared to the ternary ones, as shown in Error! Reference source not ound.. Moreover, we do not have a comprehensive idea about the metallic alloys internal arrangement of atoms, Figure 2.11 Hydrogen permeability of and their local atomic structure as well (Ni0.6Nb0.4)100-xZrx (x = 0, 30 at. %) alloys. as atom dynamics. To analyze the atom dynamics property of the amorphous membrane in local atomic level, the data are collected in XPCS experiment at the position of first sharp diffraction peak of the metallic glass at wave-vector 2.56 ∓ 0.04 Å−1. Therefore, all the pixel measurement performed at the 50 maximum static structure factor at that wave vector, which eventually gives us the information about inter-particle distance. The structure peak for both the ribbons is (2θ~ 38o) measured by CCD detector shown in Figure 2.12. We collected about 975 and 250 images for Figure 2.12 Structural measurement on a sample of Ni60Nb40 without and with Ni60Nb40 by CCD camera hydrogenation (0.6 mbar) condition at
373K with 7 seconds exposure time at the maximum structure factor region shown in the
Figure 2.13. Afterward, we dehydrogenated the sample chamber to understand metallic glass behavior. The experiment were performed with heating and cooling rate of 3 K/min.
The data processing and analyzing were done by the method describe by reference [54] and above. To check the experimental data, the XPCS measurement is planning to perform several times at same temperature and same hydrogen pressure. We will perform almost same experimental protocol for both binary and ternary alloy to compare the results of the both system.
The two-time correlation function 퐺 (푞, 푡1, 푡2) measured at Ni60Nb40 binary metallic glass in vacuum and in hydrogen at 0.6 bar at 373K for different waiting times (in vacuum waiting time was 4600 seconds and 12700 seconds for hydrogen) once temperature equilibration is obtained. In general, the atoms that have moved from initial position to different position are represented by the blue spotted regions, and the reddish regions are 51
atoms that are stationary. The broadening of the reddish line along the main diagonal from
the bottom left corner to the right top corner is proportional to the structural relaxation
time, τ. Parallel to the diagonal reddish line inside the blue region is the delay time, 푡푑 =
(푡푓 − 푡푖) where 푡푓 and 푡푖 are final time and initial time for image taken. The waiting time
of the sample inside the vacuum called ageing time represented by the equation 푡 = (푡푖 +
푡푓)/2 .
At the beginning of the experiment, when annealing time 푡푎 = 0, only diagonal will
appear. In the Figure 2.13 (a) broadening of reddish line along the diagonal from the top
side of the diagonal represent the little bit slowing down of atomic motion i.e. aging in the
system, total 975 images were taken into consideration. Addition of hydrogen, changes the
reddish region very rapidly and the atomic movement Ni and Nb become faster which
975
12700
(s)
(s)
2
t
2
t
0 330 650 650 330 0 0 330 650 975
11700 12000 12400 12400 11700 12000 11700 12000 12400 12700 t1 (s) t1 (s) Figure 2.13 (a) Intensity correlation function of relaxation time (τ, s) for Ni60Nb40 at 373
K under vacuum and (b) 1 bar H2
indicated atom rearrange themselves in a very short time. The data taken after ~12700
seconds aging time temperature considering ~ 250 image shown in Figure 2.13(b). 52
Intensity correlation function is measured at 373 K both vacuum and hydrogenated conditions showed in the Figure 2.14. The autocorrelation function (g2−1)/c showed full decay indicated atomic moment 2π/q and relaxation time τ varies with waiting time. At the beginning of the experiment sample placed inside the vacuum, designated by V with an annealing time, ta= 1600 seconds (triangle) and ta= 4600 seconds (dark blue circle) shown in the Figure 2.14. As the waiting, time increases, the system ages as signaled by the continuous shift of the decay time. The relaxation time for the plot taken with sample under vacuum shows longer relaxation time, = 946 seconds and = 1270 seconds as the aging time, 푡푎 increases from 1600 seconds to 4600 seconds. In the next step, we introduced hydrogen in the system in the same temperature. The sudden shift of the curve observed; the annealing time was 12700 seconds and shown in the Figure 2.14 by brown 53 colored triangles which strongly implies that atomic motion becomes faster due to hydrogen in a system and decay shift towards two order magnitude shorter time scale.
Addition of hydrogen causes drastically change in relaxation time, = 25 seconds. This also suggests atomic rearrangement occur at much faster rate when we introduce hydrogen in a system. In subsequent experiments, we removed the hydrogen by evacuating the chamber at same temperature 373K and observed gradual shift of the curve towards its earlier vacuum condition, which designated by vacuum, V. These shift of the curve in the right hand side causes increase in relaxation time suggesting slowing down the atomic movement. In Figure 2.14, continuing hydrogen removal from the ribbon with waiting time
16500 seconds to 39000 seconds, the relaxation time increases and atomic dynamics
Figure 2.14 Reversible Intensity correlation function of Ni60Nb40. Grey allow indicate the evolution of instantaneous and reversible dynamics of binary amorphous alloy. 54 become slower and slower. This process suggested that the atoms are trying to retract back to their original position. The dynamics slow down displayed full decorrelation 푔2(푞, 푡) to zero which means the system is relaxed into equilibrium state temporarily; however, it can be evolved different macroscopic glassy configuration [85].
The relaxation times () vs annealing time shown in the Figure 2.15 for each condition.
The initial vacuum region (V, Circle) in which the as-cast ribbon was equilibrated under vacuum, the hydrogen region (H, Diamond) during which the sample was exposed to hydrogen, and the third region vacuum (V, Star) again, during which dissolved hydrogen was purged from the alloy under vacuum at 373K. The Figure 2.15 shows that the metallic glass Ni60Nb40 system in vacuum require more time to rearrange the Ni and Nb atoms around themselves ~104푠푒푐표푛푑푠. However, introducing hydrogen in the system the structural relaxation time decreases three orders magnitude. After removing hydrogen i.e. dehydrogenation the chamber, the time require for rearranging the atom themselves are
Figure 2.15 Evolution of the structural relaxation time during hydrogenation and dehydrogenation in Ni60Nb40. 55 increasing and given proper annealing time to the system, it comeback to its initial condition. However, sufficient time is required for the system to go back to its original position suggested that a degree of hydrogen trapped inside the alloy.
The main feature of any glassy liquid system near glass transition temperature is relaxation time as mentioned above and there a distribution of relaxation time express in terms of exponent 훽 of equation (10) which is also called as “shape parameter” [86]. Shape parameter 훽 in α-relaxation is that the atomic jumps from one “cage” to nearing “cage” in different relaxation time of metallic glass leads to an exponential behavior. In glass forming liquid if 훽 < 1 then it called stretch exponential behavior and the opposite 훽 > 1 referred as compressed exponential behavior [86]. The universal behavior of supercooled liquids is stretch exponent behavior i.e. 훽 ≤ 1. The concept is that below glasses transition temperature very rapid change in atomic motion contribute to the narrow distribution of relaxation and the region which is faster than average dynamics contributed to the decay of correlation function [85], β is close to 1 but still not higher. Madsen et al. [52] paper gave us the reason to exclude two possibilities first 푔2(푞, 푡) averaged over different time interval effect on exponential behavior of any system and secondly it is not possible that atomic motion increases below glass transition temperature. This β value does not depend 56 on the time interval over which auto correlation is averaged. Figure 2.16 showed that β value is independent of wave vector (푞) and annealing time (푡푎). We conclude the fact by rescaled the dynamics in a single master curve by reporting the correlation functions as a function of the rescaled time t/τ we observe the Figure 2.16. The β values also shown in the figure indicated compressed exponential behavior of the glass as β > 1. In vacuum,
Figure 2.16 Normalized auto correlation function for Ni60Nb40 derived from two-time correlation function plotted as a function of t/ the β values are 1.85 and 1.86 respectively. Hydrogen addition causes decrease in β value
1.37. Dehydrogenation of the system causes increase in the β value (~2.03). Therefore, compressed the exponential behavior of the metallic glass does not change even addition and removal of the external gas; the universal feature of supercooled liquid is not followed here. 57
Stretch exponential behavior for a soda-silicate glass is 0.6 [40], but significantly very large compressed exponential behavior for amorphous alloys Mg65Cu25Y10 [78] and Zr67Ni33
[79] have been reported earlier. Some polymeric glasses, colloidal glasses, and nano- particle in glass former matrix shows many papers have shown similar kind of compressed exponential behavior. This type of compressed behavior cannot be explained by current universal glass theory. The most well-established fact to explain compressed exponential behavior of the glass is the relaxation of internal stress or excess free volume which store inside the glassy liquid system during the quenching during fabrication of glass [85, 86].
This compressed behavior of the glass is ballistic motion rather diffusive. Like any other
Mg and Zr- based metallic glass, the Ni-based binary alloy may be behaving similarly because of a large amount of internal stress generated during quenching and a large amount of time require from the rearrangement of the structure. In our binary system, the β values are 1.76 and 1.37 in vacuum and hydrogenated condition respectively represents compressed exponential behavior. Hydrogenated condition exponential function is relatively faster than previously observed amorphous alloy exponential function. The reason is small atom like hydrogen causes significant changes in the relaxation process. To better understand these process, we examined ternary alloy. These study will reveal whether the hydrogen causes similar changes in the atom dynamics even addition of other heavier atom like zirconium in the system. 58
The two-time correlation function 퐺 (푞, 푡1, 푡2) measured for ternary (Ni.60Nb0.40)70Zr30 metallic glass in vacuum and hydrogen at 0.6 bar at 273 K and 373K at ~3600 seconds waiting time once temperature equilibration is obtained. In the Figure 2.17 (a) shows, two- time correlation function 퐺 (푞, 푡1, 푡2) at room temperature 273K. It is interesting that after introducing hydrogen at 0.6 bar even at room temperature atomic movement is comparatively faster than room temperature vacuum condition shown in the Figure 2.17
16200 3600 (a) (c) 273K Vacuum 373K Vacuum
(s)
(s)
2
t
2
t
4050 8100 12150 12150 8100 4050
0 1200 2400 2400 0 1200 0 1200 2400 3600 4050 8100 12150 16200 t (s) t1 (s) 1
16200 (d) 3600 (b) 273K Hydrogen 373 K Hydrogen
(s)
(s)
2
2
t
t
4050 8100 12150 12150 8100 4050
0 1200 2400 0 1200 2400 3600 4050 8100 12150 16200 t1 (s) t1 (s) Figure 2.17 (a) Two-time correlation function at 273 K (b) Two-time correlation function at 273 K after introducing hydrogen at 0.6 bar, (c) Two-time correlation function at 373 K (b) Two-time correlation function at 373 K after introducing hydrogen at 0.6 bar 59
(b). At higher temperature 373K in a vacuum, atomic movement faster than room
temperature vacuum condition as shown in the Figure 2.17 (c) as it shows less broaden
diagonal spectrum than Figure 2.17 (a). However, introducing hydrogen in the system at
373K and 0.6 bar, very sharp diagonal lines are appeared shown in the Figure 2.17 (d). In
both binary and ternary alloys, the hydrogen causes significant effect on atom dynamics
due to addition of hydrogen.
The intensity correlation function showed in the Figure 2.18 (a) at 373K both vacuum and
hydrogenated conditions with almost same waiting time ~9200 seconds. In general, the
intensity correlation function is related to the density fluctuations, which provided
information about overlapping between atomic configuration and its evolution with time.
The autocorrelation function (g2−1)/c showed full decay like binary alloy. At the
beginning, when sample in vacuum with an annealing time, ta~ 9200 seconds showed
relaxation time ~ 9780 seconds. Introducing hydrogen causes a sudden shift of the curve
on the left-hand side with a relaxation time of ~375 seconds. Intensity correlation function
in case of hydrogen at room temperature 273K and 373K showed a significant change in
1.2 (b) 1.0 (a) 1.0
0.8 0.8
Under vacuum o τ = 9780 s 22 C 0.6 0.6
373 K Accelaration of dynamics
,t)-1)/c ,t)-1)/c due to hydrogen
p
p 0.4
(q (q t =1160 s (22C) 0.4 a
2
2 t =2300 s (22C) a
(g
(g t =6980 s (100C) 100oC a 0.2 0.2 t = 9200 s (V) t =9300 s (100C) a Under hydrogen a 1.20 1.25 1.30 t = 93001.35 s (H)1.40 1.45 1.50τ = 375 s1.55 t =16200 s (100C) a a 0.0 0.0 10 100 1000 10000 10 100 1000 10000 t (s) t (s) 6 Figure 2.18. (a) Intensity correlation function at 373K on vacuum and 0.6 bar 5 hydrogen (b) Intensity correlation function at room temperature and 373 K 4
3
2
1
0
-1
-2 60 the plot Figure 2.18 (b). At 273K, the annealing time is 1160 and 2300 seconds showed relaxation time increases and the decay line shifted right-hand side and showed the atomic movement become slower. At higher temperature 373K, similar results are obtained due to increase in annealing time from 6980 seconds to 16200 seconds. Increase in temperature causes faster movement of heavier atoms.
The relaxation time vs. annealing time in both vacuum and hydrogen for 373 K showed in the Figure 2.19 (a). This vacuum data (circle) clearly indicated larger relaxation time than after introducing hydrogen into it. Expanding the hydrogen data for the ternary alloy in the plot relaxation time vs. annealing time, showed in Figure 2.19 (b) almost linearly the hydrogen movement become faster with decreasing annealing time.
540 β = 1.90 510 (b) (a) 480 β = 1.74 450 β = 1.80 β = 1.90 τ =481 s 420 τ =437 s 390 τ =412 s τ =409 s 360
330 β = 2.03
Relaxation time (s) 300 τ =310 s 270 Hydrogen
6000 8000 10000 12000 14000 16000 Annealing time (s) Figure 2.19. (a) Relaxation vs annealing time both in vacuum and hydrogenated condition (b) Expanded region of Relaxation time vs annealing time at hydrogenation condition It is interesting to observe that acceleration of the atomic motion at hydrogenated condition occurs in both amorphous samples even for low H2 pressure and temperature (P = 60 MPa and T = 373 K) where the solubility of hydrogen is much higher shown. H2 permeability is usually poor due to the slow hydrogen diffusivity at such a low temperature of 273K and
373K. Internal friction studies revealed that the characteristic time for H2 jumps is only τH 61
(373 K)~0.85 μs at the probed temperature [25]. XPCS can measure the ultraslow dynamics in glasses allows us to observe the effect of hydrogenation even if the diffusion coefficient of the metallic glass [87] is ~7푥10−24 m2/s and ~2푥10−22 m2/s under vacuum and hydrogen atmosphere respectively.
The effect of hydrogen on metallic alloy explained by the free volume theory. Based on the literature, we propose [89] that Ni-based amorphous material have icosahedra clusters
Figure 2.20 (i) Icosahedra structure, (ii) hydrogen goes inside the icosahedra structure, (iii) Removal of hydrogen from icosahedra cluster. as shown in the Figure 2.20 (i) where 5 atoms of Ni (Yellow), 5 atoms of Zr (Red) and 3 atoms of Nb (Green) formed icosahedra structure. Although it is difficult to identify
“vacancy” in an amorphous structure as it requires neutron vibrational spectroscopy (which discussed later), yet it is expected that hydrogen atom prefers tetrahedral and octahedral sites of binary and ternary alloys. If hydrogen atoms go to preferred vacancy sites, the atomic cluster containing hydrogen will be lower energy barrier [88]. It is easier for an atom to rearrange themselves, which causes a sudden shift of the intensity auto-correlation function. In addition, hydrogen atoms goes inside the icosahedra cluster and expands it slightly. As a result, during dehydrogenation process, hydrogen removed from the particular sites and the whole configaration try to go back its earlier position shown in
Figure 2.20. Some energy sites like ZrH2 trapped hydrogen and it is very difficult to remove 62 it, which causes more time to go back to the icosahedra to its initial position. To understand more about binary and ternary membrane ribbons complementary extended X-ray absorption fine structure (XAFS) were performed. Extended x-ray absorption fine structure
(EXAFS) is a powerful technique to understand the atomic-level structure of disordered materials like metallic glass. Here, the experiment carried out at beamline BM23 ESRF to understand hydrogen effect on low temperature on binary and ternary alloy as the permeability of the alloys are negligible at such a low temperature. Moreover, these results also revealed about local atomic order around selected atomic species like Zr and Nb. In this work, we employed EXAFS analysis to follow the microstructural evolution under
applied hydrogen, helium loading in a Ni60Nb40 and (Ni0.6Nb0.4)70Zr30 alloy.
2.5.2 Extended X-ray Absorption Spectroscopy Results
The EXAFS experiments at the Nb K (18985 eV) edge and Zr K (17998 eV) edge were carried out in transmission at the BM23 beamline the European Synchrotron Radiation
Facility at ESRF. Figure 2.21 (a) showed the Nb K-edge and Figure 2.21 (b) Zr K-edge k3- weighted χ(k) oscillations and magnitude of their Fourier transform (FT) at room temperature in vacuum at nitrogen atmosphere. The measured EXAFS value is an average of χ(k) functions of all the absorbing atoms in the irradiated volume, the degree of regularity in local atomic arrangement around the absorbing species is proportional to the amplitude of the corresponding EXAFS [90]. In our experimental data, the amplitude of
EXAFS is approximately 40% lower in the Nb than for the Zr edge. This indicates the fact that carries a degree of short-range order (SRO) around Nb and Zr atoms. The SRO is more in Zr atom than Nb atom. These results are comparable to our atom tomography data where the Zr cluster (~7nm) formation is more pronounced than Nb cluster (~2nm). The 63 experiment also performed in hydrogenated conditions. Increasing the temperature up to
300oC both in hydrogenated and vacuum no significant changed were observed in XAFS shown in the Figure 2.22. The Zr and Nb edge have not been changed in 300oC about 1
(a) (c)
(b) (d)
Figure 2.21 (a) Nb K edge and (b) Zr K edge k3-weighted EXAFS oscillations and (c)
(d) magnitude of their Fourier transforms at room temperature in vacuum and N2 condition hour.
After increasing the temperature at 400oC, Nb and Zr K-edge k3-weighted χ(k) oscillations and magnitude of their Fourier transform (FT) in a vacuum and hydrogenated condition together shown in the Figure 2.24. Small increase in the amplitude is observed in both vacuum and hydrogenated condition from room temperature to 400oC for Zr K-edge shown in Figure 2.24 (a) and Figure 2.23. It is well observed that the hydrogenated condition difference in amplitudes is stronger than the vacuum shown in the Figure 2.23. However, in Nb k edge, χ(k) oscillations and magnitude in vacuum condition revealed a small 64
(a) (c)
(b) (d)
Figure 2.22 (a) Zr K edge and (b) Nb K edge k3-weighted EXAFS oscillations and (c) (d) magnitude of their Fourier transforms at room temperature in vacuum and Hydrogenated condition at 300oC decrease in the first peak and a small increase in the second peak. In hydrogenated condition, small decrease of the first peak and small increase of the second peak after coming back from 400oC to room temperature is observed in Figure 2.24 (b) and Figure
2.25, If the second peak is related to Nb-Zr interactions, then its increase is consistent with
Zr edge, where the first peak is related to Zr-Nb and increases after annealing. Oji et al.
[91] performed similar experiments with a different hydrogenated sample of Zr30 and
Zr40. According to their study significant changed were observed in Zr-Zr/Zr-Nb distance for both alloys. In our case, Zr-Zr/Zr-Nb distances vary at higher temperature ~400oC, which indicated the similar behavior. Sakurai et al. [92] also indicated an increase in Zr- 65
Zr distances with the addition of hydrogen in the system. The results of room temperature 66
(a) (c)
(b) (d)
Figure 2.24 (a) Zr K edge and (b) Nb K edge k3-weighted EXAFS oscillations and (c) (d) magnitude of their Fourier transforms in vacuum and hydrogenated condition at 400oC
(a) (c)
(b) (d)
Figure 2.23 Zr K edge k3-weighted EXAFS oscillations in vacuum (b) in hydrogenated condition and (c) (d) magnitude of their Fourier transforms at at 400oC in vacuum and hydrogen XAFS showed more short-range order Zr type region than Nb. The DFT calculation along 67
(a) (c)
(b) (d)
Figure 2.25 (a) Nb K edge k3-weighted EXAFS oscillations, (b) in hydrogenated condition and (c) (d) magnitude of their Fourier transforms at 400oC in vacuum and hydrogen with XAFS data from literature [89] revealed that the Ni-Nb-Zr structure are icosahedra and atom tomography results showed the cluster size are bigger in the Zr-rich regions. In metallic glasses, the icosahedra play an important role to stabilize the metal-metal structure. Although the dynamic behavior of the samples changed drastically showed in the above results of XPCS due to expansion and contraction of icosahedra structure at low temperature due to hydrogen, however, structural changes almost unnoticeable up to 300oC from XAFS results; these changes are prominent at higher temperature. Therefore, it is important to understand hydrogen dynamics inside the system at lower temperature, thus we perform inelastic neutron scattering to find position of hydrogen inside the glassy metal matrix. 68
Chapter 3 Neutron Characterization Studies of Disordered Materials
Contents
3.1 Introduction to Neutron scattering studies …………………………………..66 3.2 Inelastic neutron scattering ………………………………………………….74 3.3 Dynamic Neutron Vibrational Spectroscopy ………………………………...77 3.3.1 Basic Principle…………………………………………………….. 77 3.3.2. Experimental Details……………………………………………... 97 3.3.3. Result & Discussions……………………………………………. 101 3.4 Neutron Total Scattering experiment (HIPD)……………………………….129 3.4.1 Theory of Total Neutron Scattering ……………………………...129 3.4.2 Result and Discussions ...………………………………………... 132 3.5 Small angle neutron scattering (SANS)…………………………………….135 3.5.1 Brief Theory………………………………………………………………136 3.5.2 Result and Discussions……...…………………………………………….140
3 Neutron Characterization Studies of Disordered Materials
3.1 Introduction to Neutron scattering studies
The inelastic neutron scattering experiment performs to understand hydrogen dynamics inside the amorphous system. Neutron has no charge, and their electric dipole moment is either zero or too small to be measured by the most sensitive modem techniques. For these reasons, neutrons can penetrate far better than charged particles and able to detect smaller atom like hydrogen. Moreover, neutrons interact with atoms by nuclear forces rather than electrical. These nuclear forces are a very short range of the order of a few fermis (1 fermi
= 10-15 meter). Some of the neutron property listed in Table 3.1. 69
Table 3.1. Properties of the neutron [93]
Two important thing is in neutron that energy and momentum transfer. Therefore, if Energy
= E, Momentum = k, Wavelength =
1 So, the De- Broglie’s equation, 퐸 = ħ휔 = 푣́ ℎ푐 = 푚 푣2 2 푛
푃푙푎푛푘 푐표푛푠푡푎푡 (ℎ) ħ = , 휔 = 퐴푛푔푢푙푎푟 푓푟푒푞푢푒푛푐푦, 푣́ = 푤푎푣푒푛푢푚푏푒푟, c=speed of light, 2휋
푚푛 = 푛푒푢푡푟표푛 푚푎푠푠, v= velocity
푃푙푎푛푐푘 푐표푛푠푡푎푛푡 (ℎ) ℎ = = = ħ. 2휋⁄ 푚푛푣 푀표푚푒푛푡푢푚 (푘) 푚푛푣
2휋 푚 푣 = 푛 = 푘 ħ
It is interesting that the energy unit in neutron is meV or THz, Therefore,
1 푚푒푉 = 0.2418 푇ℎ푧 = 1.602 × 10−22퐽 = 8.066 푐푚−1
1 푀푒푉 = 106푒푉 = 9.65 × 107퐽 = 8.066 × 109 푐푚−1
푘푇 = 25푚푒푉 푎푡 푟표표푚 푡푒푚푝푒푟푎푡푢푟푒
Momentum unit is 푘푔. 푚푠−1 and neutron wavelength is Å and wave vector isÅ−1. 70
Interaction of neutron with the nucleus of the sample governs by strong nuclear force 36 meV. Instead of nuclear force, a specific interaction force consider as Fermi pseudo- potential. Two type of modes are observe here; Neutron-Lattice mode (external mode) causes due to molecules rigidly displaced from its equilibrium position and Internal mode i.e. local molecular deformation causes harmonic displacement of the atoms. Neutron elastic scattering reveals information about the atomic structure; however, inelastic neutron scattering reveals atom dynamics [94]. In XPCS experiment, we are able to measure Ni,
Nb, Zr atom dynamics inside the amorphous materials. However, we do not know about the atom dynamics of hydrogen inside the metallic glass matrix. Synchrotron x-ray is not able to detect hydrogen due to their small size as discused in the last chapter. Therefore, inelastic neutron scattering (INS) is performed. Before going to the details to inelastic neutron scattering, it is important to understand the characteristic of neutron scattering.
