Studies of Inorganic Layer and Framework Structures Using Time-, Temperature- and Pressure-Resolved Powder Diffraction Techniques

$Studies of Inorganic Layer and Framework Structures Using Time-, Temperature- and Pressure-Resolved Powder Diffraction Techniques$

Anne Marie Krogh Andersen

Department of Structural Chemistry Stockholm University, 2004

Doctoral Dissertation 2004

Department of Structural Chemistry Arrhenius Laboratory Stockholm University SE-106 91 Stockholm Sweden

Printed by Media-Tryck, Lund, 2004

ABSTRACT

This thesis is concerned with in-situ time-, temperature- and pressure-resolved synchrotron X-ray powder diffraction investigations of a variety of inorganic compounds with two- dimensional layer structures and three-dimensional framework structures. In particular, phase stability, reaction kinetics, thermal expansion and compressibility at non-ambient IV IV conditions has been studied for 1) Phosphates with composition M (HPO4)2⋅nH2O (M = Ti, IV IV Zr); 2) Pyrophosphates and pyrovanadates with composition M X2O7 (M = Ti, Zr and X = P,

V); 3) Molybdates with composition ZrMo2O8. The results are compiled in seven published papers and two manuscripts.

Reaction kinetics for the hydrothermal synthesis of α-Ti(HPO4)2⋅H2O and intercalation of alkane diamines in α-Zr(HPO4)2⋅H2O was studied using time-resolved experiments. In the high-temperature transformation of γ-Ti(PO4)(H2PO4)⋅2H2O to TiP2O7 three intermediate phases, γ'-Ti(PO4)(H2PO4)⋅(2-x)H2O, β-Ti(PO4)(H2PO4) and Ti(PO4)(H2P2O7)0.5 were found to crystallise at 323, 373 and 748 K, respectively. A new tetragonal three-dimensional phosphate phase called τ-Zr(HPO4)2 was prepared, and subsequently its structure was determined and refined using the Rietveld method. In the high-temperature transformation from τ-Zr(HPO4)2 to cubic α-ZrP2O7 two new orthorhombic intermediate phases were found.

The first intermediate phase, ρ-Zr(HPO4)2, forms at 598 K, and the second phase, β-ZrP2O7, at 688 K. Their respective structures were solved using direct methods and refined using the

Rietveld method. In-situ high-pressure studies of τ-Zr(HPO4)2 revealed two new phases, tetragonal ν-Zr(HPO4)2 and orthorhombic ω-Zr(HPO4)2 that crystallise at 1.1 and 8.2 GPa.

The structure of ν-Zr(HPO4)2 was solved and refined using the Rietveld method.

The high-pressure properties of the pyrophosphates ZrP2O7 and TiP2O7, and the pyrovanadate ZrV2O7 were studied up to 40 GPa. Both pyrophosphates display smooth compression up to the highest pressures, while ZrV2O7 has a phase transformation at 1.38

GPa from cubic to pseudo-tetragonal β-ZrV2O7 and becomes X-ray amorphous at pressures above 4 GPa.

In-situ high-pressure studies of trigonal α-ZrMo2O8 revealed the existence of two new phases, monoclinic δ-ZrMo2O8 and triclinic ε-ZrMo2O8 that crystallises at 1.1 and 2.5 GPa, respectively. The structure of δ-ZrMo2O8 was solved by direct methods and refined using the Rietveld method.

LIST OF CONTENTS

Abstract i List of Contents iii List of Enclosed Papers v 1. Introduction 1 2. Experimental Techniques 3 2.1 Synchrotron Radiation 3 2.2 Data Collection and Equipment 6 2.2.1 Time- and Temperature-Resolved Experiments 6 2.2.1.1 The micro-reaction cell 7 2.2.1.2 Translating Image Plate (TIP) camera 8 2.2.1.3 Other detectors 9 2.2.2 Pressure-Resolved Experiments 9 2.2.2.1 Diamond anvil cells 10 2.2.2.2 Pressure transmitting medium 11 2.2.2.3 Pressure determination 12 2.2.2.4 Detectors used in high-pressure experiments 13 2.2.3 Neutron Powder Diffraction 13

3. Data analysis 15 3.1 Ab Initio Structure Solution and Structure Refinement 15 3.1.1 Determination of Lattice Parameters and Space-Group Assignment 15 3.1.2 Structure Solution 16 3.1.3 Refinement of the Structure Using the Rietveld Method 17 3.2 Kinetics 19 3.3 Thermal Expansion 20 3.4 Compressibility and Equation of State 21

4. Synthesis 23

IV IV 4.1 Hydrothermal Synthesis of M (HPO4)2⋅nH2O (M = Ti, Zr) 23 IV IV 4.2 Synthesis of M X2O7 (M = Ti, Zr; X = P, V) 24

4.3 Synthesis of α-ZrMo2O8. 25

iii LIST OF CONTENTS

5. Summary and Discussion of Results 27

IV IV 5.1 Phosphates with the General Formula M (HPO4)2⋅nH2O (M = Ti, Zr) 27

5.1.1 Time-resolved Studies on the Synthesis of α-Ti(HPO4)2⋅H2O 29

5.1.1.1 Synthesis of α-Ti(HPO4)2⋅H2O in the micro-reaction cell 29

5.1.1.2 Synthesis of α-Ti(HPO4)2⋅H2O in a diamond anvil cell 30

5.1.2 Intercalation of Alkane Diamines in α-Zr(HPO4)2⋅H2O 32

5.1.3 Temperature-Resolved Experiments on γ-Ti(PO4)(H2PO4)⋅2H2O 35

5.1.4 Structure Determination of τ-Zr(HPO4)2 37

5.1.5 Temperature-Resolved Experiments on τ-Zr(HPO4)2 38

5.1.6 Pressure-Resolved Experiments on τ-Zr(HPO4)2 41 IV IV 5.2 Materials with the General Formula M X2O7 (M = Ti, Zr; X = P, V) 44

5.2.1 Pressure-Resolved Experiments on TiP2O7, ZrP2O7 and ZrV2O7 46

5.3 Molybdates with the Formula ZrMo2O8 48

5.3.1 Pressure-Resolved Experiments on Trigonal α-ZrMo2O8 49

6. Concluding Remarks 55 7. Acknowledgments 57 8. References 59

iv LIST OF ENCLOSED PAPERS

LIST OF ENCLOSED PAPERS

This thesis is based on seven published papers (II-V and VII-IX) and two manuscripts (I and VI), which are referred to in the text by their roman numerals:

I: A. M. Krogh Andersen, R. B. Nielsen and P. Norby: In-Situ Time-Resolved Synchrotron X-ray Powder Diffraction Studies of Hydrothermal Synthesis of Layered Titanium Phosphates. In manuscript.

II: A. M. Krogh Andersen and P. Norby: Structural Aspects of the Dehydration and

Dehydroxylation of Layered γ-Titanium Phosphate, γ-Ti(PO4)(H2PO4)⋅2H2O. Inorg. Chem. 37 (1998) 4313-4320.

III: A. M. Krogh Andersen, P. Norby and T. Vogt: Determination of the Formation Regions of Titanium Phosphates. Determination of the Crystal Structure of β-Titanium Phosphate,

Ti(PO4)(H2PO4), from Neutron Powder Data. J. Solid State Chem., 140 (1998) 266-271.

IV: A. M. Krogh Andersen, P. Norby, J. C. Hanson and T. Vogt: Preparation and

Characterization of a New 3-Dimensional Zirconium Hydrogen Phosphate, τ-Zr(HPO4)2; Determination of the Complete Crystal Structure Combining Synchrotron X-ray Single Crystal Diffraction and Neutron Powder Diffraction. Inorg. Chem., 37 (1998) 876-881.

V: A. M. Krogh Andersen and P. Norby: Ab Initio Structure Determination and Rietveld Refinement of a High-Temperature Phase of Zirconium Hydrogen Phosphate and a New Polymorph of Zirconium Pyrophosphate from In-Situ Temperature-Resolved Powder Diffraction Data. Acta Cryst., B56 (2000) 618-625.

VI: A. M. Krogh Andersen and S. Carlson: The high-pressure structures and properties of

τ-Zr(HPO4)2. In manuscript.

VII: S. Carlson and A. M. Krogh Andersen: High-pressure properties of TiP2O7, ZrP2O7 and

ZrV2O7. J. Appl. Cryst., 34 (2001) 7-12.

VIII: S. Carlson and A. M. Krogh Andersen: High-Pressure Transitions of Trigonal α-ZrMo2O8. Phys. Rev. B, 61 (2000) 11209-11212.

v LIST OF ENCLOSED PAPERS

IX: A. M. Krogh Andersen and S. Carlson: High-Pressure Structures of α- and δ-ZrMo2O8. Acta Cryst., B57 (2001) 20-26.

Two other papers related to the subject of the thesis have been published, but are not included in the thesis:

D. V. S. Muthu, B. Chen, J. M. Wrobel, A. M. Krogh Andersen, S. Carlson and M. B. Kruger:

Pressure-induced phase transitions in α-ZrMo2O8. Physical Review B: Condensed Matter and Materials Physics, 65(6) (2002) 064101/1-064101/5.

K. E. Lipinska-Kalita, M. B. Kruger, S. Carlson and A. M. Krogh Andersen: High-pressure studies of titanium pyrophosphate by Raman scattering and infrared spectroscopy. Physica B, 337 (2003) 221-229.

vi INTRODUCTION

1. INTRODUCTION Inorganic oxide materials with structures that consist of interconnected polyhedral elements may roughly be divided according to their structural dimensionality: 3-dimensional (3-D) framework structures, 2-dimensional (2-D) layered structures, 1-dimensional (1-D) linear chain structures and 0-dimensional (0-D) monomer structures. Typically a framework structure consists of a network of relatively rigid polyhedral units that share corners with each other. There exist a large number of framework structures important for Earth sciences, solid-state chemistry, condensed matter physics and material science. They embrace 3-D structures with corner connected tetrahedral structural units such as zeolites built from SiO4 and AlO4, octahedral units such as in perovskites like NaxWO3, or both tetrahedral and octahedral building blocks as in ZrW2O8 or ZrV2O7. Materials with 3-D structures are often nano- or microporous (e.g. zeolites, inorganic phosphates and hydrogen/hydroxy-phosphates, vanadyl pyrophosphates) and display useful catalytic properties (Vedrine, 2000; Cheetham et al., 1999). Layered 2-D structures may be defined simply as solids where the bonds are strong between atoms within parallel planes in the structure, and much weaker between atoms in adjacent layers. A single layer can therefore be regarded as a giant planar molecule. Usually atoms are covalently bonded within the layers, while weaker van der Waals forces bond adjacent layers together. The distance between the barycenters of the layers is called the interlayer distance, which is equivalent to the distance (d) between crystallographic lattice planes associated with the layers. From the point of view of intercalation, 2-D layered materials are the most frequently studied since the variation of the interlayer distance and the structural flexibility of the layers facilitate the intercalation process. Examples of layered host structures have been described for a wide range of inorganic compounds, ranging from elemental structures such as graphite, metal chalcogenides (e.g. TiS2, ZrSe2), metal oxides (e.g. MoO3,

V2O5), smectite clays and silicates (e.g. kaolinites (Al4Si4O10(OH)8), montmorillionite

(Ca0.35[Mg0.7Al3.3](Si8)O20(OH)4)) and layered phosphates and phosphonates (O'Hare, 1992; Alberti and Costantino, 1996). Applications for these types of 2-D layer structures range from uses as sorbant in renal dialysis systems, ion-exchange, water softening, chromatography and solid electrolytes to catalysis (Clearfield and Costantino, 1996).

This thesis presents results for 3-D framework structures and 2-D layered structures, with the aim to study the reaction kinetics, phase stability, thermal- and compressibility properties. Three types of inorganic materials were selected for the investigations: IV IV 1. Layered phosphates with formula M (HPO4)2⋅nH2O (M = Ti, Zr): The 2-D layered phosphates presented here have been synthesised by a technique first published by

1 INTRODUCTION

Clearfield and Stynes (1964) for the crystallisation of amorphous zirconium phosphate gel. The resulting phase from such a crystallisation was called the α-type. A second crystalline phase named γ-type was later reported by Clearfield et al. (1968). These layered phases may be considered as solid acids with the possibility for protons to diffuse in-between the regularly spaced acidic layers. Thus, considerable interest has been shown for these phases as ion exchangers in chemical processing, disposal of radioactive ions or high-temperature treatment of water. Other possible technological uses could be as protonic conductors or, because of their large active surface area and high stability, for heterogeneous acid- catalysed reactions (Clearfield and Costantino, 1996). IV IV 2. Materials with general formula M X2O7 (M = Ti, Zr; X = P, V): The MX2O7 family (Khosrovani et al., 1996 and references therein) is a class of 3-D framework phases that can be used as components in advanced ceramic materials. They are also part of a family of cubic materials that under certain conditions display isotropic negative thermal expansion - a technologically very important property. All these pyrophosphate/pyrovanadate phases also show interesting low temperature superstructures. In this thesis results for ZrP2O7, TiP2O7 and ZrV2O7 are presented. TiP2O7 and ZrP2O7 are the final products in the thermal transformation from layered titanium and zirconium phosphate. ZrV2O7 is a special compound in this class of pyrophosphate structures, since it displays negative thermal expansion.

3. Molybdates with the formula ZrMo2O8: Zirconium and hafnium molybdates are 3-D framework structures that have attracted interest to researchers because both zirconium and hafnium are major fission products in nuclear reactors (Adachi et al., 1988). For many years two forms of ZrMo2O8 were known: The low-temperature monoclinic form (Auray et al., 1987; Auray and Quarton, 1989) and a trigonal high-temperature polymorph (Auray et al., 1986;

Kletsova et al., 1989), stable between 952 and 1100 K. Trigonal ZrMo2O8, however, can be prepared at much lower temperatures due to the kinetic barrier for formation of the monoclinic phase (Samant et al., 1993). Recently a third polymorph has been discovered (Lind et al., 1998). It is a metastable cubic form that displays isotropic negative thermal expansion properties. This thesis presents high-pressure results obtained for trigonal

ZrMo2O8.

The outline of the thesis is as follows. In the next two chapters the special techniques required for in-situ experiments and the analysis of data are described. Chapter four deals with the synthesis of the investigated materials and in chapter five a summary and discussion of the obtained results is given.

2 EXPERIMENTAL TECHNIQUES

2. EXPERIMENTAL TECHNIQUES To understand the phase stability and reaction kinetics of a material at non-ambient conditions, in-situ time-, temperature- and pressure-resolved experiments have been performed. These types of studies make it possible to follow the course of the synthesis of inorganic solids under real reaction conditions and extract information that would not be obtainable from ex-situ experiments. The technique eliminates the need for quenching and isolation of products during which the product may undergo significant changes. It allows the direct observation of the formation of possible intermediate crystalline phases and their subsequent transformation into the product phase. In-situ experiments provide an easy method for testing the effect of changing reaction variables such as temperature, pH of the reaction mixture, pressure etc. It is possible to extract quantitative kinetic information from time-resolved diffraction studies, since the intensity of a Bragg reflection is generally proportional to the amount of diffracting solid - i.e. it is possible to obtain relative volume fractions from the integrated intensities. However, other factors may influence the intensities, such as compositional changes in the material, reorganisation of stacking faults or preferred orientation. In-situ temperature- resolved powder diffraction experiments make it possible to detect and structurally characterise even reversible high-temperature phases, as well as to determine their respective thermal expansion coefficients. In high-pressure experiments in-situ techniques are used since it is fairly common that high-pressure phases are non-quenchable. It is usually not possible to collect high quality X-ray powder diffraction data on normal laboratory sources for time-resolved experiments, or when the sample volume is very small (as in e.g. high-pressure experiments). Therefore all studies included in this thesis have been performed at synchrotron sources, which provide high intensity X-rays that facilitate short collecting times. Furthermore, the low divergence of synchrotron X-ray radiation is very beneficial when solving new structures.

2.1 SYNCHROTRON RADIATION For in-situ studies it is advantageous to use synchrotron generated X-rays. With lab sources slow reactions can be followed, but even with the best available rotating anode X-ray sources the time resolution is usually too low to follow most reactions. Synchrotron generated X-rays typically have intensities up to 15 orders of magnitude greater than the most brilliant laboratory-generated X-rays, as shown in Figure 1, and are produced in a wide energy range (10 to 120 keV depending on the size of the storage ring). The high X-ray intensity gives shorter exposure times and therefore better time resolution, allowing studies of very fast chemical reactions (down to milliseconds).

3 EXPERIMENTAL TECHNIQUES

High energy X-rays (short

27 wavelengths) can penetrate sample 10 containers made of e.g. stainless 24 steel. This gives the possibility to use 10 3rd generation sources relatively bulky equipment such as (e.g. ESRF, APS) 1021 hydrothermal cells or high-pressure

cells. The divergence of the beam is /0.1%BW) 2 1018 usually very low which allows /mrad 2 collection of powder diffraction data 2nd generation sources Brilliance 1015 with very high resolution, making it possible to detect very subtle 1st generation sources 1012 structural changes. The tuneable (photons/s/mm wavelength also allows utilisation of X- 9 10 Conventional ray absorption edges, for instance for X-ray source Rotating anode avoiding fluorescence problems or by 106 combining diffraction and absorption 1880 1900 1920 1940 1960 1980 2000 2020 experiments. Year Synchrotron radiation is emitted when high-energy electrons are forced on a Figure 1. Schematic representation of the historical development of available brilliance of X-rays from different bent trajectory. The electrons are sources. created by an electron gun (Figure 2) and then accelerated in a linear accelerator (linac) to nearly the speed of light. The electrons are then transferred into a small synchrotron that increases the energy of the electrons. Finally the electrons are injected into the storage ring where they circulate at constant energy for many hours. Inside the storage ring various magnets control the trajectory of the electrons. The bending magnets bend the electron beam forcing it to form a circle or rather a polygon with x sides. As the beam passes each magnet, the electrons are deviated from their path by several degrees and the change in direction causes them to emit synchrotron radiation in a forward direction. The focusing magnets (on each side of the bending magnets) keep the electrons within a beam of very small diameter. The insertion devices (wigglers/undulators) are placed on the straight sections between two bending magnets. They are made up of a complex array of small magnets that force the electrons to oscillate around a linear trajectory and thereby generating a much more intense beam of radiation than that generated by the bending magnets (Altarelli et al., 1998).

4 EXPERIMENTAL TECHNIQUES

b a c

f e d

Figure 2. Synchrotron radiation source: a) Electron gun; b) Linear accelerator (linac); c) Booster ring; d) Electron storage ring; e) Undulators/Wigglers; f) Bending magnets/Focusing magnets; g) Experimental station.

g f

d a c

Figure 3. Schematic representation of a beamline showing the principal optical elements. a) Storage ring, b) Polychromatic synchrotron radiation beam, c) Collimating mirror, d) Monochromator, e) Focussing mirror, f) Sample, g) Detector.

