Flux Growth and Physical Properties of Rare Earth Aluminides and Tetrelides Xiaowei Ma

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2013 Flux Growth and Physical Properties of Rare Earth Aluminides and Tetrelides Xiaowei Ma

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COLLEGE OF ARTS AND SCIENCES

FLUX GROWTH AND PHYSICAL PROPERTIES OF RARE EARTH ALUMINIDES AND TETRELIDES

XIAOWEI MA

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, 2013 Xiaowei Ma defended this dissertation on September 24, 2013. The members of the supervisory committee were:

Susan Latturner Professor Directing Dissertation

David Lind University Representative

Naresh Dalal Committee Member

Michael Shatruk Committee Member

The Graduate School has verified and approved the above-named committee members, and certifies that the Dissertation has been approved in accordance with university requirements.

ACKNOWLEDGMENTS

I would like to express my deepest gratitude to my advisor, Dr. Susan Latturner, for giving me the opportunity to join her group and leading me to the field of solid state chemistry. Without her excellent guidance, I would never have been able to finish my dissertation. Over the past five years, I really appreciate her kindly effort in directing me to obtain the research philosophy with warmhearted encouragement. She has been so generous to pass her broad knowledge and scientific attitude to me. She is not only a magnificent mentor but a good friend to provide personal support. I would also like to thank my committee members Dr. Shatruk, Dr. Dalal and Dr. Lind for their scientific guidance on my research. Dr. Shatruk always helped me to solve the hard problems especially concerning magnetic and electronic studies. Dr. Dalal and Dr. Lind also provided many important suggestions. I am also grateful to Dr. Lochner for kindly training me to use a lot of physical instruments. Additional thanks should be given to other members in Dr. Latturner's group, in particular, Dr. Whalen and Dr. Josiah, who provided their useful help at the beginning I joined the group. In addition, Dr. Chai, a postdoctoral associate in Dr. Shatruk's group, has taught me the electronic structure calculation. Finally, I want to thank my parents and my wife, Ling Wang, for their significant support during my graduate study.

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TABLE OF CONTENTS

List of Tables ...... viii List of Figures ...... x Abstract ...... xvi 1. INTRODUCTION ...... 1 1.1 Intermetallics and Their Applications ...... 1 1.2 Rare Earth Zintl Phases ...... 3 1.3 Flux Synthesis of Rare Earth Intermetallics ...... 4 1.4 Magnesium-based Binary Fluxes ...... 5 2. EXPERIMENTAL TECHNIQUES ...... 7 2.1 Synthesis Description...... 7 2.2 Elemental Analysis ...... 8 2.3 Structure Determination ...... 9 2.3.1 Powder and Single Crystal X-ray Diffraction ...... 10 2.3.2 Single Crystal Neutron Diffraction ...... 11 2.4 Solid State 27Al and 29Si NMR...... 11 2.5 Thermal Analysis ...... 12 2.6 Magnetic Susceptibility ...... 12 2.7 Electrical Resistivity ...... 13 2.8 Heat Capacity ...... 13 2.9 Electronic Structure Calculations ...... 14 3. SYNTHESIS AND PROPERTIES OF NEW MULTINARY SILICIDES

R5(Mg/Al)5Fe4(Al/Si)18 (R=Gd, Dy, Y) GROWN IN Mg/Al FLUX ...... 15 3.1 Introduction ...... 15 3.2 Experimental Procedure ...... 16 3.2.1 Synthesis ...... 16 3.2.2 Elemental Analysis ...... 16 3.2.3 Powder and Single Crystal X-ray Diffraction ...... 18 3.2.4 Single Crystal Neutron Diffraction ...... 18 3.2.5 Electronic Structure Calculations ...... 22 3.2.6 Magnetic Susceptibility ...... 23 3.2.7 Solid State NMR Characterization...... 23 3.2.8 Electrical Resistivity ...... 23 3.2.9 Heat Capacity ...... 23 3.3 Results and Discussion ...... 24 3.3.1 Synthesis ...... 24 3.3.2 Structure ...... 25 3.3.3 Electronic Structure Calculations ...... 32 3.3.4 Magnetic Behavior ...... 36 3.3.5 Electrical Resistivity ...... 39 3.4 Conclusion ...... 41

4. COMPETING PHASES, COMPLEX STRUCTURE, AND COMPLEMENTARY

DIFFRACTION STUDIES OF R3FeAl4-xMgxTt2 INTERMETALLICS (R=Y, Dy, Er, Yb; Tt=Si OR Ge; x<0.5) ...... 42 4.1 Introduction ...... 42 4.2 Experimental Methods ...... 43 4.2.1 Synthesis ...... 43 4.2.2 Elemental Analysis ...... 44 4.2.3 X-ray Diffraction ...... 45 4.2.4 Neutron Diffraction ...... 49 4.2.5 X-ray Photoelectron Spectroscopy ...... 50 4.2.6 Electronic Structure Calculations ...... 51 4.2.7 Magnetic Properties ...... 51 4.3 Results and Discussion ...... 52 4.3.1 Synthesis ...... 52 4.3.2 Structure ...... 55 4.3.3 Electronic Structure Calculations ...... 60 4.3.4 Magnetic Properties ...... 63 4.4 Conclusion ...... 67

5. Mg/Al FLUX GROWTH AND PROPERTIES OF M5+xMg18-xTt13 PHASES (M = Eu, Ba/Sr; Tt = Si, Ge) ...... 68 5.1 Introduction ...... 68 5.2 Experimental Procedure ...... 69 5.2.1 Synthesis ...... 69 5.2.2 Elemental Analysis ...... 69 5.2.3 TGA-DSC Measurement ...... 69 5.2.4 X-ray Diffraction ...... 69 5.2.5 Magnetic Susceptibility ...... 72 5.2.6 Electronic Structure Calculations ...... 72 5.2.7 Solid State NMR Characterization...... 74 5.2.8 Electrical Resistivity ...... 74 5.2.9 Seebeck Measurement ...... 74 5.3 Results and Discussion ...... 74 5.3.1 Synthesis and Thermal Analysis ...... 74 5.3.2 Structure ...... 75 5.3.3 Magnetic Properties ...... 79 5.3.4 Solid State 29Si MAS NMR ...... 81 5.3.5 Transport Properties ...... 83 5.4 Conclusion ...... 87 6. FLUX GROWTH AND MAGNETORESISTANCE BEHAVIOR OF RARE EARTH ZINTL PHASES EuMgTt (Tt = Sn, Pb) ...... 88 6.1 Introduction ...... 88 6.2 Experimental Procedure ...... 89