The neutron and x-ray scattering shown in Figure 3.1 taken from ref [95]. The x-rays and electron beams depicted as violate and Nuclear (Nuclear Nucleus Electron Scattering interaction) green line respectively. X-ray interacting
with electrons in the material is
Surfac e electromagnetic, whereas, with an electron Neutron beam interaction is electrostatic. The red line depicted as neutrons and it is interacting X-ray with atomic nuclei. Neutron has the very Electron Electrostatic Electromagnetic interaction interaction short-range strong nuclear force and thus Figure 3.1 Neutrons beam, x rays, and penetrate matter much more deeply than x electrons interact with material by rays or electrons [95]. In the material, if different mechanisms [95]. 71 unpaired electrons situated then it could be possible for a neutron to interact by a second mechanism. In the second mechanism, a dipole-dipole interaction occurs between the magnetic moment of the neutron and the magnetic moment of the unpaired electron.
Neutron represents dual nature; wave and particle property. The wave nature of neutron causes oscillation sinusoidally in time and space. The square of the amplitude of the wave function gives information about the probability of the neutron found from a particular point. In either case, wave or particle function represents the neutron oscillation or the probability of that particle of the neutron at a given location, depicts same mathematical result.
Characteristic of neutron scattering
Few advantages and disadvantages of neutron scattering over synchrotron X-ray or light scattering discussed below.
Advantages
1. The scattering length of neutron vary significantly with an atomic number;
therefore, a wide range of material is possible for the experiment.
2. Neutrons have low absorption and very high penetration property than light or x-
ray.
3. Neutron scattered by nuclei and X-ray scattered by atoms. The nuclei resemble of
point whereas atom sizes are comparable to the wavelength of the probing radiation.
4. In neutron scattering, both structural and dynamic property of condensed matter
possible to measure as it can transfer exact amount of momentum and energy.
72
Disadvantages
1. Generation of the neutron is very difficult. The neutron source is very expensive to
build and maintained properly. For example, the cost to run one neutron source is
almost cover the complete electric bill of USA.
2. Neutron experiment required a large amount of sample compared to X-ray or light
due to low flux. Therefore, the neutron source is limited for investigations of rapid
time-dependent processes. For NVS experiment in amorphous material requires
almost 1 gram of sample.
Neutron generation in a nuclear reactor: Chadwick [96] discovered the neutron in 1932. In nuclear fissile nuclides are U-233, U-
235, Pu-239, and Pu-241. However, U-235 and Pu-239 are commonly used to generate neutron shows in Figure 3.2. In a nuclear reactor, U-235 mainly released 2-3 neutrons per fission reaction at the energy of 2 MeV. Each fission reaction released around 200 MeV energies. This large amount of energies released as kinetic energy of the fission fragments, gamma rays and 2-3 fast neutrons. The gamma rays and fast neutrons are highly penetrating and go to the detector very easily, which cause a nuisance; thus, shielding is used around the detector. To continue the fusion reaction, light (H2O) or heavy water (D2O) moderators are used which slows down the reaction and formed thermal neutron of 0.025 eV energies.
This slow down process also helps to reduce lower beam tube energy. However, this process does not convert entire neutrons to thermal neutrons. Some of the neutrons are absorbed by radiation, or leak out of the system before going to the detector. The process of producing thermal neutrons have maintained by the collision of low atomic material; 73 water used as both moderator and coolant. The reflector minimizes the neutron leakage. Heavy water (D2O), beryllium or graphite are used to reflect back the neutron inside the core reflector. In a nuclear reactor, fission neutrons appear within 10-
14 sec of the fission event; therefore, these are called Figure 3.2 Generation of neutron prompt neutrons. Less than 1% neutron delayed during radioactive fusion reaction. These delayed neutrons play a significant role in the operation of the nuclear reactor because it controls the “nuclear chain reaction” by slow down intrinsic kinetics of overall fission reaction.
There are significant differences observed in between electrical power generation reactor and research reactor to achieve desirable flux. Usually, the core size of nuclear electric power generating reactor is very wide and 2-5% enriched U235 have used. However, the research reactors have a compact core and over 90% enriched U235 have been used. In
1942, first research was based nuclear reactor had established in University of Chicago.
Since then, worldwide 770 research and test-reactors had built.
Even though various neutron sources exist, only a few are useful for scattering purposes.
Different types of neutron sources have been used such as continuous reactors, spallation sources, some other neutron sources. Continuous reactors generate continues neutron, whereas, spallation source used for time-of-flight mode or pulsed mode.
Types of neutron scattering: To use neutron source for material characterization, it is very important to understand different types of neutron scattering. 74
1. Transmission Neutron scattering
The experiment consists of a monochromatic beam, collimation, and a neutron detector.
The beam generated from the time-of-flight method or spallation neutron source. The configuration shows in Figure 3.3. This is the simplest experiment among four types of neutron scattering. This Figure 3.3 Schematic diagram of transmission neutron scattering reveals information Transmission measurement [96] about the content of elements inside the sample and their relative fractions.
2. Elastic Neutron Scattering
The instrument consists of a monochromator, sample, and the detector shown in the Figure
3.4. The sample has scanned either step by step or by position sensitive detector. This type of neutron scattering can measure the scattered intensity with varying scattering angle (휃), if the wavelength of the neutron is λ. Suppose, Q is scattering range; then it can be written as푄 =
(4휋/휆)푠푖푛(휃/2). Diffractometers, reflectometers, and small angle scattering (SANS) instruments are Figure 3.4 Schematic diagram different types of elastic neutron scattering of diffractometer [97] instruments. They used same principle discussed above. The wave scattering range for diffractometer is greater than 5Å−1 and lower wave scattering ranges are covert by reflectometer and SANS instrument. This elastic neutron scattering reveals information about sample structures either in crystalline or disordered system.
75
3. Inelastic neutron scattering
Inelastic neutron scattering consists of the monochromator, collimator, crystal analyzer and detector shown in Figure 3.5. To resolve energy, transfer crystal analyzer has used during scattering. Although the Figure 3.5 shows quasielastic as well as inelastic method are same, however, there are certain differences observed. In quasielastic scattering, energy transfers are almost zero and inelastic scattering is finite energy transfers. Figure 3.5 Schematic diagram The triple axis, filter analyzer neutron scattering, the of quasi/inelastic scattering [97] time-of-flight and the backscattering spectrometers followed the principle of inelastic neutron scattering. These instruments are a cover wide range of energy micro to mega electron volt. Inelastic neutron scattering instruments can measure sample dynamics such as phonon, optic and other types of modes as well as structure of the materials. Diffusive modes are usually obtaining from quasielastic scattering.
4. Spin-echo neutron scattering
The spin-echo instrument consists of the similar configuration of previously discussed inelastic neutron scattering. The polarizer has added to the instrument, and crystal analyzer has replaced with spin analyzer shown in Figure 3.6. This technique measures time correlation instead of energy transfer. In this neutron spin analyzer, the number of spin precessions has tracked. The energy transfer is proportional to the difference between some spin precessions before and after the sample. The energy transfer also proportional to the neutron velocity change during scattering. As it is a time correlator, the probe times are in 76 the nanosecond range, and wave scattering ranges are in between 0.01 Å-1 and 0.5 Å-1. This spin-echo neutron scattering instrument has used for understanding diffusive motions in soft materials in condensed science. Figure 3.6 Schematic diagram of In this dissertation, elastic and inelastic neutron neutron spin echo [97] scattering have been used to understand lattice vibration as well as the structure of amorphous materials.
3.2 Inelastic neutron scattering Studies
Incoherent neutron scattering spectroscopy technique was the pioneering contribution of
Canadian physicist, Bertram Brockhouse in 1950s. In Incoherent INS spectroscopy, the local environment of the scattering atoms and the frequency measurement varies from 109 to 1014 Hz, which allows to study of the slow diffusive motion of in solids and the molecular vibration [99]. Thermal agitation causes an atom to displace from its equilibrium position, and the waves of atomic displacement have propagated throughout the entire crystal. The energy associated with these waves, or collective excitations are quantized, and the corresponding quantum of energy are known as a phonon.
When neutrons are inelastically scattered by exchanging energy with this excitation, a phonon created or destroyed in the samples and neutron loss or gain corresponding energy.
For example, a hypothetical INS spectrum of a molecular crystal and different types of possibility excitations happens across a wide frequency ranges. The elastic line (Figure 3.7 a) is due to scattering from atoms which localized in space, i.e. 휔 = 0 and inelastic lines 77
(Figure 3.7 b) result from scattering from atoms which vibrate in a periodic manner and with a fixed frequency shows in Figure 3.7 (b). The quasi-elastic scattering arises atoms jump from site to site, with is a period to which the instrument is sensitive, the elastic line
(a) (b)
Figure 3.7 Inelastic neutron scattering spectrum from a hypothetical molecular crystal (left), elastic, quasi-elastic and inelastic scattering region (right) [98] broadened by an amount that reflects the jump of the atom.
INS is complementary of the optical technique of inferred and Raman spectroscopy. It is especially suited for the study of a system containing hydrogen; incoherent scattering from proton is more than an order of magnitude stronger than from any other nucleus. Thus,
Neutron scattering particularly effective from hydrogen motion in the complex system. The total scattering cross section for hydrogen is 휎푡표푡푎푙(퐻) = 82.0 푏푎푟푛 where 휎푐표ℎ(퐻) =
1.76 푏푎푟푛 and 휎푖푛푐(퐻) = 80.3 푏푎푟푛. The hydrogen dynamics shows stronger vibration than any other heavy elements due to their large cross section area shown in the Table 3.2.
Deuterium addition causes a change in the system due to the mass of the oscillator has changed. The addition of deuterium instead of hydrogen the effective mass become doubled. Therefore the energy falls by √2 for a fixed vibrational force. Due to an order magnitude lower in scattering cross section for deuterium 휎푡표푡푎푙(퐷) = 7.64 푏푎푟푛 comparatively weak spectrum appear. Two advantages of the neutron over optical 78 technique such as Raman and Inferred that individual hydrogen can be studied because the spectrum are nit congested and also the vibration of one hydrogen atom do not interfere with other hydrogen. The Table 3.2 is show the coherent and incoherent cross section of different materials.
TableCross 3 sections.2. Cross (barns) section for(barns) 1 Å forneutrons 1 Å neutrons [93] Element σcoherent σincoherent σabsorption Hydrogen 1.74 79.60 0.1850 Deuterium 5.64 2.00 0.0030 Carbon 5.51 0.01 0.0020 Nitrogen 11.1 0.30 1.0300 Oxygen 4.15 0.09 0.0001
There are some advantage and disadvantage of inelastic neutron spectroscopy shown in
Table 3.3 [99]. The biggest practical advantage of neutron spectroscopy over the other system is that the penetration nature which permits to use aluminum for the fabrication of sample containers. However, for neutron diffraction where vanadium has used because scattering is almost entirely incoherent. Although these techniques have successfully used in crystalline material, extensive studies have not found in glass or amorphous materials due to kinematics limitation. This technique is more suitable for the study of the larger energy transfer and smaller momentum materials.
Table 3.3. Advantages and Disadvantages of Inelastic neutron Spectroscopy
Advantages of INS Disadvantages of INS Absence of selection rules, All vibrations observed Large samples needed Sensitivity to isotopic substitution especially H/D Lower resolution Ease of calculation of intensities Longer experiment time Penetrating radiation Low temperature required
79
Neutron scattering experiments are expected to reveal hydrogen dynamics of the Ni-Nb-Zr amorphous membrane. The neutron vibrational density of state is measured due to interaction of thermal neutron and exchange energy with lattice vibration by Neutron
Vibrational Spectroscopy (NVS) method. Each absorbed hydrogen atom has its characteristic vibration energies, which correspond to the specific local environment of the interstitial site [93]. Theses vibrational state can described the coordinating metal atoms and coordination geometry, and also the hydrogen-metal distance.
3.3 Neutron Vibrational Spectroscopy
In neutron vibrational spectroscopy, the density of the vibrational state is the number of vibration per wavenumber [93]. The vibrational frequency of a monoatomic crystal to a single frequency observed by Einstein. Total six vibrational frequencies are observed; three of them are transitional and three are rotational. There are usually 3푁푎푡표푚 − 6 internal vibration of isolated molecules spread over the energy range of 0 to 4400 푐푚−1. Typically, two types of dispersion curve observe – acoustic and optical.
3.3.1 Theory
In Quantum mechanics, the wavelength of the neutron wave is inversely proportional to the magnitude of the neutron velocity v =/v/ [93]. For the neutrons used in scattering experiments, the wavelength, 휆 is few angstroms. Neutron wave vector, 푘, therefore, magnitude of wave vector is 푘 = 2휋/휆. The wave vector 푘 and velocity of neutron 푣 related by the equation [93]
hk = mv (3.1) 2π 80
Where, Planck's constant represent as h, the mass of the neutron is m, and the momentum of the neutron is mv. The scattering of a neutron by a single nucleus described in terms of a cross section b. The neutron cross section usually measured in barns (1 barn = square meter) which represent the effective area presented by the nucleus to the passing neutron
[95]. The probability of neutron is to scatter in any direction with the same probability.
As indicated in Figure 3.7, elastic scattering occurs when there is no energy transfer i.e. both incident and scattered wave vector is 푘 and inelastic scattering occurs when there is both momentum and energy transfer, therefore incident and scattered wave-vector is 푘 and
푘′. Generally, the width of peaks is depending on the energy resolution of the instrument.
If the neutron beam scattered by the nucleus of the atom and travel in the 푥 direction and their plane wave represents as e푖푘푥 shown in the Figure 3.8 [95]. Due to isotropic scattering, the scattered neutron beam Figure 3.8 Neutron beam single scattering spreads as a spherical wave fronts and [95] 푏 1 amplitude is ⁄푟. Intensity of the beam possible to achieve by the amplitude factor ⁄푟.
In inelastic neutron scattering, the amount of momentum transfer represents as
ℎ ℎ 푄 = (푘 − 푘′) (3.2) 2휋 2휋 where k and 푘′ is the wave vector of the incident neutrons and scattered neutrons. The scattering wave range Q = 푘 − 푘′ is known as the scattering vector. In order to get 81 magnitude and direction of elastic scattering vector where 푘 = 푘′, so €= 0 at the scattering angle 2휃, the wave vector will be
4πsinθ 푄 = ⁄λ (3.3)
In case of inelastic scattering, where the wave vector is ≠ 푘′ , neutron will lose its energy when 푘′ < 푘 and gain its energy when 푘′ > 푘. The scattered intensity measured in a neutron diffraction experiment is called the structure factor,푆(푄). In order to calculate structure factor, 푆(푄) neutron count through the atoms of lattice both real and imaginary parts of plane wave exponential summation taken into consideration. The structure factor,
푆(푄) can be written as
1 2 2 2 푖푄.(푟퐽 − 푟퐾) − 푄 〈푢 〉 푆(푄) = 푏푐표ℎ ∑푗,푘 푒 푒 2 (3.4)
2 Where average square displacement is 〈푢 〉 and coherent scattering length is 푏푐표ℎ. Due to many atoms in the system, except at certain unique values of wave vector Q, these summations are zero. The non-zero values of structure factor is related to the structure of the crystal because the vectors 푟퐽 − 푟퐾 in represent the set of distances 푟 between different atoms 푗 and 푘 in the crystal. Elastic and inelastic scattering is possible to determine from structure factor, 푆(푄). If the values wave vector 푄 at which 푆(푄) is nonzero and wave vector 푄 is perpendicular to a plane of atoms causes scattering and if the value wave vector
푄 is any integral multiple of 2π/d where 푑 is the distance between parallel, neighboring planes of atoms, for values of Q that do not satisfy this condition, 푆(푄) = 0, that is inelastic scattering. Therefore, in inelastic scattering, scattering function 푆(푄, 휔) define as mixture of a coherent and incoherent scattering function. 82
푆 (푄, 휔) = 푆푐표ℎ (푄, 휔) + 푆푖푛푐표ℎ (푄, 휔) (3.5)
2 Total coherent cross-section is 휎푐표ℎ = 4휋〈 푏 〉 where 〈푏〉is scattering length of element,
2 2 averaged over all its isotope and spin states and 휎푖푛푐표ℎ = 4휋〈 푏 − 〈푏〉 〉 which indicates square deviation of the scattering length about its mean. Therefore, the above equation is coherent and incoherent scattering of few cross section.
The double differential cross section of neutron is the probability of the neutron scattering at a solid angle 푑훺 can be written as
푑2휎 푘′ = [(〈푏〉2푆 (푄, 휔)) + 〈 푏2 − 〈푏〉2〉 푆 (푄, 휔)] (3.6) 푑훺푑휔 푘 푐표ℎ 푖푛푐표ℎ
However, if we considered scattering angle and the energy, then
푑2휎 휎 푘′ = 푆(푄, 휔) (3.7) 푑훺푑퐸 4휋ħ 푘
dσ Thus, differential cross section as a function of energy used in elastic scattering and the 푑Ω
푑2σ integration over the energy transfer of double differential cross section used for 푑Ω푑퐸 inelastic scattering.
In order to understand hydrogen behavior in amorphous material Kirchheim [100,101] published the paper regarding hydrogen in amorphous metals. Their results showed density of hydrogen sites 푛(퐺푖) in amorphous metals are Gaussian function. According to their study,
푑푁 1 퐺 −퐺표 2 푛(퐺 ) = = 푒푥푝 [− ( 푖 ) ] (3.8) 푖 푑퐺 휎√휋 휎 83
Where 푑푁= number of sites available for hydrogen, G is the energy with the interval of 푑퐺 interval, 퐺표= mean free enthalpy related to standard state and 휎= width of the Gaussian function. In Farmi-Dirac distribution results only one electron or one proton i.e. hydrogen to occupy in the interstitial sites. Therefore, if hydrogen in state 푖 reacting with hydrogen in reference state of energy 퐺푟 , then, the hydrogen gas at one atmosphere pressure or hydrogen in normal sites can be represent as
(푉)푟 + (퐻)푖 = (푉)푖 + (퐻)푖 (3.9) where, 푉 is the vacant sites in state 푖 and 푟 respectively. Therefore, law of mass action give,
표 (푐푟 −푐푟)푐푖 퐺푖−퐺푟 표 = 푒푥푝 [− ( )] (3.10) 푐푟(푐푖 −푐푖) 푅푇
표 푐푟 = Concentration of site energy at reference state 퐺푟, 푐푟 = Concentration of hydrogen
표 energy at reference state 퐺푟, 푐푖 = Concentration of site energy at initial state 퐺푖, 푐푖 =
Concentration of hydrogen energy at initial state 퐺푖 shown in Figure 3.9.
Chemical potential at reference site 휇푟 of hydrogen in the reference state
푐푟 휇푟 = 퐺푟 + 푅푇푙푛 표 = 휇 (3.11) 푐푟 −푐푟
휇 is the chemical potential of hydrogen in the disordered material and in equilibrium condition,
표 (푐푟 −푐푟)푐푖 퐺푖−퐺푟 표 = 푒푥푝 [− ( )] (3.12) 푐푟(푐푖 −푐푖) 푅푇
푐푟 where 퐺푟 = 푅푇푙푛 표 − 휇푟 푐푟 −푐푟 84
표 푐푖 Therefore, 푐푖 = 퐺 −휇 1+푒푥푝( 푖 ) 푅푇
The above equation revealed that each energy associated with limited number of sites, so the occupancy of hydrogen will be
Figure 3.9 Potential of hydrogen in 푛(퐺) 표(퐺) = 퐺−휇 1+푒푥푝( ) disordered system where distribution in 푅푇 equilibrium sites required free enthalpy (3.13) 퐺푖- 퐺푟with respect to reference state Similar to the electron in metal, the total number of hydrogen atoms or concentration has obtained from
+∞ 푐 = 표(퐺)푑퐺 (3.14) ∫−∞
Equation (3.14) Fermi-Dirac distribution for a 푖 sites of hydrogen and 휇 is the chemical potential of hydrogen is called Fermi energy of hydrogen. So, summation over the energy level 퐺푖 to the total hydrogen concentration 푐 where the density of state 푛(퐺푖)푑퐺푖 is the concentration of the energy between 퐺푖 and 퐺푖 + 푑퐺푖 shown in Figure 3.10
+∞ 푛(퐺푖)푑퐺푖 푐 = ∫ 퐺 −휇 (3.15) −∞ 1+푒푥푝( 푖 ) 푅푇
Equation (3.15) the relation if chemical potential of hydrogen and total concentration c.
Integration of the function gave result as
퐺표−휇 2푐 = 1 ± 푒푟푓 ( ) 퐼푓 휇 > 퐺표, then it is positive, If 휇 < 퐺표 then it is negative. 휎
Therefore, 85
휇 = 퐺표 ± 푒푟푓−1 |2푐 − 1| (3.16)
Figure 3.10 In an amorphous material, potential trace for hydrogen where dissolution
from a reference state requires the G free enthalpy. 푛(퐺 푖), the distribution of the free enthalpy, 표(퐺), occupation of the equilibrium sites e is governed by Fermi-Dirac statistic [101] Their data for amorphous materials showed the linear relationship after plotting the results of chemical potential with different hydrogen concentration that satisfy the Gaussian function. The width of the function relates the width of the radial distribution function that gave an idea about the structure of the amorphous material. Therefore, hydrogen can reveal the local order or disorder of amorphous material.
In the amorphous matrix, interstitial sites that can be occupied by the hydrogen atom give rise to different free energy sites called site energies and disturbance of the site energies is called distribution of site energies [102]. He graphically represent the distribution of sites energies in amorphous and crystalline system in the Figure 3.11. 86
System potential vs distance energy distribution graphic n(E) analytical
푬 One-level 휹(푬 − 푬풐) System 푬ퟎ
풏(푬) Two-level 푬 ퟎ 풐 System 푬 (ퟏ − 풄풕)휹(풕 − 풕 ) 풐 + 풄풕휹(푬 − 푬 − 푬풕)
푬풕
풏(푬)
푬 Edge dislocation 풎푲ퟐ
푬ퟎ ퟐ푬ퟑ
풏(푬)
푬
2 Amorphous 1 퐸 − 퐸0 ퟎ 푒푥푝 − matrix 푬 휎√휋 휎
풏(푬)
Figure 3.11 Schematic presentation of potential/position curves and corresponding distribution of site energies for hydrogen in a single crystal (one-level system), in a single crystal with monoenergetic traps (two-level system). In a deformed metal with edge dislocation and in an amorphous matrix [102]
Kirchheim proposed a concept of the behavior of hydrogen in amorphous alloys using the density of site energies as discussed in above section. Chuang et al. [103] well described 87 these theories in their report. The intestinal energy sites distribution in amorphous material follow Gaussian function. The equation (3.8) density of site energy (DOSE) for hydrogen occupied in 푖th sites 푛푖(퐸) can be written as (Figure 3.11)
1 퐸−퐸 2 푛 (퐸) = 푒푥푝 [− ( 푖) ] (3.17) 푖 휎√휋 휎
Here, the chemical potential of equation (3.8) represents as different energy sites i.e. 퐸푖 is the energy sites for 푖th site. Therefore, the equation (3.17) able to described for total energy sites 푛(퐸) in normalized condition,
+∞ 푛(퐸)푑퐸 = 1 (3.18) ∫−∞
The distribution of hydrogen occupied for specific 푖th sites follow by Fermi-Dirac statistics, it can be written for specific 푖th energy sites at a temperature , 푇(퐾) as
1 퐹(퐸) = (3.19) 1+푒[(퐸−퐸푖)/푘퐵푇]
where 푘퐵 is Boltzmann’s constant. Therefore, the total occupied hydrogen sites shown by fraction of N/N0 where N is the total number of dissolved hydrogen atoms and N0 is the total number of available sites obtained from combining equation (3.18) and (3.19) given as
푁 +∞ +∞ 푛(퐸) = ∫ 퐹(퐸)푛(퐸)푑퐸 = ∫ [(퐸−퐸 )/푘 푇] 푑퐸 (3.20) 푁표 −∞ −∞ 1+푒 푖 퐵
Thus, equation (3.21) gave hydrogen vibrational density of state for amorphous material.
