Magnetic Studies of Single Crystal Intermetallics Evan M

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2008 From Paramagnetism to Spin Glasses: Magnetic Studies of Single Crystal Intermetallics Evan M. (Evan Mallory) Benbow

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COLLEGE OF ARTS AND SCIENCES

FROM PARAMAGNETISM TO SPIN GLASSES:

MAGNETIC STUDIES OF SINGLE CRYSTAL

INTERMETALLICS.

EVAN M. BENBOW

A Dissertation submitted to the Department of Chemistry and Biochemistry in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Fall Semester, 2008 The members of the Committee approve the Dissertation of Evan Mallory Benbow defended on September 25th, 2008.

Susan E. Latturner Professor Directing Dissertation

David Lind Outside Committee Member

Naresh Dalal Committee Member

Geoff Strouse Committee Member

Approved:

______Joseph Schlenoff, Chair, Department of Chemistry and Biochemistry

The Office of Graduate Studies has verified and approved the above named committee members.

TABLE OF CONTENTS

List of Figures v List of Tables viii Abstract ix 1. Chapter 1 Introduction to Molten Metals and Intermetallics 1 1.1. Molten Metal Flux 1 1.2. Intermetallics 8

2. Chapter 2 Characterization Methods 12 2.1. SEM-EDS 12 2.2. X-ray Diffraction 14 2.3. SQUID 16

3. Chapter 3 Important Solid State Physics Concepts 17 3.1. Magnetic Susceptibility and Ordering 17 3.2. Itinerant-Electron Magnetism 21 3.3. Spin Frustration 25

4. Chapter 4 Mixed Metal Flux Synthesis of Quaternary RT2TrxZn20-x compounds with T = Mn, Fe and Tr = Al, In. 27 4.1. Introduction, Characterization and Synthesis 27

4.2. RMn2TrxZn20-x compounds 33 4.2.1. In/Zn 33 4.2.2. Al/Zn 38 4.2.3. Incorporation of Manganese 39

4.3. RFe2TrxZn20-x compounds 40 4.3.1. In/Zn 40 4.3.2. Al/Zn 42 4.4. Magnetic Susceptibility 43 4.5. Conclusion 45

5. Chapter 5 Crystal growth and Spin Glass-like behavior of R6T13-xAlxMy (R = rare earth; T = Mn, Fe; M = main group) phases grown from lanthanide-rich eutectic fluxes 47 5.1. Introduction and Characterization 47 5.2. Synthesis 48 5.2.1. Iron Analogs 54 5.2.2. Manganese Analogs 55 5.2.3. Neodymium Analogs 56 5.3. R6T13-xAlxMy structural description 57 5.4. 4a site 58

iii

5.5. Fe/Al 16l2 mixed site 59 5.6. Magnetic Properties 61 5.6.1. La6Fe13-xAl1+x 62 5.6.2. Nd6Fe13-xAl1+x 66 5.6.3. La6Mn13-xAl1+x 67 5.7. Conclusion 69

6. Chapter 6 Spin Glass behavior of Isolated Tetrahedron of Iron atoms in the Geometrically Frustrated La21Fe8Sn7C12. 71 6.1. Introduction, Characterization and Synthesis 71 6.2. La21Fe8Sn7C12 structural description 77 6.3. Magnetic Properties 80 6.4. Conclusion 83

7. Chapter 7 Conclusion and Future Work 84

References 88

Biographical Sketch 95

LIST OF FIGURES Chapter 1

Figure 1.1 Materials for crucibles 1

Figure 1.2 Ni/B and Nd/Fe binary phase diagrams 3

Figure 1.3 YNi2B2C and Y2FeC4 structures 4

Figure 1.4 Ce2TMIn8 and Ce2TMIn5 structures 5

Figure 1.5 LaFe12B6 and La3.67FeC6 structures 6

Figure 1.6 Reaction setup used for synthesis 7

Figure 1.7 La(FexAl1-x)13 and La6Fe13-xAl1+x structures 9

Figure 1.8 Gd5(SixGe1-x)4 and MnFeP1-xAsx structures 10

Figure 1.9 Nd2Fe12B (left) and SmCo5 structures 11

Chapter 2

Figure 2.1 Emission of X-rays by SEM-EDS 12

Figure 2.2 EDS Spectra 13

Figure 2.3 X-ray rotation photograph 15

Chapter 3

Figure 3.1 Unpaired electrons and Magnetic Ordering 17

Figure 3.2 Strong and weak ferromagnetism hysteresis loops 19

Figure 3.3 Antiferromagnetism anisotropy 20

Figure 3.4 Rectangular 3d exchange split bands 21

Figure 3.5 Realistic 3d exchange split bands 23

Figure 3.6 Slater-Pauling curve 24

Figure 3.7 Frustration on equilateral triangle and tetrahedron 25

Figure 3.8 2D Kagome and 3D pyrochlore lattices 26

Chapter 4

Figure 4.1 The cubic RT2TrxZn20-x structure 34

Figure 4.2 Coordination polyhedral in the RMn2InxZn20-x compounds 35

Figure 4.3 Cell volumes of RT2InxZn20-x compounds versus amount of indium present in the sample. 36

Figure 4.4 Dependence of the R-In1 and R-(In2/Zn2) bond lengths in the rare-earth polyhedron on the indium content x of the compounds RMn2InxZn20-x. 37

Figure 4.5 Changes in Mn icosahedron bond lengths due to varying amount of indium present in the RMn2InxZn20-x compound. 38

Figure 4.6 Cell volumes of the RMn2AlxZn20-x versus rare-earth element size. 39

Figure 4.7 Er/Fe network in site switched Er2FeZn4.4In15.6. 43

Figure 4.8 Temperature dependence of the inverse molar susceptibility (1/χm) for YbMn2(Al5.3Zn14.7) and SmMn2(Al4.9Zn15.1). 44

Chapter 5

Figure 5.1 Image of R6T13-xAlxMy crystals. 52

Figure 5.2 Structure of R6Fe13-xM1+x compounds in addition to the local environment of the main group 4a and iron 4d sites. 55

Figure 5.3 Coordination environments for rare earth elements in the cubic La(FexAl1-x)13 and the tetragonal La6Fe13-xAl1+x. 57

Figure 5.4 Changes in unit cell parameters as a function of Fe/Al mixing. 60

Figure 5.5 La6Fe10.25Al3.75 FC and ZFC susceptibility measurements. 61

Figure 5.6 Heat capacity measurement of La6Fe10.25Al3.75. 63

Figure 5.7 La6Fe10.25Al3.75 M vs H collected at 1.8K. 64

Figure 5.8 Nd6Fe10.5Al3.5 FC and ZFC susceptibility measurements. 65

Figure 5.9 Nd6Fe10.5Al3.5 M vs H collected at 1.8K. 66

Figure 5.10 La6Mn10Al4 FC and ZFC susceptibility measurements. 68

Figure 5.11 La6Mn10Al4 M vs H collected at 1.8K. 69

Chapter 6

Figure 6.1 Image of La21Fe8Sn7C12 crystal. 72

Figure 6.2 Iron tetrahedron and iron tetrahedron with carbon. 73

Figure 6.3 La21Fe8Sn7C12 structure. 76

Figure 6.4 Iron and carbon local environments 78

Figure 6.5 Lanthanum and tin local environments. 79

Figure 6.6 La21Fe8Sn7C12 ZFC and FC susceptibility measurements. 80

Figure 6.7 La21Fe8Sn7C12 M vs H collected at 1.8K. 81

Figure 6.8 La21Fe8Sn7C12 AC susceptibility measurement. 82

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LIST OF TABLES

Chapter 4

Table 4.1. Lattice constants of the compounds RMn2TrxZn20-x. 28

Table 4.2. Crystal data for four representative RT2TrxZn20-x compounds. 30

Table 4.3 Atomic positions table for four representative RMn2TrxZn20-x compounds. 31

Table 4.4 Lattice constants of the compounds RFe2TrxZn20-x. 41

Table 4.5 Atomic coordinates for two representative RFe2TrxZn20-x compounds. 42

Chapter 5

Table 5.1. Crystallographic collection parameters for three representative R6Fe13-xAl1+x ternary compounds. 50

Table 5.2. Ternary compounds synthesized. 51

Table 5.3 Quaternary compounds synthesized. 53

Chapter 6

Table 6.1. Lattice constants of the compounds La21Fe8M7C12. 71

Table 6.2. Crystal data for La21Fe8Sn7C12. 74

Table 6.3. Atomic coordinates for La21Fe8Sn7C12. 75

Table 6.4. Selected bond lengths for La21Fe8Sn7C12. 77

viii

ABSTRACT

The main emphasis of this research was to explore molten metals (flux) as a growth medium for single crystal intermetallics. The primary characterization methods included: SEM- EDS, X-ray Diffraction, and SQUID magnetometry. The main focus was on the magnetic and structural properties of the single crystal phases.

The RT2TrxZn20-x (R = Rare Earth; T = Mn, Fe; Tr = Al, In) compounds were synthesized using Al/Zn and In/Zn eutectics. These compounds form a known structure; however, the incorporation of Mn into the structure had not been previously reported. These compounds displayed paramagnetic behavior with respect to the rare earth element present; however, the Sm analogs displayed complex Van-Vleck paramagnetism.

The R6T13-xAl1+x (R = La, Nd; T = Fe, Mn) single crystal compounds were synthesized using La/Ni and Nd/Fe eutectics. These compounds form a known structure, however, the physical and magnetic properties with respect to the anisotropy present was not adequately characterized. Also, a previously unreported substitution of manganese into these samples occurred. The iron analogs displayed type II antiferromagnetic behavior, with anisotropy effects, that can be adequately described using itinerant electron magnetism. The manganese analogs displayed ferromagnetic behavior, with strong and weak ferromagnetism occurring with respect to anisotropy. Substitution of magnetic rare earth elements, such as neodymium for lanthanum, introduces localized magnetic moments in addition to the itinerant moments.

The La21Fe8M7C12 (M = Sn, Sb, Bi, Te, Ge) single crystals were synthesized using a La/Ni eutectic. This compounds form a novel structure not reported in the literature. The magnetic properties, display spin frustration and formation of a spin glass state, with respect to the isolated tetrahedron of iron atoms within the structure. The formation of the spin glass state was confirmed, by AC susceptibility measurements, using SQUID magnetometry.

CHAPTER 1 INTRODUCTION TO INTERMETALLICS AND MOLTEN METAL FLUX Molten Metal Flux1 When investigating the physical and chemical properties of intermetallic compounds it is preferable that the material be in the form of single crystals. Powder samples have randomly oriented particles; grain boundaries, high surface to bulk ratio, inconsistent phase purity and additional impurities leftover from synthesis. These problems prevent proper characterization of physical properties within the material and obscure any anisotropy effects present. Therefore, preparation of single crystals is of considerable importance for studies of complicated systems such as intermetallics. The simplest technique for crystal growth is from a pure melt of the substance desired and there are numerous experimental techniques available to accomplish this such as zone melting, crystal pulling and Bridgman cooling. However, the desired product must melt congruently and inconveniently high temperatures or vapor pressures of materials present can complicate matters. Many materials of interest melt incongruently and therefore other techniques for single crystal growth are needed.

Figure 1.1. A list of appropriate metals for use as crucibles depending on elements used for synthesis.1

A technique that is commonly overlooked is growth of single crystals from molten metal fluxes; this can alleviate some of the problems discussed above. The main advantages of this particular technique include the growth of materials well below the melting point of reactant and products, which typically reduces thermal strain and produces fewer defects, stabilization of metastable versus the thermodynamically stable phases which is of excellent use in exploratory synthesis. Another benefit is the ease of separation of products from the molten metal flux by centrifugation, acid/base etching and preferential oxidation of the flux in the presence of oxygen. Additionally a molten metal flux can often getter impurities, reduce vapor pressure problems of reactants (such as Yb and Eu) and is a comparatively inexpensive due to the simple equipment and minimal capital needed. A metal flux should possess certain characteristics to be suitable for reaction chemistry; the metal should form a flux (i.e. a melt) at reasonably low temperatures so that normal heating equipment and containers can be used, the metal should have a large difference between its melting point and boiling point temperatures, it should be possible to separate the metal from the products, by chemical dissolution, by filtration during its liquid state, or if necessary by mechanical removal, and the metal flux should not form highly stable binary compounds with any of the reactants.2 There are disadvantages to molten metal flux growth and therefore it may not be an applicable method for crystal growth of certain compounds. An appropriate metal flux for which the desired compound will crystallize in may not be available. A crystal may grow around a pocket of flux forming an inclusion. Inclusions are a problem of excessive nucleation which can be associated with too fast a cooling rate, or supercooling of the melt by slow cooling with subsequent multiple nucleation and fast growth of large but imperfect crystals. Similar to other growth methods a molten metal flux may react with the growth container (i.e. crucible) causing impurities; in certain cases, this may assist in exploration of new phases. Figure 1.1 shows a small chart which allows selection of an appropriate crucible depending on the reactants present.

Figure 1.2. Binary phase diagrams of Ni-B (top) and Fe-Nd (bottom).3

Due to the relatively low melting points of elements such as Ga, Al, In, Sn, Pb, Hg, Zn, and Bi these have been extensively investigated for metal flux growth of single crystals.2 While elements with a low melting point are attractive for use as metal fluxes, there exist interesting examples which allow metal flux growth from elements with extremely high melting points such as Fe and Cu. Examination of binary phase diagrams

3 gives insight into ways to lower the melting points of such elements as the transition metals by combining them with other main group or rare earth elements to form a eutectic (Fig. 1.2). In the Ni-B binary phase diagram numerous eutectics are observed that significantly lowers the melting point of boron and nickel (2092ºC and 1455ºC). An excess of Ni2B was used by Canfield et al to synthesize single crystals of RNi2B2C (R = La - Lu) which helped uncover the complex interplay between magnetism and superconductivity [Fig. 1.3 (left)].4 Examination of rare earth and TM binary phase diagrams reveal a plethora of metal eutectics with significantly lowered melting points that could be used for synthesis of single crystals. Using the eutectic in the Fe-Nd binary phase diagram single crystals of Nd6Fe13-xAl1+x can be synthesized which allows for proper characterization of the magnetic properties of such a complex system containing 4 Fe sites, 2 Nd sites and the anisotropy effects due to different orientations of the crystal in a magnetic field (to be discussed later).

Figure 1.3. Structure of the superconducting YNi2B2C (left; Green = Y; Blue = Ni; Red = B; Black = C) and Y2FeC4 (right; Green = Y; Red = Fe; Black = C).

Depending on the conditions, a metal flux can be described as being reactive or nonreactive. Indium as a flux displays both reactive and nonreactive behavior, for example, several members of the Ce2TMIn8 and Ce2TMIn5 compounds have been synthesized using an excess of indium which was incorporated into the structures [Figure 5-8 1.4]. However, well formed crystals of CrSi2, WSi2, VSi2, and RESi2 grown under the same conditions have shown no incorporation of the flux.2 Another interesting example of this nonreactive behavior was the use of lithium flux to synthesize the superconducting 9 Y2FeC4 [Fig. 1.3 (right)]. This can lead to unique pairing of elements in which a reactive element and nonreactive element combine in a eutectic as a medium for growth of single crystals without incorporations of the nonreactive element. The use of a nonreactive element to form a eutectic increases the temperature range at which the metals are still molten facilitating crystal growth of metastable phases. This type of pairing in addition to combinations of two reactive elements was extensively explored as a growth medium for single crystals.

Figure 1.4. Structures of Ce2TMIn8 (left) and Ce2TMIn5 (right) synthesized by In flux. (Green = Ce, Blue= TM; Purple = In).

Many new techniques were developed while optimizing reactions to increase crystal yield especially when using the La/Ni eutectic. These metals by themselves are not typical reagents used for flux growth due to their high melting points so that inherently made synthesis initially difficult. One of the main factors in improving crystal yield when using this eutectic was utilizing a quick ramp time to the initial soak temperature and placing reactant metals between two layers of flux within the crucible. This greatly improved the quality of the melt which enhanced diffusion of the reactant elements therefore providing a better environment for crystal growth. Due to the improved quality of melt and reducing properties of the La/Ni eutectic the crucibles used would be etched by the flux thus incorporating elements such as aluminum and carbon into products. Typical flux techniques clearly state that your crucible should be inert to the reactants, however, this property was quite useful during exploratory synthesis, although uncontrollable. For example, using an alumina crucible to synthesize the La21Fe8M7C12 phase allowed for aluminum to be etched by the La/Ni

flux, yielding single crystals of the La6Fe13-xAl1+x phase which had previously only been synthesized in powder form. Another example included using a stainless steel crucible to

synthesize quaternary La6Fe13-xGaxBiy phase in which carbon was etched by the La/Ni

flux yielding single crystals of the La21Fe8Bi7C12.

Figure 1.5. Structures of LaFe12B6 (right) and La3.67FeC6 (left). (Left: Blue = La, Red = Fe, Black = B; Right: Green = La, Red = Fe, Black = C).

The use of the La/Ni eutectic allowed for exploration into pairing reactive and non-reactive reagents for growth using flux. In addition to the iron intermetallics above

synthesis of LaFe12B6 and La3.67FeC6 was achieved without any observed incorporations of nickel into the crystal structure [Fig. 1.5].10,11 This was confirmed by both SEM-EDS and X-ray diffraction. This is rather interesting considering iron and nickel can be 12,13 readily substituted for each other in structures such as RT2Zn20. Another useful result of using a flux rich in rare earths is the ease of separation of products from the melt. A typical reaction setup includes a crucible which contains the flux and measured reactants. Another crucible filled with silica wool is inverted to act as a filter during centrifugation [Fig. 1.6]. The reaction setup is then sealed under vacuum in a silica tube to prevent the formation of oxides. At the desired centrifugation temperature the reaction is removed from the oven, inverted and then placed into a centrifuge to remove the excess flux. Flux is observed pooling at the top of the reaction setup after centrifugation, typically indicating a successful reaction. After centrifugation any remaining flux attached to the surface of the crystals could be removed by controlled oxidation of the products in air. This allowed for clean single crystals to be isolated from beds of oxide powders of the rare earths created during the oxidation process. However, this process if not properly monitored can destroy air sensitive single crystals and crucibles used for synthesis.