5 EXPERIMENTAL TECHNIQUES

The intense polychromatic X-ray beam from the bending magnet, wiggler or undulator is then shaped into desired dimensions by the use of water-cooled apertures and slits. This takes place inside the main thick-walled concrete radiation shield - the so-called frontend. Outside the frontend (Figure 3) the main optical elements are typically a first collimating X-ray mirror, monochromator and second focussing mirror. To achieve effective total reflection in the X-ray regime it is common to bend very long (1 m) perfectly flat surfaces (made of e.g. Si or Zerodur®) coated with a thin layer of some heavy metal like Pt or Rh. These optical components must be operated in ultra-high vacuum (10-10 mbar) to prevent oxidation of the metal surfaces. Most beamlines use either a double-crystal or a channel-cut crystal monochromator design. In all cases, the highest resolution from the monochromator is obtained when the incoming beam is stable and well collimated. The monochromator crystal/crystals must also be able to dissipate the high heat-load and provide for vibration- free movements. Finally, the monochromatic X-ray beam is focused on the sample or detector. A monochromatic X-ray beam is used in so-called angle-dispersive diffraction mode as opposed to experiments in the energy-dispersive mode. In angle-dispersive experiments the diffracted beam intensities are detected as a function of diffraction angle. Using a position sensitive detector or an area detector makes it possible to detect a large part of the diffraction pattern at once, thereby decreasing the counting time as compared to the use of a point detector (e.g. scintillation detector). The resolution obtained from angle-dispersive experiments is usually much better than from energy-dispersive experiments and can therefore be used to obtain structural information. In energy-dispersive X-ray diffraction experiments the entire incident X-ray flux (so-called white radiation) is used directly without monochromator. The intensity spectrum of scattered X-rays from the sample is measured with a fixed-angle solid-state detector. Each Bragg reflection is characterised by an energy, which is dependent on the angle of the detector. Since no monochromator is employed the flux incident on the sample is high and sufficiently intense to probe large volume samples in thick-walled reaction vessels or perform time-resolved experiments very fast. However, the resulting low resolution data limits its usefulness for obtaining reliable structural information.

2.2 DATA COLLECTION AND EQUIPMENT

2.2.1 Time- and Temperature-Resolved Experiments.

The time- and temperature-resolved data presented in this thesis were collected at the Brookhaven Chemistry Beamline X7B (Hastings et al., 1983), National Synchrotron Light Source (NSLS), Brookhaven National Laboratory (BNL), USA and at the dedicated powder

6 EXPERIMENTAL TECHNIQUES

diffraction, BM16 (Fitch, 1996), European Synchrotron Radiation Facility (ESRF, Grenoble, France). For further information on the beamlines X7B and BM16 see: http:/www.nsls.bnl.gov/ and http://www.esrf.fr/, respectively.

2.2.1.1 The micro-reaction cell A capillary based micro-reaction cell developed at NSLS, Brookhaven (Norby, 1996) was used to study hydrothermal crystallisation and temperature-induced phase transformations in situ. The reaction cell consists a of a quartz capillary (0.5 - 1 mm diameter with 0.01 mm wall thickness) mounted using a Vespel ferrule in a Swagelock T-piece. The T-piece is mounted on a goniometer head, as shown in Figure 4. Alignment of d the capillary is easily done with the slides and arcs on b the goniometer head. An external pressure of e.g. nitrogen gas can be applied through the tubing attached to the T-piece. Depending on the applied pressure Teflon or steel tubing is used. Teflon tubing can be used up to a pressure of approximately 25 atm. c This set-up, using an open capillary with gas flow, gives the possibility to perform time-resolved studies of e.g. catalysts under operating conditions (Clausen et al., 1991). Figure 4. Capillary based micro- Depending on the type of experiment the capillary can reaction cell. a) Capillary; b) T-piece; be open or closed. Hydrothermal conditions can be c) Goniometer head; d) Tubing for application of external pressure or obtained by using a closed quartz capillary filled with gas-flow. reaction mixture or gel and applying an external pressure of nitrogen gas, while heating with a heater gun. The capillary is filled with reaction mixture using a thinner capillary mounted on a syringe The width of the X-ray beam has to be kept much smaller than the heated zone in order to limit temperature gradients across the beam and to reduce problems with transport of material by convection and diffusion. Pressures up to 45 atm can be applied inside quartz capillaries, corresponding to a maximum temperature of approximately 533 K. For hydrothermal synthesis at higher temperatures steel capillaries (1.6 mm diameter, 0.3 mm wall thickness) have been used (Norby et al., 2000). In order to obtain hydrothermal conditions at 623 K a pressure above 165 atm is necessary. In the case of steel capillaries high-energy synchrotron radiation (35-40 keV) must be used to reduce the absorption by the reaction cell and to achieve the necessary time resolution.

7 EXPERIMENTAL TECHNIQUES

When collecting temperature-resolved data an open capillary is used in order to allow water to evaporate. Typically heating rates of 15 K/min are used. When performing experiments where only a small zone is heated, the temperature at the actual sample position must be determined under as realistic conditions as possible. In the experiments carried out with the micro-reaction cell, the temperature was calibrated using a sample of microcrystalline silver, obtained by thermal decomposition of silver carbonate. The thermal expansion of silver was determined as a function of the measured temperature by profile refinement of diffraction patterns recorded during heating. The calibration curve was then determined by comparing the obtained unit-cell parameter with literature values (Kuznetsov, 1956).

2.2.1.2 Translating Image Plate (TIP) camera The Translating Image Plate (TIP) camera for time- Steel Screen resolved powder diffraction experiments was developed at the Chemistry Beamline, X7B, at the NSLS (Gualtieri et al., 1996; Norby, 1997a). An upgraded version of the TIP camera has been implemented at the Italian CRG beamline at the ESRF (GILDA) (Meneghini et al., 2001). The camera consists of a steel screen with a 3 mm vertical slit. The image plate is translated behind the slit and a continuous series of powder diffraction profiles is obtained as a function of time (Figure 5). The time resolution depends on the translation speed of the image plate and the width of the slit. Experiments with time resolution between 5 seconds and several minutes have been performed (e.g. Norby, 1997b; Norby et al., 1999; Francis et al., 1999; Ciraolo et al., 2001). A 200 × 400 mm Fuji Translating Image Plate image plate is used and the reader is a Fuji BAS2000 Figure 5. Sketch of the principle of giving a nominal pixel size of 0.1 × 0.1 mm2 (2025 × 4096 the Translating Image Plate (TIP) camera. The arrow indicates the pixels). Diffraction patterns are usually extracted from the translation of the image plate behind the steel screen. image using a 30 pixel (3 mm) wide rectangular strip of the image plate. Wavelength, sample-detector distance, image-plate tilt and zero point were determined from a diffraction pattern of a LaB6 standard (NIST SRM 660a, a = 4.15695 Å).

8 EXPERIMENTAL TECHNIQUES

2.2.1.3 Other detectors Nine-crystal multianalyser stage at BM16: At the powder diffraction beamline BM16, ESRF, a multianalyser detector system (Fitch, 1996; Hodeau et al., 1998) comprising of a rotation stage with nine scintillation detectors was used. Each detector is equipped with a Ge111 analyser crystal. The separation between each channel (detector) is about 2° in 2θ. Data are collected in a continuous scanning mode with the 2θ-arm moving at a constant rate. Thus, nine diffraction patterns are measured simultaneously, displaced from each other by 2° in 2θ. After data collection, the counts from the nine channels are rebinned to produce the equivalent normalised step scan, which is more suitable for analysis, by standard programs. Corrections in the rebinning process are due to the exact channel separation, detector efficiencies and beam current decline during data collection. The angular resolution in terms of the full width at half maximum (FWHM) of this detector system is very good - approximately 0.002° in 2θ (Norby et al., 2002). The time resolution, though, is strongly dependent on the angular range that is measured. INEL CPS120 position sensitive detector at X7B: At X7B a curved position sensitive INEL CPS120 detector (Ballon et al., 1983) was also used in the time-resolved experiments. It collects X-rays simultaneously within an arc of 120°, with a 250 mm radius of curvature. An X-ray photons are detected by the ionisation of Ar atoms that in turn are detected by a cathode where the charge moves to the right and left directions. The difference in time for the charge to arrive at each side of the detector determines its position, and thereby the X-ray photon position. The time resolution obtained in the experiments, including dead-time of electronics, was about 20 seconds. The detector was mounted on the 2θ-arm of a Huber goniometer, and the detector was calibrated by collecting 58 primary-beam positions at 2° steps in 2θ. The angular resolution (FWHM) stated by INEL is better than 0.01°, but at X7B calibration data obtained from a silicon pattern resulted in a FWHM of 0.1 - 0.2° (Ståhl, 1994).

2.2.2 Pressure-Resolved Experiments

In-situ high-pressure studies were performed at the dedicated high-pressure synchrotron beamlines ID30 (Häusermann and Hanfland, 1996) and ID9, ESRF, Grenoble, France. For further information regarding the beamlines see: http://www.esrf.fr/. The diamond anvil cell (DAC) technique was used to apply pressure on the samples while simultaneously collecting X-ray diffraction data. This technique can achieve enormous pressures by using the amplification of pressure that is obtained when two very small diamond surfaces are pressed against each other with the sample in-between. The highest pressure reported using a DAC

9 EXPERIMENTAL TECHNIQUES

is 416 GPa1 (Ruoff et al., 1990). This is well above the pressure at the centre of the earth, estimated to be 360 GPa (Holzapfel, 1996). A number of good reviews and books have been published on experimental high-pressure techniques, e.g. Jayaraman (1983, 1986), Eremets (1996), Holzapfel and Isaacs (1997) and Miletich et al. (2000).

2.2.2.1 Diamond anvil cells There are many types of DAC's described in the literature (see e.g. Force 3 mm Force

Jayaraman, 1983). The pressure Diamond generating mechanism of a DAC support consists of two opposing diamonds 2 mm with a perforated metal gasket in- Diamond between the tips (culets), as shown Gasket in Figure 6. The diamond back surfaces are supported by e.g. steel, Sample and ruby beryllium or tungsten carbide plates that are drilled in the centre to provide optical access, both for visual inspection and X-rays. This Force Force set-up is then mounted in a mechanism that can provide smooth Figure 6. Basic principle of a diamond anvil cell (DAC). and stable force on the backplates, all in order to squeeze the sample inside the perforated gasket. In normal cases the gasket is pre-indented without sample before a hole is drilled. This is done to strengthen the gasket material, which commonly consists of stainless steel or some hard metal such as tungsten or rhenium. The dimensions of the hole, typically ∅ = 0.3 mm and h = 0.2 mm for an experiment up to 10 GPa, constrain the size of the sample and the X-ray irradiated volume if parasitic peaks from the gasket material are to be avoided. In the experiments presented in this thesis two types of DAC's were used that differ essentially only in the way force is generated on the back plates and diamonds. For experiments at ambient temperatures, DAC's equipped with gas-membranes (MDAC's) to obtain the pressure generating force were used (Chervin et al., 1995; Letoullec et al., 1988). The principle of the MDAC set-up is shown in Figure 7. In the high-pressure, high- temperature (high-pT) experiments a so-called hydrothermal DAC (Bassett et al., 1993) with simple tightening screws was used. All DAC's had tungsten carbide backing plates to support

1 In the thesis pressure is expressed in GPa (gigapascal) = 104 bar. Other units of pressure commonly used are: kbar (kilobar) = 103 bar and Mbar (megabar) = 106 bar. One bar = 105 N m-2 (pascal) = 0.9869 atm = 1.0197 kg cm-2.

10 EXPERIMENTAL TECHNIQUES

the diamonds. The opening angle of the back plates was 80° for the MDAC's and 40° for the hydrothermal DAC. In the hydrothermal DAC, resistive heating is performed using molybdenum wires wrapped around the tungsten carbide seats, which support the diamond anvils. These wires can heat the anvils and the sample to a uniform and constant temperature (maximum 1473 K). Temperature is measured by thermocouples attached to the diamonds close to the sample. The maximum attainable pressure is lower at high temperature due to softening of the DAC body parts and the metal gasket.

b c

c e h He 98 bar a d i f g

k j

Figure 7. Schematic diagram of the membrane diamond anvil cell (MDAC) set-up. a) Helium bottle; b) Stainless-steel capillary tube; c) Valve; d) Leakage control; e) Pressure gauge; f) Digital pressure readout (pressure on the membrane, not on the sample); g) Cell body; h) Membrane; i) Backing plates; j) Diamonds; k) Gasket.

2.2.2.2 Pressure-transmitting medium To obtain reliable X-ray diffraction data at elevated pressures conditions around the sample must be hydrostatic (or near hydrostatic). The best way of achieving this is to use a gas- bomb for pressure generation. However, that technique can be very dangerous due to unforeseen leaks and material fatigue and is limited to pressures below 1 GPa. Therefore it is common to use liquids or condensed gases as pressure-transmitting medium. In experiments up to 10 GPa a 16:3:1 mixture by volume of methanol:ethanol:water (Fujishiro et al., 1982) was used, and at higher pressures cryogenically condensed Ar or N2 liquids were employed (Miletich et al., 2000). These liquids provide very good hydrostatic conditions and were preferred as pressure transmitting medium, but in cases where the sample might react, transform or dissolve in these liquids a silicon oil (Sigma-Aldrich no. 17,563-3) was used.

11 EXPERIMENTAL TECHNIQUES

2.2.2.3 Pressure determination The pressure inside the DAC sample chamber can be determined either by using a diffraction standard, such as sodium chloride or gold (Miletich et al., 2000), or by the use of laser-induced fluorescence in small ruby crystals. The ruby fluorescence technique (Forman et al., 1972; Piermarini et al., 1975) is the most commonly used method to determine the pressure in DAC experiments. It is based upon the 3+ observation that the R lines of ruby (Al2O3 doped with ~0.5 wt% Cr -ions) shift almost linearly with pressure. The pressure measurements were carried out using a PRL (Pressure by Ruby Lumiscence) spectrometer (BETSA, France). A small piece of ruby (~5-10 µm) was placed in the pressure medium along with the sample. The ruby was exited with an Argon-ion laser and the wavelength of the fluorescence lines were then measured with a spectrometer (see schematic diagram in Figure 8).

b c d b

R1 R2

b a Camera

Laser Spectrometer

Figure 8. Schematic diagram of a spectrometer system for pressure determination by laser induced fluorescence. a) Diamond anvil cell; b) Lenses; c) Dichroic mirror; d) Flip mirror; e) Optical fibre.

The detected fluorescence peaks are called R1 and R2. Under normal circumstances only the

R1 peak shift is determined, and the pressure is calculated using the calibration scale published by Mao et al. (1986): ⎧ B ⎫ 1904 ⎪⎡ ⎛ ∆λ ⎞⎤ ⎪ p = ⎨⎢1+ ⎜ ⎟⎥ − 1⎬ B ⎢ λ0 ⎥ ⎩⎪⎣ ⎝ ⎠⎦ ⎭⎪ where λ0 is the wavelength (694.2 nm) of the R1 line at normal temperature and pressure and the parameter B is 7.665 for hydrostatic and 5 for non-hydrostatic conditions (Mao et al., 1978 and 1986). The estimated standard deviations (e.s.d.) of the pressures were calculated from the precision in the readout of the wavelength shift and reported errors (2 %) in the pressure

12 EXPERIMENTAL TECHNIQUES

scale (Mao et al., 1986). These e.s.d.'s are probably an underestimation of the error in the absolute pressure, but should reflect the precision in the relative change in pressure. The ruby fluorescence method was also used in the high-pT experiments on the synthesis of

α-Ti(HPO4)2⋅H2O. The R1 peak shift is highly temperature dependent, and provided that the temperature is known within +/- 1 degree the calibration scales by Vos and Schouten (1991) can be used to obtain a pressure determination with reasonable precision.

2.2.2.4 Detectors used in high-pressure experiments In high-pressure powder diffraction experiments it is advantageous to use area detectors, since it gives the possibility to record the complete powder rings with short exposure times. Three detectors were used: Fastscan II, Molecular Dynamics Storm and Princeton CCD. Fastscan II (Thoms et al., 1998) was a prototype image-plate system at beamline ID30, ESRF. It used a 240 x 300 mm2 image-plate that was scanned and erased in a time-cycle of down to 11 seconds. The Molecular Dynamics Storm image-plate system consists of large (400 x 500 mm2) image-plates that are scanned by an off-line reader. At highest resolution the readout takes about 20 minutes, thus excluding it from most time-resolved studies. Finally, the Princeton system is built around an 1152 x 1242 pixel CCD with an image intensifier, and has a time-resolution of about 5 seconds.

2.2.3 Neutron Powder Diffraction

Neutron diffraction has both advantages and disadvantages over X-rays when it comes to in- situ experiments. Since many materials have low neutron absorption cross-sections, reaction vessels can be constructed that will give minimal contribution to the background in the diffraction data. Processes involving light atoms, such as reactions involving water can be followed. One disadvantage of using neutrons for in-situ experiments is the lower flux as compared to synchrotron sources. This means that at present the time resolution of neutron diffraction experiment is relatively poor, i.e. of the order of minutes rather than milliseconds. However, the development of high-flux neutron diffractometers with large surface area position-sensitive detectors, such as the D20 instrument at Institut Laue-Langevin (ILL), Grenoble, allows for faster data collection with a time resolution of seconds may be obtained (Convert et al., 1998 and 2000). The temperature-resolved neutron powder diffraction experiments presented in this thesis were carried out on the E2 powder instrument at Berlin Neutron Scattering Center (BENSC), Hahn-Meitner Institute (HMI) in Berlin. Further information about the instrument can be found at: http://www.hmi.de/bensc/. The samples were placed in open quartz tubes and heated

13 EXPERIMENTAL TECHNIQUES

(from 300 K to 700 K in steps of 10 K) in a resistance furnace equipped with an ILL-designed precision temperature controller. Powder diffraction data were collected for approximately 1 hour at each temperature. In order to remove evaporated water, the sample was kept under a flow of nitrogen gas throughout the experiment. Data were collected at 1.220 Å (Ge (311) monochromator crystal) and 2.4406 Å (PG (002) monochromator crystal). The diffractometer is equipped with a position sensitive detector, consisting of an array of 400 BF3 scintillators, that covers 80° in 2θ, in our case 8-88°.

14 DATA ANALYSIS

3. DATA ANALYSIS

3.1 AB INITIO STRUCTURE SOLUTION AND STRUCTURE REFINEMENT The determination of a crystal structure from single crystal or powder diffraction data can be divided into 3 stages (Figure 9): (1) Determination of the unit cell (indexing of the diffraction pattern) and determination of the symmetry (space- 6 8 10 12 14 16 18 20 group assignment), (2) Determination of 2θ

Indexing & space an approximate structure model, (3) group assignment

Refinement of the structure model against Structure Rietveld Solution Refinement Unit cell & Structural Final crystal the powder data. With single crystal data space group model structure this sequence is normally routine. With Figure 9. Schematic diagram illustrating the powder data, however, difficulties arise different stages in complete structure determination from powder diffraction data. because the three-dimensional intensity data is reduced into a single dimension, as a result of random crystallite orientations. This results in overlapping peaks and introduces complications at each stage of the structure determination. The overlap of non-equivalent reflections is due to either 'accidental' equality or near-equality of d-spacings of non-equivalent reflections, especially at high scattering angles (mostly in low-symmetry structures), or symmetry-imposed equality of d-spacings for well-defined groups of non-equivalent reflections (this occurs only for high-symmetry structures; e.g. for reflections {hkl} and {khl} in a tetragonal system with Laue group 4/m, d(hkl) = d(khl) but I(hkl) ≠ I(khl)) (Harris et al., 1996)).

3.1.1 Determination of Lattice Parameters and Space-Group Assignment The first step in the process is to index the reflections of the diffraction pattern, i.e. to determine the Bravais lattice symmetry and a unit cell that accounts for the peaks present. A number of auto-indexing programs are available, that work using different algorithms, broadly classified as deductive or exhaustive. Deductive programs (such as TREOR (Werner et al., 1985) and ITO (Visser, 1969)) tend to work more quickly and will index the majority of powder patterns. Exhaustive programs (such as DICVOL91 (Boultif & Louër, 1991)) sort through all the various possibilities in a systematic manner and sometime succeed where other programs fail. All programs require as input the 2θ values or d-spacings of about 20 low-angle reflections. The space group is assigned by identifying the conditions for systematic absences in the indexed powder diffraction data. If it is not possible to assign the space group uniquely, it

15 DATA ANALYSIS

may be necessary to carry out the structure solution in parallel for several plausible space groups, or to use complementary data from e.g. spectroscopic techniques.