88
For analyzing, the raw data acquire from neutron vibrational spectroscopy, the differential scattering cross section of the hydrogen atoms followed by [104]
2 ′ 1 휕 휎 = 푁 푘 휎푡표푡 ∑ 푧 푓 푆 (푄, 휔) (3.21) 푁 휕훺 퐻 푘 4휋 푗 푗 푗 푗
Where the total scattering cross section of the hydrogen isotope is 휎푡표푡, the total number
′ of hydrogen atoms represents as 푁퐻, the initial and final wave numbers is 푘 and 푘 , respectively, 푧푗 denotes the number of j-type hydrogen sites, 푓푗 represents occupation of j- type sites, the scattering function of 푗th type sites is 푆푗(푄, 휔). This structure factor only depends on sample wave vector and energy transfer. This scattering function given by
푆(푄, 휔) = 푒푥푝[−2푊(푄)][푆̃푎(푄, 휔) + 푆̃표(푄, 휔) + 푆̃표푎(푄, 휔)] (3.22)
Where 푆̃푎 represents the contribution of the acoustical (band) phonons 푆̃표 is the optical phonons, and 푆̃표푎 those of the optoacoustical phonons; -2W (Q) is the hydrogen Debye-
Waller factor [104]. 푆̃표푎 is the combination of both acoustic and optical phonon mode.
Optical mode arises due to atoms vibrate each other, however, their center of mass is fixed and their atom having opposite charges that can be excited by electric field of a light wave
[105] shown in the Figure 3.12. The acoustic mode arises when atoms and their center of mass move together along long wavelength acoustic vibration. In optical vibration, the
k k
Acoustical mode Optical mode
Figure 3.12 Transverse optical and transverse acoustical waves in a di-atomic linear lattice, illustrated by the particle displacements for the two modes at the same wavelength [112] 89 optical mode can produce sharp peak, which indicate vibration of atoms in a unit cell, vibrate against each other whereas in acoustic vibration continuous spectrum arises due to incoherent scattering. Acoustic phonon mode is outside of neutron vibrational measuring range. This value taken as approximation of an empirical function in the acoustic mode. If oscillation of hydrogen occurring in three vibrational direction 푙, 푚, 푛, therefore, the optical contribution 푆̃표 is given by
2 2 푛 2 2 푚 2 2 푙 표 1 1 1 ħ 푄 ħ 푄 ħ 푄 푆̃ = ( ) ( ) ( ) × 푛(푛휔1 + 푚휔2 + 푙휔3)훿(휔 − 푛휔1 − 푚휔2 − 푛! 푚! 푙! 6푚퐻휔1 6푚퐻휔2 6푚퐻휔3
푙휔3) (3.23)
Where 푛(휔)the Bose is factor and represent as
1 푛(휔) = [exp (ħ휔⁄ ) − 1] 푘퐵푇
These peaks are Gaussian in shape as discussed before by Kirchheim proposed.
Filter Analyzer Neutron Spectroscopy (FANS)
Neutron vibrational spectra have collected for a broad array of the hydrogenous and non- hydrogenous system by utilizing second generation FANS located at BT-4, NIST center for neutron research (NCNR). Neutron vibrational spectroscopy able to reveal atom dynamics as
a) The magnitude of the vibrational frequency directly revealed information about the
strength of the metal-hydrogen interaction and therefore, potential energy can be
determined. Lattice strain and local changes due to impurities have directly
observed. 90
b) The intensity of the neutron scattering gives information about the degeneracy of
the given level.
The vibrational inelastic neutron scattering spectrometers are available in the following places and their range, resolution shows in Table 3.4
Table 3.4. Different types of inelastic neutron vibrational spectroscopy [99]
The triple axis spectrometers consists of the monochromator, sample, analyzer crystal and detector. The flux of the triple axis spectrometer increased significantly by replacing analyzer crystal with a block of cooled Figure 3.13 The principle of Filter-analyzer polycrystalline about 15 cm thick neutron instrument beryllium filter for scattering neutron beam. This new arrangement is called Filter Analyzer
Neutron Spectrometer (FANS) shows Figure 3.13. Beryllium is ideal choice of the filter material as
a) Small absorption cross section
b) Small scattering cross section
c) Small incoherent scattering cross section 91
d) Hard phonon spectrum which tend to reduce thermal diffuse scattering
e) All above properties make this suitable for low energy neutron transmission.
FANS is a reactor-based instrument where the incident beam cross-section is 30 ×
70 푚푚2 and it has higher detector area. The monochromatic neutron beam is extracted from white beam by crystalline monochromator Cu, PG or Ge. Usually, the monochromator is either Cu (220) or polycrystalline graphite (PG) (002) or Cu (311) and
Ge (311), a combination of polycrystalline beryllium followed by block of graphite analyzer and detector.
In this FANS instrument, the monochromator neutrons of variable energy inelastically scattered from the sample, bypass though filter with a giving cutoff and detected at a fixed final energy. The filter allows neutron whose energy is less than a certain cutoff value to capture in the detector, placed behind the filter showed in the Figure 3.14. The maximum value of scattered neutron wavelength beyond which Bragg scattering is not possible because there is no atomic planes spaced far enough to diffract these long wavelength
Figure 3.14 Schematic diagram of Filter Analyzer Neutron Spectroscopy instrument [93,106] 92
neutrons [94] which indicates the neutron wavelength longer than Bragg cut-off 2푑푚푎푥 of the filter material where 푑푚푎푥 is the maximum interplaner distance. Neutron have higher wavelength than cut-off go through the filter without Bragg scattered. By scanning the incident energy of the neutron (퐸) and knowing the final energy (퐸′), the spectrum of neutron intensity measured as a function of energy loss which directly showed the vibrational density of the state weighted by the neutron cross section for the element in the material under study. Usually, beryllium is transmitting the neutron which energy is less than 40 cm-1 or 5meV and wavelength greater than 4Å beyond which the neutrons energy is Bragg scattered out of it. Sometimes even below the energy 40 cm-1 or 5 meV, neutrons are scattered more due to phonon and neutron transmission decreased. These transmissions can be improve by sharpen the energy cut-off value by cool it inside liquid nitrogen below
100K. For example, if at 5K neutron transmission is 100 %, then almost 75% at 100K and room temperature 30% transmission. If we use filter BeO filter, then the energy of neutron transmission is below 3.7 meV. Therefore, using Be and BeO filter together, we can get the energy range of 3.7 meV-5 meV. Graphite filter also use this purpose, however, their cut-off is much lower ~12 cm-1 and the resolution increased significantly by the cost of flux.
The filter-detector assemble of two-wedged converting total scattering angle range of
±2300 . The instrument is upgraded to two phases; in Phase I neutron scattered from sample at smaller angle 110O by Cu (220) and PG (002) whereas Phase II the scattering angle detected at larger scanning angle up to 230o by replacing previous the monochromator with Cu (311) and Ge (311). The scan energy range of Phase I 93 monochromator showed in the Table 3.5. Double focusing monochromators used to
Table 3.5. NVS spectrum range [106]
increase the neutron intensity for all the energies; the small crystals are arranged inside the curved surface. In phase II, double focusing monochromators will provide flux
~107 푛. 푐푚−1푠−1 approximately four times higher than phase I. These assemblies helped to collect data at larger solid an angle with high neutron intensity for all the incident energies. The monochromator rotated to the starting energy and data collected for a particular energy transfer region for saving experimental time avoid the unprofitable part of the spectrum and observe by the detector showed by the monitor. The data are collected for fixed number of incident neutrons energy (퐸) when the monochromator rotate, therefore, it eliminates the variation of incident flux due to the distribution of energy source. The energy transfer associated with the detected neutrons by varying incident neutron energy (퐸). The mean transfer energy 퐸푚 = ħ휔 (퐷푒 − 퐵푟표푔푙푖푒’푠 푒푞푢푎푡푖표푛) =
′ 퐸 − 퐸 , 퐸푚 is mean energy of scattered neutron. The monochromator rotate for next incident energy and the process it repeats. Thus, the intensity collected will be proportional to 푆∗(푄, 휔). At NIST, the neutron vibrational spectroscopy is measured by selecting incident energy (퐸) of the spectrum and detecting the final energy (퐸′) using both beryllium and graphite, the cut-of energy (퐸푐푢푡−표푓푓) value achieved 1.8 meV at 77K. However, only using Be as a filter materials display the cutoff energy 퐸푐푢푡−표푓푓~5meV which transmitted as the final energy 퐸′~3meV; resolution displayed as ~4 meV FWHM. Inserting 94
polycrystalline graphite (PG) (Bragg cutoff energy, 퐸푐푢푡−표푓푓~1.8 meV as mentioned earlier) in between two Be filter causes significant reduction of final energy 퐸′~1.2 meV with resolution become ~1.1 meV FWHM. This arrangement is chosen by empirical calculation, which showed a reduction of fast a neutron background as well as better signal to noise ratio. The different filters are separate by absorbing medium in order capture any stray Bragg diffraction neutrons. The second Be filter is placed to achieve significant improvement of background. The whole system of filters is cool to reduce thermal diffusion. The detector detected the neutron energy-loss spectroscopy at the energy range of 5-280 meV and the coverage is 9% of 4π; the detector blank consists 48 helium 3 detector.
The resolution of the filter instrument determined by the band pass of the filter and detector response. Cu (220) use for higher resolution or higher incident energy (~ 50 cm-1 up to
1600 cm-1) studies and PG (002) use for comparatively lower energy (~10 cm-1) with moderate resolution. The resolution of different types of neutron vibrational spectroscopy shown in Table 3.4. Resolution variation with incident energy depends on crystal’s mosaic spread in the certain monochromatic angle ∆휃, so differencing diffraction law 퐸 =
ℎ2 1 ∆퐸 ∆ ( 2) , we got = = ∆휃퐵푐표푡휃퐵 , therefore in the monochromator the resolution 2푚푛 퐸 degrades due to cotangent of Bragg angle, 휃.Thus, both monochromator helps to optimizing resolution and intensity during acquisition of data. The monochromator takeoff angle 2θ is from 20o to 90o and the resolution typically ~1 meV. For using two different monochromator the energy range, cover approximately 5-250 meV. 95
As the schematic cross section of the filter, detector assembly shows a block of Bi, Be, and graphite filters. The principle component of filter carriage shows below in Figure 3.15 without the Bi-section, which is removable shown in the Figure 3.15 (right). Figure 3.15
Figure 3.15 (Right) Filters (beryllium and graphite) and detector (Helium 3) of FANS instrument, (Left) Schematic diagram of Filter Analyzer Neutron Spectroscopy instrument [106] (left) shows collimator and Be filter is sequentially placed after Bi and Be filter. This collimator has placed for capturing any neutrons that are not traveling radially from the sample. These are consisting of a series of narrow parallel channels separated by thin absorbing blades. The efficiency of the slit collimators depends on following factors:
a) The uniformity of blade spacing throughout the length of collimators
b) The thickness of the absorbing blades
c) The straightness of the blade edges and the entrance and exit to the collimators
d) The microscopic neutron capture cross section of the materials.
These configurations help to reduce Be photon spurious background scattering in between
50-85 meV by placing auxiliary polycrystalline bismuth filter in front of main filter replacing spurious scattering with Bi phonon energy near 12 meV and bismuth filter can result in only a minor attenuation in sample scattering intensity concomitant with a 96 reduction in the thermal and fast neutron background from the sample [107]. There are several motors, which controls the series of scanning angles. Motor 1 in monochromator at angle θ causes movement of the monochromator to satisfy the Bragg condition for the chased neutron energy. Motor 2 monochromator at angle 2θ causes movement of monochromator drum and sample table to the angle for the chosen incident energy. The motor in sample table 3 rotates the sample. Monochromator PG (002) motor 7 and Cu (220) motor 8 help to change the individual vertical focus and motor 9 in the filter or detector carriage causes movement of the carriage. The scattering vector range (Q) and estimated flux for this instrument shown in the Figure 3.16.
Q-range as a function of energy transfer Flux estimation at the sample position
Figure 3.16 Q-range for FANS as a function of energy transfer (Right) and estimated flux at sample position (Left) [106]
The FANS instrument improvised in sensitivity from first generation instrument by two order magnitude. The updated version of FANS instrument discussed below. 97
The upgraded version of FANS instrument at NIST shown in the Figure 3.17 taken from
Udovic et al. [108]. The neutron diffracted from the sample, and some of the neutrons lose
its energy by exciting the
vibrational mode of the sample as
discussed before. In upgraded
version of FANS, neutron goes
into the bismuth filter, which
placed inside cadmium tube.
Bismuth filters require certain
properties such as high purity, Figure 3.17 Schematic diagram upgraded of Filter low hydrogen content material, Analyzer Neutron Spectroscopy instrument and small crystalline grain size
distribution to ensure sharp Bragg cut off. Instead of using coarsely polycrystalline Bi
synthesized by melt casting much better results obtained from average grain size Bismuth
meddles (~230 μm) synthesized by rapid water quenching of melted Bi dripped into a
spinning centrifuge. In the filter, this inelastically scattered neutron loses higher cutoff
energies. Graphite filter has inserted in between Be filter; the thickness of front Be filter is
15.2 cm and back is 10.2 cm, and the thickness of graphite filter is 15.2 cm. Be filter is
better than graphite filter alone and remove almost all the neutron with higher energy
5meV. However, the addition of graphite produces a better resolution, more effectively
reduces fast neutron background as well as an increase in signal to noise ratio, with a cost
of intensity. To capture unwanted neutrons within the filters 1 mm thick 10B–Al alloy 98 absorbing materials used. The collimator used in between graphite and back beryllium filter to capture any neutrons not traveling on a line joining the sample with a detector.
Usually, in NVS measurement the vibrational density of state (VDOS) background is comparatively featureless than the main vibrational spectrum [108]. However, in between
50 to 85 meV noticeable spurious spectrum observed due to Be-phonon excitation in the filter analyzer caused by elastically scattered neutron from the sample and inelastically scattered by phonon excitation. Udovic et al. [108] showed the addition of auxiliary polycrystalline bismuth layer in front of the main filter significantly reduces the spurious spectra that improve the weakly scattering system. According to their study, heavy metal like 208Pb and 209Bi are desirable quality for attenuating filter analyzer as their VDOS are much lower than the energies of interest; also they are sufficiently low neutron absorption cross section and sufficiently high coherent neutron scattering cross section and relatively low phonon energies, and higher Bragg cutoff energies than that of the pyrolytic graphite.
However, due to cost and abundance of the natural material, the 209Bi chosen for upgraded version. Their study also revealed the thickness variation of Bi causes a change in the spurious spectrum [108]. Energy dependence total cross section for polycrystalline Be, Bi,
Graphite and Pb showed in the Figure 3.18 [108] with respective Bragg cutoff energy
5meV, 1.9 meV, 1.8 meV and 2.5 meV. Below the cutoff energy, there is a marked decrease in the total cross section with respect to temperature. Therefore, it is desirable to operate filters at a lower temperature near liquid nitrogen. 99
All the above-listed factors must have optimized for high transmission and good signal to background ratio. In NIST, have an option for precollimations of 60’, 40’, or 20’ and postcollimations of 40’, 20’, or 10’; the desire resolution in our experiment is precollimation 20’ and post collimation 20’. The improvement of the Phase I intensity is due to the twenty-fold increase in detector, solid angle provided by a much larger detector bank. The entire filter assembly is routinely maintain at a temperature below 90K with liquid nitrogen to minimize intensity losses from phonon scattering in the filter materials.
Figure 3.18 This is the comparison of total cross section of beryllium and graphite crystal at 100K and 296 K (NIST) [106,108]
3.3.2 Experimental Details
Hydrogenation of all the samples including binary PdH2, ZrH2, Ni60Nb40 and ternary
(Ni0.6Nb0.4)100-xZrx (x=10, 20, 30) have carried out a fully automated, and computer- controlled volumetric apparatus (known as Sieverts apparatus, or PCT apparatus) for performing PCT measurement. It is capable of measuring isotherms from 25 to 300oC to a maximum hydrogen pressure of 60 bar. Before each test, the system calibrated with helium 100 to ensure the experimental reliability. In addition, the samples were heated under vacuum up to 300oC at least 13-14 hours in every time before starting the test to maintain the uniform testing conditions. In Sievert’s apparatus, the sample exposed to hydrogen atmosphere under incremental pressures (up to 60 bar) and allowed to absorb hydrogen at a fixed temperature (at 200oC). The absorbed hydrogen then measured by measuring the pressure drop in each step. Here, we did not perform desorption test.
Two types of aluminium sample holders required for the FANS experiments having an inner dimension (mm) 12.70Ø x 50 with volume 6.3 cm3 and 6.35Ø x 50 and 1.6 cm3. The aluminium holder contains desirable samples and sealed with an indium O- ring. For zirconium hydride sample inner dimension (mm)
12.70Ø x 50 with volume 6.3 cm3 and for amorphous ribbons
6.35Ø x 50 and 1.6 cm3 (Figure 3.19) sample holder have been used. To assemble sample holder lid, 4-40 screws and to seal the Figure 3.19 lid O-ring made of indium or lead are required. For inert aluminium sample atmosphere, all the materials placed in the helium glove box. For holder pan; inside the crystalline zirconium hydride powder pores into an aluminum pan (Ni0.6Nb0.4)80Zr20 with hydrogen foil then it presses evenly afterwards, inserted in the sample concentration 0.25 holder. In case of amorphous (Ni0.6Nb0.4)100-xZrx (x=0, 10, 20, 30) placed sample strips are covered with aluminium foil and insert into the sample holder. Correct length of indium O-ring are inserted around the groove and tighten the sample in the glove box before neutron vibrational spectroscopy measurement. 101
The filter analyzer neutron scattering instrument shown in the Figure 3.20. In this experiment, we use Cu (220) horizontal collimations before and after the monochromators.
Depending on desired resolution, the arc varies from 200 to 600.The FWHM resolutions associated with all displayed spectra depicted by horizontal bars beneath the spectra.
Figure 3.20 Filter-Analyzer Neutron Spectrometer (FANS) at the NIST Center for Neutron Research (NCNR)
Before inserting the sample in the FANS, it is required to achieve a desirable environment for the sample. Closed circle Refrigerator has used for this purpose shown in the Figure
3.21. It consists of helium gas; the compressor (operating room temperature) and cryogenic expansion cylinder (cold head) thermally linked with regenerator or thermal storage device.
The temperature range is 2-300K. The prepared sample contained aluminium holder cooled down from room to base temperature depends on the mass of the sample. Typically, one 102
hour is require to cool down the sample. In our experiment, crystalline ZrH2 takes ~ 20 minutes and amorphous (Ni0.6Nb0.4)100-xZrx (x=0, 10, 20, 30) alloys 1.5 hrs. The samples are attached to the end of sample stick (Figure 3.21 (a)) and inserted into a sample well fitted with helium exchange gas (i.e. heat exchange medium) as shown in the (Figure 3.21
(b)). The sample temperature control by adjusting heater current and helium flow through a heat exchanger accord to the sample well. The helium flow rate and heater current
Figure 3.21 (a) Sample rode and sample holder, (b) Closed circle Refrigerator, (c) Closed circle Refrigerator (schematically) manually adjusted by the temperature controller. The closed circle refrigerator shown in the Figure 3.21 (b) and Figure 3.21 (c).
In neutron vibrational spectrum measurement, first, “fastback” subtracted from all the samples because neutron with incident energy higher than the cutoff limit reaching the detector. To measure that it is necessary to block slow neutron from detectors; cadmium has placed as discussed before. The first experiment was zirconium hydride and overall time requires abound 5 hours. The overall time requires for the run is around two days for other amorphous samples. The monitor count has chosen such a way that the data collection 103 has fixed. The spectrum accommodate over several hours or overnight for the weak sample as a result statistical errors of the spectrum reduce by counting each point for a longer time.
The deduction of the background play an important role as it causes statistical errors.
3.3.3 NVS Result and Discussions
To obtain hydrogen density of states of the crystalline and amorphous materials, the solubility of hydrogen needs to determine. For this, we used a volumetric method, which gives the hydrogen /metal ratio as a function of pressure; a Sieverts apparatus used for this measurement.
Hydrogen Solubility Measurements by Volumetric methods:
We measured solubility binary PdH2, ZrH2, Ni60Nb40 and ternary (Ni0.6Nb0.4)100-xZrx (x=10,
o 20, 30) alloys at 200 C and 60 bar pressure. The Sievert results of Pd and (Ni0.6Nb0.4).80Zr0.2 at shown in the Figure 3.22 (a) and (b). To observe the condition of Sieverts apparatus, perform Palladium (Pd) experiment and try to match the data with the model Pd-H system.
The data shows (Figure 3.22) that hydrogen uptake on Palladium at 200oC is around 2.5 mmol/g, which matches the data with a model of Pd-H system [25].
Figure 3.22 Hydrogen uptake on Palladium at 200oC and 60 bar pressure (b) Hydrogen o uptake on (Ni0.6Nb0.4)80Zr20 at 200 C and 60 bar pressure 104
The amorphous ribbons cut into stripped and pour into a valve. Afterward, the experiment was done at 200oC, 60 bar for
48 hours, and we get hydrogen uptake 1.5 mmol/gram i.e. concentration around 0.25.
Then the discard valve from the main system and wait until it cools down to room temperature. Then we perform Figure 3.23 Pressure-composition isotherms of (Ni Nb ) Zr (x=0-50 at %). The data for our Filter-Analyzer Neutron 0.6 0.4 100-x x Ni60Nb40 and (Ni0.6Nb0.4)50Zr50 taken from Yamaura Spectrometer (FANS) [25, 109] experiment.
In general, the permeability of Ni-Nb amorphous alloys increases with the addition of Zr content [25] as hydrogen solubility and diffusivity increases. For comparison purpose, hydrogen solubility measurements were made on these amorphous (Ni0.6Nb0.4)100-xZrx
(x=10, 20, 30) alloys are plotted in Figure 3.23. The solubility curves for the compositions x=0 and 50 had taken from Yamaura’s experiments [25]. All the experiments were performed at 573 K. Note that Yamuara et al. [25] also performed x=10-30 at.% but we included our data instead of theirs. The solubility of hydrogen in Ni60Nb40 (x=0) is negligible at 573K. As the Zr content has increased from x=0 to 30, the solubility increases as a function composition and pressure. The exceptionally high solubility for x=50 may be due to numerous hydrogen sites available in the amorphous ribbon, leading to possible higher permeation and increased susceptibility to hydrogen embrittlement [25-92, 110]. 105
Yamaura et al. [25] reported permeation data for x=50 is 1.59 ×10-8 (mol m-1s-1Pa-0.5) at
673 K. However; the permeation decreased with temperature. Their study reveals [25] X- ray diffraction/radial distribution function (XRD/RDF) that hydrogenation of low-Zr
(x=10-20 at. %) amorphous alloys did not show changes in Zr-Zr or other elemental interatomic distances. However, for the increased Zr contents of x= 30-50 at.%, hydrogenation led to increased Zr-Zr atomic distances. These expanded Zr-Zr bond lengths by hydrogen addition allowed for better hydrogen permeation. Sakurai et al. [92] confirmed these results by using XAFS.
Oji et al. investigated Ni-Nb-Zr alloys and hydrogenated counterparts [91]; they proposed an icosahedral Ni5Zr5Nb3 model for the (Ni36Nb24Zr40)0.91H0.11 using first principle calculations. They also suggest that a distorted form of icosahedral arrangement of atoms forms a cluster for the lower Zr content alloy, for example, (Ni0.6Nb0.4)70Zr30. Oji et.al [91] and Fukuhara et al. [89] performed XAFS/XANES studies and reported that hydrogenation of the (Ni0.6Nb0.40)70Zr30 and (Ni0.6Nb0.4)60Zr40 alloy ribbons showed different results. The differences lie in their XANES results that exhibited a shoulder of prominent Ni K absorption edge with and without hydrogen for (Ni0.6Nb0.4)70Zr30. However, for
(Ni0.6Nb0.4)60Zr40 alloy ribbon they observed a shoulder around the Ni K absorption edge without any hydrogen, when hydrogenated to (Ni0.6Nb0.4)60Zr40H11, the shoulder on
XANES was not present. They implied that in the alloy with (Ni0.6Nb0.40)70Zr30, the hydrogen atom does not localize inside but outside the icosahedra cluster; However,
(Ni0.6Nb0.4)60Zr40 alloy the hydrogen atoms localize inside the icosahedra around the Nb and Zr atoms and increase the Zr-Zr, Zr-Nb, and Nb-Ni interatomic distances. Oji and 106
Fukuhara [89, 91] contradicted results of Yamaura and Sakurai [25, 92] of hydrogenated
(Ni0.6Nb0.4)70Zr30 alloy, but agreed with other results.