6.2.1 Synthesis ...... 89 6.2.2 Elemental Analysis ...... 90 6.2.3 X-ray Diffraction ...... 90 6.2.4 TGA-DSC Measurement ...... 92 6.2.5 Electronic Structure Calculations ...... 92 6.2.6 Magnetic Susceptibility ...... 93 6.2.7 Electrical Resistivity ...... 93 6.3 Results and Discussion ...... 94 6.3.1 Synthesis ...... 94 6.3.2 Structure ...... 96 6.3.3 Electronic Structure Calculations ...... 97 6.3.4 Magnetic Properties ...... 98 6.3.5 Resistivity and Magnetoresistance ...... 103 6.3.6 Thermoelectric Power of EuMgPb ...... 109 6.4 Conclusion ...... 109

7. RFe2MgxAl8-x (R=La-Nd AND Sm; x≤1): FLUX SYNTHESIS, STRUCTURE, MAGNETIC AND ELECTRICAL PROPERTIES ...... 111 7.1 Introduction ...... 111 7.2 Experimental Methods ...... 111 7.2.1 Synthesis ...... 111 7.2.2 Elemental Analysis ...... 112 7.2.3 X-ray Diffraction ...... 112 7.2.4 Solid State 27Al NMR ...... 117 7.2.5 Electronic Structure Calculations ...... 117 7.2.6 Magnetic Properties ...... 117 7.2.7 Electrical Resistivity ...... 118 7.3 Results and Discussion ...... 118 7.3.1 Synthesis ...... 118 7.3.2 Structure ...... 119 7.3.3 Electronic Structure Calculation ...... 122 7.3.4 Solid State 27Al NMR ...... 123 7.3.5 Magnetic Properties ...... 124 7.3.6 Electrical Resistivity ...... 126 7.4 Conclusion ...... 127 8. FUTURE WORK ...... 129 8.1 Introduction ...... 129 8.2 Er2Fe3Al8Si (Z=4) ...... 129 8.2.1 Experimental ...... 129 8.2.2 Structure and Magnetic Property ...... 132 8.2.3 Further Discussion ...... 135 8.3 Sm3CaFeC6 (Z=2) ...... 135 8.3.1 Experimental ...... 135 8.3.2 Structure Discussion ...... 136 8.3.3 Future Characterization ...... 139

9. CONCLUSION ...... 141

REFERENCES ...... 143

BIOGRAPHICAL SKETCH ...... 153

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LIST OF TABLES

Table 3.1 Result of SEM-EDS analysis of Al and Si (against external Al and Si standards) in R5(Mg/Al)5Fe4(Al/Si)18 products ...... 17

Table 3.2 Crystallographic data and collection parameters for R5(Mg/Al)5Fe4(Al/Si)18...... 19

Table 3.3 Atom positions and isotropic thermal parameters for Y5Mg5Fe4Al12Si6...... 20

Table 3.4 Atom positions and isotropic thermal parameters for Gd5Mg5Fe4Al12Si6 ...... 20

Table 3.5 Atom positions and isotropic thermal parameters for Dy5Mg5Fe4Al12Si6, determined by X-ray diffraction data collection...... 21

Table 3.6 Single crystal neutron crystallographic data and collection parameters for Dy5Mg2.92Fe4Al9.72Si10.36 phase ...... 21

Table 3.7 Atom positions and isotropic thermal parameters for Dy5Mg2.92Fe4Al9.72Si10.3; occupancy determined from neutron diffraction data...... 22

Table 3.8 Bond lengths in Dy5Mg5Fe4Al12Si6...... 27

Table 3.9 -ICOHP components (eV) in the four imaginary Y5Mg5Fe4(Al/Si)18 phases ...... 36

Table 4.1 Crystallographic data and collection parameters for Yb2.77FeAl3.72Mg0.28Si2, Dy3-δFeAl4-xMgxSi2, Y3-δFeAl4-xMgxGe2, Er3-δFeAl4-xMgxGe2 and Yb5Fe4Al17Si6 phases...... 46

Table 4.2 Atom positions and isotropic thermal parameters for Yb2.77FeAl3.72Mg0.28Si2...... 47

Table 4.3 Atom positions and isotropic thermal parameters for Yb5Fe4Al17Si6 ...... 47

Table 4.4 Atom positions and isotropic thermal parameters for Dy3-δFeAl4-xMgxSi2 phase...... 48

Table 4.5 Atom positions and isotropic thermal parameters for Er3-δFeAl4-xMgxGe2 phase...... 48

Table 4.6 Atom positions and isotropic thermal parameters for Y3-δFeAl4-xMgxGe2 phase...... 49

Table 4.7 Bond lengths in R3-δFeAl4-xMgxTt2 phases...... 50

Table 4.8 Bond lengths in Yb2.77FeAl3.72Mg0.28Si2 and Yb5Fe4Al17Si6...... 59

Table 5.1 Crystallographic data for Eu7.5Mg15.5Si13, Eu7.14Mg15.86Ge13 and Ba3.4Sr4.5Mg15.1Si12.9...... 70

Table 5.2 Wyckoff sites, atomic coordinates, equivalent isotropic displacement parameters [Å2] and occupancies of Eu7.5Mg15.5Si13...... 71

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Table 5.3 Wyckoff sites, atomic coordinates, equivalent isotropic displacement parameters [Å2] and occupancies of Eu7.14Mg15.86Ge13...... 71

Table 5.4 Wyckoff sites, atomic coordinates, equivalent isotropic displacement parameters [Å2] and occupancies of Ba3.4Sr4.5Mg15.1Si12.9...... 72

Table 5.5 Bond lengths in Eu7.5Mg15.5Si13, Eu7.14Mg15.86Ge13 and Ba3.4Sr4.5Mg15.1Si12.9...... 73

Table 6.1 Crystallographic data and collection parameters for EuMgSn and EuMgPb...... 91

Table 6.2 Interatomic distances in EuMgSn...... 92

Table 6.3 Interatomic distances in EuMgPb...... 92

Table 7.1 Crystallographic data and collection parameternates for RFe2MgxAl8-x (R = La-Nd and Sm)...... 113