Figure 1.6. Typical reaction setup used for synthesis.

Intermetallics An intermetallic is defined as a compound comprised exclusively of two or more different kinds of metal or metalloid atoms.14 In metallic compounds the bonding electrons are delocalized which give rise to non-directional bonding. However, in the case of intermetallic compounds bonding electrons are slightly ionic and covalent which results in directional bonding. These differences in bonding give materials of each class unique behavior. Most intermetallic compounds do not follow electron counting and oxidation number analysis, which is more easily applied in the study of halides, oxides, and chalcogenides. This makes predicting the stable composition of metallic elements which comprise the intermetallic difficult. Another source of difficulty in synthesizing intermetallics is the need for very high temperature conditions, which require induction heating or arc melting. For example, synthesis of intermetallic silicides is typically done by direct reaction of the elements under vacuum at temperatures over 1000ºC, which can only be achieved by arc welding or inductive furnaces. For the ovens to withstand such high temperatures, high temperature oxygen resistant materials and coatings made from intermetallic silicides were developed.15,16 However, these types of reactions typically yield powder polycrystalline samples which can make precise structural determination difficult and limit the ability to characterize the physical properties of the sample properly. Due to these initial difficulties, the bulk of synthetic research in solid state chemistry has focused primarily on the ionic type of materials. There are a variety of important intermetallic compounds that have interesting properties for use in industrial, commercial, and scientific applications; however some of the most important kinds are aluminum-based and silicon-based materials. Doping of aluminum alloys with rare-earth and or transition metals(TM) creates binary and ternary aluminides which often display complex structures with interesting magnetic and electronic properties.17 Silicides are of extreme importance due to their hardness, chemical stability, high melting point and the prevalence of silicon based materials in current technologies. Doping of silicides with TM yields advantageous electrical and magnetic properties which make them good materials for use in electronics and variety of new applications.18,19

Figure 1.7. Structure of cubic La(FexAl1-x)13 (left) and tetragonal La6Fe13-xAl1+x (right; Fe clusters in polyhedra view). (Green = La; Red = Fe; Blue = Fe/Al)

A variety of interesting aluminum containing intermetallics were isolated in my efforts to synthesize new compounds by flux growth techniques. Two of these phases

La(FexAl1-x)13 and La6Fe13-xAl1+x feature networks or layers of icosahedral iron clusters with complex magnetic properties [Fig. 1.7]. The cubic La(FexAl1-x)13 (0.46 ≤ x ≤ 0.92) displays various magnetic orderings depending on the amount of iron present.20 At high concentrations (0.87 ≤ x ≤ 0.92), this phase displays antiferromagnetic behavior. At slight lower concentrations (0.61≤ x ≤ 0.86) , ferromagnetic behavior is observed and with sufficient dilution of iron with aluminum (0.46 ≤ x ≤ 0.60), mictomagnetic (cluster glass) behavior is displayed. Substitution of aluminum with silicon in the cubic

La(FexAl1-x)13 structure results in magnetocaloric behavior. The properties of La6Fe13- xAl1+x will be discussed later in chapter 5.

Other remarkable intermetallics such as Gd5(SixGe1-x)4 and MnFeP1-xAsx also display the interesting phenomena called the magnetocaloric effect [Fig. 1.8].21 The magnetocaloric effect is a reversible change in the materials temperature by application or removal of a magnetic field. Upon applying a magnetic field the unpaired electrons align with the applied field which decreases entropy thus heating the material. After

removal of a magnetic field the spins of the electrons are allowed to randomize thus increasing entropy, in effect cooling the material. These compounds are of interest for refrigeration due to the increased efficiency of the process, lack of moving parts, and elimination of harmful gases used in conventional refrigeration.

Figure 1.8. Structure of Gd5(SixGe1-x)4 (left) (Green = Gd; Red = Mixed Si/Ge) and MnFeP1-xAsx (right) (Red = Mixed Mn/Fe; Blue = Mixed P/As).

The purpose of my investigations was to explore molten metals (flux) as a growth medium for isolating intermetallic compounds with unique magnetic and physical properties. Intermetallic compounds with applicable magnetic properties include the permanent magnets Nd2Fe12B, SmCo5 [Figure 1.9] and the metamagnetic Nd6Fe13-xAl1+x 22-25 which can improve the coercivity of Nd2Fe12B when present as a secondary phase. Therefore, use of 3d transition metals and rare earth metals in combination with main group elements was extensively explored. Carbon and boron additions were also of interest due to the superconducting properties of RNi2B2C and R2FeC4 (R= Y, rare earth) and possible isolation of carbon in new environments not previously observed [Fig 26,27 1.3]. With these guidelines for reactant selection the La21Fe8M7C12 and RT2TrxZn20-x

compounds were synthesized. While synthesizing analogs for the La21Fe8M7C12 phase

aluminum was etched from the crucible yielding the La6Fe13-xAl1+x compounds. The

La6Fe13-xAl1+x compound was selected for further studies due to complex and unique magnetic properties.

Figure 1.9. Structures of permanent magnets Nd2Fe12B (left) and SmCo5 (right). (Green = Nd, Sm; Red = Fe; Blue = Co; Black = B)

CHAPTER 2 CHARACTERIZATION METHODS SEM-EDS28,29 The scanning electron microscope (SEM) uses a focused beam of high-energy electrons to probe the surface of the intermetallic compounds mounted on an aluminum puck with carbon tape. This interaction of high-energy electrons with the sample produces a variety of signals; secondary electrons, backscattered electrons (BSE), diffracted BSE and photons (characteristic X-rays). Secondary electrons and BSE are commonly used for imaging samples (magnification ranging from 20X to approximately 30,000X): secondary electrons are useful for showing morphology of samples and BSE are better for illustrating contrasts in composition in multiphase samples. A secondary electron (5 eV) is emitted from the sample when the incident electron beam weakly interacts with an outer shell electron on a surface atom.

Figure 2.1. The emission of photons occurs (solid line) by excitation (dashed line) of core electrons to outer shells

Photons with wavelengths in the X-ray region of the electromagnetic spectrum is emitted when the incident electron beam interacts with the core electrons by inelastic scattering with enough energy to excite core electrons to outer shell orbitals (K, L, M), leaving vacancies. When the excited electrons fall back to various inner shell orbitals, emissions are generated that are a function of the target element and the type of orbital decay [Fig. 2.1]. Detection of characteristic X-rays for elemental analysis was achieved by Energy- Dispersive X-Ray Spectroscopy (EDS) on a JEOL 5900 SEM. A solid state EDS

detector (cooled by liquid N2) is used to separate the characteristic x-rays of different elements into an energy spectrum, and Princeton Gammatech EDS software is used to analyze the energy spectrum in order to determine the abundance of specific elements [Figure 2.2]. However, EDS detectors have difficulty with light elements (Z≤11), suffer from poor energy resolution, and cannot properly detect elements in low abundance. Therefore, this technique was used as a semi-quantitative means of elemental analysis, yielding approximate elemental ratios.

Figure 2.2. An EDS spectra collected on the cubic LaFexAl13-x compound.

X-ray Diffraction30,31 After elemental analysis has been performed, X-ray diffraction was used to determine structural information of the intermetallic phase; both powder and single crystal diffraction were used to gather this information. Single crystal diffraction was the preferred technique due to high purity single crystal products isolated using the flux growth techniques. Powder diffraction was primarily used to check phase purity of crushed single crystal products or on arc-melted compounds synthesized using traditional solid state techniques. Simple and quick screening techniques [Figure 2.3] using the single crystal diffractometer were performed to check crystallinity of the sample and to gather preliminary structural information before high resolution overnight scans were collected. The structural information gathered using these techniques is critical in understanding the physical properties of the materials studied.

(Bragg’s law)

For diffraction to occur, lattices planes of the solid material must be oriented at the Bragg angle to the incident X-ray beam. In single crystal experiments the X-ray source is held in fixed position while both the detector and the crystal are rotated through a range of angles so a 3-D sphere of diffraction data can be collected. This data is comprised of “frames” in which reflections off lattice planes in reciprocal space are collected by the 2- D plane of the CCD detector when the specific conditions of Bragg’s law are met. Refinement of the frames collected using software packages yields symmetry space group and unit cell parameters. An approximate stoichiometry is needed (determined by EDS) so that the software can correlate the intensity of the diffraction points to determine identity of atoms on specific crystallographic positions, as well as occupancies and thermal parameters. Powder samples are comprised of crystallites that are randomly oriented in all directions. For each set of lattice planes, some crystallites will be oriented so that the conditions for Bragg’s law are satisfied and diffraction will occur. Both the detector and incident X-ray beam are then scanned through a range of angles to monitor changes in diffraction. The data gathered by this technique is less redundant as compared to single crystal experiments and therefore errors are higher. These errors are related to factors

14 that are derived from the intensities of the reflections, such as occupancy and thermal parameters. The symmetry space group and unit cell parameters gathered are trustworthy, which makes this a good technique for examining phase purity. Another advantage of powder X-ray is the average unit cell parameters of numerous crystals can be determined, whereas single crystal experiments only determine the unit cell of the selected crystal.

Figure 2.3. Photograph of intensities from crystal rotated through incident X-ray beam

Accurate structure determination requires single crystal data. Crystals suitable for single crystal X-ray diffraction were selected under a microscope and shards were cleaved using a scalpel and mounted on glass fibers with epoxy. Collections between 90K and 298K were performed using a Bruker SMART CCD diffractometer with cryostat controls. The SMART, SAINT, and Shellx software packages were used for refinement of data; R-values of less than 3% were consistently acquired32,33 Single crystal refinement does not require any prior structural knowledge about the material, however if any information about occupancies, atom sites, and thermal parameters is already known refinement is simplified.

Occasionally arc-melted samples or single crystal phases would be analyzed using a powder diffractometer. The data was collected using a Rigaku CCD and KRYSTALLOFLEX powder diffractometer. Most of the data collected using this instrument was for investigating phase purity. This method requires prior structural information about the material to be entered and refined to account for the location and intensities of the reflections in the powder pattern.

SQUID34 A Superconducting Quantum Interference Device (SQUID) is a sensitive magnetometer consisting of a ring of superconductors separated by thin insulating layers to form two parallel Josephson junctions forming the coil. This is an ideal technique that measures the effect of the magnetic susceptibility of a magnetic compound on a superconducting coil in a magnetic field via the Josephson effect. Mechanical movement of the magnetic compound through the coil produces a magnetic flux, which can be measured by changes in the quantized superconducting current across the Josephson junctions. SQUID measurements that vary temperature, field, and crystal orientation measure the overall behavior of the compounds not that of the individual electrons. The various types of DC and AC measurements performed by the SQUID will be discussed in the next chapter.

CHAPTER 3

IMPORTANT SOLID STATE PHYSICS CONCEPTS

Magnetic susceptibility and magnetic ordering35 The magnetic susceptibilities of compounds of interest can be measured via SQUID (Superconducting Quantum Interference Device) or VSM (Vibrating Sample

Magnetometer). Susceptibilities are typically quoted as molar susceptibilities (χm) based on the magnetization per mole. Data acquired from a SQUID or VSM is recorded as electromagnetic units (emu). This term is proportional to the field used during the measurement, therefore, the moment measured must be divided by the field used during measurement (Oersted (Oe) or Gauss (G); these terms are equal) before dividing by the moles of the compound of interest. If the material has zero unpaired electrons, the induced magnetic moment opposes the applied field. This is referred to as diamagnetism, in these cases the susceptibility measured will be negative and usually on the order of 10-5 emu/mol and is temperature independent.

Figure 3.1. (a) Paramagnetism, (b) ferromagnetism, (c) type I antiferromagnetism, (d) type II antiferromagnetism.

However, if a sample possesses localized unpaired electrons (spins) the induced moments will align with the applied field. This behavior is referred to as paramagnetism and is temperature dependent. The susceptibility measured will be positive and should be on the order of 10-2-10-3 emu/mol at room temperature. Unpaired electrons are common for compounds containing the transition metals and rare earths elements. The spins

associated with unpaired electrons are randomly oriented at high temperatures and align with the field as the temperature is lowered [Fig. 3.1(a)]. Although elements contain core electrons (i.e. paired electrons), the paramagnetic susceptibility will dominate any diamagnetic contributions from the core electrons. Assuming no magnetic interactions,

the molar susceptibility (χm) of paramagnetic ions will obey Curie’s law.

2 2 χm = Nμβ p /3VκβT = C/T Curie Law

χm = C/(T - Θ) Curie-Weiss Law

A plot of 1/(χm) vs. T yields linear behavior for paramagnetic materials at high temperatures. This linear region can be fitted using a linear equation (y = mx + b) which,

can determine the effective magnetic moment (μeff) in Bohr magnetons from the slope. A

table of μeff for the 4f rare earth and 3d transition ions can be found in Mermin and Ashcroft.35 However, Curie’s law cannot explain deviations from linear behavior at low temperatures, therefore, Weiss introduced the concept that adjacent magnetic ions can interact thus producing alignments of electron spins (parallel or anti-parallel) yielding the Curie-Weiss law. The magnitude of the magnetic interactions can be determined via the Weiss constant (θ) using the x-intercept of the linear equation described above excluding any non-linear behavior. A positive Weiss constant indicates ferromagnetic interactions and a negative value indicates antiferromagnetic forces. Curie-Weiss behavior is observed when the ground state is the only state populated. However, some elements

(Sm, Eu) will yield non-linear behavior in a 1/(χm) vs. T plot. This is due to thermal population of low lying excited states; this is referred to as van Vleck magnetism. When the spins begin to interact with each other certain types of magnetic ordering can be observed. If the spins interacting align parallel this situation is referred to as ferromagnetism (FM) [Fig. 3.1(b)], with the corresponding ordering temperature, at

which this occurs, called the Curie temperature (Tc). There are two types of FM; weak and strong. These can often be distinguished in plots of magnetization vs. field commonly referred to as hysteresis loops. In weak (soft) FM the coercivity measured will be small where as in strong (hard) FM the coercivity will be large [Fig. 3.2]. Coercivity is the measure of the field required to flip the spins when the field applied is reversed; this is indicated by the width of the hysteresis loop.

Figure 3.2. Hysteresis measurements performed on a strong (hard) ferromagnet (left) and weak (soft) ferromagnet (right).

In contrast, if the adjacent spins align anti-parallel this is referred to as antiferromagnetism (AFM). The temperature at which this occurs is called the Neél

temperature (TN). Type I AFM occurs when neighboring spins align anti-parallel [Fig. 3.1(c)], Type II AFM occurs when FM layers are oriented anti-parallel [Fig. 3.1(d)]. If a material possesses anisotropy, the spins may prefer to align along a certain axis. This is commonly referred to as the easy axis, whereas the non-preferred axis would be called the hard axis. This can easily be determined by orienting a single crystal with respect to the magnetic field and characteristic behavior is observed when the field is applied parallel or perpendicular the preferred sublattice magnetization [Fig 3.3]. A spin flop transition occurs when the applied field is strong enough to flip the spins from the easy to the hard axis. A transition that occurs from one ordered state to another, such as AFM to FM, is called a metamagnetic transition. This can be either temperature or field induced, and results in an S shaped curve when measuring magnetization vs. field. This S shape results from a large increase in the magnetization with a very small increase in the applied field as expected when transitioning from an AFM to a FM state. The La6Fe13-

xAl1+x compounds discussed later in chapter 5 display this type of behavior. A material may be referred to as a spin-glass when a difference between field cooled (FC) and zero field cooled (ZFC) susceptibilities is observed. FC is when the material is cooled in the presence of a magnetic field and in ZFC the magnetic field is

absent. The magnetic susceptibility in weak field experiments is larger when FC then ZFC, which arises from the magnetic ions randomly freezing in orientation without any long range magnetic order. The origin of such features are typically explained in terms of magnetic frustration, due to competing ferromagnetic and antiferromagnetic exchange interactions, deformed lattices, or a random distribution of magnetic ions.

Figure 3.3. Characteristic susceptibility with the field parallel/perpendicular the preferred sublattice of magnetization for the transition within an anisotropic antiferromagnet.

However, spin-glass-like properties can be observed in systems which exhibit long range magnetic ordering. This splitting (irreversibility) between FC and ZFC susceptibility has recently been shown to originate from the magnetocrystalline anisotropy. The magnitude of the irreversibility is directly related to the coercivity.36 Exchanged biased materials can show this type of behavior and can be confirmed by shifts in hysteresis loops after field cooling the sample.37

Itinerant-Electron Magnetism (IEM)38 IEM can be used to describe the magnetic properties of metallic systems with the 3d transition metals responsible for the magnetic moments. IEM is useful for describing the magnetic properties of La6Fe13-xAl1+x, however, substitution of magnetic rare earths such as neodymium extensively complicates matters. The 4f electrons responsible for magnetic behavior in the rare earth elements are localized, whereas 3d electrons are delocalized into energy bands. The band width W depends on the interatomic separation r between magnetic atoms.

W α r-5

A simplified approach for discussing the magnetism of 3d electron bands assumes that the bands are rectangular and the density of states (DOS) remains constant over the bandwidth W. The 3d transition metals are known to possess up to 10 electrons, however IEM can only occur when less then 10 are present. Depicted below [Fig. 3.4(a)] are partially filled sub-bands with a random distribution of electrons of spin-up and spin- down behavior. With equal filling of each band no spontaneous ferromagnetic moment will be observed.

Figure 3.4. Representation of a partially depleted 3d band; (a) paramagnetism, (b) ferromagnetism

For a spontaneous ferromagnetic moment to occur, one of sub-bands must have an increase in electron population with a concurrent decrease in the other sub-band [Fig. 3.4(b)]. However, moving electrons into higher energy states of the bands increases the kinetic energy of these electrons, which typically counteracts this type of transfer.