It is well known that hydrogen permeability increases with increasing Zr content. However, increased Zr also enhances brittle failure in (Ni0.6Nb0.4)100-xZrx (x=0-30 at. %) [110]. An optimized Nb/Zr ratio in the alloy is required to prevent embrittlement for practical applications. The local atomic structure of these amorphous membranes has cited by many researchers in the literature using x-ray scattering methods [25, 89, 91], which do not directly reveal the position of hydrogen atoms in these metallic glasses. To better understand membrane permeability, it is necessary to know the H-occupancy sites within the Ni-Nb-Zr alloy. Neutron vibrational spectroscopy (NVS) can be especially helpful for determining the interstitial sites for hydrogen occupation in amorphous materials, since unlike XRD, it is a local probe not dependent on long-range order.
Rush et al. [111] previously used NVS to compare the hydrogen vibrational density of states (HVDOS) for both amorphous and crystalline TiCuHx, they identified a broad energy spectrum for the amorphous material and a much sharper spectrum at nearly the same energy for the crystalline material. In this study, we followed a similar procedure and used NVS to measure the HVDOS for hydrogenated amorphous (Ni0.6Nb0.4)100-xZrx (x=0,
10, 20, 30) and crystalline (Ni0.6Nb0.4)80Zr20, ZrH2 materials. Neutron vibrational spectra for ZrH2, NbHx, and NiZrHx reported in the literature was effectively compare to spectra for our hydrogenated amorphous Ni-Nb-Zr materials to help infer the likely H interstitial absorption sites.
107
Measurement of HVDOS by NVS: Neutron vibrational spectra were collected from the following hydrogenated amorphous ribbons: (Ni60Nb40)H0.2, (Ni0.6Nb0.4)90Zr10H0.4, (Ni0.6Nb0.4)80Zr20H0.55, and
(Ni0.6Nb0.4)70Zr30H0.7 to determine the HVDOS in each case (see Figure 3.24). NVS spectra were normalize to the same number of stoichiometric moles so that integrated peak intensities were a direct measure of H concentration.
Figure 3.24 NVS data for amorphous (Ni.60Nb.40)H0.2, (Ni.60Nb.40)90Zr10H0.4,
(Ni.60Nb.40)80Zr20H0.55, and (Ni.60Nb.40)70Zr30H0.7. Crystalline ZrH2 data is included to compare its spectral signature with those for the amorphous hydrides.
All the samples except (Ni60Nb40)H0.2 showed clear energy maxima at ~137 meV (N.B.: 1 meV ≈ 8.066 cm-1). In binary alloy, there is a small amount of H solubility due to high Ni content (Figure 3.23). The resulting spectrum is appearing as the Nb4 tetrahedral site of 108
NbHx [104]. Chang et al. [112] showed hydrogen distribution in amorphous Ni60Nb40 alloy by hydrogen thermal analysis technique and concluded the presence of Nb4 and Nb3Ni tetrahedral sites. Since the number of Nb4 sites is small, the hydrogen solubility is very low (see Figure 3.24). To the best of our knowledge, there are no other HVDOS data for
NbNiHx. There are known ordered compounds of NbNi3 and others, which still needs to investigate by NVS to determine the HVDOS due to the possible hydrogen positions.
For ternary alloy (Ni.60Nb.40)90Zr10H0.4, (Ni.60Nb.40)80Zr20H0.55, and (Ni.60Nb.40)70Zr30H0.7, the broad peaks have widths of around 100, 77, and 76 meV FWHM, respectively shown in Table 3.7. We also obtained an HVDOS for polycrystalline ZrH2, which is superimposed
(in Figure 3.24) to show the position of its vibrational band for comparison purposes. The most prominent optical phonon mode of ZrH2 also centered on ~137 meV along with a slight shoulder at 154 meV, having a width of ~20 meV FWHM that reflects the vibrational frequencies of H atoms in tetrahedrally coordinated interstitial sites comprised of four Zr atoms. Although higher-resolution instrumental collimation would reveal a clear peak splitting for the ZrH2, the lower-resolution data shown measured under the same resolution conditions as for the amorphous alloys to enable a more direct comparison. Slaggie et al.
[113] proposed a slightly distorted lattice structure in which the hydrogen resides in ZrH2 assuming the structure as FCC instead of FCT as shown in the inset of Figure 3.24.
According to their “Central Force Model” (CF), the shape of the frequency distribution of hydrogen vibration causes due to optical peak at 137meV and FWHM ~20 meV associated with the fine structure, which arises due to zirconium-hydrogen interaction. Their study
[113] tried to relate the shape of the frequency distribution of interatomic forces by 109
calculating lattice dynamics of ZrH2 in CF model assuming the ZrH2 structure as FCC instead of FCT also introduction four interatomic force
a) Zr-Zr nearest neighbor related to acoustic modes (M-M)
b) Zr-H nearest neighbor determine position of optical frequencies (M-H)
c) H-H second nearest neighbor causes splitting of the optical peak frequency (H-H)
d) H-H second nearest neighbor causes splitting of the optical peak frequency (H-H)
Therefore, in ZrH2 system, M-H interaction causes optical peak at 137 meV and FWHM
~20 meV which associated with the fine structure and with increasing temperature from
300K to 800K, the frequency of the peak lowered by 15%. Couch et al. [114] compared the data of Slaggie’s prediction of central force model with their experimental results of
ZrHx with different hydrogen concentration x= 0.54, 1.03, 1.56 and 2.00 from different initial energy 171.5 meV and 244.8 meV. Their experimental results with Slaggie’s CF model give the overall structure prediction of ZrHx structure. Couch et al. [114] showed that structure affected by the variation of zirconium and hydrogen ratio. The raw data converted to double differential cross section per hydrogen atom and then normalized using assumed cross section for zirconium (6.2b) and hydrogen (22.3b). The cross section has plotted against energy transfer ħ휔 = 퐸1 − 퐸2 where 퐸1is initial and 퐸2 is final energy. In their experimental results the optical peak arises at 137, 143 meV and 145 meV at shoulders and data varies slightly 3 meV with calculated CF model. In their ZrH1.56 does not show the peak near 154 meV indicated predominant cubic δ-phase, which also suggest ZrH2 is a
ε-phase tetragonal structure (not indicated by Slaggie [113]). Therefore, he showed that the optical peak for ZrH2 associated with ~137 meV along with a shoulder ~154 meV creates 110 due to interaction between second and third nearest neighbor in calculation, which causes split in the frequencies and suggested tetragonal structure only when infinite-wavelength vibration occurred between hydrogen atom in phase and opposite lattice zirconium atom.
This H-H interaction changes due to hydrogen concentration, which eventually affect the structure, although, earlier results showed no significant change with the change of hydrogen concentration.
Bakhsh et al. [115], and Mueller et al. [116] showed a splitting of the hydrogen vibration peak for near ~154 meV, indicating the presence of phonon dispersion due to significant hydrogen-hydrogen interactions in the long-range ordered crystal lattice for ε-phase tetragonal structure ZrH2. Malik et al. [117] performed precision total neutron cross section measurement on ZrHx (푥~1.58 ± 0.2) and compared the data of Slaggie’s “central force” model, and with Couch et al. [114] results and indicated H-H force contribute in the vibrational model suggested ZrHx structure was non-cubic probably tetragonal.
R Khoda-Bakhsht and D K Ross [115] showed that the hydrogen goes to the tetrahedral site in α phase of zirconium hydride (ZrH0.03) by inelastic neutron scattering experiment at
873K and the optical peak was observed at ~144 meV and FWHM ~ 47 meV. They attributed reasons about the hydrogen goes into tetrahedral sites instead of octahedral.
According to their study for cubic symmetry (ZrH0.03)
푐 푐 ( ) = 1.593 And ( ) = 1.6333 푎 푍푟 푎 퐼푑푒푎푙
For tetrahedron (ZrH2)
푐 푐 ( ) = 0.889 And ( ) = 1 at 80K 푎 푍푟 푎 퐼푑푒푎푙 111
In both cases, the splitting of the peak arises at higher concentration due to hydrogen- hydrogen forces. Thus, the structure is tetrahedral rather than octahedral. Their study reveals vibration frequency of regular tetrahedral site increased with decreasing M-H distance (푅−3/2) where, peak energy represent as 퐸 = 퐴푅−3/2 and A=410 meVÅ−3/2.The
Zr-H distance in hydride phases decreases from 2.083 Å to 1.973Å due to tetragonal distortion and changes frequency near 5%. Their study also revealed similar distance reduction expected in the octahedral site between metal and hydrogen and an increases peak frequency. If hydrogen goes to octahedral sites then α-Zr-H octahedral distance
(2.267 Å), which similar to Pd-H octahedral distance (1.94 Å), therefore, the frequency will be slightly higher than Pd-H frequency of vibration will be 68.5 meV. However, the frequency of all the zirconium hydride is close to ~140 meV. This relative comparison gives an idea about the conclusion of tetragonal zirconium hydride structure.
A.I. kolesnikov et al. [118] performed inelastic neutron scattering performed on the α, ε, δ phases of Zr-H in earlier years and also included inelastic neutron scattering on γ phases of ZrH in their study. Their results showed in Table 3.6. Comparing the data of different phases of ZrH, they concluded that hydrogen zirconium distance causes maximum vibrational energy in 훾 − 푍푟퐻푥 phases. Although there is some anomalies in 훼 − 푍푟퐻 interatomic distances where it showed the hydrogen-metal distances are lowered, however, the hydrogen vibration is lower than 훾 − 푍푟퐻푥. 112
Table 3.6. Energy range of different phases of Zr
Zr-H X values Energy range (meV) Zr-H Structure phases distances 훼 − 푍푟퐻푥 0.03 ≤ 푥 ≤ 0.05 ~143-144 ~2.011Å HCP
훿 − 푍푟퐻푥 0.54 ≤ 푥 ≤ 1.56 ~130-140 ~2.041Å FCC
휀 − 푍푟퐻푥 1.9 ≤ 푥 ≤ 2 ~136-138, 143-145, 154 ~2.070Å FCT
훾 − 푍푟퐻푥 ~141.5, 148.7 and 156.3 ~2.082Å FCC
Similar results of hydrogen occupied tetrahedral sites with cubic symmetry ZrHX obtained from other literature [119-121]. All the previously studied DOSE results of crystalline zirconium hydride clearly showed by Chuang et al. [103] to compare their NVS measurement of Zr-based bulk metallic glass (BMG). INS data of (Zr55Cu30Ni5Al10)99Y1
BMG at room temperature and as charged hydrogenated suggested preferably hydrogen occupy strongly bounded tetrahedral sites at ~135 meV along with Zr-deficient or octahedral like sites at ~97meV and 168 meV. Jaggy et al.[122] suggested higher hydrogen solubility due to possible hydrogen induced rearrangement to larger Zr4 tetrahedral sites in amorphous alloy. Their report [122] supported the concept of Harries by performing e.m.f measurement yielding hydrogen activity in amorphous Ni35Ti65, Ni50Zr50, and Ni65Zr35 alloys. They found that the gradual filling of Zr4, Zr3Ni and Zr2Ni2 could be possible from the experimental data and number of tetrahedral sites per metal atom in the amorphous matrix are 1.3, slightly different from Harris et al. [123] prediction f=1.9.
Recently, first principle calculation of Ni-Nb-Zr amorphous alloy showed hydrogen atom induced local rearrangement in some of the tetrahedral sites of icosahedra to fcc-like structure [124]. In our amorphous alloys, the lack of a long-range-ordered periodic structure hinders any accompanying phonon dispersion effects, and the spectra might be 113 consider more like a summation of independent contributions from all the individual interstitial H atoms. Nonetheless, the amorphous natures of these materials necessarily lead to a distribution of interstitial sites and therefore, a dispersion-like distribution of vibrational frequencies. We found that lower Zr content with other alloying elements tends to broaden the NVS peak. Comparing NVS results from all the amorphous samples, we conclude that there are more H-sites in alloys with higher Zr content; these results supported by solubility data in Figure 3.23. Therefore, hydrogen permeability of the
(Ni0.6Nb0.4)70Zr30 alloys is higher than (Ni0.6Nb0.4)80Zr20 and (Ni0.6Nb0.4)90Zr10 due to more hydrogen content in the alloy [110] (also see Figure 1.3).
To elucidate the effect of hydrogen, without changing the Zr content, we performed NVS experiments on (Ni0.6Nb0.4)80Zr20Hy with different hydrogen contents ranging from y=0.015 to 0.25 (see Figure 3.25). Over the whole concentration range, the energy distributions centered at 137 meV and the width for y=0.015 is ~51 meV narrower than comparatively higher hydrogen content alloy y=0.1, and 0.25 are 82.3 and 87.9 meV respectively, suggesting that a sequential filling of the more favorable Zr4 interstitial sites.
There is the possibility of other Zr-rich tetrahedral sites like Zr3Ni contribute to the vibrational spectrum as suggested by Harris et al. [123] in their universal model for hydrogen absorption in early transition and late transition metal for amorphous metal.
Similar sequential filling Zr4, Zr3Ni and Zr3Ni2 (0.5 ≤ x ≤ 1.0) for ZrNiHx also found in other literature [125]. Chaung et al. [121] also did not rule out similar possibilities in their
Zr-based bulk metallic glass. 114
Figure 3.25 NVS data of amorphous (Ni0.60Nb0.40)80Zr20Hy taken at different concentrations of at 4K. The data for the alloy with y=0.015(green color plot) shows a very low neutron counts. The neutron counts for the y=0.25 (blue) and 0.01 (red) shows prominent H sites associated with Zr4 tetrahedra
Samwer and Johnson [126] performed X-ray radial distribution function (XRDF) to get structural information about on Zr-rich glasses and by observing the change in nearest neighboring distance of Zr for the hydride and unhydrided sample, suggested hydrogen occupy tetrahedral sites of Zr4 and then occupy (3Zr+1Ni) tetrahedral site. Radial distribution data of amorphous ZrNiD data by Suzuki et al. [127] also suggested similar behavior. According to the study of Suzuki et al. [127], increasing in hydrogen concentration of the system, local modes of the hydrogen vibration would not affected. The local mode of vibration does not change with concentration of hydrogen due to the filling 115 of sites according to the energy, which does not have an effect on changing the local mode of vibration.
Richards showed the distribution of activation energy for hydrogen hopping in amorphous metals [102]. The main influence on the width and mean value of the distribution of hydrogen frequency depend on hydrogen and metal distance in the amorphous system. The site energy of determined by sum of the edge length of polyhedral. The activation energy of hydrogen hopping from one site to another is due to the difference between the activation energy of saddle point, which is the center of triangle face of polyhedron and equilibrium energy sites, which are the center of the polyhedron. The radial distribution function related to the dimension of the triangle and polyhedron mentioned above. Therefore, the site energy distribution closely related to the radial distribution function and change in the volume due to the addition of hydrogen. H. Kaneko et al. [128] perform inelastic neutron scattering and neutron diffraction experiment on crystalline ZrNiH2.8 and Zr2NiH4.6 and amorphous ZrNiH1.8, Zr2NiH4.4, ZrNiD1.8, Zr2NiD4.3, ZrNi, and Zr2Ni. For amorphous
Zr2NiH4.4 and ZrNiH1.8, the vibrational peak arises near 130 meV; crystalline material
FWHM and center peak shifted slightly from the amorphous vibrational peak that suggested the local position of hydrogen in Zr2Ni and ZrNi alloys are different. The coordination from RDF results showed that hydrogen or deuterium atom located two types of tetrahedral sites coordinated with four Zr atoms or three Zr and one Ni atom. It is also suggested [128] with an increase in zirconium content, the probability of hydrogen goes towards (3Zr+1Ni) site also increases. According to their results as the Zr content increases the probability of hydrogen inside three Zr and one Ni side also increases. Mittal et al.,
[129] showed inelastic neutron scattering in Zr2NiH1.9 and Zr2NiH4.6 by triple-axis 116 spectrometer. The vibrational spectra centered near 130 meV. Four types of hydrogen atom sites are available in Zr2Ni. Site 푎 and 푏 surrounded by four Zr atoms and 푐 sites are surrounded by 3Zr+1Ni and 푑 sites surrounded by 2Zr+2Ni atoms. Comparing their data with Westlake’s model, their study showed the vibrational peaks near 112, 132 and 160 meV for both Zr2NiH1.9 and Zr2NiH4.6 and later spectrum more broadened. They concluded that in Zr2NiH1.9, H atom occupies tetrahedral sites 푏 where H atom is surrounded by 4Zr atoms and Zr2NiH4.6, H atom occupies both 4Zr and 3Zr+1Ni atom.
The XRDF results of our (Ni0.6Nb0.4)70Zr30 ribbon showed an increase in both Ni-Zr and
Zr-Zr interatomic distances in addition of hydrogen [25, 92] in XAFS experiments.
Therefore, we can conclude by XRDF, XSAF, and NVS data that hydrogen trapped inside
Zr4 tetrahedral sites and then preferably goes to other sites. K. Suzuki et al. [127] showed the position of hydrogen in ZrNiDx (x=0-1.72), crystalline ZrNiHx (x=0.64-2.80) and amorphous (x=0.36-1.84) by performing neutron total scattering and inelastic neutron scattering. According to their study hydrogen and deuterium goes intestinal sites of early and late transition metal. Therefore it has a very promising hydrogen storage as well as atomic structure and dynamics of metallic glasses.
Local vibrational energy spectrum showed that for crystalline ZrNiHx (x=0.64), the vibrational peak is near 110-120 meV and shoulder appears at 80 meV and with increasing hydrogen content the shoulder disappears and x=2.8 showed three prominent peaks at 112,
123, 134 meV with 150 meV shoulder. In crystalline ZrNiH, hydrogen occupies tetrahedral sites surrounded by 4Zr atoms, and in ZrNiH3, hydrogen goes to a tetrahedral site surrounded by 3Zr and 1 Ni atom and also 3Zr and 2Ni interstitial sites. ZrNiH lattice 117
orthorhombic structure changes to triclinic and ZrNiH3, the structure, remains orthorhombic. For the amorphous ZrNiHx, the vibration of the main peak is near 130-135 meV over the hydrogen content range from 0.64-2.8. It is interesting that even at lower H content the amorphous peaks are broadened. Their radial distribution data of amorphous
ZrNiD data showed that at lower deuterium content, deuterium preferred to occupy the interstitial sites surrounded by 4 Zr. As the deuterium content increase, it goes to interstitial sites which surrounded by 3Zr and 1Ni. Their study showed that even at lower hydrogen content of amorphous ZrNIHx (x=0.30-0.48), the vibrational energy is comparatively 10-
15 meV higher than crystalline.