Table 7.2 Atom positions and isotropic thermal parameters for LaFe2MgxAl8-x...... 114

Table 7.3 Atom positions and isotropic thermal parameters for CeFe2MgxAl8-x...... 114

Table 7.4 Atom positions and isotropic thermal parameters for PrFe2MgxAl8-x...... 115

Table 7.5 Atom positions and isotropic thermal parameters for NdFe2MgxAl8-x...... 115

Table 7.6 Atom positions and isotropic thermal parameters for SmFe2MgxAl8-x...... 116

Table 7.7 Bond lengths (Ǻ) in RFe2MgxAl8-x (R = Ce -Nd and Sm)...... 116

Table 7.8 Thermal parameters for the Mg/Al 4g Wyckoff site occupied by Mg or Al separately...... 121

Table 8.1 Crystallographic data and collection parameters for Er2Fe3Al8Si...... 131

Table 8.2 Atom positions and isotropic thermal parameters for Er2Fe3Al8Si...... 131

Table 8.3 Bond lengths in Er2Fe3Al8Si...... 132

Table 8.4 Crystallographic data and collection parameters for Sm3CaFeC6...... 137

Table 8.5 Atom positions and isotropic thermal parameters for Sm3CaFeC6...... 137

Table 8.6 Bond lengths in Sm3CaFeC6...... 138

LIST OF FIGURES

Figure 1.1 Comparison of different types of materials in terms of electronic localization and charge balance ...... 1

Figure 1.2 Phase diagrams of Mg/Al, Mg/Ag and Mg/Ca...... 6

Figure 2.1 A schematic summary of the phases grown in Mg/Al flux ...... 7

Figure 3.1 SEM image of a crystal of Gd5(Mg/Al)5Fe4(Al/Si)18...... 24

Figure 3.2 Powder X-ray diffraction data for R5(Mg/Al)5Fe4(Al/Si)18 phases, compared to theoretical patterns calculated from single crystal data. Impurity peaks are observed in the experimental pattern for the Y5(Mg/Al)5Fe4(Al/Si)18 phase (indicated by asterisks) and correspond to small amounts of YFe4Al8, Mg2Si, and Al5Fe2 byproducts...... 25

Figure 3.3 Structure of R5Mg5Fe4Al12Si6, viewed down the c-axis. Aluminum and silicon atoms are light blue and dark blue respectively. Ribbons of iron-centered trigonal prisms running along the c-axis are highlighted in polyhedral mode (red). Bonds to Mg (yellow) and R (green) are omitted for clarity...... 26

Figure 3.4 Coordination environments in the R5Mg5Fe4Al12Si6 structure. Aluminum and silicon atoms are light blue and dark blue respectively. a) Mono-capped trigonal prismatic coordination of iron which share trigonal faces to form chains. b) Coordination of the rare earth ion in the 1a Wyckoff site; these sites form a chain along the c-axis. c) Coordination of the rare earth ion in the 4n site...... 28

27 29 Figure 3.5 Al and Si MAS NMR spectra of Y5Mg5Fe4Al12Si6...... 31

Figure 3.6 Partial and total density of states with variable Al/Si ratios for Y phase...... 33

Figure 3.7 Partial density of states of Y and Fe in Y5Mg5Fe4Al6Si12...... 34

Figure 3.8 Total and partial density of states of Gd5Mg5Fe4Al6Si12...... 35

Figure 3.9 COHP (eV/bond mol) of Fe-Al/Si bonds for the imaginary Y phases...... 35

Figure 3.10 Temperature dependence of magnetic susceptibility of Y5(Mg/Al)5Fe4(Al/Si)18 at different magnetic fields...... 36

Figure 3.11 Temperature dependence of magnetic susceptibility of Gd5(Mg/Al)5Fe4(Al/Si)18 at different magnetic fields...... 37

Figure 3.12 Field dependence of the magnetization for Gd5(Mg/Al)5Fe4(Al/Si)18 at different temperatures...... 38

Figure 3.13 Temperature dependence of magnetic susceptibility of Gd5(Mg/Al)5Fe4(Al/Si)18 at 100 Oe...... 38

Figure 3.14 Field dependence of magnetization for Dy5(Mg/Al)5Fe4(Al/Si)18 at 1.8 K...... 39

Figure 3.15 Electrical resistivity of R5(Mg/Al)5Fe4(Al/Si)18 (R = Gd, Y, Dy)...... 39

Figure 3.16 Heat capacity of Gd5(Mg/Al)5Fe4(Al/Si)18...... 40

Figure 4.1 SEM images of a) a representative Yb2.77FeAl3.72Mg0.28Si2 crystal and b) a typical crystal produced from reaction (Mg/Al/Si/Fe/Yb = 15/12/3/1/2) in Nb crucibles...... 52

Figure 4.2 Powder X-ray diffraction patterns of Yb2.77FeAl3.72Mg0.28Si2, Dy3-δFeAl4-xMgxSi2, Er3-δFeAl4-xMgxGe2 and Y3-δFeAl4-xMgxGe2 samples grown from Mg/Al flux reactions at optimized ratios, compared to calculated pattern for Yb2.77FeAl3.72Mg0.28Si2 (theoretical patterns for the other analogs are similar.)...... 53

Figure 4.3 Structures of (a) the title phases R3-δFeAl4-xMgxSi2, (b) the R5Fe4Al17-xMgxSi6 compounds Yb5Fe4Al17Si6 and Dy5Mg5Fe4Al12Si6, and (c) RFe2Al8-xMgx phases (R = La-Nd), all viewed down the c-axis. Capped trigonal prismatic coordinations of iron atoms are shown as red polyhedra. Rare earth, iron, aluminum, magnesium and silicon atoms are purple, red, cyan, green, and blue spheres respectively...... 56

Figure 4.4 Coordination environments of atoms in the R3-δFeAl4-xMgxTt2 structure. (a) Monocapped trigonal prismatic coordination of iron sites (red) which share trigonal faces to form chains. (b) Coordination of the 2a Wyckoff site, occupied by Mg/Al mixture. (c) Coordination of tetrel atoms in the 8i Wyckoff site. (d) Coordination of the rare earth ion in the 4h Wyckoff site. (e) Coordination of the rare earth ion in the 8j Wyckoff site. (f) Positioning of rare earth ions in an ab-plane (viewed down c-axis of unit cell); dashed lines indicate distances of less than 3.75Å (Al and Fe atoms also in this plane removed for clarity)...... 58