Therefore an effective exchange energy term Ueff per pair of 3d electrons is needed for this to be realized, and is defined as the energy gained when switching from anti-parallel to parallel spins. For such a transfer to occur Ueff needs to be large and the DOS at the

Fermi level (EF) high. After such transfer, a magnetic moment will arise and will be equal to μ = (n1 – n2)μβ, where n1 and n2 represent the number of electrons per atom for each spin state and n1 + n2 = the total number of 3d electrons per atom. Therefore, the following interaction Hamiltonian can be derived.

H = Ueffn1n2

Equally populated sub-bands yields the highest energy, therefore, electron transfer is preferred, thus lowering the energy of the system.

If [1-UeffN(EF)] > 0, (N(EF) = DOS at the Fermi level) the system is non- magnetic, however, if [1-UeffN(EF)] < 0, the 3d band is exchange split which corresponds to ferromagnetism. This condition is called the Stoner criterion for ferromagnetism, which is more commonly stated as

UeffN(EF) > 1

Using this model, it can be shown that 3d magnetism leads to moment values expressed in Bohr magnetons per 3d atom depending on the fraction of electrons transferred (p), μ = 2pnμβ. However, for a more accurate approach, the 3d bands can no longer be considered rectangular. A general shape that 3d bands possess is shown in figure 3.5, with the DOS no longer constant over the entire band. If EF is in a region where the DOS is low, the Stoner criterion may not be met, and a spontaneous moment will not form even for small transfers of electrons. A spontaneous moment may only occur where the DOS is high in the vicinity of the EF.

Using the new 3d band shapes describe simple ferromagnetism and relatively strong moments, it is possible to calculate ΔE(μ) from xpressionthe e

1 2 1 2 ΔE(μ)= N(E)EdE + N(E)EdE - (n1 - n2) Ueff 4 � � ∫ ∫ where, ��

n = N(E)dE i 0 �� The first two terms represent the ∫loss in kinetic energy and the third as the gain in exchange energy. Therefore, in order to have a ferromagnetic phase that is more stable then the paramagnetic phase the following criteria must be met.

d ( ) Δ 0 � � �� Therefore, ≤

1 2 1 1 = N(E)dE 1/ eff 1 2 1 2 � −� 2 � � −� � −� ∫ ≥ � �

Figure 3.5. The relative position of the two 3d sub-bands with opposite spin direction: (a) weak ferromagnetism, (b) strong ferromagnetism. The majority spin sub-band is lower in energy than the minority spin sub-band.

The previous situation using rectangular bands is not possible due to the EF not being constant over the sub-bands. Therefore, the two sub-bands must shift relative to each other after electron transfer so as to have the same EF (Fig. 3.5). This shift in the sub-bands allows the sub-band with larger number of electrons to be stabilized by the exchange energy with respect to the sub-band containing the lower number of electrons. The situation in Fig. 3.5(a) corresponds to the equality sign in the previous equation and is used to describe weak ferromagnetic behavior. For a given value of Ueff the optimum band shift and corresponding electron transfer between the two sub-bands has been achieved. Due to the low DOS in the minority spin band further electron transfer is prohibited due to the high kinetic energy expenditure. Therefore, both spin sub-bands will remain partially depleted even though there are enough 3d electrons available for complete filling of the majority spin sub-band. The situation in Fig. 3.5(b) corresponds to the inequality sign in the previous equation and is used to describe strong ferromagnetic behavior. The value of Ueff and the corresponding band shift is more then adequate for complete filling of the majority spin sub-band.

Figure 3.6. Slater-Pauling curve showing the variation of the 3d moment in 3d metals and alloys.38

As shown above, both weak and strong ferromagnetism in a given compounds depends on the shape of the DOS curve, the total number of 3d electrons and the value of

Ueff. Going from right to left in figure 3.6 beginning with full sub-bands, the first sub- band to become partially depleted is the minority spin sub-band, this depletion continues till the upper portion of this sub-band is empty yielding an increase in the 3d moment. Afterwards both bands will simultaneously deplete, with a concurrent shift in the sub-

bands to maintain a constant EF. This treatment yields the Slater-Pauling curve, which shows the variation in of the mean 3d moment in 3d metals as a function of average atomic number and the transition from weak to strong ferromagnetism.

Spin Frustration39 Magnetic frustration can be used to describe lattices with numerous magnetic sites that are subject to competing or contradictory constraints.40 Anti-parallel spins located on the corners of an equilateral triangle is the classic example of magnetic frustration [Fig. 3.7(a)]. A Hamiltonian can be derived for the interaction between any two spins can be written as a scalar product of the spin operators,

Hex= -2JS1·S2 the energy is minimized for collinear spin alignments. Assuming that J is negative which favors antiferromagnetic interactions and that J is equal for all nearest neighbor pairs, only two of the three spin constraints can be satisfied simultaneously. The tetrahedron which is a polyhedron comprised of four edge-sharing triangles can also be considered frustrated; only two of the four nearest neighbor interactions can be satisfied simultaneously [Fig. 3.7(b)].

Figure 3.7. Depicting frustration on an equilateral triangle and a tetrahedron39

Materials possessing frustrated equilateral triangles or tetrahedra commonly appear in 2D and 3D lattices. The most commonly studied lattices are the 2D Kagome lattice (corner sharing triangles) and the 3D pyrochlore lattice (corner sharing tetrahedra) [Fig. 3.8]. In chapter 6 an extremely rare example of an isolated tetrahedron will be presented. Frustrated materials have magnetic interactions on an energy scale set by the 2 exchange energy, Hex ~ -2JS ~kT, where T>> 0. Using Curie-Weiss law to determine

the Weiss constant Θc one can measure the sum of all exchange interactions. Using mean field theory

Θc = 2S(S + 1)/3k ΣznJn

41 where n is the nth neighbor and Jn, the exchange constant. Strong deviations from

Curie-Weiss law are expected as the temperature approaches |Θc| due to the formation of long range magnetically ordered states without the presence of frustration. For

ferromagnetic order |Θc|/Tc ~ 1, antiferromagnetic order |Θc|/Tc ~2-5, where Tc is the critical temperature below which formation of the long range magnetically ordered state

occurs. For frustrated systems |Θc|/Tc > 10 has been proposed and in cases were no long

range ordered states are observed, such as spin glasses, Tf (freezing temperature) is 42 substituted for Tc. Some materials with frustrated lattices, such as the pyrochlore lattice, do not exhibit a transition to a long range ordered state. These lattices are highly degenerate and no unique long range magnetically ordered states can emerge. Materials that possess such characteristics have been termed spin glasses, spin liquids, and spin ices.

Figure 3.8. 2D Kagome and 3D pyrcholore lattices.43 26

CHAPTER 4 MIXED METAL FLUX SYNTHESIS OF QUATERNARY

RT2TrxZn20-x COMPOUNDS WITH T = Mn, Fe AND Tr = Al, In

Introduction Eutectic mixtures of elements form melts at temperatures lower then the standard melting point of the elements; synthesis in such media is of interest as it may produce materials with fewer defects and much less thermally produced strain than those synthesized using traditional high temperature methods. These low melting molten metal fluxes help facilitate diffusion of the elements in solution and make it possible for easy removal of excess materials used for synthesis by centrifugation. In addition molten metal fluxes can often getter impurities, thus offering a cleaner environment for growth.44 We have investigated In/Zn (96.2 : 3.8 mol%, m.p. 143.5ºC) and Al/Zn (11.3% : 88.7%, m.p. 381ºC) eutectics for the growth of new intermetallic phases not accessible by traditional solid state reactions. Optimization of the reactions required varying the ratios around the eutectic point; therefore materials were synthesized in low melting mixtures near the eutectic. There are several families of ternary intermetallic phases comprised of a rare earth

(R), a transition metal (T) and either Zn, In, or Al. These include R2T3Zn14 (ordered 45 Th2Zn17 type), R6T4Al43, R2Pt7In16, and many others. There appears to be no information available at the moment on quaternary compounds comprised of a rare earth element (R), a transition metal (T), zinc, and an element of the boron group (trielide, Tr). In this work, reactions of rare earth elements and T (T= Mn, Fe) in both (In/Zn) and (Al/Zn) molten metal fluxes produced quaternary compounds with identical structure type and similar stoichiometries, RT2TrxZn20-x (2 < x < 7). The products can be

described as substituted variants of the ternary CeCr2Al20 structure, although the indium- containing phases do show some site preferences indicative of a true quaternary structure.

There have been numerous CeCr2Al20 type ternary compounds synthesized (cubic

space group Fd-3m No. 227) with high amounts of aluminum (RT2Al20) and high

46,47 amounts of zinc (RT2Zn20). However, the aluminides are formed with the early transition metals T = Ti, V, Nb, Ta, Cr, Mo, and W, and the corresponding zinc compounds contain late transition metals T = Fe, Ru, Co, Rh and Ni. Here we report the eutectic flux synthesis of quaternary compounds that contain high amounts of zinc with aluminum (RT2AlxZn20-x) and indium (RT2InxZn20-x) incorporations, with T = Mn, Fe.

Table 4.1. Lattice constants of the compounds RT2TrxZn20-x.

3 Compound a (nm) V (nm ) R1 [I>2σ(I)] * YMn2(In5Zn15) 14.7285(4) 3195.04(15) .0274 CeMn2(In4.7Zn15.3) 14.6786(2) 3162.67(7) .0253 PrMn2(In5Zn15) 14.7096(4) 3182.75(15) .0278 NdMn2(In4.5Zn15.5) 14.6522(6) 3145.64(2) .0404 SmMn2(In5.9Zn14.1) 14.8125(4) 3250.01(15) .0234 GdMn2(In5.1Zn14.9) 14.7629(6) 3217.47(2) .0273 DyMn2(In4.7Zn15.3) 14.6677(7) 3155.63(3) .0280 ErMn2(In2.8Zn17.2) 14.4419(4) 3012.13(14) .0201 YbMn2(In5.5Zn14.5) 14.7140(3) 3185.61(11) .0249

YMn2(Al3.9Zn16.8) 14.1533(3) 2835.13(10) .0250 CeMn2(Al5.3Zn14.7) 14.2489(4) 2892.71(14) .0196 PrMn2(Al7.3Zn12.7) 14.2670(2) 2904.01(7) .0210 NdMn2(Al4.8Zn15.2) 14.2499(2) 2893.58(7) .0383 SmMn2(Al4.9Zn15.1) 14.1740(14) 2847.59(5) .0233 GdMn2(Al5Zn15) 14.1761(8) 2848.86(3) .0585 DyMn2(Al4.7Zn15.3) 14.1438(4) 2829.43(14) .0182 ErMn2(Al3.6Zn16.4) 14.1287(4) 2820.37(14) .0192 YbMn2(Al5.3Zn14.7) 14.1152(3) 2812.30(10) .0204

* R1=Σ Fo − Fc /Σ Fo

Experimental Procedure Synthesis

Compounds with the formula RT2(InxZn20-x) were synthesized by combining elements in a 0.5:1:(8:2) (m.p. 280ºC) millimolar ratio. Starting materials for the preparation of these compounds were chips and powders of the rare earth elements (Metall, Strem, Cerac, Arris Int., all > 99.9%), powders of Mn, Fe (Cerac, 99.9%), Zn

(Fisher Chemical, 99.9%), Y (Cerac, 99.9%) and In shot (Alfa Aesar, 99.9%). All elements were combined in an alumina crucible which was placed in a fused silica tube; another alumina crucible was filled with silica wool and inverted on top of the reaction crucible in the silica tube to act as a filter during centrifugation. The fused silica tubes was sealed under a vacuum of 10-2 Torr, and then heated to 900°C in 10hrs, held at this temperature for 24hrs, then cooled to 800°C in 20hrs. The samples were then annealed for 24hrs at 800°C then cooled to 500°C in 60hrs, then held at this temp for 12hrs before cooling to 350°C in 15hrs. At 350°C the fused silica ampules were then inverted and placed into a centrifuge to remove excess molten flux.

Aluminum analogs of these compounds RT2(AlxZn20-x) were synthesized with Al powder (Strem, 99.9%) instead of In shot. This was accomplished by combining elements in a 0.5:1:(2:10) (m.p. 400 ºC) millimolar ratio. These reactions were prepared under the same conditions and starting materials as before except with a modified heating profile. The samples were heated to 1000°C and held there for 24hrs, then cooled to 800°C in 40hrs; again the temperature was held constant for 24hrs and then cooled to 500°C in 60hrs. Samples were then centrifuged as before. The crystals formed as cubes up to 3mm on a side, typically in large conglomerations. Aluminide crystals have a shiny metallic luster whereas the indides have a dull luster. Elemental analysis was performed on all samples using a JEOL 5900 scanning electron microscope with energy dispersive spectroscopy (EDS) capabilities. Samples were analyzed using a 30 kV accelerating voltage and an accumulation time of 40s. Surface analysis of crystals typically showed an excess of the flux in which the crystal were synthesized, so EDS was performed on the interior of cleaved crystals to improve results. Structure Refinements Samples for X-Ray diffraction were selected from the SEM plate after elemental analysis. The large crystals were cleaved into smaller pieces, which were mounted on glass fibers. Single crystal X-Ray diffraction data was collected at room temperature using a Bruker AXS SMART CCD diffractometer equipped with a Mo radiation source; lattice constants are summarized in Table 4.2. Processing of the data was accomplished with use of the program SAINT; an absorption correction was applied to the data using the SADABS

program.48 Refinement of the structure was performed using the SHELXTL package.49 The

crystallographic data is summarized with four representative RMn2AlxZn20-x and

RMn2InxZn20-x compounds listed in Table 4.2; the atomic positions are displayed in Table 4.3. Powder X-ray diffraction data was collected on several samples using a Rigaku Ultima III Powder X-Ray diffractometer with a Cu radiation source and a CCD detector. Additional details regarding the crystallographic refinements can be obtained from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (e-mail: [email protected]) on quoting the depository numbers 416909 through 416925.

Table 4.2. Crystal data for CeMn2(In4.7Zn15.3), SmMn2(Al4.9Zn15.1), YbMn2(In5.5Zn14.5), YbMn2(Al5.3Zn14.7). CeMn2(In4.7Zn SmMn2(Al4.9Zn YbMn2(In5.4Zn1 YbMn2(Al5.3Zn1 15.3) 15.1) 4.5) 4.7) Formula Weight (g/mol) 1656.30 1375.68 1689.22 1436.76 Space Group Fd-3m Fd-3m Fd-3m Fd-3m a (Ǻ) 14.6786(2) 14.1740(14) 14.7140(3) 14.1152(3) V (Ǻ3) 3162.67 2847.65 3185.61 2812.3 3 dcalc (g/cm ) 6.957 6.418 7.044 6.787 Z 8 8 8 8 Temperature (K) 298 298 298 298 Radiation MoKα MoKα MoKα MoKα 2θmax 56.24 56.81 56.09 56.37 Index ranges -19 ≤ h,k,l ≤ 19 -18 ≤ h,k,l ≤ 18 -19 ≤ h,k,l ≤ 19 -18 ≤ h,k,l ≤ 18 Reflections Collected 10064 8731 10310 8991 Unique Data/Parameters 220/18 205/20 220/18 198/20 μ (mm-1) 33.865 30.759 36.635 35.221 R1/wR2* [I>2σ(I)] 0.0253/0.0518 0.0233/0.0415 0.0249/0.0457 .0204/.0441

R1/wR2 (all data) 0.0253/0.0518 0.0250/0.0415 0.0251/0.0457 .0204/.0441 Residual Peaks/hole 0.764/-1.234 0.953/-1.248 0.874/-1.691 0.925/-1.115 2 2 2 2 2 1/2 *R1=Σ Fo − Fc /Σ Fo ; wR2=[Σ[w(Fo −Fc ) ]/Σ[w(Fo ) ]] .

Table 4.3. The atomic positions of CeMn2(In4.7Zn15.3), SmMn2(Al4.9Zn15.1), YbMn2(In5.5Zn14.5), and YbMn2(Al5.3Zn14.7). Atoms Wyckoff site X Y Z Occup. Ueq CeMn2(In4.7Zn15.3) Ce 8a 1/8 1/8 1/8 1 .0046(4) Mn 16d ½ ½ ½ 1 .0047(6) In1 16c 0 0 0 1 .0223(4) Zn1 48f .49291(10) 1/8 1/8 1 .0106(4) In2 96g 0.05696(4) 0.05696(4) 0.32973(6) 0.225(9) .0146(4) Zn2 96g 0.05696(4) 0.05696(4) 0.32973(6) 0.775(9) .0146(4)

YbMn2(In5.5Zn14.5) Yb 8a 1/8 1/8 1/8 1 .0079(3) Mn 16d ½ ½ ½ 1 .0064(6) In1 16c 0 0 0 1 .0229(4) Zn1 48f 0.49327(9) 1/8 1/8 1 .0131(3) In2 96g 0.05756(4) 0.05756(4) 0.32854(6) 0.295(9) .0183(3) Zn2 96g 0.05756(4) 0.05756(4) 0.32854(6) 0.705(9) .0183(3)

SmMn2(Al4.9Zn15.1) Sm 8a 1/8 1/8 1/8 1 .0016(3) Mn 16d ½ ½ ½ 1 .0032(4) Zn1 16c 0 0 0 0.772(4) .0145(7) Al1 16c 0 0 0 0.228(4) .0145(7) Zn2 96g 0.05940(3) 0.05940(3) 0.32472(5) 0.920(5) .0077(3) Al2 96g 0.05940(3) 0.05940(3) 0.32472(5) 0.080(5) .0077(3) Zn3 48f 0.48695(9) 1/8 1/8 0.410(4) .0048(5) Al3 48f 0.48695(9) 1/8 1/8 0.590(4) .0048(5)

YbMn2(Al5.3Zn14.7) Yb 8a 1/8 1/8 1/8 1 .0011(3) Mn 16d ½ ½ ½ 1 .0014(5) Zn1 16c 0 0 0 0.77(1) .0125(7) Al1 16c 0 0 0 0.23(1) .0125(7) Zn2 96g 0.06009(4) 0.06009(4) 0.32301(5) 0.940(8) .0071(3) Al2 96g 0.06009(4) 0.06009(4) 0.32301(5) 0.060(8) .0071(3) Zn3 48f 0.48610(13) 1/8 1/8 0.312(9) .0044(6) Al3 48f 0.48610(13) 1/8 1/8 0.688(9) .0044(6)

Magnetic Susceptibility Magnetic measurements were carried out with a Quantum Design MPMS SQUID magnetometer at temperatures between 3 and 300K. Crystals were first analyzed using EDS, then were sealed in kapton tape and placed into the magnetometer. Temperature dependent susceptibility data were collected at 500 or 1000G, and field dependence data were collected at 3K. Magnetic measurements for many of the samples were complicated by complex non-linear Curie-Weiss behavior indicative of a high amount of paramagnetic Mn-containing impurities and In inclusions.