3.1.2 Structure Solution As most approaches for structure solution from powder diffraction data depend heavily on extracting reliable intensity data, pattern decomposition constitutes an important step dictating the overall success of these approaches. In the ideal case, each peak in the powder pattern would be individually resolved, and it would then be straightforward to extract accurate intensities (I(h)). However, extraction of the intensities from the powder diffractogram is complicated by the overlap of non-equivalent reflections mentioned above. The most commonly used method to overcome this problem is 'pattern decomposition' techniques (Pawley, 1981 and Le Bail et al., 1988). These techniques adopt a least-squares approach to fit a calculated profile to the experimental powder diffraction pattern, as in the Rietveld method (see Section 3.1.3), but without the use of a structural model. In the process lattice parameters, zero point error, peak-shape parameters and background parameters are refined. The integrated peak intensities can then be determined from the fitted profile. These pattern decomposition techniques are incorporated in a number of programs including ALLHKL (Pawley, 1981), GSAS (Larson and Von Dreele, 2000), FULLPROF (Rodriguez- Carvajal, 1990) and EXTRA/EXPO (Altomare et al., 1995 and1999). An initial structural model can sometimes be derived using models from compounds with similar structures or directly from the experimental data by the Patterson method. This method does not require prior information about the phases of reflections and uses only the observed structure factor amplitudes F(h) (determined from the measured diffraction intensities I(h)). The squared structure factor amplitudes are dependent on the interatomic vectors and can be used to find e.g. heavy atom positions in the structure. The most widely used techniques for structure solution from powder diffraction data are the so-called direct methods. Direct methods is a class of statistical methods that attempt to derive knowledge of the phases α(h) directly from the measured diffraction intensities I(h). The direct methods approach is based on the fact that the observed structure factor amplitudes F(h) together with the correct (but initially unknown) values of α(h) must correspond to an electron density that is positive everywhere within the unit cell. The method does not rely on the presence of a dominant scatterer or prior knowledge of a structural fragment. Alternative methods for structure solution have been developed in recent years, e.g. Monte Carlo, simulated annealing, grid search and genetic algorithms. In these methods trial crystal structures are generated in direct space, independently of the experimental powder

16 DATA ANALYSIS

diffraction data. The suitability of each trial structure is assessed by direct comparison of the powder diffraction pattern calculated for the trial structure and the experimental powder diffraction pattern (Harris et al., 2001). If the initial structural model is a sufficiently good representation of the structure, refinement of the structure using the Rietveld method can be successful. Missing atoms can subsequently be located using difference Fourier maps. A difference Fourier map will reveal the discrepancies between the experimental powder diffraction pattern and the powder diffraction pattern calculated for the structural model. The difference Fourier map has peaks at positions in which the structural model has a deficit of electron density (e.g. when an atom is missing from the model) and troughs at positions in which the structural model has an excess of electron density (e.g. an incorrectly placed atom or an incorrectly assigned atom type).

3.1.3 Refinement of the Structure Using the Rietveld Method In the late sixties, Hugo Rietveld published two papers concerning structure refinement using neutron powder data (Rietveld, 1967 and 1969). His development of the full-profile fitting refinement method has become the most used tool to refine structure models from powder diffraction data. The Rietveld method does not require the observed intensities of the individual Bragg reflections - instead it attempts to calculate a diffraction profile that resembles the observed profile as closely as possible. The diffraction profile for the structural model is calculated using the following information: • Symmetry and lattice parameters (to determine peak positions) • Atomic positions and atomic displacement factors (to determine peak intensities) • 2θ-dependent analytical functions to describe the peak shapes and peak widths • A description of the background intensity In the refinement the calculated pattern is compared point by point with the observed powder diffraction pattern. The difference between calculated and observed pattern is minimised by least squares refinement. The quantity minimised is the residual Sy:

2 Sy = ∑w i (y i − y ci ) i where w = 1/σ 2 , y is the observed intensity of the ith step, y is the calculated intensity at i yi i ci

2 the ith step and the sum is over all data points and σ yi is the variance (Young, 1993). The shape of a peak in a powder diffraction pattern depends both on features of the instrument and the sample. Different types of peak shape functions are appropriate under different circumstances. The most widely used peak shape function for synchrotron X-ray powder diffraction data is the pseudo-Voigt function (Young and Wiles, 1982; Wertheim,

17 DATA ANALYSIS

1974). It allows the refinement of a mixing parameter (η) that determines the fraction Lorentzian of Gaussian and Lorentzian components Gaussian Pseudo-Voigt needed to fit an observed profile. The Gaussian (G), Lorentzian (L) and pseudo- Voigt (pV) profile functions are defined as follows:

4ln2 2 2 G = exp(− 4ln2(2θ i − 2θ K ) HK ) HK π

−1 4 ⎡ (2θ − 2θ )2 ⎤ L = 1+ 4 i K ⎢ 2 ⎥ Figure 10. Comparison of the Gaussian, Lorentzian HKπ ⎣⎢ HK ⎦⎥ and pseudo-Voigt peak shape. The mixing parameter for the pseudo-Voigt function shown is pV = ηL + (1−η)G 0.5. where HK is the FWHM (full width at half maximum) of the Kth Bragg reflection and η is the mixing parameter that can be refined as a linear function of 2θ, wherein the refinable variables are NA and NB ()η = NA + NB * (2θ ). A comparison of the three peak shapes is given in Figure 10. For angle dispersive data, the angular dependence of the FWHM of the peaks is usually modelled as described by Caglioti et al. (1958): H 2 = U tan2 θ +V tanθ + W where U, V and W are the refinable parameters. Several criteria of fit can be used to assess the agreement between the experimental and calculated powder diffraction patterns. Definitions of the most commonly used R-values are given in Table 1 (Young, 1993; McCusker et al., 1999). The RF is similar to the values used in single-crystal refinements, but is biased towards the model in powder diffraction and is not used actively in the refinements. It is used to estimate the reliability of the refined structure model. The Bragg intensity R-value, RB, is similar to RF except that it uses the observed and calculated intensities instead of corresponding structure factors. The two pattern R-values,

Rp and Rwp, compare the observed and calculated patterns point for point. Rwp is related to the value of the least-squares minimisation function of the powder diffraction refinement and is used actively in the minimisation. It is, however, sensitive to the background level and background subtracted data sets should be used when comparing different Rwp. The ratio of 2 Rwp and Rexp defines the goodness-of-fit, S (given as reduced χ in GSAS), which should be close to 1. As a rule-of-thumb, an S-value much higher than 1 indicates that the data have been "over collected" with a low Rexp. A value lower than 1 indicates, in a similar manner, that data was "under collected" (e.g. for very fast data collection) (McCusker et al., 1999).

18 DATA ANALYSIS

Table 1. Some frequently used numerical criteria of fit (Young, 1993). IK (obs) is the intensity of the Kth Bragg reflection determined from the experimental diffraction pattern, IK (calc) is the intensity of the Kth Bragg reflection determined from the calculated diffraction pattern, yi(obs) is the intensity of the ith data point in the experimental powder diffraction pattern, yi(calc) is the intensity of the ith data point in the calculated powder diffraction pattern, wi is a weighting factor for the ith data point, N is the number of data points in the experimental powder diffraction pattern and P is the number of parameters in the refinement.

1/ 2 1/ 2 ∑ (IK (obs)) − (IK (calc)) ) R-structure factor RF = 1/ 2 ∑(IK (obs))

∑ IK (obs) − IK (calc) RB = R-Bragg factor ∑IK (obs)

∑ y i (obs) − y i (calc) Rp = R-pattern ∑ y i (obs)

1/ 2 ⎧ 2 ⎫ ⎪∑w i (y i (obs) − y i (calc)) ⎪ Rwp = ⎨ 2 ⎬ R-weighted pattern ⎩⎪ ∑w i (y i (obs)) ⎭⎪

2 ⎛ N − P ⎞ R = ⎜ ⎟ R-expected e ⎜ 2 ⎟ ⎝ ∑w i (y i (obs)) ⎠

1/ 2 S = []Sy /(N − P) = Rwp / Re Goodness-of-fit

3.2 KINETICS Crystallisation and degradation curves for e.g. hydrothermal synthesis or intercalation processes can be determined from time-resolved in-situ diffraction data by using integrated intensities of diffraction peaks. The crystallisation/degradation curves are obtained by integrating a number of selected diffraction peaks. A 2θ-range is defined around each diffraction peak and a linear background is defined using background counts on each side of the peak. The background counts are subtracted from the total counts over the 2θ-range to give the net integrated intensity. The integrated areas of the selected reflections are added and normalised so that the maximum intensity, when the crystallisation is completed, corresponds to 100 %. The crystallisation curves can then be fitted (using least-squares methods) with a kinetic expression such as a modified Avrami expression (Norby et al., 1999):

19 DATA ANALYSIS

n α(t) = 100(1− exp(−(k(t − t0 )) )) and a similar expression can be used for the degradation curves:

n α(t) = 100(exp(−k(t − t0 )) )) where α is the percentage of crystallisation, k is a rate constant and t0 is the starting time of the crystallisation (usually interpreted as the nucleation time). The parameter n is connected to the mechanism of nucleation and crystallisation. The rate constants extracted from the crystallisation curves at different synthesis temperatures can be plotted in an Arrhenius-type plot. If the plot of ln(k) versus 1/T is linear, an apparent activation energy (EA) for the crystallisation can be determined:

ln(k) = −E A / RT The k values extracted from the crystallisation curves are, strictly speaking, not true rate constants. Therefore the derived activation energies are not true activation energies. However, the values extracted can be valuable for comparison between related crystallisation systems (Norby et al., 1999).

3.3 THERMAL EXPANSION

The coefficient of linear thermal expansion (CTE or α) is defined as unit change in length divided by unit change in temperature and is normally expressed as follows (Roy et al., 1989): l − l CTE = 0 l 0 (T −T0 ) where l is the length after temperature change, and I0 the initial length. The thermal expansion coefficient is a function of temperature, so when referring to CTE of a specific material the temperature range in which the measurements were made should also be given. Traditionally, thermal expansions of ceramics have been divided into three classes depending on their coefficient of thermal expansion.

High Expansion Group CTE > 8 ⋅ 10-6 K-1 Intermediate Group 2 ⋅ 10-6 < CTE < 8 ⋅ 10-6 K-1 Very Low Expansion Group 0 ≤ CTE < 2 ⋅ 10-6 K-1

Materials with negative thermal expansion can also be included in the last category depending on the absolute value of CTE. Technologically an expansion or contraction of the same magnitude would have the same effect on the performance of a material, but thermal

20 DATA ANALYSIS

contraction could be a useful anomaly when creating new materials with a specific thermal expansion (Roy et al., 1989).

3.4 COMPRESSIBILITY AND EQUATION OF STATE High-pressure diffraction experiments on a sample at constant temperature generally show the variation of unit-cell parameters and/or density versus pressure. It is common to find the change in unit-cell parameters fitted with a simple linear or polynomial expression. This is quite unphysical since e.g. a linear variation implies that the structure does not become stiffer at increasing pressures, while say a second order polynomial would increase the unit-cell volume at higher pressures. Nevertheless, at very low pressures a linear relationship between unit-cell volume and pressure can often be used - mainly because it will fall within the experimental error in the pressure determination. The linear compressibility, βx, has been calculated for unit-cell parameters. It is defined as follows (Nye, 1957): 1 ∆x β = − x x ∆p where x is the unit-cell volume or axis length. ∆x and ∆p are defined as the difference between measurements conditions at actual measurement and its starting value. The compressibility values were calculated by linear regression of the unit-cell parameters versus pressure and are not intended for extrapolation to higher pressures. The compressibility is used as a qualitative descriptor (with close resemblance to the expression for the thermal expansion coefficient) in a pressure range where the change in unit-cell parameters is essentially linear with pressure. A physically more accurate way of describing the compression of a material is to estimate its bulk modulus by fitting an equation of state, EoS, to the unit-cell volume data. The change in unit-cell volume with pressure is characterised by the bulk modulus, defined as: δp K = −V δV

In this study, the bulk modulus and its pressure derivative (K0') have been evaluated at zero pressure and isothermal conditions (ambient temperature). The derivation of different EoS is described in e.g. Anderson (1995) or Duffy and Wang (1998), but is out of scope for this presentation. There is in principle not an absolute thermodynamic basis for the correct form of an EoS, so that all EoS formulations are based on a number of assumptions. The validity of an EoS can only be judged in terms of its success of reproducing the experimental volume data. In the present work two EoS expressions have been used: The Birch-Murnaghan EoS 2/3 (Birch, 1947), based on Eularian strain, fe = [(V0/V) -1]/2, and expanded to third order:

21 DATA ANALYSIS

7 5 2 ⎡ − − ⎤ ⎡ ⎛ − ⎞⎤ 3 3 3 3 ⎢⎛ V ⎞ ⎛ V ⎞ ⎥ ⎢ 3 ' ⎜⎛ V ⎞ ⎟⎥ p = ⋅ K ⋅ ⎜ ⎟ − ⎜ ⎟ ⋅ 1− ⋅ (4 − K ) ⋅ ⎜⎜ ⎟ − 1⎟ 2 0 ⎢⎜V ⎟ ⎜V ⎟ ⎥ ⎢ 4 0 ⎜V ⎟ ⎥ ⎝ 0 ⎠ ⎝ 0 ⎠ ⎢ ⎜⎝ 0 ⎠ ⎟⎥ ⎣⎢ ⎦⎥ ⎣ ⎝ ⎠⎦ and the Vinet EoS (Vinet et al., 1986), derived from cohesive energies in condensed systems:

2 1 1 − ⎡ ⎤ ⎡ ⎛ ⎞⎤ 3 3 3 ⎛ V ⎞ ⎢ ⎛ V ⎞ ⎥ ⎢3 ' ⎜ ⎛ V ⎞ ⎟⎥ p = 3K ⎜ ⎟ 1− ⎜ ⎟ exp (K − 1) ⋅ ⎜1− ⎜ ⎟ ⎟ 0 ⎜ V ⎟ ⎢ ⎜V ⎟ ⎥ ⎢2 0 ⎜V ⎟ ⎥ ⎝ 0 ⎠ ⎝ 0 ⎠ ⎢ ⎜ ⎝ 0 ⎠ ⎟⎥ ⎣⎢ ⎦⎥ ⎣ ⎝ ⎠⎦ By fitting these equations to the experimental pressure (p) and unit-cell volume (V) data, the isothermal bulk modulus (K0) and its pressure derivative (K0') can be estimated. A low value of the bulk modulus corresponds to a higher compressibility of the structure and a high value indicates a more incompressible (stiff) structure. The pressure derivative of the modulus, K0', gives the curvature of the volume-pressure graph. The results from the above EoS expressions were not significantly different, but the Vinet EoS is expected to give more accurate estimation at very high pressures (100 GPa range).

22 SYNTHESIS

4. SYNTHESIS Three types of materials investigated in this thesis were synthesised at the Department of Chemistry, University of Odense, Denmark: 1) Phosphates with the general formula IV IV M (HPO4)2⋅nH2O (M = Ti, Zr) were synthesised under hydrothermal conditions; 2) IV IV Pyrophosphates and pyrovanadates with the general formula M X2O7 (M = Ti, Zr; X = P, V) were prepared by solid-state reaction at high temperature; 3) A zirconium molybdate

(ZrMo2O8) was obtained by dehydration of a basic zirconium molybdate hydrate. The obtained materials were characterised using X-ray powder diffraction, thermal analysis, 31P MAS NMR spectroscopy (on the phosphorous containing compounds) and IR spectroscopy. The powder diffraction data were recorded on a Siemens D5000 diffractometer equipped with a germanium monochromator (CuKα1-radiation, λ = 1.540598 Å). The patterns were typically recorded from 2-60° in 2θ with a step length of 0.02°. Thermogravimetric (TG) analysis was carried out using a SETARAM TG92-12 instrument. Typically the heating rate was 5 °/min and the measurements were performed in nitrogen flow. Differential Scanning Calorimetry (DSC) was performed on a SETARAM DTA92-16.18 instrument with calcined Al2O3 as reference. Heating and cooling rates of 5 and 10 °/min were used and the experiments were performed in an argon atmosphere. 31P MAS NMR spectroscopy was carried out on a Varian UNITY-500 spectrometer (11.7 T, ν(31P) = 202.3 MHz) using a Jakobsen MAS probe. IR spectra were recorded on a model 170 Fourier transform IR spectrometer, using the KBr technique (1 mg sample in 350 mg KBr).

IV IV 4.1 HYDROTHERMAL SYNTHESIS OF M (HPO4)2⋅nH2O (M = Ti, Zr). Titanium and zirconium hydrogen phosphates were prepared by hydrothermal treatment of amorphous titanium or zirconium phosphate with phosphoric acid solutions. The amorphous phosphates were prepared by dissolving TiCl4 or ZrCl4 in 2 M HCl, and subsequently adding the obtained solution to 1.25 M H3PO4. The resulting solid was allowed to stand overnight in the mother liquor and was then separated by filtration, washed with water and air-dried (Alberti et al., 1967; Paper IV). Typically the reaction mixture for hydrothermal synthesis was prepared by stirring amorphous titanium or zirconium phosphate (0.5 and 1.5 g, respectively) and 10 ml of H3PO4 for 48 hours. The resulting gel was placed in a Teflon-lined autoclave and heated according to Table 2. After cooling the products were separated from the liquid, washed with water and air-dried.

α-Ti(HPO4)2⋅H2O, γ-Ti(PO4)(H2PO4)⋅2H2O and α-Zr(HPO4)2⋅H2O have a large formation region depending on the temperature and the concentration of the phosphoric acid (Paper III and IV). τ-Zr(HPO4)2 has a very narrow window of formation and forms in conditions very

23 SYNTHESIS

near to those for the formation of zirconium pyrophosphate. It is therefore difficult to obtain samples of τ-Zr(HPO4)2 without zirconium pyrophosphate (Paper IV).

IV IV Table 2. Conditions for preparation of M (HPO4)2⋅nH2O (M = Ti, Zr). Concentration Preparation Preparation H3PO4 (M) Temp. (K) time (h)

α-Ti(HPO4)2⋅H2O 8 523 10 448-498 48 12 448-473 14 448

γ-Ti(PO4)(H2PO4)⋅2H2O 10 523 12 498-523 48 14 473-523 16 448-523

α-Zr(HPO4)2⋅H2O 10 473 12 448 48 16 423-448

τ-Zr(HPO4)2 16 463 120

IV IV 4.2 SYNTHESIS OF M X2O7 (M = Ti, Zr; X = P, V).

ZrP2O7 and ZrV2O7 were synthesised by a solid-state reaction between analytical grade

ZrOCl2·8H2O, (NH4)2HPO4 respectively NH4VO3 in molar ratios (1:2) (Korthuis et al., 1995). The reactants were first mixed by grinding in an agate mortar. The mixture was then placed in a gold crucible and heated at 973 K in air for 24 hours, and cooled rapidly by removing the crucible from the furnace. During heating, evolution of NH4Cl and NH3 was observed. The sample was then ground and heated again (973 K, 24 hours) to make sure that the reaction was complete.

∆ ZrOCl2 ⋅ 8H2O + 2(NH4 )2 HPO 4 ⎯⎯→ ZrP2O7 + 2NH3 + 2NH4Cl + 10H2O

∆ ZrOCl 2 ⋅ 8H2O + 2NH 4 VO 3 ⎯⎯→ ZrV2O 7 + NH3 + NH4Cl + HCl + 8H2O

TiP2O7 was prepared, in accordance with Soria et al. (1993), by reacting TiO2 (anatase) and

85 % H3PO4 in an autoclave for 3 hours at 473 K. The sample was dried at 373 K, ground and calcined at 973 K for 3 hours.

∆ Ti(HPO 4 )2 ⋅H2O ⎯⎯→ TiP2O7 + 2H2O Preliminary X-ray powder diffraction data on the prepared samples were identical to previously published data (Sanz et al., 1997; Khosrovani et al., 1996; Evans et al., 1998).