Figure 4.5 Total and partial density of states data for (a) Y3FeAl4Si2 (model compound for R3-δFeAl4-xMgxSi2 with no Mg in 2a site), (b) Y3FeAl4Ge2 (model for R3-δFeAl4-xMgxGe2 with no Mg) and (c) Y3FeAl3.5Mg0.5Ge2 (model for R3-δFeAl4-xMgxGe2 with 100% Mg on 2a site)...... 61

Figure 4.6 The partial density of states data for Y, Fe, Mg, Al and Ge in Y3FeAl3.5Mg0.5Ge2. Note the different DOS scales for various elements...... 62

Figure 4.7 Calculated COHP data for the three Fe-Al bonds in Yb3FeAl4-xMgxSi2 and Er3FeAl4-xMgxGe2 phases...... 63

Figure 4.8 Temperature dependence of magnetic susceptibilities (filled symbols) and inverse magnetic susceptibilities (unfilled symbols) for (a) Yb2.77FeAl3.72Mg0.28Si2, (b) Er3-δFeAl4-xMgxGe2 and (c) Dy3-δFeAl4-xMgxSi2 at 100 G. Insets show low temperature magnetic

xi susceptibility behavior. (d) ZFC and FC temperature dependence of magnetic susceptibility for Y3- FeAl4-xMgxGe2 at 100 G...... 64

Figure 4.9 The Yb 4p region of the XPS spectrum of Yb2.77FeAl3.72Mg0.28Si2. (Crystals of Yb2.77FeAl3.72Mg0.28Si2 were sputtered by 5 kV argon ions for 30 minutes to remove 3+ any surface oxidation. The main peak at ~ 350 eV can be assigned to Yb 4p3/2 and a small peak 3+ 129,130 at ~ 400 eV corresponds to Yb 4p1/2 component, indicating that the valence state of Yb ions in Yb2.77FeAl3.72Mg0.28Si2 is +3. This is in agreement with the observed bond lengths and the magnetic data. A satellite peak as reported at 366 eV arising from LS coupling is not observed, likely due to the complexity of the structure.41)...... 65

Figure 4.10 a) Field dependence of magnetization for Yb2.77FeAl3.72Mg0.28Si2, Dy3-δFeAl4-xMgxSi2 and Er3-δFeAl4-xMgxGe2 at 1.8 K. b) AC magnetization of Er3-δFeAl4-xMgxGe2 and Dy3-δFeAl4-xMgxSi2 in the applied DC magnetic field at 1.8 K...... 66

Figure 5.1 The microscopic image of an Eu7.5Mg15.5Si13 single crystal (1mm×1mm grid)...... 75

Figure 5.2 Powder X-ray diffraction data on the products of Eu7.5Mg15.5Si13 synthesis in Mg/Al flux, compared to the pattern calculated based on the single crystal structure...... 76

Figure 5.3 Thermal analysis data for a sample of Eu7.5Mg15.5Si13. Decomposition with associated loss of Mg is indicated above 900 °C...... 77

Figure 5.4 PXRD patterns of Eu7.5Mg15.5Si13 taken before and after heating to 1200 °C...... 77

Figure 5.5 Structure of Eu7.5Mg15.5Tt13 (a). Tetrelide atoms (Tt = Si or Ge) are shown in blue, 10- with the Tt4 cluster highlighted in polyhedral mode. Mg sites are indicated by yellow spheres 10- and Eu sites by purple spheres. b) thermal ellipsoid picture of the Si4 cluster; c) and d) 10- coordination environments of the Si4 cluster in different view directions...... 79

Figure 5.6 Magnetic susceptibility temperature dependence data for Eu7.5Mg15.5Si13 in different orientations; applied field is 100 G unless otherwise noted. a) Crystal oriented with c-axis parallel to applied field. Inset: data taken with different applied fields. b) Crystal oriented with c-axis perpendicular to applied field. Inset: low temperature data...... 80

Figure 5.7 Field dependence of magnetization for Eu7.5Mg15.5Si13 at 4 K. Insets show data at low fields...... 80

Figure 5.8 Magnetic data for Eu7.1Mg15.9Ge13: a) temperature dependence of magnetic susceptibility in 100 G; b) field dependence of magnetization at 1.8 K...... 81

29 Figure 5.9 Si MAS NMR data for Ba3.4Sr4.5Mg15.1Si12.9...... 82

Figure 5.10 Temperature dependence of resistivity of Eu7.5Mg15.5Si13...... 84

Figure 5.11 Density of states data calculated for Eu8Mg15Si13...... 84

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Figure 5.12 PXRD of Eu7.5Mg15.5Si13 samples pressed into two sample pellets, before (above) and after (below) the spark plasma sintering process to make the pellets...... 85

Figure 5.13 Temperature dependence of resistivity on two spark plasma sintered pellet samples of Eu7.5Mg15.5Si13...... 86

Figure 5.14 Temperature-dependent Seebeck coefficients on two spark plasma sintered pellet samples of Eu7.5Mg15.5Si13...... 86

Figure 6.1 SEM image of a single crystal of EuMgSn grown from Mg/Al flux...... 94

Figure 6.2 a) Powder X-ray diffraction patterns of EuMgSn samples from Mg/Al and Mg/Ag fluxes, compared to calculated pattern based on single crystal structure; b) Powder X-ray diffraction of EuMgSn after thermal treatment...... 95

Figure 6.3 TGA and DSC of EuMgSn...... 96

Figure 6.4 Structure of EuMgTt (Tt = Sn, Pb) viewed down the b-axis; europium, magnesium and tin (or Pb) atoms are pink, yellow and cyan respectively...... 97

Figure 6.5 Partial and total density of states data calculated for a) EuMgSn and b) EuMgPb... 98

Figure 6.6 Temperature dependence of magnetic susceptibility (χ) for EuMgSn. (a) Data for crystal oriented with b-axis parallel to the field, taken at different fields (data for 100 G, 1000 G, 1.5 T, 2 T, 2.5 T are black, red, green, blue, magenta). Solid and empty squares are for zero field cool (ZFC) and field cool (FC) respectively. Inset: 1/χ vs. T. (b) Data for crystal oriented with b-axis parallel (red) or perpendicular (purple) to the field, taken at 1000 G. Solid and empty squares are for zero field cool (ZFC) and field cool (FC) respectively. Inset: 1/χ vs. T...... 99