Results and Discussion Synthesis Synthesis in metal flux mixtures offers the opportunity to explore the comparative reactivity of two solvent metals and frequently allows lower temperature reactions due to the formation of eutectics. Removal of excess solvent by centrifugation is also facilitated by a low melting eutectic. The behavior of pure zinc, aluminum, and indium fluxes has been well-studied. Zinc and aluminum are often incorporated into the intermetallic phases that crystallize from these solvents, forming zinc–rich phases (such as Co2Zn15 50,51 and EuZn13) or aluminides (such as CeAu3Al7 and RNiAl4Ge2). Indium, on the other hand, appears to be a more inert solvent. While it has been used to synthesize indides such as CeCoIn5, it has also been used as a flux for the growth of indium-free silicides 52,53 and germanides including EuZn2Si2 , La2Zn6Ge3, and β-DyNiGe2. Si and Ge apparently form stronger interactions with the rare earth and transition metal reactants than with In, so the flux is excluded from the final products. In the absence of a reaction directing main group element such as Si or Ge, it appears indium is more likely to be incorporated into products. It is notable that the same structure and approximate stoichiometry forms from an indium-rich flux in the RMn2InxZn20-x case and from a zinc-rich flux in the RMn2AlxZn20- x case (x varies from 2 – 7 in both cases; see table 4.1). After discovering these new compounds, reproducing and optimizing the In/Zn synthesis became quite a challenge. A large amount of RIn3 was present as a secondary phase, evidenced in the X-Ray powder diffraction data. With this information and the use of phase diagrams it was decided to decrease the maximum temperature from 1000°C to 900°C; this helped remove the tendency for the reaction to form the more thermodynamically stable binary phase. Once the yield of product was optimized, another problem became apparent. The rotation photographs of numerous samples (taken using the single crystal X-Ray diffractometer) showed streaks in addition to the sharper diffraction spots due to the crystal lattice. This was attributed to our samples forming inclusions of polycrystalline indium since there was a large excess of indium in the reaction. This is a common occurrence in certain flux systems and is a byproduct of excessive nucleation which occurs due to either too fast a cooling rate or too slow of a cooling rate.44 The problem

with inclusions was only apparent in the In/Zn synthesis; the Al/Zn synthesis products were free of such defects. A variety of different transition metals were used in attempts to synthesize structural analogs in the In/Zn flux. Successful syntheses using an 8:2 In/Zn flux ratio occurred with the use of Mn and Fe, while Ti, V, Cr, Co, Ni, Cu, Rh, Ru, Ag, Au, Re, and Mo were all unsuccessful. Once all available transition metals were attempted we began to develop analogs using other Rare Earths. We were successful in isolating

RMn2(InxZn20-x) analogs with R = Y, Ce, Pr, Nd, Sm, Gd, Dy, Er, and Yb. Attempts to use La, and Eu were unsuccessful, while Pm, Tb, Ho, Tm, and Lu were not available for use. While synthesizing aluminum analogs using a Al/Zn flux ratio of 2:10 we were successful once again with Mn and Fe for the transition metals; for the Rare Earth analogs we were successful with Y, Ce, Pr, Nd, Sm, Gd, Dy, Er, and Yb. Both

RT2AlxZn20-x and RT2InxZn20-x compounds were unable to incorporate La and Eu, which may be due to size effects. Europium appears to favor the divalent state in many intermetallics; Eu2+ and La3+ have larger radii then the other rare-earth ions. Synthesis of similar compounds in Ga/Zn eutectic mixtures was not attempted due to the difficulty in distinguishing Ga and Zn in the X-ray structure, but it is expected that

R(Mn/Fe)2(GaxZn20-x) phases would form.

Manganese In/Zn Compounds

The cubic RMn2(TrxZn20-x) structure [Fig. 4.1] can be viewed as a packing of coordination polyhedra with the rare earth atoms coordinated by 16 Zinc/Tr atoms forming a Frank-Kasper polyhedron CN16 [Fig. 4.2(a)], while the transition metal rests inside a 12 coordinate icosahedron of Zn/Tr atoms [Fig. 4.2(b)]. Upon comparison of the

RMn2(Tr)xZn20-x compounds to Jeitschko’s RT2Zn20 compounds we began to notice similarities and differences to our structures.47 There is some preferential siting seen in the indium phases, with indium occupying the 16c wyckoff site and Zn occupying the 48f site, but the 96g site is occupied by a mixture of In/Zn in all the analogs. The local environment of In1 (16c) consists of a double six ring polyhedron, made from the mixed

In2/Zn2 (96g) and Zn1 (48f) sites, capped axially by two rare earth atoms [Fig. 4.2(c)]. Indium favors this site likely due to the fact that it has a higher coordination number (CN 14) then either of the other two Zn sites (CN 12). Therefore it can more readily accommodate the larger size of the indium atom. The Zn1 (48f) site rests inside a (CN 12) bicapped pentagonal prism with two transition metals in the axial position [Fig. 4.2(d)].

Figure 4.1. The cubic RT2TrxZn20-x structure viewed down the [110] direction, showing the structure as connected polyhedral. The larger dark polyhedral (CN 16) contain the rare-earth element while the smaller light icosahedra (CN 12) are centered by the transition metal.

(a) (b)

(e)

Figure 4.2. Coordination polyhedral in the RMn2InxZn20-x compounds; (a) The rare-earth element R is represented by a large green sphere, (b) Mn is represented by a small yellow sphere, (c) In is represented by a large purple sphere with equatorial lines, (d) Zn1 is represented by small gray spheres, (e) The mixed In2/Zn2 site is represented by small half red half gray spheres.

The local environment of the In2/Zn2 (96g) mixed site consists of a pentagonal prism of In and Zn comprised of the 96g, 48f, and 16c sites [Fig. 4.2(e)]. The prism is capped axially by the transition metal and rare earth with the rare earth side being truncated. During the structural refinement, the occupancy of the 96g site was initially assigned to be filled with zinc. However, the occupancy was greater than 100%. Since these compounds were grown out of an indium flux, and indium has a higher scattering power then Zn, it was decided that perhaps this site was a mixed Zn/In occupancy. Upon examination of the thermal parameters for these sites it was observed that the mixed site’s

thermal parameter was between the values for the pure In site and the pure Zn site, which further reinforced the idea that this was a mixed Zn/In site. The average indium occupancy on the 96g site for all analogs is 23.9% ± 7.4%. After refinement of this mixed Zn/In site it was observed that the unit cell volumes had a direct relationship to the amount of indium present in the sample [Fig. 4.3]. This is reasonable given that indium’s atomic radius (167 pm) is larger then the zinc radius of (134 pm) and that indium is present in large amounts. Therefore increasing or decreasing this amount would have a much larger effect on unit cell volume then the lanthanide contraction. For cases where the analogs have the same amount of indium incorporated in the structure the cell volumes do appear to follow the lanthanide contraction.

3300

3250

Å)

3200

3150 Unit Cell Volume ( Volume Cell Unit

3100

3050

3000 2 3 4 5 6 7 Indium Content

Figure 4.3. Cell volumes of RT2InxZn20-x compounds versus amount of indium present in the sample. The size of the data point is larger than error in unit cell volumes.

The amount of indium present on the 96g site strongly impacts the local environments of the rare earth [Fig. 4.2(a)] and transition metal [Fig. 4.2(b)]. The rare

36 earth Frank-Kasper (CN 16) polyhedron is made up of elements from the mixed (In2/Zn2) 96g site and the In1 16c site. The 16c site of indium tetrahedrally coordinates to the rare earth elements inside the (CN16) polyhedron. The R-In1 bond lengths show a linear dependence to the amount of indium present in the sample [Fig. 4.4]. The R- (In2/Zn2) bond lengths show this dependence as well, but what is of notable interest is that the R-In1 bond lengths are shorter then the R-(In2/Zn2) bond lengths.

3.4

3.35

R - In/Zn bond 3.3

3.25

3.2 R - In bond Bond Length (Å)

3.15

3.1 2 3 4 5 6 7 Indium Content

Figure 4.4. Dependence of the R-In1 and R-(In2/Zn2) bond lengths in the rare-earth polyhedron on the indium content x of the compounds RMn2InxZn20-x. The size of the data points is larger than the error in bond lengths.

Upon examination of the icosahedral transition metal polyhedron [Fig. 4.2(b)] similar trends in bond lengths as stated earlier were observed. The transition metal polyhedron is surrounded by elements from the 96g mixed site (In2/Zn2) and the 48f zinc site (Zn1). The Mn-(In2/Zn2) bond length shows the linear dependence on bond length due to the amount of indium present in the sample; the Mn-Zn2 bond length (48f zinc site) shows this dependence as well even though it does not incorporate indium on the site. It was observed that as the indium content increased the (In2/Zn2)-(In2/Zn2) bond

lengths increased, as did the Zn1-(In2/Zn2) bond lengths; however the Zn1-Zn1 bond lengths decreased. [Fig.4.5]. This may be a compensation for the overall expansion of the polyhedra in the structure as the amount of indium rises.

2.95

2.9

2.85

2.8

2.75

)

2.7

2.65

2.6 Bond Length (Å Length Bond

2.55

2.5 2 3 4 5 6 7

Indium Content

Mn-In2/Zn2 Mn-Zn1 In2/Zn2-In2/Zn2

Zn1-Zn1 Zn1-In2/Zn2(Short) Zn1-In2/Zn2 (Long)

Figure 4.5. Changes in Mn icosahedron bond lengths due to varying amount of indium present in the RMn2InxZn20-x compound. The size of the data points is larger than the error in bond lengths.

Al/Zn Compounds

Regarding the aluminum analogs (RMn2AlxZn20-x), the amount of aluminum on each of the three mixed sites can vary from 4-69% with no site having a preference for aluminum. This is reasonable considering the comparable size of atomic radii of aluminum (143 pm) and zinc (134 pm). Mn is again centering an icosahedron in this phase. The average Mn-Al2/Zn2 bond length for all the analogs is 275.9 ± 0.5 pm; clearly there is very little variance in this bond length even though the amount of aluminum on this site can vary from 6-69%.

After refinement of these aluminum analogs a trend in unit cell volumes became apparent. In this set of compounds the cell volume no longer has a direct relationship to the amount of triel element in the mixed sites; it is apparent that the cell size of these analogs follows the lanthanide contraction [Fig. 4.6]. This again can be attributed to aluminum’s atomic radius being of comparable size to zinc’s atomic radius; therefore the larger perturbation caused by changing the rare earth size governs volume effects.

2920

2900

2880

2860

2840

2820

2800 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Rare Earth

Figure 4.6. Cell volumes of the RMn2AlxZn20-x versus rare-earth element size. The size of the data point is larger than error in unit cell volumes.

Incorporation of manganese

Previous research has noted that RT2Al20 compounds form with the early transition elements (T = Cr, Ti) whereas the RT2Zn20 compounds incorporate the late transition elements (T = Fe, Co, Ni).46,47 This can be rationalized by atomic volume arguments. The polyhedra of these ternary structures are comprised of aluminum (with metallic radius of 143.2 pm) or zinc (with metallic radius of 139.4 pm). Therefore

assuming equally dense packing of the aluminum and zinc, the space available for the transition element is greater in the aluminides than in the zinc compounds.47 Therefore the larger early transition metals are accommodated in the aluminides, and the smaller late transition metals in the zinc phases.

This logic can be used to explain the incorporation of manganese in these

RMn2TrxZn20-x compounds. The addition of a small amount of Al or In into the zinc framework creates a slightly expanded icosohedral coordination polyhedron which is large enough to contain Mn, but not large enough to incorporate the earlier transition metals. However, indium atoms are larger than aluminum atoms and one would expect that fewer In atoms need to be incorporated to allow for Mn inclusion if size were the dominant factor. But the amounts of triel element in these compounds averages around 5 for both the In and Al containing series. This indicates that another factor such as valence electron count may play a more important role. Valence electron count (vec) can account for Mn substitution, assuming Zn has

two valence electrons and Tr elements have three. RT2Zn20 compounds reported by Jeitschko have valence electron counts that vary between 59 and 63 as the identity of the 47 transition metal and rare earth is varied. For the RMn2TrxZn20-x stoichiometry with x varying between 2 and 7 (as observed), calculated valence electron counts also range between 59 and 64, indicating a good fit to the stable valence electron count range

presented by Jeitschko. Unsubstituted RMn2Zn20 (vec = 57) would fall outside this range. It appears that substitution of Zn by a triel element with a higher vec allows transition metals with lower vec to be incorporated into the structure.

Iron In/Zn Compounds Using the same synthetic method substitution of manganese with iron readily occurs [Table 4.4], however not all analogs were synthesized but similar results would be expected. The incorporation of iron into this structure has been previously observed in 47 the form of RFe2Zn20 with no triel element present. The cell volumes of the iron analogs follow the lanthanide contraction. This is in contrast to the cell volumes of the manganese analogs which were directly related to the

amount of indium present. The absence of mixing on the 96g site yields a consistent amount of indium in the iron analogs. Synthesis using the In/Zn flux yielded incorporation of indium into the 16c site and Zn occupying the 48f and 96g site [Table 5]. Mixing of In/Zn on the 96g site is no longer observed as compared to the manganese analogs, which was previously determined to stabilize the structure in terms of vec. This mixing is not needed due to the increased vec of Fe (8 electrons) to Mn (7 electrons). The vec of the iron analogs with indium present is 61 which is within the stable range of 59-63 presented by Jeitschko.47

Table 4.4. Lattice constants of the compounds RFe2In2Zn20 and RFe2AlxZn20-x. 3 Compound a (nm) V (nm ) R1 [I>2σ(I)]* CeFe2(In2Zn18) 14.4830 3037.915 .0316 PrFe2(In2Zn18) 14.4180 2997.195 .0219 NdFe2(In2Zn18) 14.4037 2988.286 .0336 SmFe2(In2Zn18) 14.3587 2960.366 .0335 GdFe2(In2Zn18) 14.2885 2917.158 .0512 ErFe2(In2Zn18) 14.2363 2885.303 .0259 YbFe2(In2Zn18) 14.2537 2895.895 .0200

YFe2(Al4.3Zn15.7) 14.1052(3) 2806.324 .0121 SmFe2(Al4.1Zn15.9) 14.1464(9) 2830.987 .0275 GdFe2(Al4.6Zn15.4) 14.1193(2) 2814.748 .0158 DyFe2(Al4.5Zn15.5) 14.1019(3) 2804.354 .0213 ErFe2(Al3.2Zn16.8) 14.0624(4) 2780.855 .0184

Er2Fe(Zn4.4In15.6) 14.7990(3) 3241.135 .0290 *R1 = Σ||Fo|- |Fc||/ Σ|Fo|

A unique phase was isolated in which site switching occurred during synthesis [Table 4.2]. This phase features full occupancy of the 16c and 96g sites, with mixing on the 48f site, which was only previously observed for the aluminum analogs. The typical stoichiometry of these compounds ErFe2In2Zn18 was replaced with Er2FeZn4.4In15.6. This resulted in the cell volume increasing from 2885.3 nm3 to 3241.1 nm3, respectively. This is expected due to the larger atomic radius of In (167 pm) compared to Zn (134 pm). The vec of the site switched phase is 70 which is not within the stable range of 59-63 for the

non site switched compounds.47 This could indicate isolation of a metastable phase using the In/Zn flux. The magnetic properties for the iron analogs were similar to that of the manganese analogs and will be discussed later. However, this new phase now possesses magnetic nearest neighbor interactions between Er and Fe (Er-Fe 3.204 Å), whereas the former had only next nearest neighbor interactions. This new arrangement creates a network of magnetic ions and could yield interesting magnetic ordering [Figure 4.7]. However, samples for this phase were not able to be reproduced.

Table 4.5. Atomic coordinates for ErFe2(In2Zn18) and Er2Fe(Zn4.4In15.6) Atoms Wyckoff x y z Occup. Ueq site

ErFe2(In2Zn18) Er 8a 1/8 1/8 1/8 1 .00599 Fe 16d ½ ½ ½ 1 .00402 In1 16c 0 0 0 1 .01108 Zn1 48f 0.48984 1/8 1/8 1 .00967 Zn2 96g 0.05724 0.05724 0.32817 1 .01080

Er2Fe(Zn4.4In15.6) Er 16c 0 0 0 1 .03227 Fe 8a 1/8 1/8 1/8 1 .00832 Zn1 16d ½ ½ ½ 1 .00614 Zn2 48f 0.49368 1/8 1/8 0.40 .01565 In2 48f 0.49368 1/8 1/8 0.60 .01565 In1 96g 0.05738 0.05738 0.32897 1 .02205

Al/Zn Compounds Utilizing the Al/Zn flux Al has shown the ability to mix on the 16c, 48f and 96g sites, similar results were observed for the manganese analogs. The ability of Al mixing with Zn increases on these sites in the order 96g < 16c < 48f with comparable occupancies in these analogs. Similar to the iron analogs containing indium and the manganese analogs containing aluminum the cell volumes followed the lanthanide contraction. Not all

42 analogs were synthesized but similar reactivity towards the lanthanide elements would be expected [Table 4.1, 4.4].

Figure 4.7. Network of Er (Green) and Fe (Red) in site switched compound Er2FeZn4.4In15.6. In and Zn were omitted for clarity. Unit cell shown in Blue.