24 SYNTHESIS

4.3 SYNTHESIS OF α-ZrMo2O8.

Powder samples of trigonal α-ZrMo2O8 were prepared by dehydrating a basic zirconium molybdate hydrate (ZrMo2O7(OH)2(H2O)2), prepared essentially according to Clearfield and

Blessing (1972). Aqueous solutions of the reactants, ZrOCl2·8H2O and Na2MoO4·H2O, were mixed by simultaneous drop wise addition to water under continuous stirring. The obtained gel was aged overnight in the mother liquor, with continuous stirring. The gel and mother liquor was then acidified with HCl. This mixture was then heated at reflux temperature for 7 days. The obtained solid was isolated, washed with 1 M HCl and water and finally air-dried. The X-ray powder pattern was identical to the pattern in the ICDD database (no. 27-0994).

Reflux ZrOCl2 ⋅ 8H2O + 2Na2MoO4 ⋅H2O ⎯⎯→⎯⎯ ZrMo2O7 (OH)2 (H2O)2 + 2 NaOH + 2 NaCl + 6 H2O

Trigonal α-ZrMo2O8 was obtained by heating ZrMo2O7(OH)2(H2O)2 at 723 K for 18 hours in a platinum crucible in air. The product was quenched by rapid cooling to room temperature.

∆ ZrMo2O7 (OH)2 (H2O)2 ⎯⎯→ ZrMo2O8 + 3H2O X-ray powder patterns of the prepared sample were identical to the pattern published by Auray et al. (1987).

SUMMARY AND DISCUSSION OF RESULTS

5. SUMMARY AND DISCUSSION OF RESULTS

IV IV 5.1 PHOSPHATES WITH THE GENERAL FORMULA M (HPO4)2⋅nH2O (M = Ti, Zr) Layered phosphates with the general formulas IV IV α-M (HPO4)2⋅H2O (M = Zr, Ti, Sn, Hf, Pb) and IV IV γ-M (PO4)(H2PO4)⋅2H2O (M = Zr, Ti, Hf) have been studied extensively since the 1960'ies = 7.6 Å 2

because of their intercalation, ion-exchange and 00 d ion-conductivity properties (Alberti et al., 1996; Clearfield and Costantino, 1996; Suarez et al., 1998).

The structure of α-Zr(HPO4)2⋅H2O was solved using single-crystal methods by Clearfield and co-workers in 1969 (Clearfield and Smith, 1969). = 9.2 Å However, the data were not of sufficient quality 2 00 d to locate the hydrogen atoms. This was later accomplished by two groups: Troup and Clearfield (1977) using single-crystal methods and Albertsson et al. (1977) using neutron powder diffraction. Later the structures of the other α-type compounds were shown to be isostructural with α-Zr(HPO4)2⋅H2O (Bruque et al., 1995). The α-type compounds (Figure 11,

top) consist of layers built of octahedrally = 12.2 Å 002 coordinated metal atoms bound together by d 2- hydrogen phosphate groups (HPO4 ). Three 2- oxygen atoms of each HPO4 group are bonded to three different metal atoms. The fourth Figure 11. Polyhedral representations of layered oxygen (the OH group) points into the interlayer phosphates in the a-b plane. Top figure: α-Ti(HPO ) ⋅H O: Octahedra represent region, where it hydrogen-bonds to the water 4 2 2 TiO6, dark grey tetrahedra represent HPO4 and molecules. spheres represent water molecules. Middle figure: β-Ti(PO4)(H2PO4): Octahedra The existence of a second type of layered represent TiO6, dark grey tetrahedra represent PO4 and light grey tetrahedra represent H2PO4. compounds was first reported by Clearfield and Bottom figure: γ-Zr(PO4)(H2PO4)⋅2H2O: Octahedra represent ZrO6, dark grey tetrahedra represent co-workers in 1968 (Clearfield et al., 1968), who PO4 and light grey tetrahedra represent H2PO4 and spheres represent water molecules. attributed the prefix γ to the hydrated form and β Coordinates taken from Bruque et al. (1995), Paper III and Poojary et al. (1995), respectively. to the anhydrous form. The γ-type compounds

27 SUMMARY AND DISCUSSION OF RESULTS

have a larger interlayer distance than the α-type compounds. For 20 years this difference was attributed to a different type of stacking of the layers rather than a different intralayer arrangement. However, 31P MAS NMR studies published by Clayden in 1987 clearly showed that the spectra of the γ-type layers display two 31P resonances of equal intensity whereas only one is observed in the α-type layers. The conclusion made by Clayden was that the γ- layered compounds contain equal amounts of tertiary phosphate groups and dihydrogen IV phosphate groups, leading to the general formula: M (PO4)(H2PO4)⋅2H2O (Clayden,1987).

The structure of γ-Zr(PO4)(H2PO4)⋅2H2O was finally solved from powder diffraction data in 1995 (Poojary et al., 1995). The compound was shown to consist of layers built of 3- octahedrally coordinated metal atoms bound together by tertiary phosphate groups (PO4 ) - and dihydrogen phosphate groups (H2PO4 ). Within the layers, the tertiary phosphate groups are sandwiched between two layers of MO6, so that all four oxygen bind to metal atoms. In the dihydrogen phosphate groups two oxygen atoms bind to metal atoms and the two remaining oxygen atoms form hydroxyl groups that point into the interlayer region. The water molecules form a zigzag chain that runs between the dihydrogen phosphate groups (Figure

11, bottom). Recently, the structure of γ-Hf(PO4)(H2PO4)⋅2H2O was solved and found to be isostructural with γ-Zr(PO4)(H2PO4)⋅2H2O (Suarez et al., 1998; Salvadò et al., 2001). The complete structure of γ-Ti(PO4)(H2PO4)⋅2H2O has so far not been published. A Rietveld refinement of the structure was reported in the proceedings of EPDIC 3 (Salvadò et al., 1994) but no refined coordinates were given. However, it can probably be assumed that it is IV isostructural to γ-Zr(PO4)(H2PO4)⋅2H2O. The anhydrous form of γ-M (PO4)(H2PO4)⋅2H2O IV which has the general formula β-M (PO4)(H2PO4), has been shown to retain the structure of the γ-type layers (Figure 11, middle; Paper III). Unit-cell parameters and space-group symmetries for the various types of layered phosphates are summarised in Table 3.

Table 3. Crystallographic data for some zirconium and titanium hydrogen phosphates Parameters taken from: a Bruque et al., 1995; b Paper III; c Poojary et al., 1995; d Paper IV. a b c d α-Ti(HPO4)2⋅H2O β-Ti(PO4)(H2PO4) γ-Zr(PO4)(H2PO4)⋅2H2O τ-Zr(HPO4)2 a (Å) 8.6403 5.1392 5.3825 11.2611 b (Å) 5.0093 6.3126 6.6337 - c (Å) 15.5097 18.9502 12.4102 10.7688 β (°) 101.324 105.366 98.687 - V (Å3) 658.22 592.80 438.03 1365.62

S. G. P21/n P21/n P21 I41cd Z 4 4 2 8

28 SUMMARY AND DISCUSSION OF RESULTS

IV IV IV During studies of the formation region of α-M (HPO4)2⋅H2O and γ-M (PO4)(H2PO4)⋅2H2O (M = Zr, Ti) (Paper III and IV) a new zirconium hydrogen phosphate phase, with the formula

τ-Zr(HPO4)2, was discovered. Unit-cell parameters and space-group symmetry for

τ-Zr(HPO4)2 are given in Table 3 and further details about structure determination and structure model can be found in Section 5.1.4 and in Paper IV.

IV IV In the following, results for all three types of M (HPO4)2⋅nH2O (M = Ti, Zr) structures are presented. The purpose of these studies was to investigate the effect of temperature and pressure on the crystallisation and intercalation process. Furthermore, temperature- and pressure-resolved studies were used to detect and characterise thus far unknown high- temperature and high-pressure zirconium and titanium phosphate phases. Another question was, if it is possible to determine and refine the structures of new phases from temperature- and pressure-resolved in-situ powder diffraction data. Firstly, results for the α-layered structures are presented with kinetic studies of the synthesis of α-Ti(HPO4)2⋅H2O (Section 5.1.1) and intercalation of alkane diamines in α-Zr(HPO4)2⋅H2O (Section 5.1.2). Secondly, previously unknown high-temperature phases in the γ-layered compounds are presented (Section 5.1.3.) followed by the investigations on the 3-D structure of τ-Zr(HPO4)2. When it comes to τ-Zr(HPO4)2, several aspects were studied, from structure solution and refinement (Section 5.1.4), to the study of high-temperature phases (Section 5.1.5) and finally high-pressure phases in Section 5.1.6.

5.1.1 Time-resolved Studies on the Synthesis of α-Ti(HPO4)2⋅H2O.

5.1.1.1 Synthesis of α-Ti(HPO4)2⋅H2O in the micro-reaction cell (Paper I) Three sets of in-situ time-resolved data have been recorded on the formation of

α-Ti(HPO4)2⋅H2O under hydrothermal conditions; one set at beamline X7B (NSLS) and 2 sets at beamline BM16 (ESRF). The experimental details can be found in Paper I. All experiments were carried out using the micro-reaction cell described in Section 2.2.1.1. The reaction mixture consisted of amorphous titanium phosphate, prepared as described in Section 4.1, mixed with phosphoric acid (85 %) to form a gel. The data analysis was carried out as described in Section 3.2. Figure 12 shows the crystallisation curves obtained in the second experiment at BM16 and Figure 13 shows a comparison of the Arrhenius plots for all three data sets. From the slope of the Arrhenius plots the activation energies were calculated to be 41.2, 55.2 and 41.4 kJ/mol, for the BM16_1, BM16_2 and X7B data, respectively. This indicates that probably the crystallisation mechanism is the same in all three experiments,

29 SUMMARY AND DISCUSSION OF RESULTS

0 100

-1 80

-2 60 348 K

358 K -3 ln(k) 40 373 K

Crystallisation (%) -4 393 K 20 413 K -5

0 0 50 100 150 200 250 300 350 400 450 500 -6 2.0 2.2 2.4 2.6 2.8 3.0 3.2 Time (min) 1000/T (K-1) Figure 12. Crystallisation curves extracted from the isothermal in-situ experiments at Figure 13. Arrhenius plots, ln(k) versus 1000/T, temperatures between 348 K and 413 K for isothermal crystallisation of α-Ti(HPO4)2⋅H2O. (BM16_2 data). Solid curves are fits to the From the slopes of the linear regression lines, Avrami equation. apparent activation energies were derived. X7B-data, BM16_1 data, ∆ BM16_2 data but as can be seen from Figure 13, the crystallisation rate is different, probably due to differences in preparation of the reaction mixture. The diffraction data from the crystallisation of α-Ti(HPO4)2⋅H2O display anisotropic peak broadening for reflections characteristic of the directions perpendicular to the layers, which might originate from e.g. stacking disorder.

After the crystallisation it was also possible to study the transformation of α-Ti(HPO4)2⋅H2O to

β-Ti(PO4)(H2PO4) at 453 K. This transformation, which involves the change of two hydrogen phosphate groups to one tertiary phosphate and one dihydrogen phosphate group, is considerable slower than the crystallisation of α-Ti(HPO4)2⋅H2O.

5.1.1.2 Synthesis of α-Ti(HPO4)2⋅H2O in a diamond anvil cell

Time-resolved X-ray diffraction data on the synthesis of α-Ti(HPO4)2⋅H2O were collected in angular dispersive mode at ID9 (ESRF) using monochromatic radiation (λ = 0.4362 Å) and a CCD-based area-detector. An externally heated diamond anvil cell (as described in Section 2.2.2.1) was used. The pressurised sample chamber in the cell was approximately 250 µm in diameter and 80 µm in height. A gel, prepared as in Section 5.1.1.1, was loaded into the diamond anvil cell with a small ruby for pressure measurements. The temperature was monitored by Cr-Al thermocouples close to the sample, and the pressure by the previously described fluorescence technique (Section 2.2.2.3). In Figure 14, a 3-D representation of the diffraction profiles as a function of time during the crystallisation of α-Ti(HPO4)2⋅H2O at 443 K and 2.5 GPa is shown. In Figure 15, the normalised integrated intensities of diffraction lines of α-Ti(HPO4)2⋅H2O are plotted as a

30 SUMMARY AND DISCUSSION OF RESULTS

25000 100

20000 80

15000 60 Intensity

10000 40 20 Crystallisation (%) Crystallisation

T 15 ime 20

( 10 mi n) 5 0 6.0 6.5 7.0 0 4.5 5.0 5.5 0 2 4 6 8 101214161820 3.0 3.5 4.0 2theta Time (min)

Figure 14. 3-D plot for the crystallisation of Figure 15. Crystallisation curve for the α-Ti(HPO4)2⋅H2O at 443 K and 2.5 GPa. crystallisation of α-Ti(HPO4)2⋅H2O at 443 K and 2.5 GPa. function of time. The crystallisation curve was fitted using a first order Avrami-type equation. -1 The fitted values are k = 0.49 min and t0 = 1.49 min.

At 493 K and 0.8 GPa α-Ti(HPO4)2⋅H2O transforms to a previously unknown phase. Figure

16 shows a 3-D plot of the conversion from α-Ti(HPO4)2⋅H2O to the new phase, with new peaks appearing at e.g. 4.2, 5.1 and 6.5 in 2θ. The crystallisation and degradation curves in Figure 17 were fitted with the modified Avrami expression described in Section 3.2. It can be seen that the crystallisation of the new phase can be fitted by the modified Avrami expression. However, the degradation of α-Ti(HPO4)2⋅H2O does not follow the empirical expression. The deviation from ideal behaviour (degradation + crystallisation = 100%) is shown with open circles in Figure 17. The deviation can be due to an amorphous phase or structural transformations of α-Ti(HPO4)2⋅H2O during the degradation. The fitted values for -1 -1 degradation and crystallisation are kdegr = 0.055 min , kcryst = 0.109 min , ndegr = 5.23 and ncryst = 2.36.

90000 100

70000 80

50000 60

Intensity 30000

40 10000

65 Conversion (%)

20 T 60 im e ( 55 m 0 in) 50 6.0 6.5 7.0 45 4.5 5.0 5.5 35 40 45 50 55 60 65 3.0 3.5 4.0 ta 2the Time (min)

Figure 16. 3-D plot the conversion of Figure 17. Degradation/crystallisation curves for the conversion of α-Ti(HPO ) ⋅H O to a new α-Ti(HPO4)2⋅H2O to a new phase at 493 K and 0.8 4 2 2 GPa. phase at 493 K and 0.8 GPa. Open circles show the deviation from ideal behaviour.

31 SUMMARY AND DISCUSSION OF RESULTS

Attempts were made to index the pattern and determine the space-group symmetry of the new phase. From TREOR90 (Werner et al., 1985) a monoclinic unit cell similar to that of

α-Ti(HPO4)2⋅H2O (see Table 3) was obtained. The unit-cell parameters were a = 18.331 Å, b = 5.370 Å, c = 14.273 Å and β = 125.43 °. Unfortunately, the quality of the powder diffraction data did not allow further structural investigations of the new phase.

5.1.2 Intercalation of Alkane Diamines in α-Zr(HPO4)2⋅H2O 2-D layered compounds offer the possibility of intercalation. The term intercalation is used by chemists to describe the (reversible) insertion of mobile guest species into a crystalline host lattice. A large number of ex-situ investigations have been published on the intercalation chemistry of layered phosphates (Clearfield and Costantino, 1996). The majority of these investigations have been performed with α-Zr(HPO4)2⋅H2O as the host species. The reactivity of α-Zr(HPO4)2⋅H2O (and other layered phosphates) is due to the presence of Brøndsted acid groups in the interlayer region and weak forces between the layers. Species with sites able to accept protons are preferred guests and therefore large uncharged species such as cyclodextrins (Kijima and Matsui, 1986) or porphyrins (Kim et al., 1993) can be intercalated by using their amino derivatives. Alkyl monoamines and diamines, and also secondary and tertiary amines, are readily intercalated into α-Zr(HPO4)2⋅H2O from aqueous solution. The intercalation reaction is driven by the acid-base interaction between the amino group(s) and the P-OH group of the layer. Initially the amine molecules lie with the alkyl chain parallel to the layer plane and the interlayer distance increases from 7.6 Å to 10.4 Å, irrespective of the alkyl-chain length. As the amount of amine taken up by the host increases there is not sufficient room for the flat position and the amines begin to incline to the phosphate layers at increasing angle. At 50 % saturation a monolayer is formed, and at saturations above 50 % a bilayer is obtained. The composition of the fully intercalated phase is α-Zr(HPO4)2⋅2CnH2n-1NH2⋅H2O (Clearfield and Costantino, 1996). Time-resolved powder diffraction experiments on intercalation processes were carried out at beamline X7B (NSLS) using the micro-reaction cell (see Section 2.2.1.1) and an INEL CP120 position sensitive detector (see Section 2.2.1.3). Specifically, the kinetics of the intercalation of 1,6-hexanediamine (HeDA) in α-Zr(HPO4)2⋅H2O (α-ZrP) was studied. The composition of the possible intercalates of 1,6-hexanediamine in α-Zr(HPO4)2⋅H2O have previously been determined by Casciola et al. (1988) using batch titration. They showed that there exist three possible intercalates of HeDA in α-Zr(HPO4)2⋅H2O (Table 4).

32 SUMMARY AND DISCUSSION OF RESULTS

Table 4. Composition and interlayer distance for α-Zr(HPO4)2⋅H2O and the possible intercalates of 1,6-hexanediamine

(HeDA) in α-Zr(HPO4)2⋅H2O. Compound Interlayer distance (Å) α-ZrP 7.56

α-ZrP⋅0.2HeDA⋅2.5H2O 10.7

α-ZrP⋅0.5HeDA⋅1.5H2O 12.6

α-ZrP⋅HeDA⋅H2O 15.4

Figure 19. 3-D representation of a small angular

Q. W. Host Q. W. Amine solution N2 range versus time for the intercalation of 1,6- hexanediamine in α-Zr(HPO4)2⋅H2O at 283 K. The peaks shown are: Figure 18. 0.5 mm quartz capillary filled with a plug (a) 002 reflection of α-ZrP and 004 reflection of of quartz wool (Q. W.), host material α-ZrP⋅HeDA⋅H2O (α-Zr(HPO4)2⋅H2O ) and amine solution. (b) 002 reflection of α-ZrP⋅0.2HeDA⋅2.5H2O (c) 002 reflection of α-ZrP⋅0.5HeDA⋅1.5H2O (d) 002 reflection of α-ZrP⋅HeDa⋅H2O

The reaction chamber of the micro-reaction cell was a 0.5 mm quartz capillary, which was filled as shown in Figure 18. The intercalation process was started by applying an external pressure of nitrogen gas on the amine solution and thereby bringing it into contact with the host material. The experiments were performed at 4 temperatures in the range 283-318 K. The wavelength was 1.1167 Å and the time resolution was 70 seconds. Figure 19 shows the intensities of 002 reflections of host material and intercalates as a function of time for the intercalation of HeDA in α-Zr(HPO4)2⋅H2O at 283 K. The 002 reflection of the host material (a) would be expected to disappear completely as the intercalation proceeds. This, however, is not the case because the position of the 004 reflection of the intercalate α-ZrP⋅HeDA⋅H2O is nearly the same as that of the 002 reflection of the host material. The intensity data for the 002 reflection of α-Zr(HPO4)2⋅H2O were therefore corrected for the contribution of the 004 reflection of α-ZrP⋅HeDA⋅H2O. The reflections shown in Figure 19 were fitted with a Voigt profile using the FIT program in the Siemens D5000 software package. The intensities were corrected for decrease of the intensity of the primary beam. Figure 20 shows a plot of the intensities extracted for the 002 reflections of the intercalates and the host material versus time. Since the amount of crystalline material is proportional to the intensity of the reflection, rate constants for the

33 SUMMARY AND DISCUSSION OF RESULTS

4000 0

3000 -1 ) k -2

2000 ln( Intensity

-3

1000 -4

0 -5 0 20406080100120 3.25 3.30 3.35 3.40 3.45 3.50 3.55 Time (Min) 1000/T (K-1)

Figure 20. Plot of the intensities of the 002 Figure 21. Arrhenius plot for the intercalation of reflections of host and intercalates for the 1,6-diaminohexane in α-Zr(HPO4)2⋅H2O. Circles: intercalation of 1,6-diaminohexane in Consumption of α-Zr(HPO4)2⋅H2O; Triangle down: α-Zr(HPO4)2⋅H2O at 283 K. Circles: Consumption Formation of α-ZrP⋅0.5HeDA⋅1.5H2O; Squares: of α-Zr(HPO4)2⋅H2O; Triangle up: Formation of Formation of α-ZrP⋅HeDA⋅H2O. α-ZrP⋅0.2HeDA⋅2.5H2O; Triangle down: Formation of α-ZrP⋅0.5HeDA⋅1.5H2O; Squares: Formation of α-ZrP⋅HeDA⋅H2O.

consumption of α-Zr(HPO4)2⋅H2O and formation of the intercalates α-ZrP⋅HeDA⋅H2O and

α-ZrP⋅0.5HeDA⋅1.5H2O can be calculated. In this case a first order rate equation:

It = ∆I(exp(-k(t-t0))) + Ifinal where ∆I is the total change in intensity during the intercalation and t0 starting time of the intercalation, was used. At 318 K the intercalation process is too fast for determination of rate constants. Furthermore the amount of the intercalate α-ZrP⋅0.5HeDA⋅1.5H2O decreases after a short time. It appears to be converted to the other intercalate α-ZrP⋅HeDA⋅H2O. There is no reason for assuming that this conversion does not occur at lower temperatures also.