Besides the H phonon modes associated with Zr4 sites, there are several additional peaks that appear in our ternary samples for Zr=10, 20, and 30 at. %. As a comparison, we also performed NVS experiments on hydrogenated crystallized ribbons of
(Ni.60Nb.40)80Zr20H0.25. The spectra of the amorphous sample compared with the crystallized sample in Figure 3.26. Rush et al. [118] also showed similar trends for crystalline and amorphous TiCuHx alloys; observed broadening of the amorphous TiCuHx as compared to the spectrum for the crystalline alloy. Moreover, the positions of the peaks were similar to those of the amorphous sample. Other inelastic neutron experiments regarding the comparison of hydrogenated amorphous and crystalline zirconium-nickel hydrides also observed in different kinds of literature [127, 130, 131]. In Figure 3.26, we also compare amorphous (Ni0.6Nb0.4)80Zr20Hy with other related crystalline metal hydrides such as NbHx [109] and NiZrHx [132]. 118
We superimpose the data of Hauer et al. [109] for ε-NbHx (0.1 Figure 3.26. There are two sets of phonon bands (visibly split due to the higher resolution employed), one set maximized at 115.5 and 122.5 meV and the other at 157.5 and 167 meV, representing the combined spectrum of H atoms in two closely related, differently distorted Nb4 tetrahedral sites. In the crystallized sample of our ternary alloy, the NbHx peaks near 120 meV and 165 meV match. Hauer et al., [109] detailed study of inelastic (NVS) and elastic neutron scattering (NDP) to understand optical hydrogen vibration and new information about phase diagram for ε- NbHx where 0.1 Figure 3.26. NVS data of (Ni0.60Nb0.40)80Zr20H0.25 (blue) and its hydrogenated crystallized counterpart (purple). The NVS of ε NbHx (0.1 In 1980, Richter et al. [133] performed NVS on NbHx(D) obtained two fundamental peaks along with 170 meV energy peak, which is 7 meV, lower than the second harmonic motion. Usually, hydrogen dissolved in the tetrahedral sites of pure niobium and due to the symmetry of the tetrahedral sites, the localized vibration split into two parts. They found ordered to disordered transition performing NVS at a different temperature. At higher temperature 422 K, the vibrational peak shifted 10% and broadened. The deuterium atom occupies randomly distributed sites of tetrahedra. Their results also showed the broadening of the peaks occurred in the 100K energy range, which suggested 17% hydrogen occupy before phase transition. Similar results obtained from other literature suggested that the even substitution of Nb with different elements (N, O, Mo Ti, Cr), the hydrogen goes to the tetrahedral position of pure niobium [134-136].In 1983, Magerl et al. [134] showed the effect of alloying addition 120 in the NbHx system. They performed neutron vibrational spectroscopy on NbV0.008H0.005, NbN0.004H0.003, NbO0.011H0.010 and NbH0.005 at a range of temperature 4K to 250K. Their study revealed in the addition of substitutional atom V in the given system, the vibrational peaks NbV0.008H0.005 are 117 and 166 meV. At lower temperature, 78K, the peak position was almost identical to ordered ε-NbHx phase. The substitution of the system did not prevent precipitations; however, it appeared the shifting of the ε- phase boundary to a lower temperature for precipitation. For interstitial defects, such as O or N totally suppress the precipitations due to the trapping of hydrogen in the system; the vibrational peaks were near 106 and 163 meV for NbN0.004H0.003, 107 and 160 for NbO0.011H0.010. The vibrational energy peaks were much closer to α-NbH0.055 such as 106 and ~163 meV. Therefore, they concluded that the hydrogen atom trapped inside tetrahedral sites resemblance to tetrahedral interstices in pure Nb. In 1983, Richter et al. [135], extended their study of a substitutional atom with Ti and Cr and found that the trapped state of hydrogen occupies a tetrahedral site. Their NVS spectra revealed the peaks were closer to the α-NbH0.055. In 2001, Sumin et al. [136] performed neutron vibrational spectroscopy measurement for Nb0.95Mo0.05H0.3 and Nb0.8Mo0.2H0.05 at 10, 200 and 300 K. Their experiment showed that even addition of alloying element Mo did not change the vibrational peaks of pure niobium. In both cases hydrogen, atom occupies tetrahedral interstitial sites. Their experimental results showed no significant change in the hydrogen vibration in their sample as either it is in solid solution or it occupies tetrahedral interstitial sites. Usually, the hydrogen vibration possible to change in the presence of hydride phase or the type of interstitial site occupation tetrahedral or octahedral. Their study showed in all temperature hydrogen occupy tetrahedral sites and 121 hydrogen is in solid solution. In 1983, Richter et al. [135] summarized the previous results Richter and Shapiro, Rush et al., Magrel et al. [132,133,134] regarding local energy and hydrogen potential in the refractory metals. He concluded that hydrogen trapping has a strong resemblance with tetrahedral sites of pure niobium. Udovic et al. [137] performed inelastic neutron scattering to understand low H –concentration Nb95V5H1 and obtained octahedral site Nb4V2 and tetrahedral site NbV3. For pure Nb (ε- NbH0.7) the preferred site is tetrahedral, and for V the site is octahedral. The predominant peak near lower vibration 38 meV depicted octahedral site occupation in bcc metal. In Nb95V5H1 alloy, the tetrahedral vibrational energy is near 104, 137 and 151 meV. Eckert et al. [138] reported optical vibration of NbHx (with different phases) which suggested the position of the proton in the tetrahedral sites. In 1981, Rush et al. [139] studied tritium vibration in Nb metal by neutron spectroscopy. They performed an experiment on NbT0.2, NbD0.72, and NbH0.32 in the energy range of 40 to 200 meV. The vibrational data of NbT0.2 showed two dominant optical peaks near 72 and 101 meV, which indicate slight distortion tetrahedral sites in orthorhombic β phase at 295K. Due to oxygen and hydrogen impurity in tritium sample, two more peaks observed near 52 and 121 meV. The deuterium peaks observed near 86 and 120 meV. For NbH0.32, the vibrational peaks observed near 116 and 167 meV. It is important to notice that both H and D vibrations exhibit an isotopic shot with respect to T significantly less than harmonic potential. All the previous NVS results of crystalline NbHx and comparing amorphous data Ni-Nb- Zr, we believe that 120 and 165 meV reflected hydrogen vibration in tetrahedral Nb4 site. In addition to tetrahedral ZrH2 and ε-NbHx, we do not rule out the other possibilities of 122 octahedral-like sites near 97 and 168meV as suggested by Chuang et al. [103]. Due to overlapping with Nb site, it is hard to identify these type of octahedral sites. It is interesting that the density of states of the hydrogen atoms in amorphous materials found to be quite different from our crystalline counterparts as shown in the Figure 3.26, likely due to crystallization of different alloy phases in the latter materials leads to a decrease in the population of Zr4-type sites. Indeed, the fraction of hydrogen phonons associated with Zr4 sites in the crystallized ribbons is much lower than hydrogen phonon associated with Nb4 sites, in contrast to the amorphous materials. Some additional peaks are also observed in the vibrational energy range 75 to 125 meV shown in the Figure 3.26. In our crystallized ribbon of (Ni0.6Nb0.4)80Zr20H0.25, it is difficult precisely to identify the presence of possible NiZrHx peaks. Numerous studies have performed on the ZrNiHx system due to its significance in technological applications [121, 127, 140-141]. The ZrNiHx with x<0.6 suggest α phase, 0.65 γ phase is observed when ~2.5 In 1982, Westlake et al. [144] predicted Interstitial site occupation in crystalline ZrNiHx, and found that the hydrogen occupies tetrahedral sites surrounded by four Zr atoms by x- ray and neutron diffraction. X-ray data along with pressure-composition isotherms result showed stable monohydride. Four important results depicted from his study. Westlake model suggests that a) Hydrogen only occupies the sites where the radii are greater than 0.4 Å. 123 b) The larger empty site will occupy first. c) Hydrogen-hydrogen distance should be higher than 2.1 Å d) For ZrNiHx, the tetrahedral sites occupied first then it goes to site 2 and site 3. With higher hydrogen content (x=3), hydrogen goes from site 1 to site 2 and 3. However, the side 2 and 3 have smaller distance than 2.1 Å as mentioned in the third point of Westlake model suggests, therefore, it causes increase in the forces by occupying one hydrogen in site 2 and two hydrogens in site 3. X-ray diffraction results showed crystalline ZrNiH monohydride phases exists in both solid solution of H in ZrHi and ZrNiH3. According to their XRD, ZrNi and ZrNiH3 are orthorhombic, and ZrNiH is triclinic structure. The XRD results showed almost negligible peak position shift in ZrNi and ZrNiH3 indicating low solubility of hydrogen. Dihydride ZrNiH2 does not exist. Neutron diffraction of NiZrD showed deuterium occupy tetrahedral sites surrounded by Zr causes orthorhombic to the triclinic structure. Westlake also predicted that in crystalline ZrNiH3, hydrogen goes to tetrahedral sites surrounded by 3Zr and 1Ni atoms (c-site) and hexagonal hole by 3Zr and 2Ni atom (b-site) and make it orthorhombic structure. The previous study on ZrNiHx suggested only one Zr4Ni2 tetrahedra site in 훽 –phase [143, 144]. However, there are other results, which disagreed with previous results. In 1984, Benham et al. [140] showed that hydrogen atom sites in crystalline ZrNiHx (x=0.6-2.8) and compared it with Westlake’s model. According to their studies on alloys of crystalline ZrNiHx (x<0.6) showed the energy distribution at 76, 110, 126 meV and 0.6 Benham et al. [140] concluded low hydrogen content (x<0.6) hydrogen site surrounded by 124 four Zr atoms, however, with higher hydrogen content x>0.6, hydrogen progressively filled (3Zr+1Ni) and (3Zr+2Ni) sites. Their study showed as the hydrogen content increases x=3, instead of site 1, hydrogen atom goes to site 2 to site 3 which supported by Westlake model. More than one tetrahedral sites also suggested by many researchers [125, 140, 145]. Westlake’s model (1980) [143], Westlake paper (1982) [144], Michel and Gupta’s report suggested only one Zr4Ni2 tetrahedra site in 훽 –phase ZrNiHx. Jacob, Benham, Yang and Adolphi disagreed with the previous results and reported more than one occupancy sites. Adolphi’s NMR study showed three different sites in two different phases. According to their study, hydrogen occupied two inequivalent Zr4Ni2 sites for 훽 –phase and another site for γ- phase. Yang et al. study assumed three sites Zr4, Zr3Ni and Zr3Ni2 when 0.5 ≤ x ≤ 1.0 ZrNiHx. In 2006, Bowman et al. [142], reported tentative β and γ deuterium site occupancy for ZrNiDx (0.87 ≤ x ≤ 3.0) and detected phase boundaries for ZrNiDx by NVS and MAS- NMR spectra. According to their study, γ phase ZrNiH3 (trihydride) were an orthorhombic structure and had two hydrogen sites – tetrahedral Zr3Ni (2 per ZrNi) and pyramidal Zr3Ni2 site as also suggested by Westlake. It forms stable hydride at x=1, 훽 –phase ZrNiHx (monohydride), where hydrogen occupied at Zr4. However, these site better described by Irvine having 4Zr atoms and 2 Ni atoms as Zr4Ni2 site (M-H distance is 2.30 Å and 2.32 Å). 훽- phase described as NiZrHx, 0.65 ≤ x ≤ 1.0 at temperature greater than equal to 320K having only one site. In order to understand the site occupancy more clearly, they performed vibrational spectra of ZrNiD0.88 and ZrNiH0.88 at 10 and 300K. The vibrational spectra H appears at the vicinity 75.4, 102, 107.5, 111.5, 121.5 and 128 meV for ZrNiH0.88. 125 Due to the mass of hydrogen half-as-light as deuterium, the vibrational spectra shifted factor of √2 and ZrNiD0.88 vibrational spectra displayed at 54.6, 73.5, 78.1, 84.0, 90.8 and 95.3 meV. Three vibrational sites display one deuterium site and six vibrational site display two deuterium sites. At 300K, the spectra become smear out. They also compared their study with Benham’s inelastic neutron study showed three inequivalent sites for ZrNiHx and found slight discrepancy. By comparing their data with Benham et al. [140] study they proposed that previous experiment performed at 80K and spectra 76 meV along with 110, 126 meV were weak due to low resolution and Benham by mistake conclude three peaks as one hydrogen site. Due to different site energy sites in vibrational spectra as well as different knight shifts in NMR spectra. Bowman et al. [142] concluded their neutron vibrational spectroscopy results on ZrNiDx and ZrNiHx (0.87 For the β- ZrNiHx, Wu et al. [140] assigned two distinct H crystallographic sites: Zr4Ni2 octahedra and Zr4 tetrahedra instead of two inequivalent sites Zr4Ni2 in triclinic orthorhombic lattice proposed by Bowman et al. [142]. 훾-phase ZrNiH3 results showed interatrial site occupation inside Zr4 and 3Zr+1Ni interstitial site position where it followed Westlake’s model. According to their experimental results of NPD, NVS goes inside two crystallographic position Zr4Ni2 octahedral and Zr4 tetrahedral inside triclinic 푃1̅ structure instead of one Zr4 site inside distorted orthorhombic 퐶푚푐푚 structure. Their first principle calculation results showed the triclinic 푃1̅ structure have total energy ~24 eV per unit cell 126 lower than orthorhombic 퐶푚푐푚 structure and NVS results on ZrNiD0.88 showed vibrational modes at 54.6, 73.5, 78.1, 84, 90.8 meV. First three lower, modes showed deuterium position inside octahedral sites Zr4Ni2 and 84 and 90.8 meV vibrational spectra showed deuterium position inside Zr. They reported six analogous hydrogen peaks that were in the proximity of 75.4, 102,107.5, 111.5, 121.5 and 128 meV. We superimposed their spectra in our Figure 3.26. Our energy spectrum matches that of Bowman et al [142], expect in the energy range of ~80 to ~100 meV. There are some unknown peak also. We are tentatively attributed these to unknown Nb rich Nb3Ni tetrahedral sites, however in Ni60Nb40H0.2 we did not observe any density of state in this region (in Figure 3.24). The first peak of NbHX appears at ~120 MeV, which is overlapped with the ZrNiHx peak. In the literature, we found XRD data of Ni10Zr7 and NiZr [146]; Roustila et al. [147] proposed that NiZr ordered compound can easily form the hydride, NiZrH2.7. The position of hydrogen in this compound is the same as Wu et al. [140] suggested. Going back to x-ray data of Oji et al. [91] and Fukuhara et. al [89] who performed XAFS and XANES experimental results coupled with molecular dynamics calculations on (Ni.60Nb.40)60Zr40 alloy reported most stable hydrogen sites formed by a tetrahedral configuration consisting of two Zr and two Nb atoms. Our NVS data strongly suggest that the most stable sites for hydrogen in the Ni-Nb-Zr alloys are in Zr4 tetrahedra. However, it should note that the hydrogen also appears to occupy distorted Nb4 tetrahedral sites. In addition, H-sites also observe in the Zr4 and Zr4Ni2 sites in the ZrNiHx polyhedra. As the Ni atom has no affinity towards hydrogen, H vibrational modes associated with Ni-rich sites are not observe for the Ni-Nb-Zr system. Enthalpy calculation of dissolved hydrogen atom for Zr, Nb and Ni are -63,-34 and +16 kJ/mol also support this [25]. Recent first 127 principle calculation by Fujima et al. [124] showed hydrogen located preferable octahedral sites of icosahedra. Chuang et al. [121] showed hydrogen mobility in zirconium octahedral sites is an almost order magnitude higher than tetrahedral sites in Zr- based metallic glass. Due to the presence of Nb4 sites is in the same vibrational energy range of Zr octahedral sites in Ni-Nb-Zr alloy, it is difficult to identify. However, we believe these octahedral sites are responsible for higher permeation in the membrane [121, 124]. Conclusions NVS measurements of the hydrogenated amorphous alloy ribbons of (Ni0.6Nb0.4)100-xZrx (x=0, 10, 20, 30) were performed to probe the locations of hydrogen. Probable locations are suggest by comparison of our amorphous data with those known for different crystalline hydride phases. It appears that the Zr4-like interstitial tetrahedral sites are more favorable for H absorption than other sites in these amorphous structures involving Nb or Ni atoms. This is concurrent with the fact that solubility of hydrogen also increases with increasing Zr content. Although there is some indication of H atoms also populating Nb4 and Zr4Ni2 sites. Ni-rich interstices are energetically unstable sites for H atoms. However, we cannot rule out the possible existence of some mixed Zr-Nb tetrahedral or Nb-Ni octahedral interstices also capable of absorbing H atoms. The broad HVDOS distributions characteristic of these amorphous materials made it difficult to identify all the populated H-sites distinctly. Yet, in the hydrogenous crystallized NiNbZr system, we observe sharper distinct HVDOS features similar to those observed for crystalline ZrH2, NbHx, and possibly ZrNiHx, which reflect the presence of H atoms in Zr4, Nb4, and Zr4Ni2 interstitial sites, and give further support that these are the types of sites favored in the precrystallized material 128 In conclusion, NVS data clearly indicate a broad distribution of H sites in these amorphous materials, dominated by Zr4-tetrahedral interstices. Nonetheless, unlike these more stable Zr4 H traps, the various, less stable H absorption sites also mentioned previously may ultimately be responsible for enabling the facile diffusion of H atoms through these amorphous membranes. In order to understand nearest neighbor distance between the amorphous alloy, we performed high intensity neutron diffraction. 129 Table 3.7. Comparison of optical vibrational peaks of hydrogen atoms in various zirconium hydrides, niobium hydride and zirconium-nickel hydride and (Ni0.6Nb0.4)100-xZrx (x=0, 10, 20, 30) Metallic Glasses and x=20 crystalline alloy 130 131 3.4 Neutron Total Scattering experiment (HIPD) High-intensity powder diffraction (HIPD) has been performed Lujan Neutron Scattering Center at Los Alamos National Laboratory (LANSCE) to understand local structure for amorphous materials. The ribbon of (Ni0.60Nb0.40)70Zr30 was loaded in the HIPD instrument and neutron total scattering data was collected. The beam size is (1 × 5) cm2. The primary flight path is around 9 meter, and due to the proximity of neutron source to neutron diffractometer, the counting rate is high. Thus, the sample requires for HIPD experiment minimum 200mg. This kind of experiments run up to 3-4 hours. The detectors are located at the angles ± 153°, ± 90°, ± 40° and ± 14° and they covered almost ± 5°. Each detector having momentum transfer ~0.2 - 60 Å-1.The pair distribution function, 퐺(푟), was -1 generated from 푆(푄) using a Qmax of 25 Å with the program PDFgetN; details can be found in the reference [149]. 3.4.1 Theory of Total Neutron Scattering st 1 coordination shell nd 2 coordination shell Pair Distribution Function, PDF is 퐺(푟) = 푔(푟) continuum 표 1 g (r)g 0 gives a probability of finding an atom center in “푑푟” at distance ‘푟”. 푔(푟) is the ratio of a number of density of atoms at distance “푟” to the homogeneous density 0. Radial Distribution function (RDF) are also used in ) 풓 ( 품 place of PDF shown Figure 3.27. The RDF is the radial ퟎ 풏 = coordination 흆 ퟐ number 풓 흅 ퟒ ퟐ ퟒ흅풓 흆ퟎ density of atoms at a distance “푟” from the origin atom. 풏 RDF, Number of Atoms in a Spherical Shell at a distance “푟” Figure 3.27 Schematic diagram 2 of RDF and “푟 + 푑푟” is given by 4푟 표푔(푟). 132 In a powder diffraction experiment. Scattering vector 푄 give total beam of radiation from ensemble of atoms and 푆(푄) and double differential neutron cross section per unit solid angle Ω can be defined as 1 푑2휎 푘′ 푘′ 푑 = ∑푛 푏2푆푠(푄, 휔) + ∑푛 푏̅ 푏̅ 푆 (푄, 휔) (3.23) 푁 푑훺푑휔 푘 푖=1 푖 푖 푘 푖,푗=1,푖≠푗 푖 푗 푖푗 푠 푑 Where the self and distinct part of structure factor are 푆푖 (푄, 휔) and 푆푖푗(푄, 휔) respectfully, N is the atoms in the material, which contains n distinct chemical elements. 푘 and 푘′ are the initial and final wavevectors of the scattered neutron, respectively, and 푄 = 푘 – 푘’ is the scattering vector of length 4휋푆푖푛휃/휆 for a neutron of wavelength 휆 scattered at an 푐표ℎ ̅ 2 angle 2휃. The coherent neutron scattering length is 휎푖 = 4휋 푏푖 , the total cross section ̅ 2 can be written as 휎푖 = 4휋 푏푖 as mentioned earlier; therefore the incoherent scattering is 푖푛푐 푐표ℎ 휎푖 = 휎푖 − 휎푖 . Therefore, equation (3.23) written as 1 푑2휎 푘′ 푘′ = ∑푛 (푏̅̅2̅ − 푏−2)푆푠(푄, 휔) + ∑푛 푏̅푏̅푆푑 (푄, 휔) (3.24) 푁 푑훺푑휔 푘 푖=1 푖 푖 푖 푘 푖,푗=1 푖 푗 푖푗 As in the powder diffraction, the scattering only depends on ⌈푄⌉, not the diffraction, by performing integration on overall energy range the equation (3.24) written as ′ 1 푑휎 ̅̅2̅ −2 푘 = ∑푛 (푏 − 푏 ) 푆푠(푄) + ∑푛 푏̅ 푏̅ 푆 (푄, 휔) (3.25) 푁 푑훺 푖=1 푖 푖 푖 푘 푖,푗=1 푖 푗 푖푗 푠 The self-structure factor written as 푆푖 (푄, 휔) = 푐푖 as it is proportion of species 푖 in the material and distinct part of structure factor written as 푑 푆푖푗(푄, 휔) = 푐푖푐푗[퐴푖푗(푄) − 1] + 푐푖훿푖푗 (3.26) where 퐴푖푗(푄) Faber-Ziman partial structure factors and 훿푖푗 Dirac delta function. Putting these values in the above equations [150,151] 133 1 푑휎 = ∑푛 푐 푐 푏̅푏̅[퐴 (푄 − 1)] ∑푛 푐 푏̅̅2̅ (3.27) 푁 푑훺 푖,푗=1 푖 푗 푖 푗 푖푗 푖=1 푖 푖 Faber-Ziman partial structure factors 퐴푖푗(푄) is related to partial redial distribution function g(r), therefore, ∞ 푠푖푛푄푟 퐴 (푄) − 1 = 휌 ∫ 4휋푟2 [푔 (푟) − 1] 푑푟 (3.28) 푖푗 0 0 푖푗 푄푟 Rearranging the equation (3.28), ∞ ( ) 1 2 2 ( ) 푠푖푛푄푟 푔푖푗 푟 − 1 = 3 ∫0 4휋푟 푄 [퐴푖푗 푄 − 1] 푑푄 (3.29) (2휋) 휌0 푄푟 Where, 휌0 = 푁⁄푉, 푔푖푗(푟) can be written as 푛푖푗(푟) 푔푖푗(푟) = 2 4휋푟 푑푟휌푗 Where 푛푖푗(푟)= a number of particle type 푗 in between 푟 and 푟 + 푑푟. The total radial distribution and total scattering structure factor defined as 푛 ̅ ̅ 퐺(푟) = ∑푖,푗=1 푐푖푐푗푏푖푏푗[푔푖푗(푟) − 1)] (3.30) 푛 ̅ ̅ And 퐹(푄) = ∑푖,푗=1 푐푖푐푗푏푖푏푗[퐴푖푗(푄) − 1)] (3.31) The both equation (3.30) and (3.31) can be written as 1 ∞ 2 2 푠푖푛푄푟 퐺(푟) = 3 ∫ 4휋푟 푄 퐹(푄) 푑푄 (3.32) (2휋) 휌0 0 푄푟 ∞ 푠푖푛푄푟 퐹(푄) = 휌 ∫ 4휋푟2퐺(푟) 푑푟 (3.33) 0 0 푄푟 The area under the Peak gives the coordination number near an origin atom (A) within r1 and r2. Therefore, the area (A) is 푟2 2 퐴 = ∫ 4휋푟 휌0푔(푟)푑푟 (3.34) 푟1 and the coordination number (N) is 푟2 2 푁 = ∫ 4휋푟 푐푗휌0푔푖푗(푟)푑푟 (3.35) 푟1 134 3.4.2 Result and Discussions Total neutron scattering was performed at LANSCE (Los Alamos National Laboratory). The pair distribution function (PDF) data shows the number of atomic pairs separated by a distance of “푟” and therefore that serves as an excellent probe of the local structure of disordered materials. The PDF of the (Ni0.60Nb0.40)70Zr30 alloy (in Figure 3.28 a) showed Figure 3.28 (a). Pair distribution function of (Ni0.60Nb0.40)70Zr30 showing features up to ~1.8 nm.. (b) Details of overlapped regions of the first nearest neighbors distances of Ni-Ni, Ni-Nb/Ni-Zr, Nb-Nb, and Nb-Zr/Zr-Zr. well-defined features of the short-range order up to ~1.8 nm with no structural correlations at longer length scales. The first peak in the pair distribution function (PDF) plot represents the nearest neighbor atomic distances and has contributions from interatomic bond distances. This first peak has a main feature at ~0.268 nm and two high-r shoulders. The low-r feature represents bond distances involving Ni is the most prominent feature because Ni is the most common element and has the strongest neutron scattering length. The Ni- Ni distances are expected to be the shortest, however, in this case, we observed them be 135 longer (0.240-0.270 nm) as compared to the Ni-Ni distance of only 0.248 nm in the pure metallic Ni. However, the average Ni-Ni distance is probably a few hundredths of an Å shorter than the 0.268 peak; there are clearly no atom-atom pairs with average distances as short as 0.248 nm. We did not find any feature at or around 0.248 nm, concluding that there are no regions in this material where Ni coordinate mostly or entirely by Ni in this ternary alloy. Thus, it is expected that the matrix of this ribbon is Ni-rich with Nb and Zr atoms. We propose that the Ni-rich matrix with a significant number of Nb and Zr atoms randomly distributed embeds the Nb- and Zr-rich clusters. All Ni atoms appear to be bonded to significant numbers of Nb or Zr atoms, which slightly elongates the Ni-Ni distances relative to pure Ni. The higher-r part of the main feature can be expected to originate from Ni-Nb and Ni-Zr distances, which are on average slightly longer than 0.268 nm. The first high-r shoulder is centered at ~0.295 nm and can be expected to be primarily from Nb-Nb distances. The second shoulder at ~0.324 nm can be assigned to Nb-Zr and Zr-Zr distances. Table 3.8 shows the interatomic distances, note that the Ni-Nb and Ni-Zr distances could not be measured accurately. The second peak (Figure 3.28 a) in the PDF represents distances from the second and third nearest neighbor distances. At higher r values there are 5 more features in the PDF representing larger distances. These peaks are all spaced between 0.22-0.25 nm, suggesting a regular pattern in the way the polyhedra are arranged relative to each other. At longer length scales, the atomic positions are no longer correlated. Figure 3.28 (b) shows expanded the view of the first peak. 136 We also obtained interatomic distances from radial distribution function (RDF) optimizing the structure for nominal composition (Ni54Nb36Zr38), Zr-rich region (Ni49Nb23Zr56) and Nb-rich region (Ni41Nb59Zr28) compositions from the DFT-MD simulations, as showed in the Figure 3.30. The nominal composition data match with neutron total scattering experimental values. It is interesting to observe that in Nb Figure 3.29 Radial distribution function and Zr rich region the peaks shifted on the (RDF) optimizing the structure for nominal right side, concluding Ni atom bonded with composition (Ni54Nb36Zr38), Zr-rich region (Ni49Nb23Zr56) and Nb-rich region more number of Nb and Zr than the (Ni Nb Zr ) by black, red and blue color 41 59 28 nominal composition. In the Nb-rich region respectively. (Ni41Nb59Zr28), second peak of Nb-Nb distances are more prominent than other two compositions as expected. Several studies have been performed in past few decades in amorphous (Ni0.60Nb0.40)70Zr30 ribbon by x-ray diffraction to understand interatomic distances between atoms. The summary of the data for Ni- based amorphous alloy obtained from EXAFS, XRD-RDF and molecular dynamics studies shown in Table 3.8 with references. All the data of nearest neighbor found in the literature study are x-ray data, and no study have been done with a neutron to best of our knowledge. The advantage of PDF over XAFS is that later is limited to the first 1-3 coordination spheres, whereas we can access much longer interatomic distances with the PDF. The amorphous structure of (Ni0.60Nb0.40)70Zr30 has ordered up to about 1.8 nanometers. However, it is completely disordered when viewed at longer length 137 scales. The combined APT and PDF results comprehensively suggest that there is large clusters 2-7 nm in diameter will be discussed later, but there is not necessarily structural coherence across the entire length of the cluster. Table 3.8. Interatomic distance between atoms experimental study and literature References Year Alloy Ni-Ni Ni-Zr Zr-Ni Zr-Zr Nb-Nb Ni-Nb Nb-Zr Nb-Ni Zr-Nb r (nm) N r (nm) N r (nm) N r (nm) N r (nm) N r (nm) N r (nm) N r (nm) N r (nm) N Frahm et al. [153] 1984 Ni24.1Zr75.9 - - 0.262 2.35 0.262 0.84 0.317 9.66 ------ Frahm et al. [153] 1984 Ni33.3Zr66.7 - - 0.262 2.39 0.262 1.43 0.318 10.1 ------ Frahm et al. [153] 1984 Ni36.5Zr63.5 - - 0.262 2.44 0.262 1.56 0.32 8.91 ------ Lee et al. [154] 1984 Ni35Zr65 0.266 2.3 0.269 5.4 0.269 2.9 0.315 9 ------ Lee et al. [154] 1984 Ni35Zr65 0.266 2.3 0.269 7.9 0.269 4.3 0.315 9.1 ------ Frahm et al. [155] 1989 DSC Ni36.5Zr63.5 - - 0.263 3.15 0.263 1.81 0.321 5.97 ------ Lima et al. [156] 1988 Ni25Zr75 - <1.3 0.276 12.6 0.276 4.2 3.23 11 ------ Paul et al. [157] 1990 Ni24.1Zr75.9 - - 0.27 14.5 0.27 4.6 0.316 8.4 ------ Paul et al. [157] 1990 Ni33.3Zr66.7 - - 0.27 8.3 0.27 4.2 0.316 10.1 ------ Paul et al. [157] 1990 Ni36.5Zr63.5 - - 0.27 9.6 0.27 5.6 0.316 8.6 ------ Paul et al. [157] 1990 DSC Ni36.5Zr63.5 - - 0.27 10.5 0.27 6 0.324 8.6 ------ Yu. Babanov et al [158] 1995 Ni67Zr33 0.249 6.3 0.272 5 ------ J. C. de Lima et al. [159] 2003 a-NiZr2 0.267 1.3 0.267 8.4 0.267 4.2 0.321 11.6 ------ Yamura et al. [25] 2005 Ni60Nb40 0.247 6.6 ------0.294 5.8 0.266 4 - - 0.266 6 - - Yamuara et al.