Figure 6.7 Field dependence of magnetization at 4.2 K for EuMgSn crystal oriented with b-axis either parallel or perpendicular to the field...... 100

Figure 6.8 Field dependence of AC magnetization of EuMgSn at 4.2 K (AC frequency 1 Hz)...... 101

Figure 6.9 Temperature dependence of magnetic susceptibility (χ) for EuMgPb...... 102

Figure 6.10 Field dependence of magnetization at 1.8 K for EuMgPb...... 102

Figure 6.11 Field dependence of AC magnetization of EuMgPb at 1.8 K (AC frequency 1 Hz)...... 103

Figure 6.12 Temperature dependence of the electrical resistivity of EuMgSn crystal at both 0 T and 2.5 T applied fields. Inset: low temperature data...... 104

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Figure 6.13 Temperature dependence of magnetoresistance ratio (MR) for EuMgSn at an applied field of 2.5 T. Inset: low temperature data...... 105

Figure 6.14 Field dependence of resistivity for EuMgSn at 4.2 K...... 106

Figure 6.15 Temperature-dependent electrical resistivity of EuMgPb at 0T and 4T...... 106

Figure 6.16 Temperature-dependent magnetorisistance of EuMgPb (4T)...... 107

Figure 6.17 Temperature-dependent electrical resistivity of EuMgPb at different fields below 30 K. (a) H // b; (b) H⊥b...... 107

Figure 6.18 Temperature-dependent magnetoresistance of EuMgPb at different fields below 30 K. (a) H // b; (b) H⊥b...... 108

Figure 6.19 Temperature dependence of the thermoelectric power for EuMgPb...... 109

Figure 7.1 SEM image of a single crystal for NdFe2MgxAl8-x...... 118

Figure 7.2 Variable-temperature powder X-ray diffraction pattern of NdFe2MgxAl8-x...... 119

Figure 7.3 Structure of RFe2MgxAl8-x (R = La-Nd or Sm) a) viewed down the c-axis and b) viewed down the b axis. Rare earth, iron, magnesium and aluminum atoms are purple, red, green and cyan respectively...... 120

Figure 7.4 Coordination environments of a) rare earth atoms and b) Mg in the RFe2MgxAl8-x (R = La-Nd or Sm) structure...... 121

Figure 7.5 Total and partial density of states of LaFe2MgAl7 and LaFe2Al8...... 122

27 Figure 7.6 Solid state Al NMR of LaFe2MgxAl8-x...... 123

Figure 7.7 Powder X-ray diffraction pattern of LaFe2MgxAl8-x...... 123

Figure 7.8 Temperature-dependent magnetic susceptibility of LaFe2MgxAl8-x...... 124

Figure 7.9 Temperature dependence of magnetic susceptibilities of (a) CeFe2MgxAl8-x, (b) PrFe2MgxAl8-x, (c) NdFe2MgxAl8-x and (d) SmFe2MgxAl8-x...... 125

Figure 7.10 Field dependence of magnetization for RFe2MgxAl8-x (R = Ce, Pr, Nd or Sm)... .126

Figure 7.11 Temperature variation of electrical resistivity for RFe2MgxAl8-x (R= La-Nd, Sm) ...... 127

Figure 8.1 SEM image of one selected Er2Fe3Al8Si single crystal...... 130

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Figure 8.2 Structure of Er2Fe3Al8Si viewed down the b-axis. Erbium, iron, aluminum and silicon atoms are green, brown, cyan and blue respectively...... 133

Figure 8.3 Total and partial density of states for Er2Fe3Al8Si...... 134

Figure 8.4 Magnetic data for Er2Fe3Al8Si. (a) Temperature dependence of magnetic susceptibility and inverse magnetic susceptibility at 100 G. (b) Field dependence of magnetization 1.8 K...... 134

Figure 8.5 SEM image of one selected Sm3CaFeC6 single crystal...... 136

Figure 8.6 Structure of Sm3CaFeC6 viewed down the c-axis (a) and [110] direction. Erbium, iron, aluminum and silicon atoms are green, brown, cyan and blue respectively...... 138

Figure 8.7 Fe-C-C cluster viewed down the c-axis (a) and a-axis (b), and the coordination of calcium...... 139

ABSTRACT

The flux method is a very useful technique for the exploratory synthesis of rare earth intermetallics. Reactions of rare earth metals with iron and silicon (or germanium, tin, lead) in a 1:1 Mg/Al flux have yielded single crystals of a series of new complex intermetallic phases. The structures of products were determined by single crystal X-ray diffraction or neutron diffraction. Reactions with early rare earths (R=La-Nd, Sm) produce RFe2MgAl7 phases which are substituted variants of the LaFe2Al8 type. NdFe2MgAl7 and SmFe2MgAl7 show antiferromagnetic ordering with Néel temperatures (TN) of 7.8K and 12K respectively. An electrical resistivity upturn was observed at ~11K for SmFe2MgAl7, consistent with the TN.

Reactions with later rare earth elements (Gd, Dy) produce R5(Mg/Al)5Fe4(Al/Si)18 which forms in a new P4/mmm symmetry structure (a=11.655(2)Å, c=4.0668(8)Å for Dy analog). The single crystal neutron diffraction data of the Dy analog distinguished the Mg, Al and Si sites, indicating a stoichiometry of Dy5Mg2.92Fe4Al9.72Si10.36. The Gd and Dy analogs exhibit antiferromagnetic transitions with TN= 11K and 6.9K respectively. Reactions with ytterbium, erbium, dysprosium, or yttrium produce R3FeAl4-xMgxTt2 (R = Yb, Dy, Er, Y; Tt = Si, Ge) which has a new structure type in the P4/mbm space group (a=13.3479Å, c=4.0996Å); neutron diffraction data confirmed the partial incorporation of Mg into one Al site, leading to a formula of Yb3FeAl3.72Mg0.28Si2.

Er2Fe3Al8Si crystallizes as a substituted variant of the orthorhombic Nd2Co3Al9 type. No magnetic ordering was observed for Yb3FeAl4-xMgxSi2 and Er2Fe3Al8Si.