Arrhenius plots for the consumption of α-Zr(HPO4)2⋅H2O and formation of

α-ZrP⋅0.5HeDA⋅1.5H2O and α-ZrP⋅HeDA⋅H2O are plotted in Figure 21. That the Arrhenius plots appear to be linear indicate that only one rate-determining step is involved. Activation energies for the processes are: 103.5 kJ/mol for the consumption of α-Zr(HPO4)2⋅H2O and

104.5 kJ/mol respectively 69.1 kJ/mol for the formation of α-ZrP⋅0.5HeDA⋅1.5H2O and

α-ZrP⋅HeDA⋅H2O.

34 SUMMARY AND DISCUSSION OF RESULTS

5.1.3 Temperature-Resolved Experiments on γ-Ti(PO4)(H2PO4)⋅2H2O (Paper II)

The thermal transformations of the layered phosphate, γ-Ti(PO4)(H2PO4)⋅2H2O, were studied using thermogravimetric analysis (TG), differential scanning calorimetry (DSC), X-ray powder diffraction and in-situ temperature-resolved X-ray powder diffraction experiments. The transformation from γ-titanium phosphate to cubic titanium pyrophosphate, TiP2O7, proceeds via a number of intermediate phases which can be summarised as follows:

appr. 323 K 373 K γ − Ti(PO4 )(H2PO4 ) ⋅ 2H2O ⎯⎯→⎯⎯⎯ γ'−Ti(PO4 )(H2PO4 ) ⋅ (2 − x)H2O ⎯⎯→⎯⎯ β − Ti(PO4 )(H2PO4 ) − x H2 O - (2− x) H2 O 748 K 1023 K ⎯⎯→⎯⎯ Ti(PO4 )(H2P2O7 )0.5 ⎯⎯→⎯⎯ TiP2O7 - 0.5 H2 O - 0.5 H2 O

The first transformation from γ-Ti(PO4)(H2PO4)⋅2H2O via γ'-Ti(PO4)(H2PO4)⋅(2-x)H2O to

β-Ti(PO4)(H2PO4) is the most interesting regarding in-situ data. Several authors have already described this dehydration in the literature (La Ginestra and Massucci, 1979; Kobayashi and Yamazaki, 1983; Llavona et al., 1985), but only La Ginestra mentions the possibility of a two- step transition with the formation of an intermediate phase. The TG measurements in the temperature range 298 to 523 K indicated that γ-Ti(PO4)(H2PO4)⋅2H2O loses 2 molecules of crystal water between 323 and 373 K, leading to the formation of the anhydrous phase,

β-Ti(PO4)(H2PO4). The DSC measurement, however, clearly shows that the dehydration

Figure 22. 3-D representation of the transformation of γ-Ti(PO4)(H2PO4)·2H2O to β-Ti(PO4)(H2PO4) via the intermediate, partially dehydrated phase, γ'-Ti(PO4)(H2PO4)·(2-x)H2O (x~1). The pattern of γ'-Ti(PO4)(H2PO4)·(2-x)H2O (x~1) is indicated by a thicker linewidth at 342 K.

35 SUMMARY AND DISCUSSION OF RESULTS

Table 5. Crystallographic data for γ-Ti(PO4)(H2PO4)·2H2O and its high-temperature forms. Parameters taken from Paper II.

γ-Ti(PO4)(H2PO4)⋅2H2O γ'-Ti(PO4)(H2PO4)⋅(2-x)H2O β-Ti(PO4)(H2PO4) a (Å) 23.742(1) 23.678(1) 19.105(3) b (Å) 6.346(1) 6.269(1) 6.316(1) c (Å) 5.179(1) 5.032(1) 5.144(1) β (°) 102.54(1) 102.43(2) 105.29(2) V (Å3) 761.69(19) 729.43(19) 598.74(18)

Space group P21 (no. 4) P21 (no. 4) P21/n (no. 14) T (K) 311 342 371 takes pla ce in two steps, with the formation of an intermediate phase. The intermediate phase, in the following γ'-Ti(PO4)(H2PO4)⋅(2-x)H2O, contains approximately 1 mol of crystal water. This observation is supported by the temperature-resolved in-situ data collected at beamline X7B (Figure 22). Experimental details for the in-situ data are given in Paper II. The unit-cell parameters for the new phase were determined using the auto-indexing program TREOR90 (Werner et al., 1985), which came up with a unit-cell similar to that of

γ-Ti(PO4)(H2PO4)⋅2H2O (see Table 5). The unit-cell parameters for all patterns in Figure 22, obtained by indexing of the observed d-spacings using the program CELLKANT (Ersson, 1990), are plotted versus temperature in Figure 23. From the unit-cell parameters that were obtained from the in-situ data it was possible to gain some information about the structural changes that take place during the transformations.

The formation of γ'-Ti(PO4)(H2PO4)·(2-x)H2O (x~1) at 342 K is characterised by a decrease of 4 % in unit-cell volume which is due to a shortening of the b- and c-axis (by 1.1 and 2.9 % respectively), while the parameter that gives the interlayer distance (a⋅sin(β)/2) is close to constant (0.2 % smaller). When the anhydrous phase, β-Ti(PO4)(H2PO4), is formed at 348 K a large decrease (18 %) in unit-cell volume is observed. This decrease is due to the reduction of the interlayer distance from 11.5 Å to 9.2 Å (and with that the interlayer parameter). The length of the b- and c-axis, however, increase slightly. So the conclusion is that the formation of the partially hydrated intermediate phase γ'-Ti(PO4)(H2PO4)·(2-x)H2O (x~1) is characterised by an intralayer contraction rather than an interlayer rearrangement and that the formation of β-Ti(PO4)(H2PO4) (with the elimination of the rest of the crystal water) causes a relaxation of the structure of the layers.

36 SUMMARY AND DISCUSSION OF RESULTS

The transformation from 775.0 750.0 β-Ti(PO4)(H2PO4) to the end product, 725.0 cubic titanium pyrophosphate, was 700.0 3 also studied but mainly on quenched 675.0 Volume (Å ) 650.0 samples. This transformation takes 625.0 600.0 place in two steps. In the first step at 575.0 748 K 0.5 moles of water per formula 24.00 23.00 unit is lost, leading to the formation of 22.00 a layered pyrophosphate 21.00 a-axis × sin(β) (Å)

(Ti(PO4)(H2P2O7)) where adjacent 20.00 layers are joined by P-O-P bridges. It 19.00 18.00 was found that the transformation goes 6.36 through a poorly crystalline 6.34 intermediate with strong anisotropic 6.32 b-axis (Å) broadening of peaks, which has 6.30 interlayer components in their indices. 6.28

Peaks with no interlayer component in 6.26 5.08 their indices do not display anisotropic 5.06 5.04 broadening. It was concluded that the 5.02 structure of the layers is retained 5.00 c-axis × sin(β) (Å) 4.98 during the transformation and that the 4.96 4.94 interlayer distances varies due to 4.92 4.90 partial hydroxyl condensation (see 310 320 330 340 350 360 370 Temperature (K) Figure 6 in Paper II). In the second step at 1023 K the final 0.5 moles of Figure 23. Changes in lattice parameters versus water per formula unit is lost and the temperature for the dehydration process from γ-Ti(PO4)(H2PO4)·2H2O via γ'-Ti(PO4)(H2PO4)·(2-x)H2O end product, cubic titanium (x~1) to β-Ti(PO4)(H2PO4) pyrophosphate is formed.

5.1.4 Structure Determination of τ-Zr(HPO4)2 (Paper IV). As mentioned in Section 4.1, this new phase was discovered during studies of the formation region of α-Zr(HPO4)2⋅H2O and γ-Zr(PO4)(H2PO4)⋅2H2O. The new phase, which we gave the prefix τ, has a very narrow formation region and forms under conditions very close to those for cubic zirconium pyrophosphate, ZrP2O7 (see Figure 1 in Paper IV). The new zirconium hydrogen phosphate phase was characterised using 31P MAS NMR spectroscopy,

37 SUMMARY AND DISCUSSION OF RESULTS

thermogravimetric analysis, infrared spectroscopy and density measurements (details can be found in Paper IV). It was concluded that the formula should be written as: τ-Zr(HPO4)2.

The structure of τ-Zr(HPO4)2 was solved from single-crystal synchrotron X-ray diffraction data recorded on a small crystal (25 × 25 × 50 µm) at beamline X7B, NSLS and high-resolution neutron powder diffraction data collected at the high-resolution neutron powder diffractometer (HRNPD), at the high-flux beam reactor (HFBR), Brookhaven National Laboratory. Further details about the data collection and structure solution can be found in Paper IV. Unit-cell parameters and space group are listed in Table 3. Contrary to the layered titanium and zirconium hydrogen phosphates described in Section 4.1, this phase has a three-dimensional framework structure built from ZrO6 octahedra and HPO4 tetrahedra. In the framework there are channels extending along the c-axis. The OH groups of the hydrogen phosphate groups are pointing into these channels, forming hydrogen bonded spirals (Paper

IV). A polyhedral representation of τ-Zr(HPO4)2 in the a-b plane can be found in Figure 25.

5.1.5 Temperature-Resolved Experiments on τ-Zr(HPO4)2 (Paper IV and V)

Thermogravimetric analysis of τ-Zr(HPO4)2 shows that the compound loses 1 molecule of water per formula unit at 673 K, which corresponds to the condensation of the hydrogen phosphate groups to form pyrophosphate. The results from DSC measurements show that there are two transitions, one reversible at 598 K and one irreversible at 683 K. The recorded temperature-resolved data (beamline X7B) shown in Figure 24 corroborate the existence of the two intermediate phases before the final transition to cubic zirconium pyrophosphate (which is not complete in the figure). Patterns of the two intermediate phases are indicated in the figure.

Figure 24. 3-D representations of the in-situ powder diffraction data versus temperature. The transformation of τ-Zr(HPO4)2 to cubic ZrP2O7 is shown. Patterns of pure ρ-Zr(HPO4)2 and β-ZrP2O7 are indicated in the figure with thicker line width. * indicates cubic ZrP2O7. 38 SUMMARY AND DISCUSSION OF RESULTS

Table 6. Parameters for τ-Zr(HPO4)2 and its high-temperature phases Parameters taken from: a Paper IV; b Paper V; c Khosrovani et al. (1996) (converted from the 3 × 3 × 3 supercell).

a b b c τ-Zr(HPO4)2 ρ-Zr(HPO4)2 β-ZrP2O7 α-ZrP2O7 a (Å) 11.2611(1) 8.1935(2) 8.3127(5) 8.247 b (Å) - 7.7090(2) 6.6389(4) - c (Å) 10.7688(1) 5.4080(1) 5.3407(3) - V (Å3) 1365.62(1) 341.59(2) 294.74(3) 560.90

Space group I41cd (no.110) Pnnm (no. 58) Pnnm (no. 58) Pa3 (no. 205) Temp. (K) Ambient 598 778 Ambient Z 8 2 2 4

RF2 - 0.0706 0.0420 -

Rp 0.030 0.0305 0.0285 -

wRp 0.040 0.0415 0.0367 -

The unit-cell parameters for the two intermediate phases, ρ-Zr(HPO4)2 and β-ZrP2O7, were determined using TREOR90 (Werner et al., 1985). Integrated intensities were extracted using GSAS (Larson and Von Dreele, 2000) and EXTRA (Altomare et al., 1995). The extracted intensities were then used as input for the direct-methods program SIRPOW92 (Cascarano et al., 1992; Altomare et al., 1994), which in both cases produced a suitable starting model. The Rietveld refinements were carried out using GSAS (Larson and Von

Dreele, 2000). Unit-cell parameters, symmetry and other parameters for τ-Zr(HPO4)2,

ρ-Zr(HPO4)2, β-ZrP2O7 and α-ZrP2O7 are summarised in Table 6.

An illustration of the structural changes over the transformation from τ-Zr(HPO4)2 to α-ZrP2O7 is given in Figure 25. In the transformation of τ-Zr(HPO4)2 to ρ-Zr(HPO4)2 at 598 K the main structural changes are the reduction in symmetry and a disorder of the HPO4 tetrahedra into two phosphorous and oxygen sites with 50% probability each. Over the ρ-Zr(HPO4)2 to

β-ZrP2O7 transition at 688 K a condensation takes place at one of the disordered phosphorous sites, while the symmetry remains the same. Finally, cubic α-ZrP2O7 is formed at 1243 K by changing the energetically less favorable four and six ring configuration of polyhedra in β-ZrP2O7 to only five rings (Figure 26). Figure 27 shows an example of neutron powder diffraction data, collected on the E2 instrument at BENSC, HMI, Berlin, during heating in the temperature range 550-650 K on a non-deuterated sample of τ-Zr(HPO4)2. The two phase transitions from τ-Zr(HPO4)2 to

ρ-Zr(HPO4)2 at 590 K and then to β-ZrP2O7 at 630 K can be seen. One can note the significant decrease of the background during the condensation process. The removal of

39 SUMMARY AND DISCUSSION OF RESULTS

598 K

a a b b 688 K

1243 K

a a b b

Figure 25. Polyhedral representations of τ-Zr(HPO4)2 (top left), ρ-Zr(HPO4)2 (top right), β-ZrP2O7 (bottom right) and cubic α-ZrP2O7 seen along [001]. Dark grey octahedra represent ZrO6 and light grey tetrahedra represent HPO4/PO4. The dashed lines in the top right figure indicate where the condensation takes place.

3000

2500

2000

1500

1000 Intensity 500

640 T

e m 620 p

r a 600 t u

r e 580 ( Figure 26. Schematic representation of the 4-, K ) 5- and 6-rings of corner-connected polyhedra 560 38 40 28 30 32 34 36 in β-ZrP2O7. Projected along [100] to the left 22 24 26 and [011] to the right. 2theta Figure 27. In-situ neutron powder diffraction data on the thermal transformations of τ-Zr(HPO4)2.

40 SUMMARY AND DISCUSSION OF RESULTS

water (Zr(HPO4)2 → ZrP2O7 + H2O) causes 172.0 the incoherent scattering contribution to τ-Zr(HPO ) 171.5 4 2 decrease. Some Rietveld refinements were 171.0 performed on the data, but unfortunately the ρ-Zr(HPO4)2 quality of the data was not good enough to 170.5 locate the hydrogen atoms or to gain any 170.0 ) 3 more information about the behaviour of the 169.5 hydrogen atoms during the transformations. 149.0 The thermal expansion coefficient of Volume (Å β-ZrP2O7

τ-Zr(HPO4)2 and its high-temperature phases 147.0 has been determined from the in-situ α-ZrP O synchrotron X-ray powder diffraction data. 145.0 2 7 Figure 28 shows the variation of the unit-cell volume versus temperature, and the resulting 143.0 200 400 600 800 1000 1200 thermal expansion coefficients for Temperature (K) τ-Zr(HPO4)2, ρ-Zr(HPO4)2, β-ZrP2O7 and Figure 28. Unit-cell volume per zirconium atom -7 -1 -5 -1 versus temperature for τ-Zr(HPO4)2 and its high- α-ZrP2O7 became -7.8⋅10 K , -2.6⋅10 K , temperature phases. 4.2⋅10-5 K-1 and 9.2⋅10-6 K-1, respectively.

Thus, τ-Zr(HPO4)2 shows almost zero expansion up to about 500 K and could therefore be useful as component in advanced materials. The strong negative thermal expansion of ρ-

Zr(HPO4)2 would also be of potential use, but the reversibility of its transitions could make it unsuitable in applications.

5.1.6 Pressure-Resolved Experiments on τ-Zr(HPO4)2 (Paper VI).

Two high-pressure transformations were observed for τ-Zr(HPO4)2 in a study at beamline ID30, ESRF, up to 13.8 GPa. Experimental details can be found in Paper VI. The new high- pressure phases were assigned the prefixes ν and ω and the transformations occur below 10 GPa:

1.1GPa 9.5GPa τ − Zr(HPO 4 )2 ⎯⎯→⎯⎯ ν − Zr(HPO 4 )2 ⎯⎯→⎯⎯ ω − Zr(HPO 4 )2

Selected diffraction patterns of τ-Zr(HPO4)2, ν-Zr(HPO4)2 and ω-Zr(HPO4)2 are shown in Figure 29. Indexing of the two new high-pressure phases were performed using the auto- indexing programs DICVOL91 (Boultif and Louër, 1991) and TREOR97 (Werner et al., 1985).

The unit-cell parameters, symmetries and compressibilities of τ-, ν- and ω-Zr(HPO4)2 are summarised in Table 7. Figure 30 shows the change in unit-cell volume versus pressure for

τ-, ν- and ω-Zr(HPO4)2. It can be seen that the τ-ν and ν-ω transitions involve a reduction in

41 SUMMARY AND DISCUSSION OF RESULTS

1400 ω−Zr(HPO4)2 τ−Zr(HPO4)2 12.0 GPa 1300 ) 3

1200 ν−Zr(HPO4)2 ν−Zr(HPO4)2 2.52 GPa 1100 Volume (Å ω−Zr(HPO4)2 τ−Zr(HPO4)2 1000 0.21 GPa

900 2 4 6 8 10 12 14 02468101214 2θ Pressure (GPa)

Figure 30. Unit-cell volume changes versus Figure 29. In-situ diffraction patterns for pressure. Increasing and decreasing pressures τ-Zr(HPO4)2, ν-Zr(HPO4)2 and ω-Zr(HPO4)2. are indicated by open and filled markers, respectively. The unit-cell volumes for ν- and ω-Zr(HPO4)2.have been multifplied by 2 for easy comparison with τ-Zr(HPO4)2

Table 7. Parameters for τ-Zr(HPO4)2 and its high-pressure phases. Parameters taken from a Paper IV; b Paper VI.

a b b τ-Zr(HPO4)2 ν-Zr(HPO4)2 ω-Zr(HPO4)2 Crystallographic data Pressure (GPa) Ambient 2.52(3) 10.73(3) a-axis (Å) 11.2611(1) 7.61374(13) 7.7226(7) b-axis (Å) - - 6.3941(8) c-axis (Å) 10.7688(1) 10.4266(3) 10.0056(9) Volume (Å3) 1365.62(1) 604.418(18) 494.07(10)

Space Group I41cd P41212 or P43212 Orthorhombic Z 8 4 - Compressibility (10-2GPa-1)

βV 1.48 1.99 0.77

βa 0.55 1.09 0.37

βb - - 0.09

βc 0.40 0.74 0.26

unit-cell volume of about 6 and 8 %, respectively. From the values for linear volume -2 -1 compressibility in Table 7 one can note that ν-Zr(HPO4)2 (βV = 1.99⋅10 GPa ) is more -2 -1 compressible than τ-Zr(HPO4)2 (βV = 1.48⋅10 GPa ), while ω-Zr(HPO4)2 is considerable -2 -1 harder (βV = 0.77⋅10 GPa ). The unit-cell volumes for τ- and ν-Zr(HPO4)2 are from Rietveld refinements of the structures, while the volumes for ω-Zr(HPO4)2 come from Le Bail profile

42 SUMMARY AND DISCUSSION OF RESULTS

fitting. The τ-ν transition shows hysteresis but was not completely reversible within the time of the experiment. The ν-ω transition appears to be reversible.