Magnetic Susceptibility

There is no evidence of magnetic ordering down to 3K in any of the RT2TrxZn20-x compounds presented. This can be attributed to the large separation of the magnetic species (the rare earth ions are over 6Å apart); the lack of magnetic interactions is not unexpected. Compounds containing rare earth metals with low magnetic moments (i.e. Ce3+, Pr3+) show slight deviations from Curie-Weiss behavior due to the presence of

small amounts of paramagnetic Mn impurities; these were also apparent in the data for the analog containing non-magnetic Y3+. The susceptibility of such impurities has a much less detrimental effect on the data for compounds of rare earths with larger magnetic moments, which display Curie-Weiss behavior.

100 9 (a)

8 7 6 5 4

(emu/mole Yb) 3

m 2 χ

1/ 1 0 0 10 20 300 400 Temperature (K)

40 ) 35 (b) 30 25 20 (emu/mole Sm

m 15 χ 1/ 10 5 0 0 10 200 30 400

Temperature (K)

Figure 4.8. Temperature dependence of the inverse molar susceptibility (1/χm) for (a) YbMn2(Al5.3Zn14.7) and (b) SmMn2(Al4.9Zn15.1).

The magnetic moments derived from the data agree with the theoretical values for the rare earth element, and the low Weiss constants are another indication of little to no

interaction between magnetic ions. Magnetic susceptibility data for the YbMn2Al5.3Zn14.7 analog is shown in Figure 4.8(a); the fit indicates a trivalent state for ytterbium, with no 3+ sign of fluctuating or mixed valency (observed µeff = 5.01µB; theoretical µeff for Yb =

4.54 µB). The data for SmMn2Al4.9Zn15.1 is more complex, as shown in Figure 4.8(b); it indicates that this compound strongly deviates from Curie-Weiss behavior. This is likely due to the complex van Vleck paramagnetism typically associated with Sm atoms in cubic symmetry.54 Concurrence of the experimental magnetic moments with the theoretical values for the rare earth ions indicates that the manganese atoms show diamagnetic behavior in these compounds. This is in agreement with studies of other multinary R/T/main group intermetallics containing low stoichiometric ratios of transition metals T.45d, 51, 53c Paramagnetic manganese is observed for intermetallic compounds that are comparatively rich in Mn; RMn4Al8 and RMn6Al6 have the same crystal structure, but only the latter material has magnetic Mn species.55 On the other hand, Zintl phases (comprised of very electropositive metals—such as Na, Ca, Eu—in combination with main group metals or metalloids such as Tl, Ge, P, Bi) containing small amounts of Mn usually feature 56 paramagnetic manganese ions, as seen in the compound Ca14MnP11. However, these compounds are more ionic in nature and lend themselves to being viewed as charge balanced materials with localized electrons producing a specific oxidation state/formal charge on each atom. Intermetallics such as the ones studied in this work can seldom be understood this way. While they may contain a very electropositive element whose oxidation state is obvious/measurable (such as Ca2+ or Nd3+), the electrons donated by these elements are not localized on another specific atom or atoms in the structure; they are essentially delocalized in bands created by orbital overlap. The Mn d-band for the

RMn2TrxZn20-x structures is likely located below the Fermi level and will therefore be filled, rendering the Mn magnetically silent. Band structure calculations would be useful in studying this aspect of these compounds.

Conclusion We have shown that mixed metal fluxes are suitable media for the successful growth

of RT2TrxZn20-x, (T = Mn, Fe) quaternary substituted variants of the ternary RT2Tr20

structure. Substitution of zinc by a specific amount of triel (Al or In) produces the correct size and valence electron count to allow the incorporation of Mn atoms into these phases. Although Fe analogs were also developed and presented further investigations are needed for the site switching behavior observed when synthesizing in In/Zn flux.

CHAPTER 5 CRYSTAL GROWTH AND SPIN GLASS-LIKE BEHAVIOR

OF R6T13-xAlxMy (R = RARE EARTH; T = Mn, Fe; M = MAIN GROUP) PHASES GROWN FROM LANTHANIDE-RICH EUCTECTIC FLUXES

Introduction Due to their high melting points, La (m.p. 918ºC) and Ni (m.p. 1455ºC) are not ideal elements for use as molten metal solvents (flux) to synthesize single crystal products. However, when combined in an 88:12 wt% ratio they form a eutectic with a melting point of 532 ºC. This flux is being explored as a medium for the growth of new intermetallic phases. The use of molten metal solvents enhances diffusion of the reactants, provides a wide temperature range for single crystal growth, and allows isolation of products by means of centrifugation to remove the excess flux. In many instances, these molten metals act not only as solvents, but also as reactants which can be incorporated in the final product (i.e. reactive flux). The La/Ni metal eutectic flux is a unique system that combines a reactive component (lanthanum) with an inert component

(nickel). We have crystallized numerous Fe-based intermetallics such as La21Fe8M7C12, 57,58 LaFe12B6, and La6Fe13-xAl1+x from this flux mixture without any Ni incorporation .

The magnetic and structural properties of R6Fe13-xM1+x (R = early rare earth, M =

Si, Ge, Al, Au, Ag…) with the La6Co11Ga3-type tetragonal structure have attracted the interest of many research groups.59-61 The structure, shown in figure 5.2, consists of iron- rich layers separated by layers comprised of R and M, stacked along the c axis. The binary variant of this phase (R6Fe14) does not exist; a third element is required to mix into

the 16l2 and 4a sites to stabilize the structure (resulting in ternary variants such as

La6Fe13-xAl1+x), and a fourth element can also be incorporated in the 4a site to create

quaternary analogs such as La6Fe10Al3P1. Due to technological applications much of the

focus has been on the Nd6Fe13Si variant due to its presence as an impurity phase which can enhance coercivity in Nd-Fe-B permanent magnets.62 Few studies have been

performed on the La analogs, due to the inability to synthesize single crystals of this peritectic phase using arc-melting techniques and the common occurrence of impurities such as α-Fe and La3Al.

In this work, large single crystals of a variety of La6Fe13-xM1+x analogs have been grown from La/Ni eutectic. The structural variations with the identity of M and the filling of the mixed and partially occupied sites have been explored and will be crucial to tailoring the magnetic properties of these phases. We have also explored Nd/Fe and

La/Mn eutectic to crystallize additional R6TxAlyMz analogs. All the members of this family exhibit either temperature or field induced first-order magnetic phase transitions and are attractive systems for applications in materials science and for the study of fundamental magnetic properties such as itinerant-electron magnetism (IEM). The magnetic properties of these R6Fe13-xM1+x compounds are controversial with various magnetic ordering models being proposed based on results of a variety of studies including susceptibility measurements (SQUID and VSM), Mossbauer spectroscopy, X- Ray and neutron diffraction. Understanding the magnetic behavior is complicated by competing intralayer and interlayer ordering mechanisms. The exploration of the La analogs is crucial to isolating the behavior of the iron layers in the absence of competing magnetic ordering mechanisms in the rare earth layers. These properties will be investigated through a combination of magnetic susceptibility and heat capacity measurements. Experimental Procedure Synthesis

Starting materials for preparation of La6Fe13-xAl1+x and La6Fe13-xAlxMy phases were powders of the rare earth metal La (METALL Rare Earth Ltd and Acros, purity > 99.9%), powders of Fe, Bi, Sb, (Strem Chemicals, 99.9%), Cu, Au, P (Alfa Aesar >99.9%), Ag (PremIon >99.9%), Ge (Cerac >99.9%), chips of Pb (Fisher Scientific >99.7%), and In (Alfa Aesar >99.9%). Chips cut from ingots of La/Ni eutectic (88:12 wt%, Alfa Aesar 99.9%, m.p. 532ºC) were used for the flux reagent. The standard reactant amounts were 1mmol of La, 1.5mmol Fe, 0.5mmol Al and a variable molar amount of M layered between ~1g of La/Ni flux in an alumina crucible. This was placed in a fused silica tube; another alumina crucible was filled with silica wool, inverted and

48 placed on top of the reaction crucible to act as a filter during centrifugation. The silica tube was then sealed under a vacuum of 10-2 Torr. Various heating profiles were investigated (vide infra), but the best results were obtained by heating to 1000°C in 3hrs, holding at this temperature for 12hrs, then cooling to 850°C in 10hrs. The samples were then annealed for 48hrs at 850°C then cooled to 600°C in 84hrs. At 600°C the fused silica ampoules were then inverted and placed into a centrifuge to remove excess molten flux. Due to the high lanthanum content, the La/Ni eutectic flux is an aggressive reducing agent that will leech Al from alumina crucibles; this resulted in our initial synthesis of the La6Fe13-xAlx phases. The reactivity of the flux also allows for a unique way to remove any excess flux attached to the crystals by leaving the products out overnight. The La-rich flux oxidizes in air, and the product crystals can be picked out of the rare earth oxide/nickel powder. This is a rather nice side effect of using this flux for growth, as it allows isolation of the product without using solvents which could damage the single crystal. Due to the layered growth habit of this system, any remaining flux on the surface of the crystal can be removed by shearing off a small layer of the crystal using a scalpel if scraping is not successful. The crystals are sufficiently air stable to allow extended handling and storage under standard conditions, but were stored in a dry box as a precaution to prevent any degradation.

Elemental analysis. Elemental analysis was performed on all samples using a JEOL 5900 scanning electron microscope with energy dispersive spectroscopy (SEM-EDS) capabilities. Samples were analyzed using a 30 kV accelerating voltage and an accumulation time of 40s. Surface analysis of crystals typically showed good stoichiometric ratios for the La, Fe, and Al. The M elements however, would not resolve nicely from surface measurements; therefore EDS was performed on the interior of shattered crystals to confirm its presence. Because of the possibility of Ni contamination from the flux the samples were also monitored for this element, but it was not observed in any of the scans.

X-ray diffraction. Small interior shards were cleaved from the large single crystals grown in flux and analyzed by EDS. The crystals were mounted on glass fibers using epoxy, and single-crystal X-ray diffraction data for each compound was collected at room temperature on a Bruker AXS SMART CCD diffractometer. Data processing was then performed using the program SAINT; an adsorption correction was applied to the data using the SADABS program.63 The structure was solved using direct methods and refined with the SHELXTL package of programs.64 Table 5.1 contains crystallographic collection parameters for ternary phases synthesized.

Table 5.1. Crystallographic collection parameters for three representative R6Fe13-xAl1+x ternary compounds.

La6Fe10.5Al3.5 La6Mn10Al4 Nd6Fe10.5Al3.5 Formula Weight (g/mol) 1514.32 1490.77 1546.30 Space Group I4/mcm I4/mcm I4/mcm a (Ǻ) 8.2168(4) 8.4533(3) 8.1513(6) c (Ǻ) 23.6986(22) 23.9345(20) 23.1413(31) V (Ǻ3) 1600.03 1710.32 1537.59 3 dcalc (g/cm ) 1.572 1.447 1.670 Z 4 4 4 Temperature (K) 298 298 298 Radiation MoKα MoKα MoKα 2θmax 56.59 56.55 56.64 -10 ≤ h ≤10 -11 ≤ h ≤11 -10 ≤ h ≤10 -10 ≤ k ≤ 10 -11 ≤ k ≤ 11 -10 ≤ k ≤ 10 Index ranges -31 ≤ l ≤ 31 -31 ≤ l ≤ 31 -30 ≤ l ≤ 30 Reflections Collected 11045 11674 10670 Unique Data/Parameters 566 597 548 μ (mm-1) 24.55 22.20 29.08 R1/wR2 [I>2σ(I)] 0.0291/0.0563 0.0285/0.0584 0.0197/0.0411 R1/wR2 (all data) 0.0291/0.0563 0.0286/0.0584 0.0198/0.0411 Residual Peaks/hole (e/Å3) 1.310/-1.233 5.24/-0.849 1.542/-0.942

Magnetic susceptibility. Magnetic susceptibility measurements were performed with a Quantum Design MPMS SQUID magnetometer at temperatures between 1.8 and 400K. Anisotropic measurements were performed on clean single crystals sealed in kapton tape in specific orientations with respect to the applied field. Field cooled and zero-field cooled temperature dependence measurements were collected at 2000G with field dependent measurements collected at 1.8K.

Table 5.2. Ternary compounds synthesized. *Occupancy of site refined as mixed Fe/Al. ‡Occupancy of site refined as mixed Mn/Al. Iron M Compound Occupancy of Occupancy a (Å) c (Å) R1 16l2 site of 4a site La6Fe10.7Al3.3 0.29234 0.57/0.43* 8.2327 23.8036 0.0229

La6Fe10.5Al3.5 0.34435 0.10/0.90* 8.2168 23.6986 0.0291

La6Fe10.4Al3.6 0.27251 0.35/0.65* 8.2297 23.7924 0.0257

La6Fe10.4Al3.6 0.32017 0.15/0.85* 8.2352 23.7904 0.0352

La6Fe10.4Al3.6 0.31518 0.09/0.91* 8.2294 23.7678 0.0193

La6Fe10.3Al3.7 0.29553 0.09/0.91* 8.2268 23.7734 0.0355

La6Fe10.2Al3.8 0.28612 0.08/0.92* 8.2368 23.8004 0.0328

La6Fe10.1Al3.9 0.27418 0.04/0.96* 8.2342 23.7772 0.0283

La6Fe10.1Al3.9 0.24289 0.09/0.91* 8.2365 23.7495 0.0424

La6Fe10Al4 0.23265 0.03/0.97* 8.2380 23.7039 0.0268 ‡ La6Mn10Al4 0.20547 0.15/0.85 8.4533 23.9345 0.0285 ‡ La6Mn10Al4 0.19277 0.23/0.77 8.4406 23.9366 0.0436 ‡ La6Mn9.9Al4.1 0.20459 0.12/0.88 8.4647 23.9202 0.0450

Nd6Fe11Al3 0.48966 0.01/0.99* 8.1335 23.1026 0.0206

Nd6Fe10.5Al3.5 0.36670 0.01/0.99* 8.1513 23.1413 0.0197

Results and Discussion Synthesis The facility with which crystals of iron-rich intermetallics can be grown from a commercially-available La/Ni eutectic has led to the crystallization of a wide range of

ternary La6Fe13-xAl1+x (Table 5.2) and quaternary La6Fe13-xAlxMy compounds (Table 5.3). This allows investigation of the effects of stoichiometry variation on the structure, and will also facilitate the characterization of effects on magnetic behavior (to be published in another manuscript). We have also expanded the study of rare earth/transition metal eutectic flux chemistry to the Nd/Fe and La/Mn systems to explore further variation of the ternary and quaternary compounds. Our initial synthesis was aimed at generating single crystals of a new iron carbide intermetallic. However, due to the aggressive reducing nature of the La/Ni flux, Al was etched from the alumina crucible used for synthesis, which yielded single crystals of the ternary La6Fe13-xAl1+x phase (Fig. 5.1). So far this compound has only been synthesized using traditional arc melting techniques yielding impure polycrystalline samples,

although Canfield, et al. have investigated growth of Nd6Fe13-xAl1+x in melts rich in Nd and Al relative to their desired product.65 These compounds are peritectic phases which melt incongruently; as such it is difficult to isolate pure bulk samples and single crystals using traditional stoichiometric synthesis. This inability to synthesize single crystals limits the ability to perform accurate characterization and contributes to the difficulty in understanding the magnetic properties of these materials.

Figure 5.1. Image displaying typical morphology of R6T13-xAlxMy phases viewed parallel the c-axis captured using an SEM. The white powder is La2O3 from excess La/Ni flux attached to surface becoming oxidized.

Table 5.3. Quaternary compounds synthesized. The 4a site of quaternary compounds refined as partially occupied. †Occupancy of site refined as mixed Fe/Si. Iron M Compound Occupancy of Occupancy a (Å) c (Å) R1 16l2 site of 4a site

La6Fe10Al3Si1 0.26129 1 8.2118 23.5818 0.0208 † La6Fe10.5Al2.7Si0.8 0.32631 0.17/0.83 8.2083 23.6073 0.0246 † La6Fe10.5Al2.7Si0.8 0.32339 0.21/0.79 8.2101 23.6200 0.0248

La6Fe9.8Al3.2P1 0.21195 1 8.2408 23.7478 0.0230

La6Fe9.9Al3.1S0.92 0.21319 0.91495 8.2394 23.7587 0.0403

La6Fe10.2Al2.8Cu0.49 0.29194 0.49124 8.2227 23.6992 0.0359

La6Fe10.4Al2.6Ga0.63 0.34833 0.62529 8.2123 23.6766 0.0337

La6Fe10.1Al2.9Ga0.63 0.27834 0.62677 8.2228 23.7053 0.0383

La6Fe10.5Al2.5Ge0.74 0.36655 0.74174 8.2123 23.6418 0.0316

La6Fe9.5Al3.5Ge0.76 0.13127 0.76046 8.2428 23.6757 0.0240

La6Fe9.9Al3.1As1 0.23362 1 8.2542 23.8681 0.0302

La6Fe10.2Al2.8Se0.37 0.30875 0.37369 8.2230 23.6664 0.0263

La6Fe9.9Al3.1Se0.37 0.23239 0.36613 8.2328 23.7444 0.0219

La6Fe10.2Al2.8Ag0.37 0.30923 0.36921 8.2224 23.6871 0.0411

La6Fe9.7Al3.3Ag0.54 0.18055 0.53497 8.2474 23.7586 0.0284

La6Fe9.8Al3.2Ag0.66 0.20943 0.65930 8.2498 23.7812 0.0435

La6Fe10.4Al2.6In0.55 0.34691 0.54929 8.2418 23.8782 0.0307

La6Fe10.4Al2.6Sb0.73 0.35085 0.73214 8.2375 23.7998 0.0214

La6Fe9.8Al3.2Sb0.92 0.20841 0.91680 8.2583 23.8653 0.0243

La6Fe9.4Al3.6Sb0.95 0.10985 0.94628 8.2691 23.8903 0.0278

La6Fe10.1Al2.9Au0.22 0.28818 0.21993 8.2296 23.7113 0.0247

La6Fe10.4Al2.6Pb0.65 0.35552 0.64401 8.2368 23.9253 0.0226

La6Fe9.8Al3.2Bi0.32 0.19354 0.31773 8.2389 23.7525 0.0433

La6Fe9.4Al3.6Bi0.47 0.09074 0.46467 8.2695 23.9019 0.0445

La6Fe10Al3Bi0.60 0.20160 0.59827 8.2534 23.8842 0.0694

La6Fe10.1Al2.9Bi0.75 0.26249 0.75250 8.2752 23.9842 0.0389

La6Fe10.4Al2.6Bi0.84 0.34722 0.83897 8.2522 23.9511 0.0216

La6Fe9.5Al3.5Bi0.91 0.12478 0.90852 8.2842 24.0373 0.0218

La6Fe10.6Al2.4Bi0.91 0.39547 0.91206 8.2417 23.9813 0.0232

La6Mn10.5Al2.5Sb0.91 0.37755 0.90912 8.4175 23.9515 0.0213

Nd6Fe11.5Al1.5Sb0.5 0.61634 0.50303 8.1144 23.1155 0.0314

During synthesis the heating program was varied in attempts to increase crystal yield and size. Changes to cooling rates and dwell times had minimal effect on crystal growth; however, changes in the initial ramping had the most drastic effects. Utilizing a quick initial ramp time of 3 hours provided a better melt of the La/Ni flux which yielded a more liquid environment to facilitate crystal growth. Using a 6 hour ramp time typically resulted in a very poor melt of the La/Ni flux and no reaction would occur.