Common structural features in the RFe2MgAl7, R5(Mg/Al)5Fe4(Al/Si)18 and

Yb3FeAl4-xMgxSi2 phases include chains of face-sharing mono-capped FeAl6 trigonal prisms, and preferential siting of Mg on specific Al sites. DOS calculations indicate that substitution of Mg for Al slightly destabilizes the structure. The presence of vacancies on the rare earth sites or the silicon substitution for aluminum are likely able to compensate for the structure destabilization, leading to the formation of pseudo gaps close to the EF. Reactions with europium and light tetrelides Tt = Si or Ge with iron in the Mg/Al flux produce compounds that do not incorporate iron or aluminum. Instead, these reactions yield ternary Zintl phases Eu6Mg17Tt13, crystallizing in the hexagonal Ba5Mg18Si13 structure type.

Study of the magnetic anisotropy reveals that Eu6Mg17Si13 orders ferromagnetically (TC=12K) with a slight hysteresis when the c axis is oriented parallel to the field. Reactions with europium

xvi and heavier tetrelides Tt = Sn or Pb yield ternary Zintl phases EuMgTt, crystallizing in the orthorhombic TiNiSi structure type. Magnetic and electrical studies indicate that both compounds show large magnetoresistance up to -30% and -25% at their Néel temperatures (10.9 K and 13.9 K), respectively.

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CHAPTER ONE

INTRODUCTION

1.1 Intermetallics and Their Applications Intermetallics are compounds comprised of two or more metallic or semimetallic elements. It is necessary to clarify the difference between intermetallics and conventional metal alloys though intermetallics can be considered as alloys in a broad sense. Metal alloys can be described as a combination of very similar metals, often exhibiting mixing of different metals on crystallographic sites. These compounds therefore have a large phase width, as demonstrated by the brass family of Cu1-xZnx in which x can range from 0 to 1. Intermetallic compounds are comprised of combinations of metals and/or metalloids which are different enough in size and electronegativity that each element will have a distinct preferred site in the crystal structure and there will be little mixing; as a result, these phases usually have a small (or zero) phase width. Intermetallics often exhibit some degree of charge transfer from the more electropositive metals (which can become recognizably “cationic”) to the more electronegative metals or metalloids. However, unlike the case of salts, the electrons are not localized on a specific atom and there is not an exact charge balance of cations and anions; instead, the electrons are delocalized, making intermetallics good conductors. A comparison is shown in Figure 1.1.

Figure 1.1 Comparison of different type of materials in terms of electronic localization and charge balance

Due to the partially ionic characteristic of intermetallics, interest in these phases goes beyond their mechanical properties and extends to their magnetic and electronic behaviors. For instance, the presence of rare earth cations often produces interesting magnetic properties due to the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the localized magnetic spins on the rare earth ion with the conduction electrons, leading to long range order. RKKY-induced 1

1 magnetic ordering is seen for intermetallics such as RE2AlGe2 (RE= Tb-Tm, Lu) , RE12Co5Bi 2 3 (RE= Y, Gd, Tb, Dy, Ho, Er, Tm) , REAu2In4 (In = La, Ce, Pr, Nd) . Many compounds such as 4 5 6 7 YbNiAl2 , CeFe2Al10 , Ce(Pt1-xIrx)2Si2 and Ce3Pd20Ge(Si)6 exhibit the Kondo effect, in which the conduction electrons can be affected by the localized magnetic spins. Superconducting 8 9 behavior was discovered in a lot of intermetallic compounds like Nb3Sn , MgB2 , LuRh4B4 10,11 12 (Tc=11.7 K) and LnNi2B2C (Ln=Y, Tm, Er, Ho or Lu) (Tc is up to 11.7 K) , some of which can be explained well with the BCS theory. Geometric frustration and spin glass behavior is also 13 14 15 interesting as shown in intermetallics such as CoxNbS2 , CePd3+xGa8-x and La21Fe8Sn7C12 . Aluminum-containing and silicon-containing intermetallics (Al and Si are present simultaneously in many cases) are important materials and have received much attention for uses such as structural materials and coatings. Thin films of refractory phases such as TiSi2 and CoSi2 are used as diffusion barriers in microelectronics, facilitated by their excellent bonding to silicon.16 Silicon is often added to metal alloys to strengthen them, causing precipitation hardening from formation of adventitious secondary silicide phases, such as microcrystals of

CaMgSi in magnesium alloys and Al12Mn3Si2, Al8Fe2Si, and the “π-phase” Al9FeMg3Si5 in 19-22 aluminum alloys. Aluminides such as Ni3Al can be used as a light-weight automotive body material.23 γ-TiAl has promising mechanical property and corrosion resistance as high-temperature engine components.24,25 FeAl is a good substitute of stainless steel with excellent corrosion and oxidation resistance.26,27 Many transition metal silicides and aluminides also have interesting magnetic or transport properties; Fe3Si is a ferromagnetic metal, while FeSi2 is a small bandgap semiconductor of interest as a thermoelectric material.17,18 Aluminides containing rare earths and/or transition 28 metals can also possess interesting magnetic and electrical behaviors like La2NiAl7, RAu3Al7 29 30-35 (R = Ce-Nd, Sm, Gd-Lu), CeT2X8 (T = Fe, Co; X = Al, Ga) . In this work, the flux synthesis and physical characterization (magnetic and transport properties) of rare earth aluminides and silicides were explored. In some cases, the reactions with heavier IVA group elements (Ge, Sn and Pb) were also explored in order to study the effect of chemical pressure on the structures.

1.2 Rare Earth Zintl Phases Zintl phases are named after Eduard Zintl, who pioneered their exploration in the 1930s. Zintl phases are traditionally viewed as compounds that contain electropositive alkali or alkaline-earth metals and electronegative group 13, 14 or 15 p-block elements (except B, Al, C, N and P). Zintl phases can be viewed as a special subset of intermetallics since they combine metals and metalloid elements. However, in the case of Zintl phases, charge balancing is achieved; the electrons donated by the electropositive element are located on the more electronegative metalloid (or clusters of metalloid atoms), so these phases are usually semiconducting. Unlike isolated simple anions (e.g. Cl- in NaCl) in salts which follow electronic octet rules, metalloid atoms in the Zintl phases will often bond to each other to form different types of polyanionic clusters or anion networks (e.g. in NaTl, instead of forming isolated Tl- anions, thallium atoms link together into a three-dimensional quasi-infinite anionic diamond network). Zintl phases are mostly electronically balanced and follow the octet rule considering the localized covalent bonds among the anions; this is known as the Zintl-Klemm concept.36 The Zintl-Klemm concept can be extended to model the creation of vacancies; Zintl phases such as