Space-group assignment could be made for ν-Zr(HPO4)2 but it was not possible to distinguish between the two enantiomorphic space group symmetries P41212 or P43212. The data quality for ω-Zr(HPO4)2 was too poor for a reliable space-group assignment and further structural investigations.

The structure of ν-Zr(HPO4)2 was solved by transforming the structural coordinates of

τ-Zr(HPO4)2 to the new space-group symmetry and refined using GSAS (Larson and von Dreele, 2000). Fractional coordinates as well as selected bond distances and angles can be found in Paper VI. The new structure is very similar to the structure of τ-Zr(HPO4)2, with tilting and distortion of the ZrO6 and PO4 polyhedra to accommodate the increased pressure - but with a significant change in hydrogen-bonding scheme. The hydrogen bonding has changed from spirals in both anti-clockwise and clockwise sense along the c-axis of τ-Zr(HPO4)2 to spirals that turn only in one direction when propagating along the c-axis of ν-Zr(HPO4)2 (Figure 31). This change of hydrogen bonding pattern is possibly due to the smaller void a vailable to the oxygen and hydrogen atoms at higher pressures.

1.1 GPa

b a b

Figure 31. Polyhedral representation of τ-Zr(HPO4)2 and ν-Zr(HPO4)2 along the c-axis. Dark grey octahedra represent ZrO6 and light grey tetrahedra represent HPO4.

During compression the metal oxygen bond distances do not show large changes neither for

τ- nor ν-Zr(HPO4)2. The changes in bond distances, however, are more linear after the τ-ν transition, indicating that the oxygen movements have become more restricted in

ν-Zr(HPO4)2. Calculations of ZrO6 and PO4 volumes for all data on τ- and ν-Zr(HPO4)2 showed that there is no large changes in polyhedral volumes during compression. However, large changes (10-20°) are observed for the Zr-O-P angles up to the τ-ν transition, while

43 SUMMARY AND DISCUSSION OF RESULTS

smaller (1-5°) changes occur after the transition. This is consistent with a picture of fairly rigid polyhedra that tilt to accommodate increasing pressure.

In summary, this part of the thesis described a wide range of investigations on phosphates of IV IV the type M (HPO4)2⋅nH2O (M = Ti, Zr) comprising the determination of the activation energy for the crystallisation of α-Ti(HPO4)2⋅H2O, the study of pressure effects on this crystallisation, the study of the 1,6-hexanediamine intercalation in α-Zr(HPO4)2⋅H2O, the detection of a new intermediate high-temperature phase γ'-Ti(PO4)(H2PO4)⋅(2-x)H2O stable between 323 and

373 K, and the structure determination of novel τ-Zr(HPO4)2 featuring a 3-D framework structure. A high-temperature in-situ examination of the latter compound revealed two new high-temperature phases, ρ-Zr(HPO4)2 and β-ZrP2O7. Generally, high-temperature IV IV transformations of M (HPO4)2⋅nH2O (M = Ti, Zr) materials end with complete dehydration IV and/or dehydroxylation leading to formation of cubic pyrophosphate phases M P2O7 with 3-D framework structures. In view of the high-pressure phase transformations found for

τ-Zr(HPO4)2 it was of interest to investigate cubic ZrP2O7 at elevated pressures. Additionally, also studies of TiP2O7 and ZrV2O7 were performed. The latter compound is a negative thermal expansion material and it has been shown by Speedy (1996) that materials displaying negative thermal expansion may also undergo pressure amorphisation. Thus, a comparative investigation of the high-pressure behaviour of these structurally very similar compounds appeared to be very interesting.

IV IV 5.2 MATERIALS WITH THE GENERAL FORMULA M X2O7 (M = Ti, Zr; X = P, V).

TiP2O7, ZrP2O7 and ZrV2O7 are members of a large

IV V family of cubic M X 2 O7 (M = Si, Ge, Sn, Pb, Ti, Zr, Hf, Mo.....; X = P, V, As) compounds (Khosrovani et al., 1996 and references therein). The ideal framework structure is built of corner connected MO6 octahedra and linear X2O7 (pyrophosphate, pyrovanadate, pyroarsenate) units (Figure 32). The 'parent' structure type of these phases, ZrP2O7, was described by Levi and Peyronel in 1935. In the ideal parent structure

(space-group symmetry Pa3 , Z = 4) the X O units Figure 32. Ideal structure for MX2O7 2 7 compounds, consisting of corner sharing fall on the 3-fold axis with the bridging oxygen on an MO6 octahedra and XO4 tetrahedra.

44 SUMMARY AND DISCUSSION OF RESULTS

inversion center, constraining the X-O-X angles to 180°. This leads to an unreasonably short

X-O-X bridging bond in the X2O7 units, built by two connected XO4 tetrahedra. Linear X-O-X bonds are furthermore energetically less favorable than bent X-O-X bond angles of approximately 145° (Cruickshank, 1961). Linear X2O7 units in the MX2O7 family are partially or completely avoided by distortion of the ideal cubic structure, resulting in a 3 × 3 × 3 superstructure (space-group symmetry Pa3 , Z = 108). The expansion to the 3 × 3 × 3 superstructure removes 96 of the 108 X2O7 groups of the unit cell from the 3-fold axis, allowing them to adopt X-O-X angles less than 180° (Norberg et al., 2001). The first example of a 3 × 3 × 3 superstructure was published in 1963 by Völlenkle et al. for GeP2O7. Similar superstructures have since been reported for e.g. SiP2O7 (Tillmans et al., 1973), TiP2O7

(Sanz et al., 1997; Helluy et al., 2000; Norberg et al., 2001), ZrP2O7 (Hagman and

Kirkegaard, 1969; Chaunac, 1971; Khosrovani et al., 1996) and ZrV2O7 (Khosrovani et al., 1997; Evans et al., 1998; Withers et al., 1998). The assumption that the 3 × 3 × 3 superstructure at low temperature is cubic for all MX2O7 compounds has recently been 31 questioned. The 'true' symmetry of ZrP2O7 has by P solid-state NMR (King et al., 2001) and electron diffraction (Withers et al., 2001) been shown to be the orthorhombic Pbca. Generally, materials expand when heated, i.e. they have a positive coefficient of thermal -5 -1 expansion. TiP2O7 displays positive thermal expansion, 1.1×10 K (Taylor, 1988), in the temperature range from 298 to 1273 K (Figure 33, 8.84

8.82 bottom). The thermal expansion of ZrP2O7 might ZrV2O7 be considered normal from room temperature to 8.80 8.78 about 560 K (Figure 33, middle). At this 8.76 temperature it undergoes a transition to the 8.748.30 simple cubic structure, followed by low positive 8.28 ZrP2O7 thermal expansion (from 563 to 883 K it is about 8.26 3.5 × 10-6 K-1) (Khosrovani et al., 1996). 8.24 8.00 There has been a considerable interest in 7.98 materials that have the unusual property of 7.96 contracting when heated, i.e. materials with a 7.94 TiP O negative coefficient of thermal expansion. 7.92 2 7 Negative thermal expansion materials are of 7.90 7.88 interest for use in composites and substrates to 200 300 400 500 600 700 800 900 1000 1100 1200 1300 counterbalance the positive thermal expansion of Temperature (K) other materials. Materials with zero (or close to Figure 33. Thermal expansion behaviour for zero) thermal expansion are used for various TiP2O7, ZrP2O7 and ZrV2O7. Data taken from: Taylor (1988), Khosrovani et al. (1996) applications in optics, electronics and other fields and Withers et al. (1998 and 2001),

45 SUMMARY AND DISCUSSION OF RESULTS

where exact positioning of parts is crucial. As pressure-induced phase transformations are likely to degrade the performance of composites, it is desirable to fully characterise the high- pressure behaviour of negative thermal expansion materials. A good understanding can only be gained by in-situ studies. Several members of the MX2O7 family show low or even negative coefficients of thermal expansion. In MX2O7 materials the tendency to exhibit negative thermal expansion behaviour increases as the unit-cell edge increases. The thermal expansion coefficient actually becomes negative in the cases of e.g. ZrV2O7, HfV2O7, ThP2O7 and UP2O7 (Taylor, 1988; Khosrovani et al., 1996; Sleight, 1998).

ZrV2O7 undergoes two phase transitions at 350 and 375 K. The first transition leads to an incommensurately modulated phase, recently characterised by electron diffraction (Withers et al., 1998). The second transition at around 375 K leads to the simple cubic cell. Below 375

K ZrV2O7 displays positive thermal expansion (Figure 33, top) which can be related to an 'unfolding' of the polyhedra while gradually approaching a high symmetric structure with 180° V-O-V angles. Above 375 K and all the way up to the decomposition temperature of about 1073 K the compound shows strong and isotropic negative thermal expansion (CTE = - 7.1×10-6 K-1 (400-500K)) (Korthuis et al., 1995; Khosrovani et al. 1997; Evans et al., 1999). Explanations for the strong negative thermal expansion properties of ZrV2O7 above 375 K have been given by Korthuis et al. (1995), Pryde et al. (1996), Sleight (1998) and recently by Evans

(1999). Increasing temperatures will cause the 375K-1073 K

VO4 tetrahedra in ZrV2O7 to rotate and simultaneously diminish the distance between the centres of the tetrahedra. This will give a reduction in volume (Figure 34). The gain in energy by bending the V-O-V angle away from 180° at increasing temperatures is balanced by the stiffness of the ZrO6 octahedra. In the case of Figure 34. Illustration of linked VO4 ZrP2O7 the size of the XO4 tetrahedra decreases tetrahedra, rotating to induce negative thermal expansion. Dark and light circles and the effect of rotations becomes smaller, thus indicate vanadium and oxygen atoms, resulting in positive thermal expansion. respectively.

5.2.1 Pressure-Resolved Experiments on TiP2O7, ZrP2O7 and ZrV2O7 (Paper VII).

Pressure-resolved synchrotron X-ray studies of TiP2O7, ZrP2O7 and ZrV2O7 have been performed. The purpose was to investigate if these three compounds, with similar structures but different thermal expansion coefficients, would show different behaviour under pressure.

46 SUMMARY AND DISCUSSION OF RESULTS

Of specific interest was the possible link between negative thermal expansion and 1.00 pressure amorphisation, reported by Speedy 0.95

(1996). 0.90 0 Synchrotron powder diffraction experiments 0.85 V/V were performed at beamline ID30 and ID9 0.80

(ESRF) up to maximum pressures of 40.3, 0.75

20.5 and 6.4 GPa for TiP2O7, ZrP2O7 and 0.70

0 5 10 15 20 25 30 35 40 45 ZrV2O7, respectively. The experimental Pressure (GPa) details can be found in Paper VII. As can be seen in Figure 35, the behaviour of the Figure 35. Change in unit-cell volume versus pressure for TiP2O7 (circles), ZrP2O7 (squares) and negative thermal expansion material ZrV2O7 ZrV2O7 (triangles). The volume data were normalised with respect to the reported unit-cell volumes at differs from that of the positive thermal ambient conditions. Solid lines represent fits of the Vinet equation of state to the volume data. expansion materials TiP2O7 and ZrP2O7. The two latter compounds compress smoothly up to the highest measured pressure. For ZrV2O7 the situation is different, it transforms from cubic symmetry to pseudo-tetragonal (orthorhombic) symmetry at 1.38-1.72 GPa with splitting of a majority of the peaks, and finally it becomes X-ray amorphous at 4 GPa. The findings for TiP2O7 are corroborated by recent infrared and Raman spectroscopy studies performed in collaboration with the research group of Prof. M. B. Kruger (University of Missouri). They showed smooth compression of TiP2O7 up to 49.4 GPa (Lipinska-Kalita et al., 2003). In a further collaboration with Kruger's group, the phase transition pressure and amorphisation of ZrV2O7 were confirmed by Raman and infrared spectroscopy up to 4.5 GPa (Goedken et al. 2003).

The major peaks of the new high-pressure phase, β-ZrV2O7, could be indexed using TREOR97 (Werner et al., 1985) and DICVOL91 (Boultif and Louër, 1991), resulting in a small tetragonal cell (a = 8.3075 Å, c = 8.4029 Å) with close relation to the original small cubic cell (a = 8.7653 Å). Possible space groups are P4212 or P 421m (0k0: k = 2n being the only reflection condition). However, the high-pressure phase also shows superstructure peaks (see Figure 36), which were analysed using SUPERCELL (Rodriguez-Carvajal, 1998) and CELLKANT (Ersson, 1990). The most probable solution obtained from both programs was a 2 × 3 × 3 supercell of the small tetragonal cell. The parameters of the resulting orthorhombic unit cell were: a = 16.644 Å, b = 24.914 Å and c = 25.229 Å. Possible space- group symmetries are (no special reflection conditions in the indexed pattern): P222, Pmm2, Pmmm, Pm2m or P2mm. The change in unit-cell axes versus pressure over the phase transition at 1.5 GPa is shown in Figure 37.

47 SUMMARY AND DISCUSSION OF RESULTS

200 201 2.97 GPa 102 211 002 112 8.9 111 202 311 220 113 222 8.8 a (α)

8.7 200 0.15 GPa 8.6 a (β) 210 211 311 8.5

8.4 220 c (β) 111 Unit-cell parameters (A) 222 8.3 302 321 8.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Pressure (GPa) 5 6 7 8 9 10 11 2θ° (λ = 0.4512Å) Figure 37. Change in unit-cell parameters versus pressure for ZrV2O7. Filled and unfilled circles Figure 36. Indexed patterns of cubic α-ZrV2O7 at represent data collected at ID9 and ID30, 0.15 GPa and the new pseudo-tetragonal high- respectively. pressure phase, β-ZrV2O7, at 2.97 GPa. The indices are for the small cubic and tetragonal unit cells.

The differences in unit-cell volume compressibility between TiP2O7, ZrP2O7 and ZrV2O7 are best analysed using an EOS (see Section 3.4). In Figure 35, the solid lines were fitted to the volume data using the Vinet EOS, with resulting bulk modulus of 42, 39, 21, and 17 GPa for

TiP2O7, ZrP2O7, α- and β-ZrV2O7, respectively. To a first approximation these differences in bulk modulus can be explained by the atomic sizes in the respective compound. The vanadium atom is larger (and more compressible) than phosphorous, which makes ZrV2O7 more compressible than ZrP2O7 and zirconium is larger than titanium rendering TiP2O7 the least compressible material in this series.

In summary, both TiP2O7 and ZrP2O7 compress to very high pressures, while ZrV2O7 becomes amorphous at pressures above 4 GPa. The pressure amorphisation of ZrV2O7 is linked to its negative thermal expansion properties because flexible V-O-V bond angles, such as the ones described in Figure 34, may vary during compression without breaking bonds (Speedy, 1996). Thus, a nucleation can occur under pressure where the polyhedral framework of ZrV2O7 crystallises in many structural configurations, rendering the material more or less amorphous. Another compound that displays negative thermal expansion is

ZrMo2O8, which inspired to perform the high-pressure investigations below.

5.3 MOLYBDATES WITH THE FORMULA ZrMo2O8.

Until very recently, two different polymorphs of ZrMo2O8 were known: A monoclinic low- temperature phase (β-ZrMo2O8: a = 11.433 Å, b = 7.935 Å, c = 7.460 Å, β = 122.32°, space

48 SUMMARY AND DISCUSSION OF RESULTS

group C2/c, Z = 4), which transforms reversibly into a trigonal high-temperature form

(α-ZrMo2O8: a = 10.1409 Å, c = 11.7097 Å, space group P 3c , Z = 6) at temperatures around

952 K (Auray et al., 1986; Kletsova et al., 1989). Recently, a third form, cubic γ-ZrMo2O8 (a = 9.1304 Å, space group Pa3 , Z = 4) was prepared and studied extensively by Lind and co- workers (Lind et al., 1998, 2001a, 2001b and 2002). This cubic polymorph displays isotropic negative thermal expansion and is related to the much-studied ZrW2O8 (Mary et al., 1996;

Evans et al., 1996; Perottoni and Jornada, 1998) and HfW2O8 (Evans et al., 1996). Cubic

ZrMo2O8 is metastable and transforms readily to the trigonal polymorph when heated to temperatures over 663 K. The origin of the negative thermal expansion in ZrW2O8, HfW2O8 and ZrMo2O8 is different from the one described earlier for

ZrV2O7. It has been shown by Mary et al. (1996) and Pryde et al. (1996) that the negative thermal expansion in ZrW2O8 can be attributed to low-frequency phonon modes. A phonon mode is a cooperative vibrational mode of all atoms in a solid. If a rocking motion of the polyhedra is possible without distortions of polyhedra, or interference with other polyhedra (Figure 38), a low frequency phonon mode exists that can be exited even at low temperatures. These modes are also called 'rigid unit Temperature modes', or RUMs, as the polyhedra remain mostly undistorted (i.e. rigid). Comprehensive studies of the high-pressure properties of

ZrW2O8 have been reported, showing a cubic to orthorhombic transition a 0.2 GPa and pressure induced amorphisation above 1.5 GPa (Evans et al., 1996; Perottoni and da Jornada,1998; Jorgensen et al. 1999). A link between negative thermal expansion and pressure amorphisation has been reported by Speedy (1996). Reports of high-pressure studies Figure 38. Schematic on cubic γ-ZrMo2O8 have been published by Lind et al. (1998 representation of how rigid polyhedra in a 2-D perovskite and 2001b). These reports inspired to do pressure-resolved can undergo low energy volume reducing oscillations. experiments on trigonal α-ZrMo2O8, with the aim to investigate phase stability and possible pressure amorphisation.

5.3.1 Pressure-Resolved Experiments on Trigonal α-ZrMo2O8 (Paper VIII and IX).

Trigonal α-ZrMo2O8 displays anisotropic thermal expansion properties, with a slightly negative expansion for the a-axis and strongly positive for the c-axis (Mittal et al., 1999). The structure of α-ZrMo2O8 was originally solved from single-crystal data (Auray et al., 1986;

49 SUMMARY AND DISCUSSION OF RESULTS

Serezhkin et al., 1987). Unit-cell parameters are given in Table 8. α-ZrMo2O8 consists of a

2-D network with layers perpendicular to the c-axis, which are formed from ZrO6 octahedra linked together by MoO4 tetrahedra. Three of the four oxygen atoms of the molybdate tetrahedra are linked to different zirconium atoms. The fourth oxygen atom points into the interlayer region. α-ZrMo2O8 has electrically neutral layers bonded together by van der Waals forces between the oxygen pointing into the interlayer space and its closest neighbours. Polyhedral representations of the structure are shown in Figure 39.