Iron compounds We are able to synthesize a variety of single crystal iron-based intermetallics using the La/Ni flux, such as the metamagnetic phase LaFe12B6, La6Fe13-xM1+x, 57,58 La3+dFeC6, and a new compound La21Fe8M9C12 (M = Bi, Sb, Sn). All these structures feature iron clusters, layers, or networks interspersed with lanthanide ions. SEM-EDS elemental analysis of the crystal interiors showed no incorporation of Ni into any of the Fe-based intermetallics discussed above. Examining the refined crystallographic data also showed no indication of a heavier element in the Fe sites. If iron is present in the reaction mixture, the nickel in the solvent eutectic behaves as an inert flux—an element that serves to dissolve the reactants, but is not incorporated into the products. Many examples of inert flux behavior have been reported, such as the growth of Si and Ge phases (including CrSi2, WSi2, RSi2, and α-RNiGe2) using indium as a flux, and the growth of a wide variety of rare earth transition metal phosphides from tin flux.66-68 It appears that one can use the non-reactive flux properties of Ni in a La/Ni eutectic to lower the melting point of La thus facilitating growth of single crystal products and non- thermodynamically stable iron-rich phases. If iron is not present in the reaction or is present in small amounts, the nickel in the flux is reactive; for instance, crystals of

La5Ni2-dSi3 and La5Ni2Sn (the latter with the Cr5B3 structure type) are grown from reactions of Si or Sn in the La/Ni flux. One of the main byproducts for this synthesis was an orthorhombic LaNiAl phase which forms hexagonal shaped rods and is easily 69 distinguishable from the La6Fe13-xM1+x phase which forms rectangular plates (Fig. 5.1). Use of a La/Fe eutectic (91.5/8.5 mole %; m.p. 780 ºC) was also explored;

aluminum was added to this flux in an attempt to crystallize La6Fe13-xAl1+x. However these attempts thus far have yielded single crystals of the structurally related cubic

La(FexAl1-x)13 phases (Fig. 5.3). These compounds previously have been synthesized using arc-melting techniques. The higher melting point of the eutectic, higher soak temperatures (1050 ºC) and higher centrifugation temperature (815 ºC) used for the

La/Fe eutectic could indicate that the LaFe13-xAlx phase is more thermodynamically stable then the La6Fe13-xM1+x phase. Work by Chan et al. have shown similar results with gallium flux in isolating Ce2PdGa12 and CePdGa6 intermetallics utilizing different heating profiles and centrifugation temperatures.70-71

Figure 5.2. Displaying the structure of R6Fe13-xM1+x compounds in addition to the local environment of the main group 4a (left) and iron 4d (right) sites.

Manganese analogs

There have been several reports of successful Mn doping into the cubic La(TxAl1- x)13 (T = Fe, Co) phases, however these manganese phases are stabilized by transition metals with higher VEC.72-73 Attempts have not been made to replace Fe with Mn in the

tetragonal R6Fe13-xM1+x phase according to the literature. Using manganese instead of iron as a reactant in the La/Ni flux synthetic method successfully yielded ternary

La6Mn13-xAl1+x and quaternary La6Mn13-xAlxMy phases (Table 5.1, 5.3). Comparing

55 ternary analogs of La6Mn10Al4 and La6Fe10Al4 a ~6% increase in cell volume (Table 5.2) and both the a- and c-axis parameters increased quasi-linearly.

A ternary La6Mn10Al4 phase grown in La/Ni eutectic showed a slight Ni impurity

(~2%); whereas the quaternary La6Mn10Al3Sb0.92 displayed a larger Ni impurity (~30%), which was confirmed by SEM-EDS on the crystals exterior and interior. However, which site the Ni incorporation occurred could not be confirmed by X-ray diffraction. Another indication of Ni incorporation is seen during centrifugation; no noticeable removal of molten flux occurs, indicating a shift away from the low-melting eutectic ratio due to the reduction of the amount of nickel in the solution as the product crystallized.

The absence of a pure (containing only manganese) cubic La(MnxAl1-x)13 phase in addition to the nickel impurity present in the tetragonal phases reinforces that transition metals with higher VEC are needed to stabilize the formation of manganese icosahedra. Use of a La/Mn (83/17 mole %; m.p. 701 ºC) eutectic was explored for growth of these phases without Ni impurities; however current attempts have been unsuccessful.

Neodymium compounds

Attempts to grow single crystals of R6Fe13-xM1+x phases with R = Nd were successful using a Nd/Fe (79.5/20.5 mole %; Alfa Aesar) flux with a melting point of ~685ºC, using the same elemental ratios for the reactants as before. Each soak point in the heating profile was raised by 100 ºC to accommodate the higher melting point of this flux. Not all quaternary variants were attempted; however preliminary results show elements that were able to be incorporated into the 4a site include Al, Fe, and Sb. Other groups have recently had success growing Nd containing phases using Nd as the flux.65

Cell volumes of ternary Al analogs R6Fe13-xAl1+x show a ~3.9% decrease in cell volume going from R = La to R = Nd. The dominant decrease in length occurred along the c-axis which is in good agreement with previously reported results.74 Substitution of Mn for Fe was also explored in the Nd systems (by adding Mn to the Nd/Fe eutectic reactions). This results in an expansion in the unit cell as the larger Mn replaces Fe.

Complete substitution was not achieved and accurate stoichiometries for Nd6(Fe/Mn)13- xAl1-x phases were difficult to determine. Elemental analysis to determine stoichiometry

was not reliable due to overlap of Mn and Fe peaks in the EDS spectra, and the electron density of the elements is too similar to distinguish in the X-ray diffraction data.

Structure description

The structure of R6Fe13-xM1+x (R = rare earth, M = Si, Ge, Al, Au, Ag…) is shown

in Figure 5.2; it consists of Fe(4d, 16k, 16l1, 16l2) rich layers separated by layers comprised of R(8f, 16l) and M(4a), stacked along the c axis. The 2-D iron slabs can be

described as layers of icosahedral Fe clusters with Al mixing on the 16l2 Fe site

(outermost or capping site of the layer). This Fe/Al mixing also appears in La(FexAl1- x)13 (0.46 ≤ x ≤ 0.92) which crystallizes in the cubic NaZn 13-type structure and is composed of a 3d network of icosahedral clusters of Fe atoms with Al distributed randomly at the apex of the icosahedrons.75 Other similarities include the La local

environment (Fig. 5.3). In the cubic La(FexAl1-x)13 the La atom rests in a snub cube coordination sphere of Fe and Al atoms; the coordination environment of the La2 8f site

in tetragonal La6Fe13-xM1+x consists of a half snub cube of Fe and Al atoms with a square pyramid cap consisting of 4 La1 atoms forming the base with the M element forming the

peak. It is of interest to note that no pure LaFe13 phase exists and that Al is necessary for the formation of the icosahedral Fe clusters76.

Figure 5.3. La(FexAl1-x)13 structure (left) with a comparison of coordination environments for rare earth elements in the cubic La(FexAl1-x)13 (middle) and the tetragonal La6Fe13-xAl1+x (right).

4a site Attempts to replace Al on the 4a site (within the La layer) revealed some new interesting facts about this structure not previously observed. During synthesis of the

ternary phase La6Fe13-xAl1+x, restricting the amount of Al to less then stoichiometrically needed results in incorporation of Fe onto the 4a site. This can be confirmed by examining the occupation of the 4a site on numerous Al analogs synthesized; in many cases, the XRD data indicates an electron density higher than Al itself. Refinement of this site as a mixture of Al and Fe indicates occupation in the range of 2% to 57% Fe. The amount of Fe present on the 4a site shows no noticeable trends in relationship to the unit cell parameters. The presence of Fe on this site has not been previously reported and could contribute to the difficulty in understanding the magnetic properties of the system. Attempts to synthesize ternary phases with other main group elements besides aluminum were unsuccessful; however substitution of the 4a site by different main group elements in the presence of Al readily occurs, producing the many quaternary variants

La6Fe13-xAlxMy (Table 5.3). Electronegative main group elements readily incorporate into this site, likely stabilized by the surrounding environment of electropositive lanthanum ions. We can confirm the incorporation of Pb, Bi, Sb, In, P, Si, As, Ag, and Ge into the 4a site. Attempts to incorporate S, Se, Ga, Cu, and Au yielded single crystal products but the 4a site occupancy (and the resulting stoichiometry) is not clear due to the fact that partial occupancy of these elements produces similar electron density as an aluminum atom or a Fe/Al mixture. Stoichiometries in Table 5.3 are based on refinements with the 4a site partially occupied by the main group element. Multiple attempts at synthesizing analogs containing Sn and Te were unsuccessful at obtaining any products. Occupation of the 4a site, listed in table 5.3, is affected by a number of variables. One is clearly the size of the element M; analogs with smaller M (Al, Si, P, and As) atoms achieving near 100% occupancy of this site. Quaternary analogs containing larger elements such as Bi was synthesized in which the occupation of the 4a site varied from 32% to 95% by increasing the molar amounts of Bi loaded in the reaction. These Bi containing analogs (highlighted in table 5.2) display an increase in the c-axis parameter with increased occupation of the 4a site with Bi. Therefore it can be seen that large main

group elements like Bi (182 pm) have the ability to disturb the packing of the La (187 pm) layer where as smaller elements like Al, Si. P, and As cause very small perturbations

in the packing which can be masked by the more dominant changes occurring at the 16l2 site. However, the a-axis parameter seems to have a linear dependence not on the 4a site

but rather between the Fe and Al mixing on the 16l2 site. A further discussion of this trend will be discussed below. The valence electron count (VEC) may also play a role, but this is less clear.

Fe/Al mixed 16l2 site

The 12 coordinate 16l2 Fe3/Al3 mixed site is the outermost, capping site of the iron layers and possesses a mirror plane as its only symmetry element. The 5 La atoms distort the local environment and enforce a greater volume, which is better suited to accommodate the larger Al atom (143 pm) compared to Fe (126 pm). The 16l2 mix site incorporates only iron and aluminum even in the presence of other main group elements. Syntheses carried out at 950 ºC consistently displayed ~20% Fe on this site; the VEC of the main group element appeared to have little influence on the Fe/Al ratio at the 16l2 site.2 A unique aspect of this site was ability to consistently increase the amount of iron incorporated by increasing the maximum dwell temperature while holding the amounts of reactants constant. Using a 1|1.5|0.5 mmol ratio of La|Fe|Al in 1 g of La/Ni flux were able to increase the amount of Fe on the Al site from 23.3% to 24.3% and 27.4% at temperatures of 1000ºC, 1050ºC, and 1100ºC respectively. By varying both the soak temperature and molar amounts of Al added we were able to synthesize analogs with Fe in the range of 5-50% incorporation on this site. (highlight in table 5.3)

Examination of unit cell size trends in La6Fe13-xAl1+x revealed interesting dependencies of unit cell parameters on the 16l2 mix site. A linear relationship between the amount of Fe present on this site and the unit cell parameters was noticed (Fig. 5.4), with the a-axis decreasing as the amount of Fe present increased. This trend would be expected considering the smaller radius of Fe compared to Al. However the c-axis increases as the amount of iron on the 16l2 site increases. Likewise, the overall cell volume increases as the amount of iron increases.

23.83 8.239

8.238 23.81

8.237 23.79

8.236 (Å) 23.77 axis

axis (Å) 23.75 8.235 c- a-

8.234 23.73

8.233 23.71 %Fe on 16l2 site 8.232 23.69 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3

Figure 5.4. Changes in unit cell parameters as a function of Fe/Al mixing on the 16l2 site. (a-axis, filled circle; c-axis open circle)

Examination of Fe bond lengths on numerous analogs versus %Fe content displays linear trends in which all the Fe-Fe and Al-Fe bond lengths decrease with increasing Fe content. However, this decrease results in more compact Fe layers, this is in contrast to the increase in the c-axis observed with increasing iron content. Bond length analysis on Al only analogs revealed a noticeable decrease in bond lengths between the Fe/Al 16l2 site and La1 16l site with increasing Al content while the bond length changes between the Fe/Al 16l2 site and La2 8f site were negligible. This is unexpected considering the larger radius of Al compared to Fe, therefore this might be an indicator that increasing the presence of Al on the Fe/Al 16l2 site promotes bonding character between Fe and La lattices and vice versa. Using an IEM treatment the 3d bands are split into majority and minority spin sub-bands with the latter being higher in energy and the relative position of these sub-

bands shift with changes in the Fermi energy level.77 Decreasing the number of electrons (doping Fe with Al) filling these bands increases the splitting of the bands with the minority spin sub-band shifting to higher energy while the majority spin sub-band shifts to lower energy. The resulting increase in energy of the minority spin sub-band increases overlap with the higher energy 5d bands present on rare earth elements promoting bonding character between the iron and rare earth lattice. Electronic band structure calculations would need to be performed to confirm this prediction.

Magnetic Properties

) -4 (emu/gram) (x10 (emu/gram)

Figure 5.5. La6Fe10.25Al3.75 FC and ZFC susceptibility measurement H = 0.2T. (Primary axis H║ c-axis open circle; Secondary axis H┴ c-axis filed circle) Inset: Depicting type II AF structure.

La6Fe13-xAl1+x

The magnetic properties of the R6Fe13-xAl1+x (R = La, Pr, Ce, Nd) have been thoroughly studied by a variety of groups.65, 78-79 Initially there was a large disparity in the proposed magnetic ordering properties with antiferromagnetism, ferrimagnetism, and ferromagnetism all being reported.80-83 However, most of these conflicting models are most likely due to polycrystalline samples limiting characterization and traces of the

ferromagnetic R2Fe17 and α-Fe impurities. The most recent and promising low temperature magnetic structure consists of a Type II antiferromagnetic structure [Fig. 5.5 (inset)]. This features ferromagnetic layers of Fe and R with an antiferromagnetic translation occurring across the 4a site along the c- axis.84 This leads to 3 separate intralayer ordering mechanisms, FM Fe-Fe, FM R-Fe, and FM R-R and 2 competing interlayer ordering mechanisms across the 4a site, AF R-M-R and FM R-M-R.65,85 Substituting La for a magnetic rare earth element eliminates the R- Fe and R-R magnetic ordering and allows study of the FM intralayer Fe-Fe mechanism and the AF ordering of the alternating FM Fe layers.

Susceptibility measurements on La6Fe13-xAl1+x were performed with H║ c-axis (Fig. 5.5). Our studies show an easy axis of magnetization in the basal plane with a spin flop to the hard axis (axial) occurring around ~115K due to the moments of the iron lattices approaching each other in the applied field.59 This spin flop occurs at low temperatures in weak fields (~0.01T) and shifts to higher temperatures with increasing field (~0.2T). However, applications of higher fields (~1T-3T) cause the transition to broaden and shift to lower temperatures again. High field experiments (5T-7T) cause the AF spin flop to disappear yielding a spectra typical of a saturated ferromagnet. Above the AF spin flop transition a long tail is displayed in the susceptibility which does not fit to Curie-Weiss behavior for paramagnetic materials, however, indications of FM are shown by a positive Weiss constant. Heat capacity measurements were performed (Fig. 5.6) which yielded no fluctuations near the spin flop temperature. However, above 200K fluctuations are observed in both 0T and 1T. This behavior fits well with the concept of long range FM order breaking up into short range FM ordering of spin clusters above the spin flop temperature of the Fe layers unit the paramagnetic

state is reached.86 However, there is an change in the slope of the heat capacity curve near the spin flop transition temperature.

Cp- 0T

Cp -1T

0.4

0.2 Heat CapacityHeat (J/gK)

0.0 0 100 200 300 Temperature (K)

Figure 5.6. Heat capacity measurement of La6Fe10.25Al3.75. Fluctuations near 300K are from grease used to adhere crystals to measurement puck.

Magnetization experiments with H║ c-axis at 1.8K (Fig. 5.7) display the typical S- shaped curve associated with metamagnetic transitions (MMT). This AF-FM MMT occurs with a clear jump at a field ~2T. A slight hysteresis (coercivity) is noticed which indicative of the spins of the iron layer is gradually rotating against the magnetocrystalline anisotropy.74

Comparing ZFC and FC (H║ c-axis) susceptibilities spin-glass-like behavior is observed below the spin flop transition (Fig. 5.5). This intrinsic property occurs only in fields less then ~2T and is the result of the spins aligning along the easy axis of magnetization (basal plane) when ZFC and eventually rotating to the hard axis (with application of field) as the coercivity decreases with increasing temperature.