“K4Si23” actually contain a specific amount of framework vacancies. In the actual structure

K4Si22□1, vacancies in the silicon framework create 3-bonded silicon with a net negative charge to balance the cation charge.37 Zintl phases are commonly semiconductors with a small band gap. Using a binary Zintl phase NaSi as an example, the Na+ cations in the structure are expected to formally transfer electrons to the Si- anions. Due to the presence of anion clusters (in the case of NaSi, silicon 4- + forms Si4 clusters balanced by 4 Na cations; this compound is sometimes denoted as Na4Si4), the antibonding combination of Si-Si bonds will be pushed up in energy. The top of the valence 4- band with respect to Si4 anions is occupied by the lone pairs rather than the strong Si-Si bonding orbitals. Therefore, a small band gap will be formed between the Si-Si bonding and antibonding orbitals. Zintl phases are mostly diamagnetic with the exceptions of compounds containing Eu2+ or Mn2+ which exhibit paramagnetic behavior.36 If the alkali or alkaline-earth cations are substituted by electropositive rare earth ions such as Eu2+, the compound will become a rare earth Zintl phase, which provides the connection between Zintl phases and intermetallics. Due to the presence of 4f electrons, the rare earth Zintl phase will be more metallic and a pseudo gap

3 instead of a real band gap will be formed at the Fermi level. Since most of the rare earth ions possess a magnetic moment, the conduction electrons could be affected by the localized magnetic moment in the case that the 4f bands are close to the Fermi level. This interaction between conduction electrons and magnetic moments can lead to some interesting transport 38 properties like magnetoresistance behavior. Some example compounds are EuGaSi, EuIn2M2 39, 40 41 42 (M = As, P) , EuGa2M2 (M = As, P) and EuxCa1-xB6.

1.3 Flux Synthesis of Rare Earth Intermetallics The arsenal for the synthesis of intermetallic compounds includes various approaches such as high temperature annealing, floating zone method, high pressure method and molten metal fluxes. High temperature annealing of reactant elements is a traditional method for the synthesis of various binary or ternary intermetallic phases. Before the reaction, the solid state reactants are often ground to powders to increase the contact surfaces among the elements and sometimes arc melting is helpful to achieve homogeneity of reactant mixture. A high temperature is required to create sufficient diffusion and overcome reaction barriers. In this way, the reactions generally end up with thermodynamically favorable phase.43, 44 This high temperature method allows careful control over product composition and is scalable to a large amount of products. Unfortunately, the traditional method allows very little control during the heating of samples and polycrystalline phases or tiny single crystals are often produced, which highlights the advantage of flux synthesis method. Flux reactions utilize low-melting metals or salts as solvents and promote the formation of crystals by slowly cooling down the reaction mixture. The solvent environment can enhance the diffusion and lower the activation energy barrier, which allows isolation of metastable products. The slow cooling rate often leads to growth of large single crystals of products.45-47 Therefore, the molten flux technique is an appealing tool for exploratory synthesis of new single crystal phases. This work mainly focused on the synthesis in metal fluxes. To be a good flux, the metal should have a relatively low melting point but a high boiling point so that there is enough room to control the temperature variation with the normal heating equipment. A low melting point also enables removal of the flux from products by decanting while still molten. Also, the metal flux should not yield thermodynamically stable phases with the reactants, which is especially important for the exploratory synthesis.

Many metal elements have been successfully used as flux reaction solvents.1 Al, Sn, Pb, Ga and In fluxes are quite productive and a large variety of new phases have been synthesized and characterized in these melts. In addition, Li, Na, Cu, Co and Zn fluxes were also reported to be used for the synthesis of carbides, borides and nitrides. The use of mixed fluxes composed of two metal elements can further lower the melting point due to eutectic formation and incorporate more elements as reactants, which is especially helpful to the exploratory synthesis. This work is going to focus on the growth and physical characterization of rare earth intermetallics in Mg-based binary fluxes.

1.4 Magnesium-based Binary Fluxes Using binary fluxes composed of two metal elements in large amounts can lower the melting point due to the formation of eutectics, although it introduces additional complexity since one or both of the flux metals may act as reactants and be incorporated into the products. However, if the goal is to explore compounds with new structures, the addition of a second metal may be able to tune the reaction environment and contribute to the formation of metastable phases. Magnesium, a lightweight alkaline earth metal, has a melting point of 650 oC. When it is combined with other elements in specific molar ratios, eutectics can form and the melting point will be lowered further. Figure 1.2 shows the phase diagrams of Mg/Al, Mg/Ag and Mg/Ca. The Mg/Al phase diagram contains a wide low melting range (~460 oC) between 35-60% Mg, and 50 only two known binary phases, Mg2Al3 and Mg17Al12. This allows for many different Mg/Al ratios to be explored as fluxes. Previous research in our group has found that Mg/Al mixtures are particularly good solvents for the formation of silicides, allowing for growth of CaMgSi single crystals.51 The large crystal size enabled the study of the physical properties of this phase, resulting in discovery of a metal to semimetal transition at around 50K. The Mg/Ag phase diagram exhibits the formation of a Mg/Ag eutectic at the molar ratio = 0.85/0.15, and the melting point is ~440 oC. This eutectic can also be used for the exploratory synthesis. The Mg/Ca flux (see Figure 1.2c) shows two eutectic points: Mg/Ca=0.3/0.7 (446 oC) and 0.9/0.1 (517 oC), both of which are of interest to use as fluxes. As a very reducing media, the Mg/Ca flux might be suitable for dissolving oxidizing p-block elements and forming stable multinary phases.

(a) (b)

(c)

Figure 1.2 Phase diagrams of Mg/Al, Mg/Ag 48 and Mg/Ca 49.