Pressure-resolved X-ray synchrotron studies on α-ZrMo2O8 were performed at ID30, ESRF. The experimental details can be found in Paper IX. The experiments showed that trigonal

α-ZrMo2O8 undergoes two phase transitions in the investigated pressure range up to 9.5

GPa. At 1.1 GPa α-ZrMo2O8 transforms to the monoclinic high-pressure phase δ-ZrMo2O8. A second phase transition from the δ phase to a triclinic ε-ZrMo2O8 phase takes place in the pressure range 2 - 2.5 GPa. In connection to these experiments, Raman, IR spectroscopy and optical-absorption results, obtained in collaboration with Professor Kruger (University of Missouri), have confirmed the phase-transition pressures (Muthu et al., 2002). The unit-cell parameters for the δ phase were determined using the auto-indexing program DICVOL91 (Boultif and Louër, 1991). Systematic absences in the monoclinic pattern (h00 (h = 2n + 1), 0k0 (k = 2n + 1), hk0 (h + k = 2n + 1) and h0l (h = 2n + 1)) indicated three possible space groups (C2, Cm or C2/m). In the absence of any other indications the space group with the highest symmetry, C2/m, was chosen. The choice of space group was later corroborated by the structure solution and refinements. Integrated intensities were extracted using the EXTRA module in EXPO (Altomare et al., 1999) and a structural model was obtained using direct methods in the SIRPOW module of the same program. Rietveld refinements were performed using GSAS (Larson and Von Dreele, 2000). Unit-cell parameters, space group and final R-values for the refinement of α-ZrMo2O8 and δ-ZrMo2O8 are given in Table 8.

Indexing the second high-pressure phase (ε-ZrMo2O8) proved not to be straightforward. The auto-indexing programs TREOR97 (Werner et al., 1985), DICVOL91 (Boultif and Louër, 1991), KOHL (Kohlbeck and Hörl, 1978) and LZON (Shirley and Louër, 1978) linked in the CRYSFIRE suite (Shirley, 2000) were tried before a reasonable triclinic unit cell was found. The triclinic solution has similar dimensions to those found for the δ phase (Table 8). It was not possible to distinguish between the two possible space-group symmetries P1 and P 1 . Rietveld refinements were performed for 15 pressure points up to the second phase transition at 2.5 GPa. The patterns collected above 2.5 GPa were fitted using the Le Bail method in GSAS. The change in unit-cell parameters obtained from the Rietveld refinements versus pressure are plotted in Figure 40 and 41. The figures show that the variation of the

50 SUMMARY AND DISCUSSION OF RESULTS

Table 8. Parameters for α-ZrMo2O8 and its high-pressure phases Parameters taken from Paper VIII and IX.

α-ZrMo2O8 δ-ZrMo2O8 ε-ZrMo2O8 Crystallographic data a (Å) 10.14778(9) 9.7966(3) 5.4268(7) b (Å) - 5.98422(17) 10.255(2) c (Å) 11.6780(2) 5.28547(18) 5.1234(6) α (°) 90 90 97.155(12) β (°) 90 93.069(2) 93.394(9) γ (°) 120 90 101.450(13) V (Å3) 1041.46(2) 309.42(2) 276.25(8) Space group P3c (no. 163) C2/m (no. 12) P1or P 1 (no. 1 or 2) Z 6 2 - Pressure (GPa) 0.32 1.64 2.65

RF2 0.033 0.046 -

Rp 0.006 0.006 -

wRp 0.009 0.010 -

Compressibility (10-2GPa-1)

βV 5.07 4.24 1.10

βa 0.34 1.50 0.38

βb - -0.32 0.35

βc 4.26 3.08 0.52 unit-cell parameters is linear within the experimental error. Therefore the compressibility of the various unit-cell parameters could be determined using the equation given in Section 3.4. The results are given in Table 8. Fractional coordinates, bond distances and angles as well as the difference profile plot for the Rietveld refinement can be found in Paper IX. The volume compressibilities of α-ZrMo2O8 and δ-ZrMo2O8 are 4-5 times higher than the value for the triclinic ε phase. In fact, the compressibility for ε-ZrMo2O8 is close to the value reported for α-ZrW2O8 (Jorgensen et al., 1999). The a-axis in the α-phase has a quite low compressibility and splits into the a- and b-axis of the δ phase at the transition. After the transition the a-axis is further compressed while the b-axis expands. The compressibility of the c-axis is larger than the other axes both before and after the transition. This is easily explained when one considers that both the α- and δ- phases consist of layers in the ab plane. This means that most of the pressure increase is accommodated by a decrease of the interlayer distance (Figure 39).

Before the transition at 1.1 GPa, α-ZrMo2O8 accommodates the increased pressure by displacive movements of oxygen, thereby tilting and distorting the ZrO6 and MoO4 polyhedra

51 SUMMARY AND DISCUSSION OF RESULTS

1.1 GPa

a a b b

1.1 GPa

b a c a

Figure 39. Polyhedral representations of α-ZrMo2O8 on the left and δ-ZrMo2O8 on the right. Dark octahedra represent ZrO6 and light tetrahedra represent MoO4.

12.0 1050 α 11.6 1000 c(α) δ 11.2 ) 950 3

900 10.8 c(δ) Volume (Å 850 Axis Length (Å) 10.4 a(α) ε b(δ) 800 10.0 a(δ)

750 9.6 012345678910 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (GPa) Pressure (GPa) Figure 41. Change in unit-cell parameters Figure 40. Change in volume versus pressure versus pressure for α-ZrMo2O8. The for α-ZrMo2O8. The unit-cell volume data for δ- monoclinic axes of δ-ZrMo2O8 have been and ε-ZrMo2O8 have been multiplied by 3 for transformed according to b = 3 ⋅ b and easy comparison with α-ZrMo2O8. Solid lines α δ are least-squares fits to the volume data. cα = 2⋅sinβδ⋅cδ for comparison with α-ZrMo2O8. Solid lines are least-square fits to the unit-cell data.

52 SUMMARY AND DISCUSSION OF RESULTS

(Figure 39). The driving force for these structural changes before and over the α-δ phase transition is likely to be packing effects. The compressible anions (oxygen) achieve a more symmetrical arrangement and effective packing in δ-ZrMo2O8 as compared to the less effective packing in α-ZrMo2O8. Thus, bonding distances, angles and polyhedral volumes

(ZrO6 and MoO4), which display a fairly complex behaviour before the transition, become almost linear after the transition.

CONCLUDING REMARKS

6. CONCLUDING REMARKS

IV IV The studied cases of layer and framework structures, M (HPO4)2⋅nH2O (M = Ti, Zr), IV IV M X2O7 (M = Ti, Zr; X = P, V) and ZrMo2O8, show that in-situ studies at elevated temperatures and pressures, as opposed to studies of quenched samples, are crucial for the understanding of phase stability and structural relations. Especially, properties such as thermal expansion and pressure-induced contraction of materials are necessary to study at experimental conditions using in-situ techniques. It is also evident that any phase involved in a reversible phase transition at high temperature or pressure cannot be detected from samples quenched to ambient conditions.

As an example one can look at τ-Zr(HPO4)2: It has reversible phase transitions both with increased temperature and pressure. In the transformation of τ-Zr(HPO4)2 to α-ZrP2O7, the first intermediate, ρ-Zr(HPO4)2, would be impossible to detect without in-situ methods.

Similarly, the second high-pressure phase, ω-Zr(HPO4)2, would have been missed if a study had been performed on quenched samples. The presented in-situ X-ray powder diffraction experiments have been very fruitful in the collection of data for the simultaneous determination of phase stability, symmetry and structural changes, as well as thermal expansion and compressibility. From a technical point of view, it seems that the use of high-flux synchrotron radiation is necessary in time-resolved experiments, while for static structural information lab-source data and neutron diffraction data are valuable. Otherwise, it must be stressed that it is the combination of data from different sources like NMR, TG, DSC, as well as neutron and X-ray diffraction that makes it possible to obtain the most reliable determination of the properties of phases and structures.

Future projects for the investigated type of compounds would be to perform in-situ experiments on similar chemical systems as the ones studied here, to obtain a larger amount of data. This would facilitate a more complete analysis of the chemical reactivity and reaction kinetics for these systems. The high-pressure experiments can be improved by development of simultaneously heating and pressurising samples in the DAC - a technique that is complicated, not only because of the difficulty to precisely determine the temperature in the DAC, but also because calibration of pressure at elevated temperatures can be difficult.

There are also a number of high-temperature phases (e.g. γ'-Ti(PO4)(H2PO4)⋅(2-x)H2O,

Ti(PO4)(H2P2O7)0.5) and high-pressure phases (e.g. ω-Zr(HPO4)2, ε-ZrMo2O8 ) in the investigated systems for which the structure should be determined.

ACKNOWLEDGMENTS

7. ACKNOWLEDGMENTS

First of all I would like to thank my supervisors Professor Rolf Norrestam and Dr. Ulrich Häussermann for giving me the opportunity to finish this thesis at the Structural Chemistry Department, Stockholm University. I am also grateful for their comments and criticism of this manuscript.

I also want to thank Professor Poul Norby, Oslo University, for his supervision and collaboration throughout the last decade and for introducing me to world of synchrotron radiation.

Furthermore, I would like to thank the beamline managers, Dr. Jon Hanson (X7B, NSLS) and Dr. Andy Fitch (BM16, ESRF), for their invaluable help with all experimental problems at the beamlines.

Finally, I wish to thank my family (especially Stefan, Sofia and my parents) for their patience and support throughout my studies. It took a long time, but now it is finally finished!

REFERENCES

8. REFERENCES Adachi, T.; Muromura, T.; Takeishi, H. and Yamamoto, T.: Metallic phases precipitated in

UO2 fuel II. Insoluble residue in simulated fuel. J. Nucl. Mater., 160 (1988) 81-87. Alberti, G.; Cardini-Galli, P.; Costantino, U. and Torracca, E.: Crystalline insoluble salts of polybasic metals - I. Ion-exchange properties of crystalline titanium phosphate. J. Inorg. Nucl. Chem., 29 (1967) 571-578. Alberti, G.; Casciola, M.; Costantino, U. and Vivani, R.: Layered and Pillared Metal(IV) Phosphates and Phosphonates. Adv. Mater., 8 (1996) 291-303. Alberti, G. and Costantino, U.: Layered Solids and Their Intercalation Chemistry in Comprehensive Supramolecular Chemistry, Volume 7 (Solid-State Supramolecular Chemistry: Two- and Three- Dimensional Inorganic Networks), pp. 1-23. Volume Editors: G. Alberti and T. Bein. Pergamon Press, 1996. Albertsson, J.; Oskarsson, Å.; Tellgren, R. and Thomas, J. O.: Inorganic Ion Exchangers. 10.

A Neutron Powder Diffraction Study of the Hydrogen Bond Geometry in α-Zr(HPO4)2⋅H2O. A Model for the Ion Exchange. J. Phys. Chem., 81 (1977) 1574-1578. Altarelli, M.; Schlachter, F. and Cross, J.: Making Ultrabright X-ray. Radiation a billion times brighter than the sun's is illuminating a host of scientific and technical phenomena. Scientific American, December 1998, 66-73. Altomare, A.; Cascarano, G.; Giacovazzo, C.; Guagliardi, A.; Burla, M. C.; Polidori, G. and Camalli, M.: SIRPOW.92 - a program for automatic solution of crystal structures by direct methods optimized for powder data. J. Appl. Cryst., 27 (1994) 435-436. Altomare, A.; Burla, M. C.; Cascarano, G.; Giacovazzo, C.; Guagliardi, A.; Moliterni, A. G. G. and Polidori, G.: EXTRA: a program for extracting structure-factor amplitudes from powder diffraction data. J. Appl. Cryst., 28 (1995) 842-846. Altomare, A.; Burla, M. C.; Camalli, M.; Carrozzini, B.; Cascarano, G. L.; Giacovazzo, C.; Guagliardi, A.; Moliterni, A. G. G.; Polidori, G. and Rizzi, R.: EXPO: a program for full powder pattern decomposition and crystal structure solution. J. Appl. Cryst., 32 (1999) 339-340. Anderson, O. L.: Equations of state of solids for geophysics and ceramic science. Oxford University Press, 1995. Auray, M.; Quarton, M. and Tarte, P.: New Structure of High-Temperature Zirconium Molybdate. Acta Cryst., C42 (1986) 257-259. IV IV Auray, M.; Quarton, M. and Tarte, P.: Crystal Data for Two Molybdates M (MoO4)2 With M = Zr, Hf. Powder Diffraction, 2 (1987) 36-38.

Auray, M. and Quarton, M.: Revised Crystal Data of Zr(MoO4)2, L. T. Form. Powder Diffraction, 4 (1989) 29-30.

59 REFERENCES

Ballon, J.; Comparat, V. and Pouxe, J.: The blade chamber: A solution for curved gaseous detectors. Nucl. Instr. Meth. Phys. Res. 217 (1983) 213-216. Bassett, W. A.; Shen, A. H.; Bucknum, M. and Chou, I-M.: A new diamond anvil cell for hydrothermal studies to 2.5 GPa and from -190 to 1200 °C. Rev. Sci. Instrum., 64 (1993) 2340-2345. Birch, F.: Finite Elastic Strain of Cubic Crystals. Phys. Rev., 71 (1947) 809-824. Boultif, A. and Louër D.: Indexing of Powder Diffraction Patterns for Low-Symmetry Lattices by the Successive Dichotomy Method. J. Appl. Cryst., 24 (1991) 987-993. Bruque, S.; Aranda, M. A. G.; Losilla, E. R.; Olivera-Pastor, P. and Maireles-Torres, P.: Synthesis Optimization and Crystal Structures of Layered Metal(IV) Hydrogen

Phosphates, α-M(HPO4)2⋅H2O (M = Ti, Sn, Pb). Inorg. Chem., 34 (1995) 893-899. Caglioti, G.; Paoletti, A. and Ricci, F. P.: Choice of Collimators for a Crystal Spectrometer for Neutron Diffraction. Nucl. Instrum., 3 (1958) 223-228. Cascarano, G.; Favia, L. and Giacovazzo, C.: SIRPOW.91 - a direct-methods package optimized for powder data. J. Appl. Cryst., 25 (1992) 310-317. Casciola, M.; Costantino, U.; Di Croce, L. and Marmottini, F.: Intercalation of α,ω- Alkyldiamines in Layered α-Zirconium Phosphate and the Inclusion Behaviour of Some of the Intercalates Obtained. J. Incl. Phenom., 6 (1988) 291-306. Chaunac, M.: Étude cristallographique du pyrophosphate de zirconium. Bull. Soc. Chim. Fr., (1971) 424-429. Cheetham, A. K.; Férey, G. and Loiseau, T.: Open-Framework Inorganic Materials. Angew. Chem. Int. Ed., 38 (1999) 3268-3292. Chervin, J. C.; Canny, B.; Besson, J. M. and Pruzan, Ph.: A diamond anvil cell for IR microscopy. Rev. Sci. Instrum., 66 (1995) 2595-2598. Ciraolo, M. F.; Hanson, J. C.; Norby, P. and Grey, C. P.: An In-situ X-ray Powder Diffraction Study of the Adsorption of Hydrofluorocarbons in Zeolites. J. Phys. Chem. B, 105 (2001) 2604-2611. Clausen, B. S.; Steffensen, G.; Fabius, B.; Villadsen, J.; Feidenhans'l, R. and Topsoe, H.: In situ cell for combined XRD and on-line catalysis tests: studies of copper-based water gas shift and methanol catalysts. J. Catal., 132 (1991) 524-535. Clayden, N. J.: Solid-state Nuclear Magnetic Resonance Spectroscopic Study of γ-Zirconium Phosphate. J. Chem. Soc., Dalton Trans., (1987) 1877-1881. Clearfield, A. and Stynes, J. A.: The Preparation of Crystalline Zirconium Phosphate and Some Observations on its Ion Exchange Behaviour. J. Inorg. Nucl. Chem., 26 (1964) 117- 129.

60 REFERENCES

Clearfield, A.; Blessing, R. H. and Stynes, J. A.: New Crystalline Phases of Zirconium Phosphate Possessing Ion-Exchange Properties. J. Inorg. Nucl. Chem., 30 (1968) 2249- 2258. Clearfield, A. and Smith, G. D.: The Crystallography and Structure of α-Zirconium Bis(monohydrogen orthophosphate) Monohydrate. Inorg. Chem., 8 (1969) 431-436. Clearfield, A. and Blessing, R. H.: The Preparation and Crystal Structure of a Basic Zirconium Molybdate and its Relationship to Ion Exchange Gels. J. Inorg. Nucl. Chem., 34 (1972) 2643-2663. Clearfield, A. and Costantino, U.: Layered Metal Phosphates and Their Intercalation Chemistry in Comprehensive Supramolecular Chemistry, Volume 7 (Solid-State Supramolecular Chemistry: Two- and Three- Dimensional Inorganic Networks), pp. 107- 149. Volume Editors: G. Alberti and T. Bein. Pergamon Press, 1996. Convert, P.; Hansen, T.; Oed, A. and Torregrossa, J.: D20 high-flux two-axis neutron diffractometer. Physica B, 241-243 (1998) 195-197. Convert, P.; Hansen, T. and Torregrossa, J.: The High Intensity Two Axis Neutron Diffractrometer D20 First Results. Mater. Sci. Forum, 321-324 (2000) 314-319. Cruickshank, D. W. J.: The Rôle of 3d-Orbitals in π-Bonds between (a) Silicon, Phosphorus, Sulphur, or Chlorine and (b) Oxygen or Nitrogen. J. Chem. Soc., 83 (1961) 5486-5504. Duffy, T. S. and Wang. Y.: Pressure-volume-temperature equations of state in Ultra-High- Pressure Mineralogy: Physics and Chemistry of the Earth's Deep Interior, Reviews in Mineralogy, Editor Hemley, R. J., Volume 37, 1998, pp. 425-457. Eremets, M.: High Pressure Experimental Methods, Oxford University Press, 1996. Ersson, N. O.: CELLKANT: Program for the refinement of unit-cell parameters. University of Uppsala, Sweden, 1990. Evans, J. S. O.; Mary, T. A.; Vogt, T.; Subramanian, M. A. and Sleight, A. W.: Negative

Thermal Expansion in ZrW2O8 and HfW2O8. Chem. Mater., 8 (1996) 2809-2823. Evans, J. S. O.; Hanson, J. C. and Sleight, A. W.: Room-Temperature Superstructure of

ZrV2O7. Acta Cryst., B54 (1998) 705-713. Evans, J. S. O.: Negative thermal expansion materials. J. Chem. Soc., Dalton Trans., (1999) 3317-3326. Fitch, A. N.: ESRF Annual Report 1995/1996: BM16. Fitch, A. N.: The High Resolution Powder Diffraction Beam Line at ESRF. Mater. Sci. Forum, 228-231 (1996) 219-222. Forman, R. A.; Piermarini, G. J.; Barnett, J. D. and Block, S.: Pressure Measurement Made by the Utilization of Ruby Sharp-Line Luminescence. Science, 176 (1972) 284-285.