[25] 2005 (Ni0.6Nb0.4)70Zr30 0.25 1 0.266 1.3/7.4 0.266 1.8 0.32 9/12.9 0.292 6 0.268 5.1 0.311 2.2/15.9 0.268 7.7 0.311 2.1 Sakurai et al. [94] 2005 (Ni0.6Nb0.4)70Zr30 0.263 0.67±0.08 0.316 4.4±2.2 ------ Yamuara et al.[25] 2005 (Ni0.6Nb0.4)50Zr50 0.25 0.3 0.266 1.2/6.6 0.266 0.7 0.32 9/10.7 0.292 5.6 0.269 5.1 0.311 2.5/15.8 0.269 7.7 0.311 1 Sakurai et al. [94] 2005 (Ni0.6Nb0.4)50Zr50 - - 0.264 4.2±0.6 0.316 7.9±1.9 ------ Junji Saida et al.[160] 2007 Ni30Zr70 0.248 1.3 - - 0.27 2.6 0.319 9.4 ------ Oji et al. [91] 2009 (Ni0.6Nb0.4)70Zr30 - - - - 0.263 3.3 0.324 5.4 0.324 5.4 0.255 1.5 - - Oji et al. [91] 2009 (Ni0.6Nb0.4)60Zr40 - - - - 0.263 2.6 0.325 5.1 - - 0.325 5.1 0.254 0.9 - - Hua Tian et al. [161] 2012 Ni62.5Nb37.5 2.48 ------3.05 - 2.63 - - - 5.5 - - - Yang et al. [162] 2013 Ni60Nb40 0.273 ------0.282 0.28 ------ Yang et al. [162] 2013 Ni61Nb39 0.273 ------0.282 0.279 ------ Yang et al. [162] 2013 Ni62Nb38 0.273 ------0.281 0.279 ------ Yang et al. [162] 2013 Ni63Nb37 0.272 ------0.282 0.278 ------ Yang et al. [162] 2013 Ni64Nb36 0.273 ------0.281 0.279 ------ Experimental 2015 (Ni0.6Nb0.4)70Zr30 ~0.240-0.270 >~ 0.268 - - - - ~0.295 >~ 0.268 ~0.324 - - - - - 3.5 Small angle neutron scattering (SANS) Small-Angle Neutron Scattering (SANS) is a technique for polymers, colloids or glassy materials characterization of clusters in the nanoscale size range [96]. To get cluster information for our amorphous system, SANS was performed. SANS is not directly scattered from individual atoms rather the scattering takes place from aggregates of atoms. This instrument used for understanding the structural information at a coarser level than the atomic level. The intensity of scattering depends on the scattering length densities of the elementary volume in the size range 10 Å to 1000 Å. 138 Small-Angle Neutron Scattering (SANS) able to detect the structure in materials on the 10- 9 m to 10-6 m scale. If the neutron wavelength, λ, and scattering angle, θ, then the interatomic distance determine by the length scale of d= λ/ θ. Cold neutrons have long wavelength 5 Å -20 Å (FWHM is 10 to 30 % ) and tight beam collimation. Scattering vector Q range from 0.001 Å-1 to 0.45 Å-1 and the scattered angle is less than 1o. Therefore, in the instrument, one can achieve the 푑-spacing from 6,300 Å down to 14 Å. There are certain advantages and disadvantages of small angle neutron scattering and small angle x-ray scattering. Small angle neutron scattering (SANS) can measure density fluctuations and as well as composition fluctuations due to their ability of deuteration. However, small angle x-ray scattering (SAXS) can measure only density fluctuation. Low- intensity neutron flux is a disadvantage of this technique over small angle x-ray scattering, where flux is an order of magnitude higher. 3.5.1 Brief Theory Von Hove scattering law showed number of neutron scattering per incident neutron is 1 푘′ ∞ 퐼(푸, €) = 푏 푏 ∫ 〈푒−푖푄.푟푘(0)푒−푖푄.푟푗(푡)〉 푒−푖€푡푑푡 (3.36) ℎ 푘 푗 푘 −∞ Where the summation is over the pair of j and k nuclei located at position 푟푗(푡) and 푟푘(0) with a scattering length of 푏푗 and 푏푘 at the time 푡 and 0. 〈… 〉 indicates over all the possible thermodynamic states of sample. The wave-vector 푘 scattered in the outgoing plane wave vector 푘’, 139 In the case of small angle neutron scattering, the interatomic distances are larger than the magnitude of Q; an integral can replace the overall sum of equation (3.36). The integral extended throughout the samples. Therefore, it can be described as 2 퐼(푸) = |∫ 푏(푟) 푒−푖푄.푟푑3푟| (3.37) Where, b(r) is the scattering length over the entire sample. In SANS, scattering length density of matrix is the 푏푚 and scattering length of particle 푏푝 over the matrix. Therefore, the difference depicted by (푏푝 − 푏푚), called contrast factor. These value separated matrix to particles. Therefore, equation (3.37) can be written as 2 2 −푖푄.푟 3 퐼(푸) = (푏푝 − 푏푚) 푁푝 |∫ 푒 푑 푟| (3.38) 푣푝 In the above equation integral taken over the volume of the specific particle (푉푝) and a number of such particle throughout the sample. The integration of 푒푖푄.푟 is called form factor. Description of Instruments: The reactor based small angle neutron scattering of the NG3 instrument at the NIST Center for Neutron Research is discussed here [95, 151]. Cold source neutrons transported inside the neutron glide, which usually coated with Ni58 or nature Ni and these neutrons are internally reflected through at a specific wide critical angle. Transmission of neutron through cold sources causes 1% neutron energy loss per meter. For undesirable neutron and gamma rays Be and Bi, filters are used respectively; the neutron transmits through the neutron glide having the wavelength more than 4 Å. The filters used for small angle neutron scattering angle having 15 cm and 20 cm thick. The better efficiency of these filters can 140 achieve by cooled down to liquid nitrogen temperature (77 K). However, coved guide, which transmits only wavelengths above a cutoff value, causes no gamma rays in the beam, as there is no direct line-of-slight from the reactor; therefore, no filter such as Bi is needed. Neutron flux is possible to increase by using the optical device as it can keep the neutron beam away from the direct line-of-sight, therefore, crystal filters are possible to eliminate, as it is lower the neutron flux. The optical device consists of tapered neutron guides that transmit only reflected neutrons. Figure 3.31. Schematic diagram of Small angle neutron scattering [97] Small angle neutron scattering instrument consists of the neutron source, Be and Bi-filter, neutron guide, velocity selector, beam shutter, guide sector, alternative sample position, the sample chamber and 2D detector as shown in the Figure 3.31. The mechanical velocity selector is installed to match up variable speed and pitch of the monochromator. The collimation used in SANS is a circular collimator, and it consists of a circular source and sample apertures. The pre-sample flight path evacuates, and the beam is collimated. The pre-sample flight path is around 15 m and post sample flight path is 13 m. However, these flight paths are adjustable and varying from 1 to 20 m depending on intensity and resolution required for the experiment. The source to sample distance varied from 3.5-15 m and the detectors to sample distance is 1.3-13.2m. 141 More neutron guides are included in between pre-sample flight path as shown in the Figure 3.31. These neutron guide sections contain more reflecting inner surfaces of the collimation system, which help easy beam insertion. By varying the effective way adjusting source-to- sample distance, desire flux, and instrumental resolution possible to achieve. The incident neutron (NG3) having the area of 6 × 6 cm2. Therefore, simplified small angle neutron scattering configuration consists of a certain number of guides inserted into the neutron beam, then a source aperture, followed by a series of empty beam positions up to the sample aperture placed inside the sample chamber shown in the Figure 3.32. The sample chamber consists of a translation frame, and the sample size is 0.5 to 2.5 cm diameter. Usually, the sample chamber able to hold many samples and experiment possible to perform without removing the sample from the chamber. Cryostats, electromagnets, ovens, shearing devices, etc. are accommodated in the sample chamber to approximately cooled and heated from 263 K to 473K. This temperature controlled oversized sample environment are placed on a 22’ Huber sample table, which is rotated around a vertical Figure 3.32. Schematic diagram of the principle of small angle neutron scattering [97] axis; translated in and out of the neutron beam. 142 The high counting rate 2D area detector has been installed in the SANS instrument as shown in the Figure 3.31 having 0.5cm to 1 cm resolution. This type of area detector is typically gas detector having 128 × 128 cells. The special resolution achieved by the detector is 0.508 × 0.508 cm2, where the electromagnetism goes from 0 to 9 Tesla; In the back of the detector preamplifiers are placed. Then amplifier is placed right after that. Then timing unit, as well as coincidence unit, placed. Altogether these set up produce the histogram and mapping of the data and store onto the computer. To carry high voltage and power, flexible hose is installed for display the experimental results. Experimental Details: The small angle neutron scattering experiment have been carried out at NG7 30 m SANS instruments at NIST. All the amorphous samples (Ni0.6Nb0.4)100- xZrx (x= 0 to 20) and one crystallized (Ni0.6Nb0.4)80Zr20 are hydrogenated by Sieverts apparatus discussed above in the section 3.3.3. Titanium cells are used to perform SANS experiment. The hydrogenated samples are placed in between the cells. The sample holder consists of two quartz windows shown in the Figure 3.33. The windows are sealed with an Figure 3.33 Sample holder for SANS O-ring. There are four screws to hold the experiment complete assembly. 143 3.5.2 Result and Discussions The well-known fact about SANS experiment on amorphous material that the signal is contributed about 푄−4 surface states due to surface roughness, chemical composition or oxide layers. The hydrogenated samples showed the data intensity vs q (Å-1). It is interesting that (Ni0.6Nb0.4)90Zr10 and crystallized (Ni0.6Nb0.4)80Zr20 showed significant contribution from the samples. These samples revealed significant length scales of the possible stoichiometric inhomogeneity. All the amorphous spectra suggest that, even though amorphous alloys are supposed to be “homogeneous” metallic glass, there greater than ~30 Å domain objects are visible shown in the Figure 3.34. The crystallized sample (Ni0.6Nb0.4)80Zr20 indicated the objects are around 60 Å in size. The cluster formation inside the amorphous material is revealed in some extend. We proposed the inhomogeneity arises due to icosahedra cluster inside the matrix. To understand exact object size of icosahedra clusters further, it required lower scattering vector, Q range than SANS or look for a different instrument. In the future study, UNSANS should be performed where the Q range value is 0.0003 nm-1 to ~0.1 nm-1 instead of 0.008 nm-1 to 7.0 nm-1 (SANS) and it can determine the object size 0.1 μm to 20 μm. However, 144 we performed atom probe tomography to observe cluster formation inside the matrix. Next chapter has discussed the clustering and the atom probe tomography technique. Figure 3.34 Small angle neutron scattering data of (Ni0.6Nb0.4)100- xZrx (x= 0 to 20) and one crystallized (Ni0.6Nb0.4)80Zr20 145 Chapter 4 Clustering Studies in Amorphous Materials: Atom Probe Tomography (APT) Contents 4.1 Introduction ………………………………………………………………...142 4.2 Theory ……………………………………………………………………...145 4.3. Experimental Detail ……………………………………………………….149 4.3.1 Sample preparation by Focused Ion Beam ……………...... 149 4.3.1 Local Electrode Atom Probe (LEAP) ...…………………………151 4.4 Results and Discussion …………………………………………………… 155 4 Atom Probe Tomography 4.1 Introduction Small Angle Neutron Scattering does not reveal significant information about cluster. As mentioned earlier these amorphous materials have a lack of long-range order, despite these materials show high hydrogen permeability, excellent electrical transport properties, and under certain conditions show superconductivity [163]. However, the nature of internal atomic arrangement of these thin ribbons, generally between 30 to 60 m, have not understood, entirely. Several studies have been performed [25, 91, 163] in the past decade to understand the atomic arrangement of (Ni0.60Nb0.40)70Zr30 glassy ribbons. There are reports of icosahedral structure formation of ~0.55 nm average size inside the ribbon [89, 91], although fundamental understanding of the cluster formation inside the matrix and internal atomic arrangement of atoms in this amorphous ribbon is still lacking. 146 Atom probe tomography has performed to understand the nature of short-range order in Ni-Nb-Zr amorphous alloys. To address these issues earlier, we performed the experiment on the membrane alloy ribbon by HIPD and SANS. Now, the tests were conducted by Atom Probe Tomography (APT) to understand the homogeneity of these alloys and to determine the existence of clusters and, if present, their average sizes, and compositions. These APT data allowed us to reconstruct three-dimensional structures revealing Nb-rich and Zr-rich clusters embedded in a Ni-rich ternary matrix whose compositions deviated from the nominal overall composition of the membrane. Historical perspective of atom tomography: Muller, Panitz, and McClane at the Pennsylvania State University discovered the atom probe tomography in 1967 [165 - 167]. However, the concept comes in 1928 due to the calculation of the time Figure 4.1. The detection range vs resolvable features. required to ionize an atom The name (S)TEM stands for (scanning) transmission electron microscopy, EELS- electron energy loss in a vacuum. In 1955, spectroscopy, EDS- energy dispersive X-ray Muller’s microscope was spectroscopy, SEM -scanning electron microscopy and first able to observe atoms tof -SIMS –time of flight secondary ion mass- spectroscopy [165] by human eye by field ion 147 microscopy. Atom probe is a combination of field ion microscopy and mass spectra, which identify atoms and create an image. TEM and SEM can resolve 0.02 nm on a surface, yet atom tomography is required because detection range of APT is much different from other microscopes; also, it provides the very high spatial resolution for chemical analysis. Figure 4.1 describes detection range as well as the spatial resolution of microscopes. It is clear that single microscope is not able to cover the whole detection range. Together TEM and Field Electron Emission Microscope 1935 Field Ion Microscope 1951 Atom Probe Field Ion Microscope Muller, Panitz and McClane 1967 1-D Atom Probes Imaging Atom Probes Topagraphiner 1969 1973 1978 Scanning Tunneling Microscope Pulsed Laser Atom Probes 1981 Kellogg and Tsong 3-D Atom Probes 1979 Atomic Force Microscope 1987 Mapping Atom Probes Muller Position Sensitive Atom Probes 1986 Cerezo, Godfrey, Smith Scanning Probe Instruments 1988 Tomographic Atom Probes Blavetter and Menand Scanning Atom Probes 1990 Nishikawa 1993 Local Electrode Atom Probes Kelly, Larson, Camus 1993 Figure 4.2 History of development of Local electrode atom tomography adapted from ref [164] 148 APT together can resolve clusters even in the amorphous materials. The evolution of atom probe tomography shown in Figure 4.2 4.2 Theory In 2003, Kelly et al. [167] commercially developed local electrode atom probe (LEAP). A sharp cryogenically cool needle-shaped specimen, radius <100 nm placed close to the local electrode. The specimen prepare by electropolishing or focus ion beam technique [167]. The advantage of the local electrode has lower- amplitude standing and pulse voltages, which eventually increase the field view. The pulse repetition rates increase due to lower pulse amplitude. Central aperture of the local electrode precisely aligns the apex of the specimen shown in Figure 4.3. In APT, high voltage ~10-15 kV and high electric field ~1010 V/m required in between sample and local electrode (Alfred Cerezo). The final alignment performed under ultra-high vacuum <10-8 Pa. To initiate the field evaporation in voltage-pulsed mode, a positive voltage applied to the sample and negative voltage is applied to the local electrode. This applied field evaporate the atoms as ions accelerated Figure 4.3 Schematic diagram of Local electrode atom probe (LEAP). The local electrode, specimen and towards the detector and crossed delay line detector shown [167]. created ‘hot spot,’ i.e., it is 149 require changing aperture. The chemical nature of the specimen can be determined by adding sub-nanosecond voltage to the DC voltage. It causes different time-of–flight of each ion and determines to calculate mass to charge. The magnification can achieve ~106. In the laser-pulse mode, the sample target with a laser beam and evaporation of atom start and go towards imaging detectors. In both cases, the depth information possible to get by a sequence of evaporation of events and position of an atom determine by the ions, which hit the detector. It is important to remember that the electrical conductivity of laser pulse mode must be greater than 102 S/cm and the heavily doped semiconductor can achieve this. The temperature require for laser pulse is small at 100-200 K; the field of evaporation reduce, as the temperature is increased. The LEAP has a position sensitive cross delay line detectors. These delay line detectors consist of a micro-channel plate (MCP) and conductive lines. The ion goes towards the multichannel plate and creates several secondary electrons, which detect by delay line anode. The conductive lines are placed behind MCPs. If the ion Figure 4.4 Schematic diagram of is detected, then, the signal affects both X and Y delay-line detector [165] coordinates 푋퐷 and 푌퐷 respectively shown in Figure 4.4. If the physical length of conductive line is 퐿푥 , 푇푥1 and 푇푥2 are the signal propagation time at the end of the conductive lines and the total propagation time of the signal is 푇푝푥, therefore, the position of the each ion can be determined by the coordinate of 푋퐷 and 푌퐷 , 150 푇푥1−푇푥2 푌퐷 = 푋퐷 = 퐿푥 (4.1) 푇푝푥 In Atom Probe Tomography, removal of atoms from the surface layer occurs by field ionization and field evaporations. In this technique depending upon materials around 10- 40Vnm-1, intense electric fields are applied. This field breaks atom bonds and pulls the atoms while one of the electrons remains at the surface which causes ionization of the atom. The field evaporation occurs at two stages. a) Thermally activated ion escape b) Post field ionization The first phenomena thermally activated process happens due to the escape of ion to overcome an activation energy barrier. The electric field reduces these activation barriers and helps to escape the ion. The schematic diagram of atomic state transfer to the ionic state shown which also called charge-draining electric field escape mechanism in Figure Figure 4.5 (a) The atom detached from the surface shown by grey atom and black atom [165]. (b) The charge-drained electron field evaporation escape mechanism [167]. 151 4.5. The Y and X-axis show atomic and ionic potential energy as a function of distance along the escape path respectfully. The ion escape from the surface usually follows the charge draining mechanism Figure 4.5 [165]. In the above Figure 4.5, 0 designated as a neutral atom in the electric field region. The energy of atom bond with and without field F are 훬표 and 훬퐹 shown Figure 4.5. After introduction electric field, the surface atom partially ionize. Electron charge reduced and made ion entirely charged due to the nucleus, which goes along the escape path. Therefore, ion cross the activation energy barriers. After ion escape from the surface, the charge of the ion is 푠푒 where s is 1, 2 or 3 depending on chemical nature of the ion and e is the positive charge. Usually, the post field ionization occurs into a higher charge state when ion depart from the surface; the change of the ion is ne where n is the negative charge. In field evaporation, the speed of the surface atom i.e. the rate constant 푘 indicates the speed of the surface atom ionizes into charge state s. Arrhenius equation can determine the rate constant, −푄(퐹) 푘 = 퐴푒푥푝 (4.2) 푘퐵푇 Where 퐴 is the pre-exponential factor, 푇 is the operating temperature of the atom probe, 푘퐵푇 is Boltzmann constant, and 푄(퐹) is the activation energy to escape the atom from the surface to change state 푠. Initially, the temperature of the instrument is 푇표 and the field is 퐹표. The activation energy is higher; therefore, rate constant is low. Suppose the rate constant is 푘표 and it equation (4.2) expressed as −푄(퐹표) 푘표 = 퐴푒푥푝 (4.3) 푘퐵푇표 152 Therefore, to evaporate the atom from the surface, it shows that the rate constant depends on temperature or applied voltage. 4.3 Experimental details 4.3.1 Sample preparation by Focused Ion Beam Usually, electro-polishing, micro polishing, and pulse polishing techniques have used to prepare the samples. However, preparation of amorphous ribbon specimen for atom probe tomography method is rather complex. The Focused Ion Beam (FIB) has used to prepare amorphous sample shown in Figure 4.6. The material used in FIB due to (a) the material cannot be electro-polish, (b) the specimen geometry prevents the use of traditional specimen fabrication techniques or (3) the specimen is to be prepared for a specific site. Figure 4.6. Focused Ion Beam apparatus (FIB) at Northwestern University 153 Here, a fine needle with circular cross-section (~38 nm) and a taper angle <5o is made by using Focused Ion Beam (FIB) apparatus. This instrument combined with scanning electron microscope. The small radius of the tip of the specimen required creating a high field for evaporation. The taper angles made to analyze the specimen to the depth ~100 nm to 1μm. We start with the amorphous ribbons of ~35μm thickness and extract a needle with the tip normal to the length of the needle, i.e. the total length of the needle is very short ~35μm or so and the diameter in the nanometer range. We show scanning electron microscopic images obtained during processing in the FIB instrument. Figure 4.7 (a) shows Figure 4.7 Sample preparation inside Focused Ion Beam apparatus (FIB) at Northwestern University the surface of the ribbon in the FIB instrument, (b) shows Pt coating on the surface of interest, (c) and (d) shows trenching of areas near the sample to extract the parallelepiped- 154 shaped sample by “cut away” FIB milled from the surface. (e) Shows micromanipulator attached the sample to a needle in the FIB instrument for extraction of the sample called “lift away.” Image (f) shows sample separated from the original ribbon, and attached to a support post; (g-m) shows the annular milling pattern for sharpening the needle. Series of annular milling have performed by a Gallium progressively smaller inner diameter and beam current. (n) Shows transfer of the sample to the holder of LEAP atom tomography instrument, (o-p) show final needle shape <100 nm, (q) show the sample needle mounted on the sample holder of the LEAP atom tomography Cameca instrument. Note that three to four sample needles possible to mount on this holder. 