-5 (emu/gram)

M -15

-25

-35 -7 -5 -3 -1 1 3 5 7 H (T)

Figure 5.7. La6Fe10.25Al3.75 M vs H collected at 1.8K. (H║ c-axis filled diamonds; H┴ c- axis open diamonds)

Magnetization and susceptibility (H┴ c-axis) experiments display typical antiferromagnetic behavior which suggests that the magnetic properties of the iron lattice are more greatly affected when H║ c-axis (Fig. 5.7). A slight decrease in the spin flop

transition temperature with increasing fields is noticed and contrasts with large shift

observed with H║ c-axis. A previously unreported irreversibility is observed in these compounds indicated by the slight differences in FC and ZFC magnetic susceptibilities below the spin flop transition with H┴ c-axis (Fig. 5.5); this is typically a characteristic feature of a spin glass. However, it has been shown that spin-glass-like behavior of magnetically ordered systems originates from the magnetocrystalline anisotropy and is related to the magnitude and the temperature variation of the coercivity.87

11.0 2.9 10.0 2.7

) -4

9.0 -3 2.5

8.0 (x10 2.3

7.0 2.1 emu/(gram) x10 (emu/gram) (emu/gram) χ 6.0

1.9 χ

5.0 1.7

4.0 1.5 0 50 100 150 200 250 300 Temperature (K)

Figure 5.8. Nd6Fe10.5Al3.5 FC and ZFC susceptibility measurement H = 0.2T. (Primary axis H║ c-axis open circle; Secondary axis H┴ c-axis filed circle)

Nd6Fe13-xAl1+x

Similar magnetic measurements were performed with H║ c-axis on single crystals of the neodymium containing phase for comparison (Fig. 5.8). These compounds display the same AF spin flop of iron lattices at 232K with a two-step magnetic ordering of the rare earths sites at 77K (FM Nd2-Fe) and (FM Nd2-Nd1) at 9K. 59,74, 88-90 The Nd2 8f site ordering is shifted to higher temperatures due to it close proximity to the FM Fe layers and the stronger than normal R-Fe coupling noticed for this compound in comparison to other rare-earth transition metal compounds.85-86 Application of high fields (1T-4.8T) will saturate these transitions with reentrant behavior at ~5T.65 In ZFC experiments similar spin-glass-like behavior is observed and is resulting from the competition between the easy and hard axis discussed above for the lanthanum analogs.

100

-20

(emu/gram) -40 M -60

-80

-100 -7 -5 -3 -1 1 3 5 7 H (T)

Figure 5.9. Nd6Fe10.5Al3.5 M vs H collected at 1.8K. (H║ c-axis filled diamonds; H┴ c- axis open diamonds).

Magnetization experiments with H║ c-axis at 1.8K (Fig. 5.9) display a shift in the MMT to a higher field ~4T and is more abrupt when compared to the lanthanum analog. A larger coercivity is observed at the MMT which indicates that coupling of the iron lattice to the magnetic rare earth lattice increases the coercivity.

Susceptibility experiments with H┴ c-axis (Fig. 5.8) display an increased

susceptibility which is in agreement with neodymium possessing a larger role with H┴ c- axis.65 The Nd2 site orders at a higher temperature the compared to theNd1 site however the Nd1 site dominates at lower temperatures due to the site containing twice as much magnetic rare earth. Effects of this are displayed with a low temperature FM transition preceded by a cusp from 100K-10K which is not observed for lanthanum analogs in addition to an increase in the magnitude of the irreversibility as compared to the lanthanum analogs. A low temperature spin reorientation has been shown to originate at the Nd sites due to the absence of a spin reorientation in the Fe lattice in low temperature

Mossbauer spectra of La6Fe13-xAl1+x and could be the source of the AF cusp observed in the ZFC susceptibility.74

Magnetization experiments with H┴ c-axis display typical AF behavior up to a field of 5T (Fig. 5.9) with a more pronounced S shape is present compared to the lanthanum analogs which supports additional MMT’s reported within the neodymium lattice in addition to reentrant FM behavior observed at fields of 5T -7T.65 Due to coupling of localized rare earth moments to delocalized iron moments proposing exact magnetic models is difficult.

La6Mn13-xAl1+x

Substitution of iron with manganese yields strong FM (Tc ~200K, Coercive Field

= 1T) behavior with H║ c-axis (Fig. 5.10). The presence of strong FM behavior indicates easy axis behavior along c which is in contrast to the iron analogs. The difference between ZFC and FC susceptibilities is an artifact of removing the field used during centering process due to the large coercivity.87 The large coercive field present in the

ternary La6Mn13-xAl1+x (Fig. 5.11) is most likely due to doping of the manganese with nickel in the center of the icosahedrons which acts as a strong FM whereas manganese typically acts as a weak FM. Using XAFS manganese was shown to prefer the corners of

67 the icosahedrons whereas late transition metals such as cobalt preferred the center site in 72 the cubic LaCo13-xMnx.

6.0 4.7

5.0 4.2 )

-4 3.7 ) 4.0 -5 0 3.2 (x1 3.0 2.7

2.0 2.2 (emu/gram) (x10 (emu/gram) χ (emu/gram) (emu/gram)

1.7 χ 1.0 1.2

0.0 0.7 0 50 100 150 200 250 300 Temperature (K)

Figure 5.10. La6Mn10Al4 FC and ZFC susceptibility measurement H = 0.2T. (Primary axis H║ c-axis open circle; Secondary axis H┴ c-axis filed circle)

Susceptibility experiments with H┴ c-axis show a two step FM ordering (Fig. 5.10). The ordering observed at ~200K is attributed to FM intralayer ordering with a FM interlayer ordering occurring at lower temperatures. The irreversibility observed in the magnetic susceptibility is greater in comparison to the iron analogs. This is due to the larger coercivity noticed in the manganese analogs and is in good agreement with the increase in irreversibility observed with a corresponding increase in coercivity.87 M vs. H experiments show an increase in coercivity of the compounds at fields greater then 1T possibly due to FM interlayer ordering (Fig. 5.11).

1.5

0.5

-0.5 (emu/gram) M -1

-1.5 -7 -5 -3 -1 1 3 5 7 H(T)

Figure 5.11. La6Mn10Al4 M vs H collected at 1.8K. (H║ c-axis blue filled diamonds; H┴ c-axis open diamonds)

Conclusion In summary a new method for synthesizing single crystals in molten metal flux in a eutectic ratio comprised of early rare earth and 3d transition metals. This technique has been applied for growth of the ternary R6T13-xAl1+x (T = Fe, Mn; R = La, Nd)) compounds with the ability to incorporate other main group elements in the rare earth lattice in the presence of aluminum to form quaternary R6TxAlyMz compounds. Smaller main group elements fully occupy the 4a site in the rare earth lattice whereas larger elements can be synthesized with varying occupancy. A previously unknown iron impurity is observed on the 4a site in the presence of aluminum and could provide additional complications when determining the magnetic properties of these compounds. In addition increasing the iron content on the 16l2 site

69 appears to decrease the coupling of the rare earth and iron lattices which could help explain some of differences in magnetic properties being reported.

Synthesis of the ternary La6Fe13-xAl1+x compounds in single crystal form has allowed a more thorough study of the properties of the magnetically coupled iron lattices. Application of field parallel the hard axis displays Type II antiferromagnetic behavior with a spin flop transition (Tn ~113K; B = 0.2T) and a field induced metamagnetic transition from AF to FM. A low temperature spin-glass-like behavior in ZFC experiments is noticed due the moment of iron lattices preferring the easy axis of magnetization before aligning with the hard axis with increased temperature as the coercivity decreases. Susceptibility experiments with the field parallel the easy axis displays irreversibility between ZFC and FC susceptibilities with the magnitude related to the coercivity, which is a measure of the magnetocrystalline anisotropy.

Susceptibility experiments on the ternary Nd6Fe13-xAl1+x compounds are consistent with results reported in the literature. However, irreversibility is observed with the field parallel the easy axis of magnetization and its magnitude of splitting ZFC and FC susceptibilities is larger compared to the lanthanum analogs as expected due to the increase in coercivity by doping with neodymium.

Substitution of iron with manganese yielded a ternary La6Mn13-xAl1+x analog not previously reported. Susceptibility experiments with the field parallel the hard axis display strong ferromagnetic behavior (Tc ~200K; B = 0.2T) with a coercive field of 1T, most likely due to the slight nickel impurity which stabilizes the formation of manganese icosahedrons. At low temperatures the spin-glass-like behavior is observed similar to the iron analogs. Application of field parallel the easy axis displays a two step magnetic behavior with a ferromagnetic intralayer (Tc~200K) and interlayer (Tc~20K) interactions. The irreversibility between the ZFC and FC susceptibilities is easily observed due to the increase in coercivity. Future work is needed to explore the effect of substituting different main group elements in the rare earth lattice in addition to increasing its partial occupancy on the magnetic properties. Heat capacity measurements have displayed the formation of a cluster glass phase above 200K in the La6Fe13-xAl1+x compounds and need further investigation.

CHAPTER 6 SPIN GLASS BEHAVIOR OF ISOLATED TETRAHEDRON OF IRON ATOMS IN THE GEOMETRICALLY

FRUSTRATED La21Fe8Sn7C12

Introduction Pöttgen and Jeitschko et al. are responsible for the discovery of many known inorganic carbides. These typically feature interstitial carbon atoms (C1) although some feature C2 and C3 units such as Sc3C4, with a unit cell that features 12 C1, 2 C2 and 8 C3 units.91 There are relatively few inorganic compounds containing carbon that are known in comparison to other elements such as aluminum and silicon which have been thoroughly studied for their unique electronic and physical properties. Carbides are typically known for their hardness (i.e WC, and steel), but inorganic carbides such as

Y2FeC4 and LaNi2B2C also display superconductivity with the latter revealing the relationship between superconductivity and magnetism.92-93 Synthesis of new carbide phases increases the probability for isolating carbon in unique environments with interesting physical properties.

Table 6.1. Lattice constants of the compounds La21Fe8M7C12. Compound a (Å) R

La21Fe8Bi7C12 16.5212(5) 0.0293 La21Fe8Sb7C12 16.3999(3) 0.0195 La21Fe8Sn7C12 16.6032(4) 0.0233 La21Fe8Te4.9Al2.1C12 16.2911(7) 0.0421 La21Fe8Ge5.7Al1.3C12 16.1589(4) 0.0207

In an effort to synthesize new carbide compounds use of molten metal solvents (flux) as a growth medium was explored. Our previous efforts in using the La/Ni (88:12 wt %; m.p. 530 ºC) eutectic for growth of single crystals have yielded many interesting phases such as La6T13-xAl1+x (T = Fe, Mn), LaFe12B6, and La3.67FeC6 in addition to the

novel cubic phase La21Fe8M7C12 (FM-3M, #225; M = Bi, Sb. Sn, Te, Ge) [Fig. 6.1; Table 6.1].94-96 This new phase features an isolated tetrahedron of iron atoms edge capped by carbon in a network of La/M [Fig. 6.2, 6.3]. Isolated tetrahedrons of magnetic atoms with

Jij equal are typically studied by theoretical/computational methods and have been referred to as “toy problems” due to the lack of real materials possessing such features.97- 98

Figure 6.1. SEM image showing morphology of La21Fe8Sn7C12 single crystal.

Tetrahedrons of magnetic atoms are associated with geometrically frustrated magnets and commonly studied using materials possessing the cubic pyrochlore structure 99 (A2B2O7), such as Mn2Sb2O7. The pyrochlore structure features a 3d network of corner sharing tetrahedra with interesting ground states without long range magnetic order, such as spin glasses, spin ices and spin liquids.100 Conventional spin glasses are commonly described using randomness (disorder) and competing exchange interactions, however some pyrochlores display spin glass ordering without apparent chemical disorder whose ground states are not well defined both experimentally and theoretically.101 Therefore, investigations into the properties of an isolated tetrahedron could provide useful information for the study of materials possessing geometric frustration without

possibilities of long range magnetic ordering. Single crystals of the cubic La21Fe8Sn7C12 have been characterized by means of SEM-EDS, X-ray diffraction and AC/DC SQUID. The magnetic properties deviate from Curie Weiss behavior below 130K with a spin

glass transition (TSG) observed below 5K.

Figure 6.2. Iron tetrahedron (left), iron tetrahedron with carbon (right).

Experimental Procedure Synthesis Starting materials for preparation were powders of lanthanum (METALL, Acros, purity > 99.9%), powders/chips of Fe, Bi, Sb, Sn, Ge, Te, and C (Strem Chemicals, 99.9%), and chips ground from ingots of commercially available La/Ni eutectic (88:12 wt%, Alfa Aesar 99.9%). All elements were combined stoichiometric 1 mmol ratios sandwiched between layers of La/Ni eutectic (~1.2g total) and placed in an alumina crucible sealed in a fused silica tube under vacuum of 10-2 Torr. In addition to the alumina crucible containing the reactants another alumina crucible was filled with silica wool and inverted in the silica tube to act as a filter during centrifugation. The eutectic fluxes used are aggressive enough reducing agents to leech Al from the alumina crucible which can be limited by utilizing an initial soak temperature of 950°C with a short soak (6hrs). However, the leeching of aluminum increases the crystal yield. The fused silica ampoule was then heated to 950°C in 3hrs, held at this temperature for 12hrs, then cooled

to 850°C in 10hrs. The samples were then annealed for 48hrs at 850°C then cooled to 600°C in 84hrs. At 600°C the fused silica ampoules were then inverted and placed into a centrifuge to remove excess molten flux. Any flux remaining on the surface can be removed mechanically or by controlled oxidation in air. Products were stored in a dry box to prevent oxidation. The crystals were stable enough in air to allow overnight X- Ray collections under ambient conditions.

Stoichiometric synthesis of the La21Fe8Sn7C12 was achieved by arc melting on a water cooled copper hearth. The reactants were measured in stoichiometric ratios and wrapped in tin foil before arc melting to prevent loss reactants. The reaction pellet was flipped and arc melted several times to ensure homogeneity. Powder X-ray diffraction was used to determine phase purity of the arc melted pellet.

Table 6.2. Crystal data for La21Fe8Sn7C12. La21Fe8Sn7C12 Formula Weight (g/mol) 4338.86 Space Group Fm-3m (#225) a (Ǻ) 16.6032(4) V (Ǻ3) 4576.94(19) 3 dcalc (g/cm ) 6.297 Z 4 Temperature (K) 298 Radiation MoKα 2θmax 56.43 Index ranges -22 ≤ h ≤ 22 -22 ≤ k ≤ 22 -21 ≤ l ≤ 22 Reflections collected 15699

Unique data/parameters 337/21 μ (mm-1) 25.28 R1/wR2* [I>2σ(I)] .0233/.0533 R1/wR2 (all data) .0233/.0533 Residual peaks/hole (e/Å3) 3.22/-1.18

* R1 = Σ||Fo|-|Fc||/Σ|Fo|; 2 2 2 2 2 1/2 wR2 = [Σ[w(Fo - Fc ) ]/Σ[w(Fo ) ]]

Elemental analysis. Elemental analysis was performed on all samples using a JEOL 5900 scanning electron microscope with energy dispersive spectroscopy (SEM-EDS) capabilities. Samples were analyzed using a 30 kV accelerating voltage and an accumulation time of 40s. Scans of the surface and interiors of the crystals typically showed good stoichiometric ratios for the La, Fe, M, and Al. Stoichiometric ratios could not be resolved for carbon due to limitation of EDS with light elements (Z< 11). Because of the possibility of Ni contamination from the flux the samples were also monitored for this element, but it was not observed in any of the scans.

X-ray diffraction. Small interior shards were cleaved from the large single crystals grown in flux and analyzed by EDS. The crystals were mounted on glass fibers using epoxy, and single-crystal X-ray diffraction data for each compound was collected at room temperature on a Bruker AXS SMART CCD diffractometer. Data processing was then performed using the program SAINT; an adsorption correction was applied to the data using the SADABS program.102 The structure was solved using direct methods and refined with the SHELXTL package of programs.

Table 6.3. Atomic positions of La21Fe12Sn7C12. All occupancies equal to 1. Atoms Wyckoff x y Z Ueq site La1 48h 0 0.169892 0. 169892 0.00894 La2 32f 0.365001 0.365001 0.365001 0.00799 La3 4b ½ ½ ½ 0.01693 Fe 32f 0.195605 0.195605 0.195605 0.00880 Sn1 24e 0.288942 0 0 0.01085 Sn2 4a 0 0 0 0.01018 C 48g 0.109637 ¼ ¼ 0.01454

Magnetic susceptibility. AC and DC magnetic susceptibility measurements were performed with a Quantum Design MPMS SQUID magnetometer at temperatures between 1.8 and 300K.

Susceptibility measurements were performed on clean single crystals sealed in kapton tape. ZFC and FC temperature dependence measurements were collected at various fields with field dependent measurements collected at 1.8K.

Figure 6.3. The structure of the cubic La21Fe8Sn7C12. (La = Green, Sn = Blue, Fe = Red, C = Black)

Table 6.4. Selected bond lengths for La21Fe8Sn7C12. Bond Length (Å) La1-La1 3.7620(15) x 1 La1-La1 3.9891(7) x 4 La1-La2 3.9816(4) x 4 La1-Sn1 3.4444(8) x 2 La1-Sn2 3.9891(1) x 1 La1-Fe1 3.3033(17) x 2 La1-C1 2.6176(99) x 2

La2-La1 3.9816(4) x 6 La2-La3 3.8823(9) x 1 La2-Sn1 3.4121(7) x 3 La2-Fe1 3.1520(9) x 3 La2-C1 2.7329(23) x 3

La3-La2 3.8823(9) x 8 La3-Sn1 3.5042(13) x 6

Sn1-La1 3.4444(8) x 4 Sn1-La2 3.4121(7) x 4 Sn1-La3 3.5042(13) x 1

Sn2-La1 3.9891(1) x 12

Fe1-Fe1 2.5544(39) x 3 Fe1-C1 1.9154(106) x 3 Fe1-La1 3.3033(17) x 3 Fe1-La2 3.1520(9) x 3

C1-La1 2.6176(99) x 2 C1-La2 2.7329(23) x 2 C1-Fe1 1.9154(106) x 2

Results and Discussion Structural Description The atomic coordinates and crystallographic information of the novel cubic

La21Fe8Sn7C12 phase been determined by single crystals X-ray diffraction [Table 6.2, 6.3]. The unit cell is shown [Fig. 6.3] and features an isolated iron tetrahedron edge capped by carbon [Fig. 6.2] in an extensive La/Sn network. Although substitution of tin

77 readily occurs with Bi, Sb, Te, and Ge, [Table 6.1] only the tin analog will be discussed with bond lengths presented in table 6.4. The Fe1 (32f) site that forms the tetrahedron resides at the base of an intergrowth of a trigonal prism and trigonal anti-prism [Fig. 6.4]. The trigonal prism is formed by carbon and iron atoms with the carbon base nearest the iron atom. The trigonal anti- prism is comprised of lanthanum atoms (La1 and La2) with the base comprised of La2 atoms nearest the iron atom. Although aluminum has been observed in the structure, occupancy refinement of the iron site shows no incorporation of aluminum. The carbon (48g) site that edge caps the iron tetrahedron is centered within a distorted octahedron of lanthanum and iron atoms [Fig. 6.4]. The La1 and Fe1 atoms form the distorted equatorial plane with the La2 atoms capping axially.