61 REFERENCES

Francis, R. J.; O'Brien, S.; Fogg, A. M.; Shiv Halasyamani, P.; O'Hare, D.; Loiseau, T. and Ferey. G.: Time-Resolved In-Situ Energy and Angular Dispersive X-ray Diffraction Studies of the Formation of the Microporous Gallophosphate ULM-5 under Hydrothermal Conditions. J. Am. Chem. Soc., 121 (1999) 1002-1015. Fujishiro, I.; Piermarini, G. J.; Block, S. and Munro, R. G.: Viscosities and Glass Transition Pressures in The Methanol-Ethanol-Water System. In High Pressure in Research and Industry, Proceedings of the 8th AIRAPT Conference, edited by, Backman, C. M.; Johannisson, T. and Tegner, L., Volume II (1982), pp. 608-611. Goedken, A. M.; Muthu, D. V. S.; Krogh Andersen, A. M.; Carlson, S. and Kruger, M. B.:

High-Pressure Raman and Infrared Study of ZrV2O7. (2003) In manuscript. Gualtieri, A.; Norby, P.; Hanson, J. and Hriljac, J.: Rietveld Refinement using Synchrotron X-ray Powder Diffraction Data Collected in Transmission Geometry using an Imaging-

Plate Detector: Application to Standard m-ZrO2. J. Appl. Cryst., 29 (1996) 707-713. IV IV Hagman, L.-O. and Kierkegaard, P.: Note on the Structures of M P2O7 (M = Ge, Zr, and U). Acta Chem. Scand., 23 (1969) 327-328. Harris, K. M. D. and Tremayne, M.: Crystal Structure Determination from Powder Diffraction Data. Chem. Mater., 8 (1996) 2554-2570. Harris, K. M. D.; Tremayne, M. and Kariuki, B. M.: Contemporary Advances in the Use of Powder X-Ray Diffraction for Structure Determination. Angew. Chem. Int. Ed., 40 (2001) 1626-1651. Hastings, J. B.; Suortti, P.; Thomlinson, W.; Kvick, Å. and Koetzle, T. F.: Optical design for the NSLS Crystallography Beam Line. Nucl. Instr. Meth., 208 (1983) 55-58. Häusermann, D. and Hanfland, M.: Optics and Beamlines for High-Pressure Research at the European Synchrotron Radiation Facility. High Pressure Research, 14 (1996) 223-234. Helluy, X.; Marichal, C. and Sebald, A.: Through-Bond Indirect and Through-Space Direct Dipolar Coupling 31P MAS NMR Constraints for Spectral Assignment in the Cubic 3 × 3 ×

3 Superstructure of TiP2O7. J. Phys. Chem. B, 104 (2000) 2836-2845. Hodeau, J. L.; Bordet, P.; Anne, M.; Prat, A.; Fitch, A. N.; Dooryhee, E.; Vaughan, G. and Freund, A.: Nine crystal multi-analyser stage for high resolution powder diffraction between 6 and 40 keV. Proceedings SPIE (SPIE Conference on Crystal and Multilayer Optics, San Diego, 1998), 3448 (1998) 353-361. Holzapfel, W. B.: Physics of solids under strong compression. Rep. Prog. Phys., 59 (1996) 29-90. Holzapfel, W. B. and Isaacs, N. S. (editors): High-Pressure Techniques in Chemistry and Physics. A Practical Approach. Oxford University Press, 1997. Jayaraman, A.: Diamond anvil cell and high-pressure physical investigations. Rev. Mod. Phys., 55 (1983) 65-108.

62 REFERENCES

Jayaraman, A.: Ultrahigh pressures. Rev. Sci. Instrum., 57 (1986) 1013-1031. Jorgensen, J. D.; Hu, Z.; Teslic, S.; Argyriou, D. N.; Short, S.; Evans, J. S. O. and Sleight, A.

W.: Pressure-induced cubic-to-orthorhombic phase transition in ZrW2O8. Phys. Rev. B, 59 (1999) 215-225. Khosrovani, N.; Korthuis, V.; Sleight, A. W. and Vogt, T.: Unusual 180° P-O-P Bond Angles

in ZrP2O7. Inorg. Chem., 35 (1996) 485-489.

Khosrovani, N.; Sleight, A. W. and Vogt, T.: Structure of ZrV2O7 from -263 to 470°C. J. Solid State Chem., 132 (1997) 355-360. Kijima, T. and Matsui, Y.: A new type of host compound consisting of α-zirconium phosphate and an aminated cyclodextrin. Nature, 322 (1986) 533-534. Kim, R. M.; Pillion, J. E.; Burwell, D. A.; Groves, J. T. and Thompson, M. E.: Intercalation of Aminophenyl- and Pyridinium-Substituted Porphyrins into Zirconium Hydrogen Phosphate: Evidence for Substituent-Derived Orientational Selectivity. Inorg. Chem., 32 (1993) 4509- 4516. King, I. J.; Fayon, F.; Massiot, D; Harris, R. K. and Evans, J. S. O.: A space group 31 assignment of ZrP2O7 obtained by P solid state NMR. Chem. Commun., (2001) 1766- 1767. Kletsova, R. F.; Glinskaya, L. A.; Zolotova, E. S. and Kletsov, P. V.: Crystal structure of

zirconium molybdate Zr(MoO4)2. Sov. Phys. Dokl., 34 (1989) 185-187. Kobayashi, E. and Yamazaki, S.: Studies of Inorganic Ion Exchangers. VI. The Formation Region and Dehydration Behaviour of Various Titanium(IV) Bis(hydrogenorthophosphate) Hydrates. Bull. Chem. Soc. Jpn., 56 (1983) 1632-1636. Kohlbeck, F. and Hörl, E. M.: Trial and error indexing program for powder patterns of monoclinic substances. J. Appl. Cryst., 11 (1978) 60-61. Korthuis, V.; Khosrovani, N.; Sleight, A. W.; Roberts, N.; Dupree, R. and Warren Jr., W. W.:

Negative Thermal Expansion and Phase Transitions in the ZrV2-xPxO7 Series. Chem. Mater., 7 (1995) 412-417. Kuznetsov, V. G.: РЕНТГЕНОГРАФИЧЕСКИЙ АНАЛИЗ ПРИ ВЬІСОКИХ И НИЗКИХ ТЕМПЕРАТУРАХ. (X-ray analysis at high and low temperatures.) Zh. Neorg. Khim., 1 (1956) 1548-1558. La Ginestra, A. and Massucci, M. A.: Titanium and Zirconium Acid Phosphate Dihydrates: Thermal Behaviour and Phase Changes of their Hydrogen, Sodium and Strontium Forms. Thermochimica Acta, 32 (1979) 241-256. Larson, A. C. and Von Dreele, R. B.: 'General Structure Analysis System (GSAS)', Los Alamos National Laboratory Report, LAUR 86-748, 2000.

Le Bail, A.; Duroy, H. and Fourquet, J. L.: Ab-Initio Structure Determination of LiSbWO6 by X- ray Powder Diffraction. Mat. Res. Bull., 23 (1988) 447-452.

63 REFERENCES

Letoullec, R.; Pinceaux, J. P. and Loubeyre, P.: The Membrane Diamond Anvil Cell: A New Device for Generating Continuous Pressure and Temperature Variations. High Pressure Research, 1 (1988) 77-90. Levi, G. R. and Peyronel, G.: Struttura Cristallografica del Gruppo Isomorfo (Si4+, Ti4+, Zr4+, 4+ 4+ Sn , Hf )P2O7. Z. Kristallogr., 92 (1935) 190-209. Lind, C.; Wilkinson, A. P.; Hu, Z.; Short, S. and Jorgensen, J. D.: Synthesis and Properties of

the Negative Thermal Expansion Material Cubic ZrMo2O8. Chem. Mater., 10 (1998) 2335- 2337. Lind, C.; Wilkinson, A. P.; Rawn, C. J. and Payzant, E. A.: Preparation of the negative

thermal expansion material cubic ZrMo2O8. J. Mater. Chem., 11 (2001a) 3354-3359. Lind, C.; VanDerveer, D. G.; Wilkinson, A. P.; Chen, J.; Vaughan, M. T. and Weidner, D. J.: New High-Pressure Form of the Negative Thermal Expansion Materials Zirconium Molybdate and Hafnium Molybdate. Chem. Mater., 13 (2001b) 487-490. Lind, C.; Wilkinson, A. P.; Rawn, C. J. and Payzant, E. A.: Kinetics of the cubic to trigonal

transformation in ZrMo2O8 and their dependence on precursor chemistry. J. Mater. Chem., 12 (2002) 990-994. Lipinska-Kalita, K. E.; Kruger, M. B.; Carlson, S. and Krogh Andersen, A. M.: High-pressure studies of titanium pyrophosphate by Raman scattering and infrared spectroscopy. Physica B, 337 (2003) 221-229. Llavona, R.; Garcia, J. R.; Suarez, M. and Rodriguez, J.: Synthesis of γ-Titanium Phosphate. Study of the Solids Obtained by Using Water or Acetone as Washing Agents. Thermochimica Acta, 86 (1985) 281-289. Mao, H. K.; Bell, P. M.; Shaner, J. W. and Steinberg, D.: Specific volume measurements of

Cu, Mo, Pd, and Ag and calibration of the ruby R1 fluorescence pressure gauge from 0.06 to 1 Mbar. J. Appl. Phys., 49 (1978) 3276-3283. Mao, H. K.; Xu, J. and Bell, P. M.: Calibration of the Ruby Pressure Gauge to 800 kbar Under Quasi-Hydrostatic Conditions. J. Geophys. Res., 91 (1986) 4673-4676. Mary, T. A.; Evans, J. S. O.; Vogt, T. and Sleight, A. W.: Negative Thermal Expansion from

0.3 to 1050 Kelvin in ZrW2O8. Science, 272 (1996) 90-92. McCusker, L. B.; Von Dreele, R. B.; Cox, D. E.; Louër, D. and Scardi, P.: Rietveld refinement guidelines. J. Appl. Cryst. 32 (1999) 36-50. Meneghini, C.; Artioli, G.; Balerna, A.; Gualtieri, A. F.; Norby, P. and Mobilio, S.: Multipurpose imaging-plate camera for in-situ powder XRD at the GILDA beamline. J. Synchrotron Rad., 8 (2001) 1162-1166. Miletich, R.; Allan, D. R. and Kuhs, W. F.: High Pressure Single-Crystal Techniques in High- Temperature and High Pressure Crystal Chemistry. Rewievs in Mineralogy and Geochemistry, Editors Hazen, R. M. and Downs, R. T., Volume 41, 2000, pp. 445-519.

64 REFERENCES

Mittal, R.; Chaplot, S. L.; Lalla, N. P. and Mishra, R. K.: X-ray diffraction study of anisotropic

thermal expansion in ZrMo2O8. J. Appl. Cryst., 32 (1999) 1010-1011. Muthu, D. V. S.; Chen, B.; Wrobel, J. M.; Krogh Andersen, A. M.; Carlson, S. and Kruger, M.

B.: Pressure-induced phase transitions in α-ZrMo2O8. Phys. Rev. B, 65 (2002) 064101-1- 064101-7.

Norberg, S. T.; Svensson, G. and Albertsson, J.: A TiP2O7 superstructure. Acta Cryst., C57 (2001) 225-227. Norby, P.: In-Situ Time Resolved Synchrotron Powder Diffraction Studies of Syntheses and Chemical Reactions. Mater. Sci. Forum, 228-231 (1996) 147-152. Norby, P.: Synchrotron Powder Diffraction using Imaging Plates: Crystal Structure Determination and Rietveld Refinement. J. Appl. Cryst., 30 (1997a) 21-30. Norby, P.: Hydrothermal Conversion of Zeolites: An in Situ Synchrotron X-ray Powder Diffraction Study. J. Am. Chem. Soc., 119 (1997b) 5215-5221. Norby, P.; Nørlund Christensen, A. and Hanson, J. C.: Crystallization in Nonaqueous Media of Co- and Mn-Substituted Microporous Aluminophosphates Investigated by in Situ Synchrotron X-ray Powder Diffraction. Inorg. Chem., 38 (1999) 1216-1221. Norby, P.; Hanson, J. C.; Fitch, A. N.; Vaughan, G.; Flaks, L. and Gualtieri, A.: Formation of

α-Eucryptite, LiAlSiO4: An In-Situ Synchrotron X-ray Powder Diffraction Study of a High Temperature Hydrothermal Synthesis. Chem. Mater., 12 (2000) 1473-1479. Norby, P.; Dinnebier, R. and Fitch, A. N.: Decomposition of Silver Carbonate; the Crystal

Structure of Two High-Temperature Modifications of Ag2CO3. Inorg. Chem., 41 (2002) 3628-3637. Nye, J. F.: Physical Properties of Crystals. Oxford University Press, 1957, pp.145-146. O'Hare, D.: Inorganic Intercalation Compounds in Inorganic Materials, p 165-235. Edited by D. W. Bruce and D. O'Hare. John Wiley & Sons Ltd., 1992. Pawley, G. S.: Unit-Cell Refinement From Powder Diffraction Scans. J. Appl. Cryst., 14 (1981) 357-361. Perottoni, C. A. and da Jornada, J. A. H.: Pressure-Induced Amorphization and Negative

Thermal Expansion in ZrW2O8. Science, 280 (1998) 886-889. Piermarini, G. J.; Block, S.; Barnett, J. D. and Forman, R. A.: Calibration of the pressure

dependence of the R1 ruby fluorescence line to 195 kbar. J. Appl. Phys. 46 (1975) 2774- 2780. Poojary, D. M.; Shpeizer, B. and Clearfield, A.: X-Ray Powder Structure and Rietveld

Refinement of γ-Zirconium Phosphate, Zr(PO4)(H2PO4)⋅2H2O. J. Chem. Soc., Dalton Trans., (1995) 111-113.

65 REFERENCES

Pryde, A. K. A.; Hammonds, K. D.; Dove, M. T.; Heine, V.; Gale, J. D. and Warren, M. C.:

Origin of the negative thermal expansion in ZrW2O7 and ZrV2O7. J. Phys.: Condens. Matter., 8 (1996) 10973-10982. Rietveld, H. M.: Line Profiles of Neutron Powder-Diffraction Peaks for Structure Refinement. Acta Cryst., 22 (1967) 151-152. Rietveld, H. M.: A Profile Refinement Method for Nuclear and Magnetic Structures. J. Appl. Cryst., 2 (1969) 65-71. Rodriguez-Carvajal, J.: 'FULLPROF: A Program for Rietveld Refinement and Pattern Matching Analysis', Abstracts of the Satellite Meeting on Powder Diffraction of the XV Congress of the IUCr, Toulouse, France, 1990, p.127. Rodriguez-Carvajal, J.: SUPERCELL. Program to Index Superstructure Reflections. LLB, France, 1998. Roy, R.; Agrawal, D. K. and McKinstry, H. A.: Very Low Thermal Expansion Coefficient Materials. Annu. Rev. Mater. Sci., 19 (1989) 59-81. Ruoff, A. L.; Xia, H.; Luo, H. and Vohra, Y. K.: Miniaturization techniques for obtaining static pressures comparable to the pressure at the centre of the earth: X-ray diffraction at 416 GPa. Rev. Sci. Instrum., 61 (1990) 3830-3833. Salvadò, M. A.; García-Granda, S. and Rodríguez, J.: An Investigation on the Structure of Gamma Titanium Phosphates from X-ray Conventional Powder Diffraction Data. Mater. Sci. Forum, 166-169 (1994) 619-624. Salvadò, M. A.; Pertierra, P.; García-Granda, S.; Barcina, L. M.; Llavona, R. and Rodríguez,

J.: Hydrogen bond network of the layered phosphates γ-Zr(H2PO4)(PO4)⋅2H2O and

γ-Hf(H2PO4)(PO4)⋅2H2O determined by neutron powder diffraction. Z. Kristallogr., 216 (2001) 326-330. Samant, M. S.; Dharwadkar, S. R.; Phadnis, A. B. and Namboodiri, P.N.: Thermoanalytical

investigation on the solid state synthesis of pure zirconium molybdate (ZrMo2O8). Mater. Chem. Phys., 35 (1993) 120-125. Sanz, J.; Iglesias, J. E.; Soria, J.; Losilla, E. R.; Aranda, M. A. G. and Bruque, S.: Structural

Disorder in the Cubic 3 × 3 × 3 Superstructure of TiP2O7. XRD and NMR Study. Chem. Mater., 9 (1997) 996-1003.

Serezhkin, V. N.; Efremov, V. A. and Trunov, V. K.: The Crystal Structure of α-Zr(MoO4)2, the High-Temperature Modification of Zirconium Molybdate. Russian J. Inorg. Chem., 32 (1987) 1566-1570. Shirley, R. and Louër, D.: New powder indexing programs for any symmetry which combine grid-search with successive dichotomy. Acta Cryst., A34 (1978) S382.

66 REFERENCES

Shirley, R.: The CRYSFIRE System for Automatic Powder Indexing: User's Manual, 2000. The Lattice Press, 41 Guildford Park Avenue, Guildford, Surrey GU2 7NL, England. Sleight, A. W.: Compounds that Contract on Heating. Inorg. Chem., 37 (1998) 2854-2860. Soria, J.; Iglesias, J. E. and Sanz, J.: Effect of Calcination on Titanium Phosphate produced

by H3PO4 Treatment of Anatase. J. Chem. Soc., Faraday Trans., 89 (1993) 2515-2518. Speedy, R. J.: Models for Amorphization in Compressed Crystals. J. Phys.: Condens. Matter 8 (1996) 10907-10918. Ståhl, K. and Hanson, J. C.: Real-Time X-ray Synchrotron Powder Diffraction Studies of the Dehydration Processes in Scolecite and Mesolite. J. Appl. Cryst., 27 (1994) 543-550. Suárez, M.; Barcina, L. M.; Llavona, R.; Rodríguez, J.; Salvadó, M. A.; Pertierra, P. and García-Granda, S.: Synthesis, crystal structure and intercalation behaviour of hafnium phosphate dihydrogenphosphate dihydrate. J. Chem. Soc., Dalton Trans., (1998) 99-102.

Taylor, D.: Thermal Expansion Data XII. Complex oxides: AB2O6, AB2O7, A2B2O7 plus complex aluminates, silicates and analogous compounds. Br. Ceram. Trans. J., 87 (1988) 39-45. Thoms, M.; Bauchau, S.; Häusermann, D.; Kunz, M.; Le Bihan, T.; Mezouar, M. and Strawbridge, D.: An improved X-ray detector for use at synchrotrons; Nucl. Instr. Meth. Phys. Res. A. 413 (1998) 175-184 Tillmanns, E.; Gebert, W. and Baur, W. H.: Computer Simulation of Crystal Structures Applied to the Solution of the Superstructure of Cubic Silicondiphosphate. J. Solid State Chem., 7 (1973) 69-84. Troup, J. M. and Clearfield, A.: On the Mechanism of Ion Exchange in Zirconium Phosphates. 20. Refinement of the Crystal Structure of α-Zirconium Phosphate. Inorg. Chem., 16 (1977) 3311-3314. Védrine, J. C.: Partial oxidation reaction on phosphate-based catalysts. Topics in Catalysis, 11 (2000) 147-152. Vinet, P.; Ferrante, J.; Smith, J. R. and Rose, J. H.: A universal equation of state for solids. J. Phys. C: Solid State Phys., 19 (1986) L467-L473. Visser, J. W.: A fully automatic program for finding the unit cell from powder data. J. Appl. Cryst., 2 (1969) 89-95. Vos, W. L. and Schouten, J. A.: On the temperature correction to the ruby pressure scale. J. Appl. Phys., 69 (1991) 6744-6746.

Völlenkle, H.; Wittmann, A. and Nowotny, H.: Über Diphosphate vom Typ Me(IV)P2O7. Monatsh. Chem., 94 (1963) 956-963. Werner, P. E.; Eriksson, L. and Westdahl, M.: TREOR, a semi-exhaustive trial-and-error powder indexing program for all symmetries. J. Appl. Cryst., 18 (1985) 367-370.

67 REFERENCES

Wertheim, G. K.; Butler, M. A.; West, K. W. and Buchanan, D. N. E.: Determination of the Gaussian and Lorentzian content of experimental line shapes. Rev. Sci. Instrum., 45 (1974) 1369-1371. Withers, R. L.; Evans, J. S. O.; Hanson, J. and Sleight, A. W.: An in Situ Temperature-

Dependent Electron and X-ray Diffraction Study of Structural Phase Transitions in ZrV2O7. J. Solid State Chem., 137 (1998) 161-167. Withers, R. L.; Tabira, Y.; Evans, J. S. O.; King, I. J. and Sleight, A. W.: A New Three-

Dimensional Incommensurately Modulated Cubic Phase (in ZrP2O7) and Its Symmetry Characterization via Temperature-Dependent Electron Diffraction. J. Solid State Chem., 157 (2001) 186-192. Young, R. A. and Wiles, D. B.: Profile Shape Functions in Rietveld Refinements. J. Appl. Cryst., 15 (1982) 430-438. Young, R. A.: The Rietveld Method. R. A. Young (Ed.). IUCr Monographs on Crystallography 5, Oxford University Press, 1993.