4.3.2 Local Electrode Atom Probe (LEAP) High-purity nickel (35.1 wt. %), niobium (33.3 wt. %) and zirconium (31.6 wt. %) particles were mixed and arc-melted to produce alloy buttons of Ni42Nb28Zr30 at the DOE AMES Laboratory in Iowa. This ternary ribbon, usually designated as, (Ni0.60Nb0.40)70Zr30, fabricated by melt spinning under an argon atmosphere at CSIRO Laboratory, Brisbane, Australia. The cooling rate for fabrication of this type of amorphous ternary ribbon was ~106 K/s. X-ray diffraction analyses performed on the ribbon (~50 m thick) confirmed the amorphous nature of ribbon. The Atom Probe Tomography instrument at NUCAPT facility located at the Northwestern University, Evanston, Illinois has shown in Figure 4.8. The small section of ~30 m long parallelepiped extracted from the Ni42Nb28Zr30 amorphous ribbon and ion machined in the form a needle and sharp tip (~20 nm). The sample transferred to a Cameca Amtek Local Electrode Atom-Probe (LEAP) sample chamber shown in Figure 4.8. In this LEAP 4000X, 155 Si has an ultrafast detection of up to 360 million ions per hour. This instrument consists of the focused laser beam and the local electrode. This is the only laser pulse instrument having capabilities of analyzing microtip array shown in Figure 4.7(q). Few reasons of the microtip array discussed below [164]. a) In the APT, the microtip arrays have analyzed directly from Figure 4.8 LEAP (local electrode atom probe) one to another. instrument used at Northwestern University b) The tips coated with thin films ofused organic in our and studies. inorga nic materials. c) These tips also solved the purpose for extraction from the wafer or other bulk materials. The LEAP instrument has better than 0.3 nm in three dimensions, and high analytical sensitivity of ~1 atomic parts per million (appm) over volumes of greater than 106 nm3 (100 nm × 100 nm × 100 nm). Despite some detector inefficiencies, this is the best probe available for studying the internal arrangement of atoms. a pulsed laser beam with a wavelength of 355 nm (ultraviolet) and 20 pJ pulse energies to activate atom-by-atom field evaporation, with a pulse repetition frequency of 500 kHz and a specimen stage temperature of 30 K. More details can found in the reference [168 - 170] 156 4.4 Results and Discussions Atom Probe Tomography (APT) had performed on the needle-shaped specimen of (Ni0.60Nb0.40)70Zr30 from the thin alloy membrane. The alloying elements Ni, Nb, Zr and their respective isotopes had detected by using mass spectroscopic analyses from pulsed laser field evaporation of the atoms. Each ion evaporated from surface goes towards detector by time-of-flight method. Taking potential and kinetic energy of the ion consideration, time-of-flight converted to the mass-to-charge ratio (M). The detection of an ion by mass (푚) to charge (푛) state ratio represented by histogram called mass spectrum. Some electrons removed from the ion usually having is a charge of 1-4.If we consider, ion detach from the surface without any velocity then, 푚 푡푓푙푖푔ℎ푡 − 푡0 푀 = = 2푒푉 푛 퐿푓푙푖푔ℎ푡 Where, V is the applied voltage between the specimen and the local electrode, 푒 is the elementary charge of an electron, 퐿푓푙푖푔ℎ푡 is the length of flight distance, 푡푓푙푖푔ℎ푡 time required to flight, 푡0 is the time shift. The unit of mass-to-charge ratio expressed by Daltons (Da). Sometimes it also given as atomic mass unit (amu). Due to high mass resolution, this time-of-flight mass spectrometer can identify individual isotopes of all elements. In a pulsed laser, the detection efficiency of the spectrum is around 50-60% as the ions removed from the specimen by evaporation of atom [167]. This loss appears due to the interaction of ions in the interchannel region of a microplate in the detector. There are certain issues of the mass spectrometer i.e. hydrides, pulse replicas, etc. Sometimes large broad peaks appeared due to a high voltage of the pulse. The mass spectra show the elemental profile 157 in the mass range ~28 to 65 mass-to-charge-state ratio shows in Figure 4.9 (a). The mass range is minimum mass-to-charge ratio and the maximum mass-to-charge ratio of the experimental specimen. Mass spectra of our sample have allowed identifying unknown mass peaks as well as the distribution of the isotopes. Some cases isobaric overlap could be possible to occur such as 58Fe+ and 58Ni+. For clarity, we expand the three sections, where the peaks have populated as shown in Figure 4.9 (b, c, and d). The expanded range of 27-66 amu show isotope peaks of Ni+2 (58, 60, 61, 62, and 64) and Zr+3 (90, 91, 92, 94, and 96) in Figure 4.9 (b). In the range of 43.5-50 amu, peaks of Zr+2 (90, 91, 92, 94, and 96), and one Nb+2 (93) are observed in Figure 4.9 (c). The peaks of Ni+1 (58, 60, 61, 62, Figure 4.9 (a) The overall mass spectra 0.02 bins 27-66 amu for the area shown in Figure. (b) Expanded region of the spectra in 0.02 bins 27-66 amu (c) expanded region of the spectra in 0.02 bins 43.5-50 amu, (d) expanded region of the spectra in 0.02 bins 50-66 158 and 64), and other impunities are observed in Figure 4.9 (d). In the below plot, the isotopic ratio is maintained. There is some overlap of Ni with Zr peaks, but there is no overlap of the 93Nb3+ (96.906 Da) with the 93Nb2+ (46.453 Da) or other Zr or Ni peaks. These peaks have identified by masses of the periodic table and known isotopic fingerprints. Peaks associate with minor isotopes such as some Ni with Zr peaks have hidden due to overlapping of other peaks or high background. The isotope mass numbers, atomic mass, and isotope abundance and the charged states of the elements Ni, Nb and Zr shown in Table Table 4.1 Periodic Table of isotopes for mass spectroscopy 4.1. In Atom Probe Tomography, individual ions collected in the detector, and these are required to reconstruct the 3D position of the specimen. The real space of the specimen constructed in 푥, 푦, 푧 coordinates from calculating captured ion collecting time series of 2D positions in the detector coordinates. The surface of Ni-Nb-Zr amorphous ribbon tip evaporated one atom layer to another. The standard 3D reconstruction appears due to evaporated atom from the specimen and detector hit positions (푋 and 푌) into real-space coordinates, where 푥 and 푦 contained in the plane normal to the specimen axis at the current 159 apex position [171]. 푍-axis depicted the depth of ion along based on the ionic volume and imaged area of the specimen surface. The atom hitting at the detector used to identify the same layers of the atom as well as the position of the atoms. The 3D reconstruction of the image occurs by two-step after collecting the data. First, raw time of flight data conversion to the time-of-flight measurement by correcting voltage and flight path, ion position determination in 3D coordinates 푥, 푦, 푧 from detector hitting position of the ion and layer by layer atom evaporation sequence. Second, 3D image reconstruction by analyzing the volume of the image and identify the atoms. The position of the ion in the 3D coordinate (푥, 푦, 푧) determined from the position of ion hitting the detector (푋퐷, 푌퐷) shown in the Figure 4.10. If the voltage is 푉퐷퐶 and radius of the specimen tip is 푟, then specimen radius will be 푉 푟 = 퐷퐶 푘 × 퐹 Where, 퐹 is evaporation potential and 푘 is a geometric factor. Usually, sample tip is conical in shape where 푘 = 3.5. In a point projection, magnification (푀) determined as the distance between distance and sample and detector (퐿) and radius of curvature of the specimen (푟), therefore 푆푝푎푐푖푛푔 표푛 푑푒푡푒푐푡표푟 (푙) 퐿 + 휉푅 퐿 푀 = = ≈ 푠푝푎푐푖푛푔 표푛 푠푎푚푝푙푒 (푙표) 휉푅 휉푅 Where, 휉 image compression factor and 휉푅 is reconstruction center. The magnification of 6 atom probe tomography is usually 10 mm/nm. Therefore, detector position (푋퐷,푌퐷) display original coordinate position (푥, 푦) of ion 푋 푌 푥 = 퐷 , 푦 = 퐷 푀 푀 160 Figure 4.10 Schematic diagram of field line and detector [adopted from ref 171] Coordinate 푧 display depth direction calculating series of evaporation of the specimen and volume increment [171], 푎푡표푚 푣표푙푢푚푒 푧 = 푧 + ∆푧 = 푧 + 0 푖푛푖푡푖푎푙 푑푒푡푒푐푡표푟 푒푓푓푖푐푖푒푛푐푦 × 푠푢푟푓푎푐푒 푎푟푒푎 This unique property of atom probe tomography is unparalleled with any other electron microscope. Three-dimensional reconstruction of the atom tomography data of the glassy alloy (Ni0.60Nb0.40)70Zr30 shows the distribution of Ni, Nb, and Zr atoms in an 113 nm×109nm×99nm cube in Figure 4.11 (a). The average composition of the amorphous matrix of this ribbon is Ni=42 at. %, Nb=28 at. %, and Ni=30 at. % although the exact nature of the short range order (SRO) is not known. Each dot represents the different atomic position of different atoms. Concerning the atomic arrangement of the Ni-rich matrix, we do not know the exact nature of the three-dimensional coordination of the Ni-rich region; perhaps there may be a distorted icosahedra arrangement as observed in the SRO of FCC 161 alloys. Figure 4.11 (b-d) shows a rather uniform distribution of individual ions of Ni (blue), Nb (Green) and Zr (Red) atoms in the sample volume of 100x100x100 nm3. Figure 4.11. Atom probe 3D reconstruction of a portion of the (Ni0.60Nb0.40)70Zr30 needle shaped specimen showing (a) ~ 20.1 million atoms of Ni, Nb and Zr, and other small impurities in a section 113×109×99 nm3 volume, (b) Ni atoms (isolated), (c) Nb atoms (isolated) and Zr atoms (isolated) More detailed analyses of a randomly selected APT data in a small volume slice of 113×5×99 nm3 in the original volume of 113×109×99 nm3 cube revealed inhomogeneous amorphous structure with clusters embedded in the Ni rich-matrix, as shown in as dotted lines Figure 4.12 (a). Sections 푦 and 푧 directions shown in Figure 4.12 (b) and (c). The global composition of this metallic glass was in agreement with measured value by the APT. We will discuss the detection of the Nb-rich clusters in the matrix first. The matrix has 28 at.% Nb, but varying the concentration greater or less than 28 at.% we observe Nb- 162 rich clusters of a different composition than the nominal ones (Figure 4.12 (d)); other atoms Figure 4.12 Atom probe 3D reconstruction of a portion of the (Ni0.60Nb0.40)70Zr30 sample in a cropped volume of 113×5×99 nm3 showing all the Ni, Nb, and Zr atoms, (b) view in y-direction, (c) view in z-direction, (d) Iso34-Nb, (e) Iso34-Nb with Nb atoms (isolated) (f) Iso34-Nb with Ni atoms (isolated), and (g) Iso34-Nb with Zr atoms (isolated). 113×109×99 nm3 cube are not represented in this figure. In Figure 4.12 (e), we show Nb atoms above and below the threshold iso-concentration of 34% Nb, which shows the same clusters as seen in Figure 4.12 (d) but superimposed with lower concentration Nb-atoms. The position of the clusters remains the same when this 34% Nb atoms superimposed with the Ni (Figure 4.12 (f)), and Zr (Figure 4.12 (g)) atoms. We designate this Nb-rich cluster as Phase I in the matrix of Ni-rich atoms. In a similar manner, designate Zr-rich (Phase II) in the Ni-rich matrix. These results clearly suggest phase separation even at room temperature in the amorphous alloy (Ni0.60Nb0.40)70Zr30 ribbon with Nb and Zr-rich clusters. 163 To illustrate this, an APT 3D-construction and proximity concentration profile on a nano- 3 scale of the Ni42Nb28Zr30 alloy in an 113 x 109 x 99 nm region shows all the atoms of Ni, Nb, and Zr superimposed as dots (Figure 4.12 (a). In Figure 4.12 (b), only Nb-enriched atom clusters shown whose average composition is Ni31.78Nb46.5Zr21.2, omitting all other Ni and Zr atoms for clarity. An area at the bottom of Figure 4.13 (b) selected for a line scan on this small area, as shown in the inset. A proxigram concentration profile created, 3D construction of 3D view of only Nb all Ni-Nb-Zr Atoms rich clusters (units-nm) overlapped x-axis (a) (b)+40 +20 0 -20 -40 z - axis 50 93 + 40 Nb 30 60Ni+ 20 10 58 + Concentration (At.%)Concentration Ni 0 -6 -5 -4 -3 -2 -1 0 +1 Distance (nm) Figure 4.13 APT 3D-construction and proximity diagram on Ni42Nb28Zr30 alloy in a 100 nm x 100 nm cube in which all the atoms of Ni,Nb,Zr are superimposed as dots. Figure 2(b) shows only the Nb-enriched clusters, and excludes the Ni and Zr atoms for clarity. The average composition of the Nb-rich clusters is Ni31.78Nb46.5Zr21.2 (green), different from the nominal alloy composition. A proxigram shows the composition variation of the 93Nb+, 60Ni2+, and 58Ni+ isotopes 164 averaging over all Nb-enriched clusters, as schematically shown in the inset for one cluster. The proxigram (concentration vs. distance) shows the composition variation of the 93Nb+ and 58Ni+ isotopes detected using the mass spectrometer across a small line of ~10 nm extending from point A to C. The point B shows the interface at zero marks, i.e., at the interface of the particle “C” and the matrix. As the scan approaches the interface, the Nb concentration increases and that of Ni decreases. A proxigram with a partial mass spectrum (in b) obtained by scanning ~7 nm distance along the line A-B-C (in the inset image) that shows a variation of Nb, and Ni at the interface (at point B) in one of the Nb-rich cluster (dark green). Figure 4.13 (c) shows the matrix of Ni atoms (blue in c) superposed with Nb 34% isoconcentration (dark green). To the best of our knowledge this first time, we have shown these three phases. It suggests that possibility of icosahedron type coordination may exist in these types of glasses based on theoretical studies [172]. The average composition of the specimen is possible to determine by mass spectra where the composition is simply computed from the proportions of atoms of each species. Suppose an element j that is part of a multi-component material containing i different elements. The composition 퐶푗 can be define as [165] ∑푀푚푎푥(퐽) 푁 (푀) 푀푚푖푛(푗) 푎푡 퐶푗(푎푡. %) = × 100 ∑ ∑푀푚푎푥(푖) 푁 (푀) 푖 푒푙푒푚푒푛푡 푀푚푖푛(푖) 푎푡 푁 (푗) 푁 (푗) = 푎푡 × 100 = 푎푡 × 100 ∑푖 푒푙푒푚푒푛푡 푁푎푡(푖) 푁푎푡 165 Where the number of an atom having mass M is 푁푎푡(푀), a total number of an atom is 푁푎푡 from part of any range, and 푁푎푡(푗) is the total number of atoms of the species 푗. In the mass spectrum, the maximum and minimum range showed as 푀푚푎푥(푖) and 푀푚푖푛(푖). The above equation gives atomic ratio and values in atomic percentage. For statistical variation, the precision, σj , of the composition measured by 퐶푗(1 − 퐶푗) 휎푗 = √ 푁푎푡 The average composition of the ribbon as measured by the mass spectra is Ni=41.89 at.%, Nb=26.14 at.%, Zr=31.97 at.% is very close to the original alloy composition of Ni=42 at.%, Nb=28 at.%, Zr=30 at.% of the arc melted alloy button. Note that effort had made to make measurements away from the clusters. Table 4.2 shows the composition of Nb and Zr enriched cluster, which is distinctly different from the nominal composition of the alloy. Table 4.2. Composition of Phase I (Nb-rich cluster), Phase II (Zr-rich cluster), and overall composition of the alloy from the atom probe tomography studies. at.% Abbreviation Elemental Concentration (at.%) Phase Name Ni Statistical Nb Statistical Zr Statistical error error error Overall Nominal Ni42Nb28Zr30 42 - 28 - 30 - Overall measured by APT Ni42Nb26Zr32 41.89 + 0.07 26.14 + 0.04 31.97 + 0.07 Phase I (Nb-rich cluster) Ni32Nb46Zr22 31.8 + 0.6 46.5 + 0.4 21.7 + 0.7 Phase II (Zr-rich cluster) Ni39Nb18Zr44 38.6 + 0.8 17.9 + 0.3 43.45 +1.1 Phase III (matrix) NiXNbYZrZ 41.97 + 0.07 26.05 + 0.03 31.98 + 0.07 A section of 60×60×30 nm3 (3,631,236 atoms) was chosen in this case (Figure 4.14 (a-b). The Zr Phase cluster are clearly seen superimposed with Ni and Zr atoms in Figure 4.14 (c). Figure 4.14 (d) shows superimposed Zr and Nb (high concentrations) with all Nb background atoms (without Ni atoms). To observe the distribution of isolated Zr-rich clusters (in red color) in a small volume shown in Figure 4.14 (e); other atoms are left out 166 for clarity the spatial distribution of both Nb- and Zr-atoms in the (Ni0.60Nb0.40)70Zr30 ribbon shown in Figure 4.14 (f). These shows that even there is a cluster in the homogeneous amorphous matrix. Figure 4.14 A section of 60×60×30 nm3 (b) Enlarge section of 60×60×30 nm3 (c) Clusters of Ni and Nb in NI-Zr matrix (d) Cluster of Zr in the matrix (e) Phase separation cube with zirconium rich phase with depleted Niobium (red color), (f) Niobium rich phase with depleted Zirconium (green color) with Zirconium rich phase. The cluster size of Niobium is comparatively bigger than the cluster size of zirconium 167 So far, we have the cluster configuration in the amorphous matrix, but the actual short- range order cannot be determined due to lack of resolution of the APT. In the literature, we found Kelton et al. [173] reported the experimental demonstration of Frank hypothesis in 2003. The Frank hypothesized that the barrier to nucleation of crystallographic phases gives rise to local icosahedra in the liquid. Kelton showed that in Ti39.5Zr39.5Ni21 alloy undercooled liquid state, local structure contained a significant degree of short-range order (SRO) icosahedra, with no long-range periodicity by calculating XRD structure factor. He also showed the nucleation barrier decreases due to the formation of icosahedra phase and proved Frank’s hypothesis. Their study first revealed the growth of icosahedra short-range order structure inside amorphous matrix with decreasing temperature of the alloy. Many other researchers later reported metallic glass systems have a significant degree of order within the amorphous matrix. In 2009, Oji et al. [91] reported icosahedral structure in (Ni0.60Nb0.40)70Zr30 and (Ni0.60Nb0.40)60Zr40 alloys using XAFS data and other computational models. Further studies by Fukuhara and Inoue [89] using XANES confirmed that these glassy alloys had formed icosahedra short-range order. We propose that the Nb-rich (Phase I) and Zr-rich (Phase II) clusters have interconnected distorted icosahedra embedded in Ni- rich matrix. There are other examples of Zr-based amorphous alloys that showed phase separation and nano-scale icosahedra precipitates in a single amorphous phase by APT at comparatively high temperatures, just below the glass transition temperature [174]. In 2004, Martin’s study combined SAXS, TEM and APT data [174]. The icosahedra phases obtained just above the glass transition temperature. However, they are not able to detect these phase separation in an amorphous state. They explained their nanocrystalline microstructure as primary crystallization of icosahedra phase. 168 We propose a similar type of icosahedral structure appears in our ribbon at room temperature [89, 91, and 174]. In another paper by Hono et al. [175] obtained three- dimensional APT data along with high-resolution electron microscopy (HREM) in and observed clustering of Cu and Si petitioning just before primary crystallization in the Fe73.5Si13.5B9Nb3Cu1 amorphous alloy. Their study revealed these clustering helped to form heterogeneous nucleation sites for primary crystallization of the material. Shariq and Mattern [176] reported phase separation in Ni66Nb17Y17 alloy, in which a Y-rich phase depleted of Nb and vice-versa observed in an APT experiment. They also found two interconnected amorphous phases similar to what we observed in our Ni-Nb-Zr alloy. Further study revealed melt-spin process have a significant effect on phase separation of the alloy. The cooling rate is higher in roller contact side of the amorphous ribbon. Therefore, early stage of decomposition observed on that side rather than the non-contact side. There are reports of amorphous thin films in the immiscible copper–niobium system, in which phase separation observed even at low temperatures, 200 °C [178]. Mattern et al. [179] studied as-quenched Cu46Zr47−xAl7Gdx metallic glasses and found that the cluster formation was dependent on the Gd content (푥) in the alloy; this formation is favorable at higher temperatures due to pre-crystallization nucleation and growth. The cluster size they found 2-5 nm inside the amorphous matrix. In order to understand detailed local cluster structures inside these Ni-based amorphous ribbon by considering the experimental APT data, DFT- MD simulation were performed. The result suggests that the amorphous structure consists of different types of icosahedra shown in the Table 4.3; these icosahedra consists of 12 atoms (Voronoi index (0 0 12 0)) and most of them are Ni and Nb centered. The Nb- and Zr-rich clusters in the alloys have 169 different icosahedral chemical formulas as expected shown in Table below. The DFT simulation reveals the average size of single icosahedron is ~0.56 nm. Table 4.4 Different icosahedra configurations for Nb-rich (Ni41Nb59Zr28) and Zr-rich (Ni49Nb23Zr56) with centered atom in parenthesis calculated by DFT-MD. Icosahedron Ni41Nb59Zr28 Ni49Nb23Zr56 1 Ni2Nb7Zr3 (Zr) Ni3Nb4Zr5 (Nb) 2 Ni4Nb4Zr4 (Nb) Ni2Nb4Zr6 (Nb) 3 Ni4Nb6Zr2 (Nb) Ni4Nb2Zr6 (Ni) 4 Ni2Nb5Zr5 (Nb) 5 Ni1Nb7Zr4 (Ni) 6 Ni3Nb6Zr3 (Ni) 7 Ni4Nb5Zr3 (Ni) Average over icosahedra Ni16Nb30Zr18 Ni9Nb10Zr17 Average over all Ni31Nb49Zr26 Ni33Nb18Zr48 The Figure 4.15 showed snapshot of (a) nominal composition (Ni54Nb36Zr38 ), (b) Zr-rich region (Ni49Nb23Zr56) and (c) Nb-rich region (Ni41Nb59Zr28) where Ni, Nb and Zr atoms are represented by grey, cyan and green balls respectively. The atoms with icosahedra clusters represented by red atoms revealed that the Nb rich cluster is composed of 7 icosahedra (~3.9 nm) and Zr- rich cluster is composed of 3 icosahedra (~1.7 nm) which are similar to the experimental data shown in Figure 5. The cluster typically observed in small region composed of hundred atoms and it is randomly arrange throughout the glass. The APT experimental and DFT-MD simulation shows that the cluster sizes in these metallic glasses between 2-5 nm as a function of different alloying additions. Fujima et al.[20] reported 8 icosahedra of Ni5Nb3Zr5 single unit in (Ni0.60Nb0.40)60Zr40 alloy using first 170 principle calculation; according to their calculation local icosahedra structure are stable in the amorphous phase at room temperature. All the literature mentioned above and our APT data suggested that phase separation might be a common behavior in the majority of the amorphous materials at room temperature, soon after the ribbons are made. Going back to our alloy system, addition Zr to the base (c) Ni Nb Zr (a) Ni54Nb36Zr38 (b) Ni49Nb23Zr56 41 59 28 Ni2Nb7Zr3 Ni3Nb4Zr5 Ni2Nb7Zr3 Figure 4.16 DFT-MD calculation: Snapshots of various ternary metallic glasses which are formed during the fast quenching from high temperature of 3000 K with the cooling rate of 1.08 x 1014s-1. Red balls in the periodic simulation box represent the atoms within icosahedral clusters. Green, cyan and grey balls represent the Zr, Nb and Ni atoms, respectively. alloy Ni60Nb40 to increase the hydrogen permeation rate. It is possible that the phase separation or cluster formation at room temperature is enhanced due to the addition of Zr in the Ni-Nb-Zr amorphous alloy as the empirical atomic size of zirconium (rZr=155 pm) is much larger than of Ni (rNi= 135 pm) and that of Nb (rNb=145 pm); the more the Zr in the Ni-Nb-Zr alloy, greater the tendency for phase separation [179]. Zhu’s et al. [179] TEM result of Ni-Nb-Zr bulk metallic glass reveals Ni3Nb, NiNb and Ni10(NbZr)7 and the 171 structures depend on Zr content shown in the below Figure 4.17. As the Zr content increase the Ni10(NbZr)7 phase also increased shown in the Figure 4.17. Kim et al. [180] showed in Ni-Nb-Zr amorphous ribbon have Ni10Zr7. (a) (b) (c) Figure 4.17 Bright field TEM image of bulk metallic NI-Nb-Zr glass and the composition is (a) Ni61.5Nb37.5Zr1 (b) Ni61.5Nb31.5Zr7, (c) Ni61.5Nb29.5Zr9. As zirconium content increase the microstructure become different (Zhu, 2008) [179] In our study, we also propose considering Martin and DFT simulation that in Ni-Nb-Zr amorphous alloy just before crystallization can produce (푵풊 − 푵풃 − 풁풓 풂풎풐풓풑풉풐풖풔) → 푎푚표푟푝ℎ표푢푠 + 푖푐표푠푎ℎ푒푑푟푎 푐푙푢푠푡푒푟 + 푁푖10푍푟7 + 푢푛푘푛표푤푛 푝ℎ푎푠푒푠 We determined the cluster size of Nb-rich as ~2 nm, and Zr to be ~5 nm from Figure 4.14 which indicates that each cluster in the Zr-rich cluster, have ~7 interconnected icosahedra, and the Nb-rich cluster may have only ~3 interconnected icosahedra. The cluster sizes in this metallic glass between 2-5 nm as a function of different alloying additions [178]. The number of atoms in a 2 nm diameter precipitate is about 80-120 atoms in the reconstruction or 160-240 atoms in nature, taking into account the 50% detection efficiency of the LEAP. If the coordination polyhedra have 12-14 atoms, that is about 15-20 individual "building 172 block" icosahedra not counting that of course every single one of the 160-240 atoms have their own coordination polyhedron consisting of the 12-14 atoms surrounding them. Fujima et al. [181] reported 8 icosahedra of Ni5Nb3Zr5 single unit in (Ni0.60Nb0.40)60Zr40 alloy using first principle calculation; according to their calculation, local icosahedra structure are stable in the amorphous phase at room temperature. Similar size of the structure also revealed by Mattern [178] in the Cu-based amorphous alloy. Conclusion: Atom tomography studies unambiguously show cluster formation within the matrix of the amorphous Ni-rich ternary alloy. Specifically, Nb-rich phase of Ni32Nb46Zr22 (cluster size~ 2nm size ) composed of 3 icosahedra, and Zr-rich phase of Ni39Nb18Zr44 (cluster size~ 5 nm size) composed of 7 icosahedra embedded in the Ni-rich ternary alloy matrix of Ni42Nb28Zr30; phase separation in Ni-Nb-Zr amorphous alloy, without prior annealing to crystallization; have not been reported earlier to the best of our knowledge. 173 Chapter 5 High-Pressure Studies on Disordered Materials: Diamond Anvil Cell (DAC) Contents 5.1 Introduction…………………………………………………………………169 5.2 Diamond Anvil Cell (DAC) and Raman Spectroscopy…………………….169 5.3. Experimental Details ………………………………………………...... 