Figure 6.5. Local environments for iron and carbon. (Fe1 = Left, C1 = Right)

The La1 (48h) and La2 (32f) site reside within complex low symmetry local environments [Fig. 6.5]. However, the La3 (4b) site is coordinated by 8 lanthanum in a square prism face capped by 6 tin atoms [Fig. 6.5]. The Sn1 (24e) site is coordinated by 9 lanthanum atoms in a square anti-prism monocapped axially [Fig. 6.5]. A slight aluminum impurity etched from the alumina crucible by the La/Ni flux can be observed on this site [Table 6.1]. The Sn2 (4a) site is weakly coordinated by 12 lanthanum in a cuboctahedral array [Fig. 6.5]. This site features extremely long bond lengths (Sn2-La1

3.9891 Å) and a high thermal parameter (Ueq = 0.01018), which is indicative of the tin atom “rattling” within the cuboctahedron. Similar behavior is observed for heavy atoms in skutterudite and clatharate thermoelectric materials which impedes thermal transport.103,104

Figure 6.5. Local environments for lanthanum and tin. (La1 = Top Left, La2 = Top Right, La3 = Center, Sn1 = Bottom Left, Sn2 = Bottom Right)

Figure 6.6. ZFC temperature dependence of the DC susceptibility for La21Fe8Sn7C12; H=100G, TSG = 4K. Inset: depicting divergence of ZFC and FC susceptibility.

Magnetic Properties

Susceptibility measurements on single crystals of La21Fe8Sn7C12 with H= 100G displays Curie-Weiss behavior above 130K [Fig 6.6]. A Curie-Weiss fit of the high temperature linear region between 130-300K yields μeff = 4.71μβ per iron atom and θc= - 3+ 619.5K. The μeff is smaller than that typically found for Fe (μeff =5.9 μβ), which is common for magnetically frustrated systems. The Weiss constant (θc) is proportional to the sum of the exchange interactions (Jij); a large negative c θis symbolic of an antiferromagnetic system which experiences spin frustration. The large antiferromagnetic coupling of spins is responsible for the non-linear behavior observed in the temperature dependent susceptibility. The applied magnetic field appears to cause fluctuations in the measured μeff and reaches a maximum (μeff = 5.54 μβ) near H = 180G

with decreases in the measured μeff with increasing and decreasing field. A decrease in θc was observed with an increase in the applied field.

Figure 6.7. M-H curves at 1.8K. Inset: Observed hysteresis.

Below 5K a separation between ZFC and FC susceptibilities is observed (TSG = 4K, H = 100G) [Fig. 6.6 inset]. This separation of ZFC and FC susceptibilities indicates a spin glass transition, with the transition shifting to lower temperatures with an increase in applied field. This transition is no longer observed with H > ~750G. The magnetization measured as a function of field at 1.8K, M(H), does not saturate at the highest field of 7T [Fig. 6.7]. A slight hysteresis is observed at 1.8K with a coercivity of ~200 G [Fig. 6.7 inset]. The hysteresis and the inability to saturate the sample are consistent with the expected behavior of a spin glass.

The real component of the AC magnetization should exhibit a sharp and

frequency dependent cusp (TSG) in the case of a spin glass. Figure 6.8 shows the real part

(m’) of the AC magnetization of La21Fe8Sn7C12 measured at µ0Hdc = 5 Oe at various frequencies (ω = 1, 10, 100, 1000Hz). The peak shifts to higher temperatures and decreases in intensity with increasing frequency. A two point smoothing function of

adjacent averaging was applied using Origin graphing software to determine TSG. The

Mydosh parameter (φ = ΔTSG/[TSG*log (ω)]) is a quantitative measure of the frequency shift of a spin glass system and was determined to be φ = 0.054. This value is within the estimated range (0.004-0.08) for spin glass systems.105

Figure 6.8. Temperature dependence of the real component of the AC magnetization, m', for La21Fe8Sn7C12 with different frequencies (ω). Inset: the variation of ΔTSG/TSG with log[ω].

Conclusion

The DC and AC magnetization data support spin glass behavior in La21Fe8Sn7C12. However, there is no detectable disorder between neighboring iron atoms which contradicts commonly used models to explain the origin of spin glass behavior. Recent theoretical calculations have shown that introduction of weak exchange randomness (disorder) can induce spin freezing and that the disorder strength is proportional to the spin glass transition temperature.97 A possible explanation of this weak disorder could be attributed to the aluminum impurity on the 24e site causing random strain in the surrounding lanthanum network. Any perturbations in the lanthanum network would generate a slight distortion in the local environment of the iron atom thus causing weak disorder in the exchange interactions between neighboring iron atoms allowing for the formation of the spin glass state. This weak bond disorder between iron atoms is not detectable via X-ray diffraction. However, x-ray absorption fine structure (XAFS) experiments could be used to detect any disorder in Fe-Fe interactions. It is possible to synthesize pure phases without the aluminum impurity however, the crystal yield is not yet sufficient for magnetic characterization.

In conclusion, a new cubic compound La21Fe8Sn7C12 has been synthesized using a molten metal flux. This compound features isolated tetrahedrons of iron atoms which are frustrated. The magnetic properties indicate a spin glass transition without detectable disorder between the magnetic ions. The observed fluctuations in the μeff need further investigations.

CHAPTER 7 CONCLUSION AND FUTURE WORK

The prevailing theme of my research was the use of flux as a growth medium for synthesizing single crystals. The typical reagents used for flux chemistry (i.e. Ga, Sn, In…) have been thoroughly investigated by other research groups; therefore the emphasis of my study was using metal eutectics as the growth medium. The main focus was on exploratory synthesis, although many known compounds were synthesized with a select few garnering extra attention. When reexamining a known phase one must make sure the study is a worthwhile endeavor with clear benefits.

Utilizing In/Zn and Al/Zn eutectics a new quaternary variant RT2TrxZn20-x (R =

rare earth; T = Mn, Fe; Tr = Al, In) of a known phase in the CeCr2Al20 structure type was synthesized. Zinc-rich phases of this structure type are able to incorporate the late transition metals whereas aluminum-rich phases incorporate the early transition metals. However, creating a mixed Al/Zn or In/Zn phase we were able to incorporate manganese into this structure type which was not previously observed. The paramagnetism of these compounds is due to the rare earth ions, which are far enough apart in the structure to

show no magnetic interactions. An interesting site switched analog Er2FeZnxIn20-x was synthesized; however, these results were not reproducible. Efforts to isolate this phase might be of interest. This compound could feature interesting magnetic ordering due to the close proximity of the rare earth ions and transition metals. In an effort to synthesize more magnetically interesting compounds a eutectic comprised of La/Ni was investigated. These are not typical reagents used for flux chemistry and could potentially yield new compounds. An interesting aspect of this eutectic was the ability to synthesize numerous intermetallics containing iron without any incorporations of nickel detectable by SEM-EDS. However, this technique is limited in its ability to detect elements in relatively small abundance; therefore, secondary ion mass spectrometry (SIMS) experiments should be performed to confirm the absence of nickel incorporations. The use of air-sensitive reagents for flux growth allows for isolation of clean crystals by controlled oxidation of any remaining flux attached to the crystals

surface after centrifugation of the reaction to remove the flux. Due to the aggressive nature of this eutectic towards the alumina crucible an aluminum impurity was often incorporated into the products during synthesis. To avoid this, future syntheses should be done in different crucibles such as niobium, although the more inexpensive alumina crucibles are useful for initial exploratory work.

The tetragonal La6Fe13-xAl1+x compounds have been previously studied by many research groups. These compounds possess alternating layers rich in iron and lanthanum respectively, stacked along the unique axis. However, this compound had previously been observed in polycrystalline forms. This made characterization of the magnetic ordering difficult especially with respect to the anisotropy of the system. Therefore, an investigation into the properties using single crystals could vastly improve the understanding of such a system. The use of itinerant electron magnetism is very useful for comprehension of the magnetic and structural properties of this compound. These compounds display classic antiferromagnetic anisotropy effects with respect to the spin flop transition and the preferred axis of magnetization. In addition, a metamagnetic transition from the antiferromagnetic to ferromagnetic state is observed as the applied field is increased. Quaternary variants of this compound have been synthesized and need further investigation as to the effect on the magnetic properties upon changing the electron density within the lanthanum layers. Substitution of strontium for lanthanum provides another method for tuning the electron density within the layers and its effect on magnetic properties should be investigated. The effect of flux components, reaction heating profile and centrifugation

temperature on the synthesis of La6Fe13-xAl1+x and the structurally related LaFe13-xAlx compounds should also be investigated. The former phase crystallizes out of La/Ni flux, but attempts to grow it out of the La/Fe eutectic led only to the latter cubic phase. This may be a factor of the temperature of the reaction and the centrifuging (higher in the case of the La/Fe reactions), or the presence of nickel may determine which phase is crystallized. Carrying out a La/Fe/Al reaction in both La/Ni and La/Fe fluxes using identical temperature profiles would be informative.

Substitution of manganese for iron in the La6Fe13-xAl1+x compounds has not been previously observed; this greatly affects the magnetic properties. Results indicate that

formation of a stable manganese phase requires an addition of a transition metal with a higher valence electron count such as nickel or iron. This analog displays ferromagnetic properties with anisotropy effects and a change in the easy axis of magnetization. The unique axis of the crystal displayed strong ferromagnetic behavior while the non-unique axis displayed weak ferromagnetic behavior. This analog could be useful for the study of the magnetocaloric effect and merits further investigation.

The Nd6Fe13-xAl1+x analog has received the most attention in the research community as it was first observed as a secondary phase in the strong permanent magnet

Nd2Fe14B and improved its coercivity. This analog was synthesized for a comparison using an Nd/Fe eutectic. The magnetic properties of this analog are significantly more complex due to the presence of localized rare earth moments in addition to the itinerant properties of the iron layers. Substitution of manganese for iron readily occurs, which yields more complexities in the magnetic properties. An interesting study would be to synthesize various analogs with increasing amounts of manganese and track changes in the structural and magnetic properties. However, determination of stoichiometry and structural properties cannot be achieved by SEM-EDS or X-ray diffraction. Due to these limitations SIMS should be used for stoichiometric determination as it is a highly sensitive analysis technique. As stated before the main goal of my investigations was for exploratory synthesis due to the ability of the flux to stabilize metastable or kinetically stable phases. Through use of the La/Ni eutectic a new phase La21Fe8M7C12 (M = Sn, Sb, Bi..) was synthesized. This compound features isolated tetrahedra of iron atoms edge capped by carbon in an extensive network of lanthanum and main group elements. Magnetic property

investigations on the La21Fe8Sn7C12 analog revealed antiferromagnetically frustrated iron atoms with formation of a spin-glass state below 5K. The spin-glass properties were confirmed by AC SQUID measurements which was used to determine the Mydosh parameter φ = 0.054. This family of compounds definitely merits further investigations into changes in the magnetic properties due to rare earth and main group substitution. The formation of the spin glass state is most likely due to disorder between iron atoms in the tetrahedron that is not detectable by X-ray diffraction. However, other techniques such as low temperature neutron diffraction could detect this distortion and possibly

provide insight into the fundamentals of spin glass behavior state in magnetically frustrated compounds. The binary phase diagrams of the early rare earth metals (such as La, Ce, Pr, Nd) and the late transition metals (Fe, Co, Ni, Cu) all feature eutectics at a lanthanide-rich ratio; this is a rich area for flux growth synthesis. Investigations into other molten metal eutectics such as La/Co should be performed. This eutectic features a melting point lower than La/Ni and possesses a larger ratio of transition metal to lanthanum. These features make it an ideal growth environment for isolation of new or metastable compounds with unique magnetic properties.

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BIOGRAPHICAL SKETCH

Evan Mallory Benbow

Field of Interest Inorganic solid state chemistry and materials science

Education Iowa State University, B.S. in Chemistry, 2003 Florida State University, Ph.D. in Inorganic Chemistry, 2008

Research Experience Florida State University, 2003-2008. Graduate Advisor: Dr. Susan E Latturner. Synthesis of single crystal intermetallics using metal flux. Ternary and quaternary compounds comprised of a rare-earth element, a late transition metal, and main group elements were grown from molten metal binary eutectic mixtures. Structural, physical, and magnetic properties were investigated with regard to complex magnetic ordering and anisotropy effects.

Iowa State University, 2001-2003. Undergraduate Advisor: Dr. Gordon J Miller. Solid state chemistry of intermetallics. Ternary and pseudo-binary phases containing an early rare-earth element, a late transition element and aluminum or silicon were synthesized by arc-melting and use of high temperature furnaces. The structural, electronic, and magnetic properties were investigated.

Teaching Experience Florida State University Directed Undergraduate Research, Nate Falb, Spring08 General Chemistry, CHM 1045L, Teaching Assistant, Fall03, Spring04, Summer05 General Chemistry, CHM 1046L, Teaching Assistant, Fall04, Spring05 General Chemistry, CHM 1045R, Teaching Assistant, Fall05, Spring06 Chemistry Tutor, 2001-present

Awards and Memberships The National Scholars Honor Society Golden Key Honor Society Best poster Florida Inorganic Materials Symposium (FIMS 2007) Merck Index award for achievement in undergraduate research

Presentations

“Magnetic properties of the intermetallic phases RET13-xAl1+x (RE = La, Nd; T = Fe, Mn).” Benbow E. M., Florida Annual Meeting and Exposition of the American Chemical Society, Orlando, FL, 2008

“Structural and Magnetic Investigation of Fe9(FexAl1-x)4 Distorted Icosahedra.” Benbow, E. M., North American Solid State Chemistry Conference, Texas A&M University, College Station, 2007

“Mixed Metal Flux Synthesis of Quaternary RT2TrxZn20-x Compounds, T = Mn, Fe and Tr = Al, In.” Benbow, E. M. and S. E. Latturner., Florida Annual Meeting and Exposition of the American Chemical Society, Orlando, FL, 2006

“Synthesis and structural characterization of new Ce-Ni-Al and La-Ni-Al compounds.” Benbow, E. M. and Miller, G. J., NSF Solid State Chemistry Summer Program, Clemson University, Clemson, SC, 2001

Posters

“Planes, Chains, and Tetrahedra: An Investigation of Rare Earth/Iron Intermetallics.” Benbow, E. M. and S. E. Latturner., Florida Inorganic Materials Symposium, University of Florida, Gainesville, 2007

“Synthesis of new intermetallic phases from zinc eutectic fluxes.” M. Stojanovic, E. Benbow, J. Whalen, and S. E. Latturner., Solid State Chemistry Gordon Research Conference, 2006

“Synthesis of new intermetallic phases from zinc eutectic fluxes.” M. Stojanovic, E. Benbow, J. Whalen, and S. E. Latturner., Transatlantic Frontiers of Chemistry, Durham NH, 2006

“Synthesis of new intermetallic compounds from metal eutectic fluxes.” M. Stojanovic, E. Benbow, and S. E. Latturner., Solid State Chemistry Gordon Research Conference, 2004

“Crystallographic and Magnetic Studies of Al23Ce4Ni6: A New Ternary Intermetallic Compound in the Aluminum-Cerium-Nickel Phase Diagram.” Gout, D., Benbow, E. M. and Miller, G. J., 34th Great Lakes Regional Meeting of the ACS, Minneapolis, MN, 2002

“Crystallographic and Magnetic Studies of Al23Ce4Ni6: A New Ternary Intermetallic Compound in the Aluminum-Cerium-Nickel Phase Diagram.” Gout, D. Benbow, E. M. and Miller, G. J., Gordon Conference on Solid State Chemistry, New London, NH, 2002

Publications

Benbow, E. M., Latturner, S. E. “Mixed-metal flux synthesis of quaternary RMn2TrxZn20-x compounds with Tr = Al, In.” Journal of Solid State Chemistry. 179(12), 2006, 3989-3996

Gout, D., Benbow, E., Gourdon, O., and Miller, G. J. “Composition-Structure Relationships in Polar Intermetallics: Experimental and Theoretical Studies of LaNi1+xAl6-x (x = 0.44).” Inorganic Chemistry. 43(15), 2004, 4604-4609

Gout, D., Benbow, E., Gourdon, O., and Miller, G. J. “Theoretical studies on cerium nickel aluminides: polar intermetallics with heavy fermion behavior.” Journal of Solid State Chemistry. 176(2), 2003, 538-548

Gout, D., Benbow, E., Gourdon, O., and Miller, G. J. “Crystallographic, electronic and magnetic studies of Ce4Ni6Al23: a new ternary intermetallic compound in the cerium- nickel-aluminum phase diagram.” Journal of Solid State Chemistry. 174(2), 2003, 471- 481

Gout, D., Benbow, E., and Miller, G. J. 2002. “Structure and bonding consequences in the pseudo-binary system Ln5Si3-xMx (Ln = La, Ce or Nd; M = Ni or Co).” Journal of Alloys and Compounds. 338(1-2), 2003, 153-164