173 5.4 Result and Discussions……………………………………………………...175 5 High-Pressure Studies on Disordered Materials: Diamond Anvil Cell (DAC) 5.1 Introduction High-pressure permeability behavior of amorphous material Ni42Nb28Zr30 has performed by Diamond Anvil Cell (DAC) and Raman Spectroscopy. The primary function of DAC is to increase pressure in the amorphous material and rearrange the structure; this eventually helps to understand hydrogen permeation through the membrane more easily as the pressure plays a significant role in coal gasification system. 5.2 Diamond Anvil Cell and Raman Spectroscopy Diamond Anvil Cell The DAC is a high-pressure device that use to generate high pressure by squeezing a sample in a small area between two opposed diamonds configuration shown in Figure 5.1. The sample has placed in the hole of a gasket inserted between the polished culets of two 174 diamonds. The culet is small area is the tip of the diamond to create a small flat portion, and the size of the culet is crucial for determining the amount of pressure applied to a sample. The pressure applied to the sample roughly estimated by the following relation, where pressure is equal to force divided by area. Considerably Figure 5.1 Diamond Anvil cell high pressure is possible to attain by reducing the surface area of the culet. There are several types of DACs used depending on the type of experiments, require pressures and temperatures conditions. The detailed description of DAC found in the several literatures [182-183]. The diamond anvil has made of tungsten carbide or hardened steel backing to withstand huge pressure. Diamonds are possible to glue by epoxy due to their high thermal conductivity and low thermal expansion. In our experimental setup, we use DAC, which have the cylindrical external shape of four-post where out of four screws, two screws are left handed, and two are right handed. These four independent set of screws used for parallel and concentric alignments. The most important factor of DAC is to make the diamonds align as much as possible. Therefore, it can deliver a similar amount of pressure throughout the sample. Breaking the diamond occur in the cell due to the wrong alignment. For performing alignment, microscope, and transmitted-reflected lights have used. For DAC concentric alignment, parallel surface alignment i.e. touching both surface each other also performed. The interference rings i.e. fringes should be minimum when it look from the top. Usually, less than four interference rings are good for alignments. Therefore, the culets are placed for parallel alignments to concentric nature. Lateral movement of the samples has 175 prohibited after the sample placed in the culets. A metallic sheet such as inconel, rhenium, copper or beryllium has placed in between diamonds, called gasket. The gasket material has chosen to depend upon experimental pressure. In the amorphous ribbon, copper- beryllium gasket used in order go up to 10 GPa pressure. The gasket also creates uniform pressure through the whole volume of the sample indicates hydrostatic or quasi-hydrostatic medium. For making extremely, small hole in the gasket, electric discharge machine (EDM) has used. The gaseous medium in the sample chamber, hydrostatic pressure is required. After proper alignment of diamond and sample, the screws are tightened properly. After preparing the cell, the standard procedure is to introduce a few ruby chips above the diamond to calculate the pressure by empirical relation. The composition of Ruby is 3+ (sapphire (Al2O3)+(~0.05% Cr )) by weight. Due to chemical inertness, it causes a minimum reaction to the experimental samples. After introducing ruby chips, the DAC are closed, and the visible laser is illuminated on the ruby particles. Ruby particles are produced two peaks, R1 (694.2 nm) and R2 (692.8 nm) under ambient pressure. Increasing pressure R2 peak shifted, and it is useful for empirical relation [184]. To understand hydrogen permeability, the interaction of hydrogen with the amorphous sample on (Ni60Nb40)70Zr30 and Ni60Nb40 experiments were performed using Raman spectroscopy. Raman spectroscopy: Raman spectroscopy is a technique to determine vibrational, rotational and low-frequency modes of the molecules [185]. High-pressure mode change in the system due to DAC is possible to measure by Raman spectroscopy. In 1928, C.V Raman discovered Raman scattering. In this scattering technique, the molecules are going to an excited state from the 176 ground electronic state by visible light (laser) [186]. The incident and the resulting spectrum having new wave-number and the energy difference between two vibrational excitation represents as Raman spectrum. Suppose, the incident wave number is 푣0 and it is excited by laser beam then the final wavenumber will be 푣 = 푣0 + 푣푚 where, 푣푚 is the transition between rotational, vibrational and electronic states. If the molecule is elastically scattered, i.e., the radiation without a change in the frequency comes to its initial state called Rayleigh scattering. The intensity of Rayleigh scattering is about 10−3 of the incident radiation. However, the scattered light frequency shifted depend upon the energy spacing between the vibrational modes. If the molecule goes initial state to higher vibrational state (푣 = +1), it gives rise to the spectrum call Stokes scattering and if the opposite phenomena where (푣 = −1) resulting anti-Stokes scattering shown in Figure 5.2. Figure 5.2 Schematic diagram of Raman scattering [187] 177 Usually, the intensity of Stoke scattering is higher than anti-Stoke scattering. Here, this technique is required to understand hydrogen permeation behavior through the membrane under high pressure. 5.3 Experimental Details To understand hydrogen permeability, the interaction of hydrogen with the amorphous sample on (Ni60Nb40)70Zr30 and Ni60Nb40 experiments were performed by Diamond Anvil Cell using Raman spectroscopy. To begin with, diamonds are inserted into the anvil cylinder and piston are placed. About 800µm diameter, culet have aligned into the cells for 500µm diamenter sample. Four screws have attached to the each side of the cell. It required tightening these in such a way that the diamonds are centered as much as possible. Mono-focal microscope is used to observe the position of the diamond. Usually, it required to make the diamonds closer, usually 1 mm apart then piston and cylinder are inserted together. Next step is to hammer both sides of the diamond and align the cell through other two screws, then loosen and tighten the screws every time, so that the diamonds are alignment is proper. In the monofocal microscope, the brighter diamond is the lower diamond. Few ruby particles placed on the diamond as discussed before and the gasket is placed in between the diamond, which create an impression in the gasket due to pressure of the diamond; gaskets are removed. The electric discharge machine (EDM) is used to make a hole in the gasket inside that particular impression. EDM prepared gasket hole inserted in between the diamond. Next, the sample (Ni0.6Nb.40)80Zr20 with 500µm has placed inside the gasket and tighten the DAC again shown in Figure 5.3 (a). Very carefully, hydrogen is loaded to the one side of 178 the Diamond Anvil Cell to understand whether the Sample vibrational and rotational movement Gasket are changing inside 500 µm 800 µm the sample after Figure 5.3 (a) (Ni0.60Nb.40)70Zr30 with diameter 500µm at increasing the 800µm culet at pressure 1.37 GPa (b) (Ni0.6Nb.40)70Zr30 with diameter 500µm at 800µm culet at pressure 2.25 GPa pressure on it. The Raman spectroscopy has measured at Carnegie by a red laser having a wavelength of 635 nm shown in Figure 5.4. The appearance of the samples shows below is before and after the pressure inside the diamond anvil cell. Figure 5.4 In-situ Raman spectroscopy for high pressure using diamond anvil cell at Carnegie Institute of Washington. 179 5.4 Result and Discussions Raman spectroscopy is measured on the mechanically prepared (Ni60Nb40)70Zr30 surface of the sample, at the sample-H2 interface, and in the surrounding H2 for reference. Raman spectra for (Ni60Nb40)70Zr30 are plotted in the pressure range 0.2-2.7 GPa shown in Figure 5.5 (a). The blue and the red plots represent the spectra on the foil and in the H2-rich region. Figure 5.5 (b) shows results of a binary alloy, Ni60Nb40 in the pressure range 0.3 to 3 GPa. It is interesting to find that above 2.5 GPa; there is a red shift in the H-H frequency on the Figure 5.5 (a) Raman spectra of Zr30 with H2 loading (b) Zr=0 with H2 loading at different pressures foil in comparison to pure H2 (Figure 5.5 b) indicative of an interaction between the foil and the H2 molecules not observed in the other sample. However, the interaction between foil and hydrogen is not very prominent in the actual mechanically prepared sample. The vibron peaks for hydrogen in the sample (hydrogen + sample), outside of the sample (pure hydrogen) and the edge of the surface shown in the below Table 5.1. Roton peaks are not 180 much important for our experiment and vibrons are more sensitive shown in Figure 5.6. The peaks are matched with Raman data of hydrogen at room temperature [188]. Table 5.1. Roton and vibron peak The interaction between foil and hydrogen is not very prominent in mechanically prepared sample. We repeated experiments using samples (Ni0.6Nb0.4)70Zr30 and Ni60Nb40 prepared by FIB; The Raman data are shown in Figure 5.7. The data obtained from mechanically Figure 5.6 (a) Roton peaks of hydrogen for binary alloy (b) Vibron peaks of hydrogen in binary alloy machined and FIB fabricated samples yielded the same results shown Figure 5.8, suggesting the sample preparation did not have any effect. 181 Figure 5.8 Raman results from the mechanically milled and FIB fabricated DAC samples showing no Other experiments attempted to understand the diffusion behavior of the amorphous membrane. Thus, a new set of experiment had performed to understand hydrogen diffusion through the amorphous (Ni60Nb40)70Zr30 membrane using DAC system. (c) A schematic of the DAC is shown in Figure 5.9(a). In these experiments a different strategy was used; hydrogen absorbing material such as graphite (-350 mesh and >99.99% purity) has placed between the KBr and sample (Figure 5.9 (b)). Figure 5.9 (b through d) show different arrangements explored with the (Ni60Nb40)70Zr30 ribbon sample. Note that the KBr is placed below the graphite layer. Raman spectroscopy performed on both sides of the DAC; it has observed that the hydrogen placed on the top side has not detected on the top side (Figure 5.9 (b) after pressurizing to 2.8 GPa. The result suggests that the hydrogen 182 diffused into the sample. However, by flipping the DAC (a) to expose the bottom side toward the Laser side we could detect the hydrogen vibron. Green laser pointer has used for the Raman spectra (wavelength of 520nm) to measure the hydrogen vibron peak. It has proposed that the hydrogen may have diffused into the sample but Not to Scale (b) not permeated through the thickness. Typically, hydrogen solubility is higher at lower temperatures, but KBr Figure 5.9. (a) Schematic of the kinetic is very slow, with the application of GPa level Diamond Anvil Cell with the pressure, the hydrogen solubilized in the membrane. hydrogen diffusion set up. (b) The permeation requires pressure differential between schematic showing the sample (Ni0.60Nb0.40)70Zr30, graphite the top and bottom, which was not present. We can only layer, and the KBr layers with suggest that hydrogen solubilize in the membrane at head-space for hydrogen gas. room temperature and 2.8 GPa. We decided to remove the graphite and introduce only KBr. In our next experiment, two holes are drilled with a diameter of ~80 µm in the sample; the diameter of the sample is 500µm and thickness is 54µm. The hole sizes were ~80 µm drilled using EDM; the distance between two holes was also ~80 µm. One of the ~80µm holes is filled with hydrogen gas and other filled with KBr. The hydrogen filling of the diamond anvil cell was performed using the cannister showing in Figure 5.10(a) and the diamond anvil cell shown in Figure 5.10 (b). It is expected lateral diffusion of hydrogen ion through the membrane to the KBr filled the hole. The schematic of the sample (shown in red) pressed between the diamonds (shown in blue) in Figure 5.10 (c). The gasket was 183 plastically deformed to compress the sample disk such that thickness of the gasket (hatched in blue) after the compression was the same as the sample, as shown schematically in Figure 5.10 (d) i.e. the top and bottom of the sample are compressed and sealed between the diamonds. Figure 5.10 (e) and (f) show photomicrographs of the actual sample and the gasket, before and after compression, clearly showing that there are no paths for hydrogen to flow across the thickness of the membrane, after compression. Figure 5.10 (g) shows the holes filled with hydrogen gas and the KBr in the sample membrane. Then the sample with KBr and H2 were compressed further, and Raman data has obtained by aligning the Laser Figure 5.10. (a) Photo of the canister used for loading hydrogen at CIW, (b) Diamond thickness sample, (d) schematic of the gasket and the sample (red), before and after compression, (e) optical micrograph of (Ni0.60Nb0.40)70Zr30 disk in the Cu-Be gasket before compression, (f) after compression, (g) samples with two hole made by EDM machine one filled/compacted with KBr, and the other with hydrogen, (h) sample at 8.8 GPa, (i) sample at 8.8 GPa after 24 hours. on the hydrogen-filled hole and next by aligning with the hole filled with KBr. Series of measurements were made at different pressures. As expected we observed hydrogen vibron peak in the hydrogen-filled (yellow) hole. However, by aligning KBr filled (blue hatched region) hole with the green pointer laser, we did not observe any hydrogen vibron, 184 even after repeated measurement in different regions of the KBr pellet at the same pressure. After that, several experiments were performed by changing the pressure very slowly to observe hydrogen vibron peak in the KBr. By changing the pressure from 2 kbar to 8.8 GPa, we did not observe any hydrogen vibron in the KBr. Unfortunately, in this experiment, we could not observe the hydrogen diffusion from the hole with H2 gas to the hole with KBr significantly. Therefore, these experiments were terminated; we start another approach to understand hydrogen diffusion in the system with water. Based on all these previous trails, we decided to use water as the hydrogen absorbing medium (eliminate graphite and KBr below the sample). A stepped hole (top diameter~ (a) Before (b) Gasket After Top Side Gasket (b) (d) Clathrate Membrane Wax 0.07 m Bottom Side 0.08 m (c) (e) Clathrate Sample Gasket 540µm ~54µm H O Cavity 2 Sample 500 µm 190 µm Bottom Side 0.07 m Bottom Side 0.08 m Figure 5.11. (a) Schematic diagram of the sample and the gasket (b) Before compression- photomicrograph of top side of the membrane sample (500 µm), (c) Before compression- photomicrograph of bottom side smaller cavity for H2O (190 µm); sample can be seen through the water droplet, (d) After compression-clathrate formation due to hydrogen and water interaction at 1.2 GPa pressure, (e) After compression- photomicrograph of clathrate at 2.75 GPa pressure. 500 m, and bottom diameter 190m) have made in the Cu-Be gasket (~540 m) thick. 185 A (Ni60Nb40)80Zr20 membrane sample has placed in the top part of the gasket and a water droplet at the bottom. A schematic diagram of the gasket with the sample embedded in it shown in Figure 5.11 (a). Photomicrographs of the actual sample, before applying pressure, viewed from the top and bottom are shown in Figure 5.11 (b and c), respectively. Next, we loaded hydrogen in the above top cavity and Raman spectra as obtained on both sides of the sample. We observed a microstructural change and clathrates were found on the bottom side of the sample, due to hydrogen interaction with water as shown in Figure 5.11 (d) at 1.2 GPa and in Figure 5.11 (e) at 2.75 GPa. Raman spectra of the ribbon with the interaction of hydrogen only show in Figure 5.12 (a) and interaction of hydrogen with H2O on the other side formed clathrate shown in the Figure 5.12 (b). These clathrate formation peaks are matched with the reference [189]. To summarize, the most significant finding is that high pressure can solubilized hydrogen in the membrane material at room temperature at ~1.28 GPa 16000 1.2 GPa 5000 (a) 1.2 GPa (b) Diamond 14000 4000 12000 10000 3000 Diamond 8000 2000 6000 Intensity (A.U) Intensity Clathrate Intensity (A.U) Intensity H2 Roton H2 vibron 4000 1000 2000 0 0 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 -1 Raman Shift (cm-1) Raman Shift (cm ) Figure 5.12. (a)Hydrogen vibron peaks observed by Raman spectra on the top side of Figure 10 (f). Raman spectra of the ribbon sample(shown in brown) on the top side(in Figure 10(a)) and the (gamorphous) Raman spectra s ampleof the water (b) clathrate Raman on spectrathe bottom ofside the shown clathrate as H2O cavity (H2 O+Hin Figure2) 10(a)formation illustrating on the the hydrogen solubility in the sample. bottom side cavity shown at 1.2 GPa 186 Synchrotron X-ray diffraction study of this ribbon has conducted at 16ID-B, HPCAT (0.4066Å and 25μm focused beam). The compiled data taken at different pressures shows phase transformation initiating at ~6 GPa as illustrated in Figure 5.13. Synchrotron data showed the sample started to crystallize ~6 GPa and it almost crystallizes at 7.6 GPa. Figure 5.13. Synchrotron x-ray diffraction Conclusion: Raman spectra measurement by high-pressure diamond anvil cell results showed the at 1.2 GPa hydrogen started to pass through the membrane. Synchrotron XRD Diamond Anvil Cell results revealed that the 7.6 GPa pressure required making amorphous to crystallization transition, although further study is needed in high pressure to understand the complete behavior of the membrane. 187 Chapter 6 Summary & Future Study 6 Summary & Future Study The mitigation of greenhouse gas emissions on the environment led to the development of non-polluting hydrogen fuel cell use in automobiles. Syngas produced from coal gasification is converted to H2 and CO2 gasses by the water shift reaction. Metallic membranes are used to separate H2 from CO2 and other gasses obtained from the water shift reaction of coal-derived syngas. Commercial crystalline Pd-Ag membranes are widely Nb and Zr rich Atom Clustering in Ni matrix By Atom Tomography and SANS Atom dynamics of hydrogenated Ni- based Membranes And icosahedra Cluster formation Aging of Metallic Neutron Hydrogen Glass: Relaxation Vibrational Density Times by of States synchrotron XPCS Position of Hydrogen in Clusters Figure 6.1 A schematic showing determination of local atomic structure from neutron vibrational spectroscopy (NVS), total neutron scattering (HIPD-PDF), and atom – tomography (APT). Reversible expansion of icosahedra cluster by insertion of hydrogen determined using APT and XPCS. Position of hydrogen in clusters determined by NVS and XPCS. Overall, the aging property of the Ni-based metallic glass membranes, which performed Nb- and Zr- rich clusters in Ni matrix. 188 used for this purpose, but Pd is an expensive strategic metal. Thus inexpensive Ni-Nb-Zr alloys, typically, 35-40 m thick ribbons made by melt spinning methods are studied here. The permeation property of amorphous membranes are known, however, the mechanism of permeation and the nature of the local atomic order of the amorphous membranes was not fully understood. In this section, we show consolidated results from this study. First, the most significant result came from the dynamic aging studies of Ni-Nb and Ni-Nb-Zr alloy ribbons; typically, 35-40 m thick ribbons made by melt spinning methods. In metallic glasses, a small change in macroscopic behavior causes a large change in atom dynamics. The atom dynamic studies from XPCS data revealed relaxation times (), i.e. is the time taken to anneal or rearrange atoms towards a more stable state in the glassy material at a certain temperature. In these glassy materials, there are internal stresses as the solid is out of equilibrium. These systems always have the propensity to relax towards more stable states as a function of time. Our measurements involve finding the positions of speckles in reciprocal spaces by measuring the changes in the position of speckles with time by using XPCS methodology. These XPCS data for both binary and ternary alloy ribbons were measured that showed fast atom dynamics of Ni, Nb, and Zr, particularly when exposed to hydrogen. Hydrogen interaction with the amorphous binary Ni60Nb40 alloy showed a dramatic change in relaxation time decreasing from vacuum= 1276 sec to H2 =25 sec, suggesting an interaction of hydrogen prompts faster aging and atom dynamics. In addition, the effect of alloying Ni60Nb40 with elements that have a high solubility of hydrogen, such as the addition of Zr that formed (Ni0.60Nb0.40)70Zr30 alloy increased the permeability by two orders of magnitude. In this study, the reason for increased solubility of H2 in the 189 ternary (Ni0.60Nb0.40)70Zr30 alloy because of faster atom dynamics, which decreased from vacuum = 9780 sec to H2 = 375 sec. It should be noted that movement of heavier atoms (Ni, Nb or Zr) was detected with synchrotron experiments, although it is implied that hydrogen atoms movements persist. In the ternary schematic (Figure 6.1-left corners) the APT results show Nb- and Zr-rich clusters formed in a Ni-rich amorphous matrix, and and DFT-MD simulation revealed that the clusters are consist of 7 and 3 interconnected icosahedra throughout the matrix. The experimental results match with simulation. correlating the XPCS data with that of APT shows reversible expansion of clusters by insertion of hydrogen with decreasing the relaxation time (). Next, we correlate the results of XPCS with inelastic neutron studies (Figure 6.1-bottom corners). However, the synchrotron XPCS is not sensitive to hydrogen atoms; there is neutron vibrational spectroscopy (NVS) data gave the positions of the hydrogen atoms in the polyhedra. The main results show (i) the most prominent phonon modes of ZrH2 are around ~137 meV, where vibrational frequencies of Zr tetrahedral site of hydrogen reside, (ii) The Ni60Nb40 (without any Zr content) did not show significant neutron counts as the hydrogen is very low (from our previous results), as such we did not observe any peak in the NVS pattern, (iii) the distorted Nb4 tetrahedra contributing a distribution of phonon energies near 120 and 165 meV, (iv) we did not observe any obvious H-sites associated solely with Ni, however, H-sites associated mixed element such as crystalline ZrNiH cannot be ruled out. Now consider the right corner and the middle of the schematic triangle (Figure 6.1 – bottom right and middle) that shows total neutron scattering (HIPD-PDF) results which give the 190 nearest neighbor distances between the Ni-Ni, Ni-Nb, Nb-Zr, Zr-Zr atoms in the amorphous (Ni0.60Nb0.40)70Zr30 alloy revealed well-defined features of the short range order up to ~1.8 nm with no structural correlations at longer length scales. The Data match with DFT-MD simulation.This means that there is some order beyond the length scale of a single icosahedral unit but that there is not structural order across the entire length of a cluster. The high pressure Diamond Anvil Cell (DAC) study of the amorphous ribbons by Raman Spectroscopy reveals hydrogen passes through the membrane at 1.2 GPa and the high pressure XRD study reveals the amorphous ribbons become crystalized at ~7 GPa. Now considering the ternary schematic (Figure 6.1- top and right-hand EXAFs corner) the APT results show Zr-rich cluster sizes of ~ 7 nm and Nb-rich clusters of ~2 nm, but not the short range order (SRO). The Extended X-ray absorption fine structure (EXAFS) data revealed the SRO is more in Zr-cluster than Nb-cluster, which correlates our APT data. Combining the NVS, HIPD-PDF, EXAFs and APT (Figure 6.1- right side) shows the overall local atomic structure of the amorphous ribbon. Together, the atom dynamics with and without hydrogen, and cluster formation is determined in the membranes. In conclusion, these studies show the atom dynamics with and without hydrogen, local atomic structure of the amorphous ribbon and interconnected icosahedra cluster formation inside the membranes. Based on the dissertation, some additional experimental works possible to carry out. Even with knowing the dominant characteristic bonding length for the mix of all possible coordination polyhedra it will be difficult to guess the actual geometry, configuration and/or distortions of the actual physical coordination neighborhoods. This is where 191 atomistic simulations come into play. The dissertation requires further work to determine the universal behavior of smaller atom such as carbon; nitrogen causes similar dynamical changes like hydrogen inside binary and ternary amorphous alloys. Further, work in synchrotron high-pressure diamond anvil cell possible to reveal amorphous to amorphous transition. Altogether, this study reveals the fundamental behavior of Ni-based amorphous alloys with and without hydrogenation. 192 7 References 1. N.E. Amadeo, M.A. Laborde, Hydrogen production from the low-temperature water- gas shift reaction: kinetics and simulation of the industrial reactor, International Journal of Hydrogen Energy, 20, 12, 949–956 (1995) 2. S.M. Kim, W. M. 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