CHAPTER TWO

EXPERIMENTAL TECHNIQUES

2.1 Synthesis Description Exploratory synthesis in the Mg/Al flux was carried out with the goal of combining electropositive and electronegative elements. In excess Mg/Al flux, electropositive metals such as rare earth and alkaline earth metals were combined with electronegative elements such as the p block metals and metalloids such as C, Si, Ge, Sn, Pb, Se, Te, etc. A large variety of reactions were attempted; Gd5(Mg/Al)5Fe4(Al/Si)18 was the first new complex multinary phase discovered, which will be discussed in detail in chapter 3. Gd5(Mg/Al)5Fe4(Al/Si)18 was grown from a reaction of Mg/Al/Si/Gd (15/15/2/1 mmols) and Fe was incorporated from the etching of stainless steel crucible. It was discovered that adding Fe element to the reactants could significantly enhance the yield. Subsequently, the experiments were extended to other rare earth elements and tetrels with a starting Mg/Al/Tt/Fe/R reactant ratio of 15/15/2/1/1 mmols (Tt = Si, Ge, Sn, Pb; R = La to Yb). Surprisingly, the reactions with different rare earth elements produced compounds with different structure types, as summarized in Figure 2.1.

Figure 2.1 A schematic summary of the phases grown in Mg/Al flux

Magnesium has a high vapor pressure (10-4 torr at 327 ° C ) and it is strongly reducing, so open crucibles and crucible materials such as alumina are not feasible. The Mg-based flux reactions (Mg/Al, Mg/Ca and Mg/Ag) have to be done in closed metal crucibles. The most

7 common closed crucibles in our group are stainless steel crucibles and Nb crucibles, which can be welded shut by arc-melting. Low cost stainless steel crucibles contain tiny amount of impurity elements such as C, Ni, Cr, Co, Mn; all products grown in these vessels much be analyzed for accidental incorporation of these elements. After the reaction ratios were optimized in stainless steel crucibles, the same reaction should be repeated in pure Nb crucibles so that relatively pure single crystals can be obtained for further physical characterization. To carry out flux reactions, reactants as received from different companies were weighed out in the desired ratio and loaded into a stainless steel crucible in a dry box. The steel crucible was welded shut in an argon-filled glovebox and then sealed into fused silica tubes under vacuum. All reaction ampoules were placed in a muffle furnace and heated from room temperature to 950°C in 10 h, held at 950 °C for 10 h, cooled to 750°C in 80 h, and held at 750 °C for 24 h, at which point the reaction ampoules were quickly removed from the furnace, flipped and centrifuged to let the excess Mg/Al molten flux decant off the product crystals which adhered to the crucible walls. The steel crucibles were then cut open with a tube cutter and single crystals can be removed with some rod tools. If the products are air sensitive, the operation can be done in the dry box and accordingly products will be stored away from the air.

2.2 Elemental Analysis After single crystal products are obtained, elemental analysis is needed to determine the elements contained in the crystals. Scanning electron microscope - Energy dispersive spectroscopy (SEM-EDS) and X-ray photoelectron spectroscopy (XPS) are good techniques for the elemental analysis, with the former method being very convenient. SEM-EDS analysis was performed using a JEOL 5900 scanning electron microscope (30 kV acceleration voltage) equipped with PGT Prism energy dispersion spectroscopy software. This technique uses a high energy beam of electrons which scans across the sample. The electron beam ejects core electrons from atoms in the sample; these ejected electrons are detected to image the sample surface. Ejection of these core electrons leaves vacancies which are filled by relaxation of electrons in higher energy shells of the atoms. The difference in energy of the electron shells (for instance, a 3s electron relaxing down to fill a void in a 1s shell) is characteristic of the atom; the energy is released as an X-ray which is detected by a spectrometer.

Each different element in a sample will emit specific X-ray energies and can therefore be distinguished. For SEM-EDS measurements, selected crystals were arranged on double-sided carbon tape adhered to an aluminum sample puck. Each crystal was cleaved to expose inner portions to acquire more accurate elemental analysis of the bulk sample and avoid erroneous readings due to residual flux coating on the surface. Several spots on each crystal were analyzed for 60 s at each location. Aluminum and silicon pieces were used as external standards to improve the quantification of these elements. XPS spectra were obtained on a Physical Electronics PHI 5100 series XPS with a non-monochromated dual anode (Mg and Al) source equipped with a single channel hemispherical energy analyzer. The Al Kα X-ray source (15 kV and 30 mA) was used. When the incident X-ray photons with sufficient energy hit the surface of a material, the inner shell electrons of an atom can be knocked out as photoelectrons. By detecting their kinetic energy, the characteristic binding energy corresponding to certain element will be obtained. Beside the elemental identification, the valence states can also be figured out. Single crystals were placed on a carbon tape adhered to a XPS stage puck. To avoid the effect of impurities on the surface, the XPS spectra were collected after sputtering with Ar ions (5 kV) for 30 minutes.

2.3 Structure Determination X-ray and neutron diffraction techniques play very important roles in determining the structure of crystals. Crystals can be viewed as infinite ordered stackings of layers of atoms. These layers of atoms are separated by distances on the order of angstroms, which is the same magnitude as the wavelength of X-rays. Crystals can therefore act as diffraction gratings for X-ray beams. The diffraction methods are based on the wave interferences following Bragg's law, as described in Equation 2.1:

(2.1)

where is the wavelength of incident beam (X-ray or neutron), d is the distance between two parallel crystal planes, θ is the incident angle and n is an integer.

At a certain angle of θ, when the diffracted X-ray or neutron beams exhibit a path difference (2dsinθ) that is equal to one or multiple wavelengths (n), the diffraction will be detected. Otherwise, the light waves will destructively interfere and will not be detected. Knowing the d spacings of the various layers of atoms in a crystal, the lattice parameters of the structure will be calculated according to the equations corresponding to the structure types.52 The advantage of X-ray diffraction is the convenient operation with commercially available powder or single crystal X-ray diffractometers. However, X-ray beams interact with the electrons and the diffraction intensity depends on the number of electrons. This makes detection of light elements difficult because of their small number of electrons. Also, if a compound contains two elements with very similar numbers of electrons, it will be difficult to distinguish the atoms in an X-ray diffraction experiment. Neutron diffraction, in comparison, is realized through the interaction between a neutron beam and atom nuclei. So there is no limitation applied to the light elements and neighboring elements. The disadvantage of neutron diffraction is the complexity of generating a neutron beam, so experiments must be carried out in certain places like national labs in the U.S or Europe.

2.3.1 Powder and Single Crystal X-ray Diffraction

For all the phases studied in this work, single crystal diffraction data were collected at room temperature on a Bruker APEX2 single crystal diffractometer with a Mo Kα radiation source. Selected crystal samples were broken into suitable size and small spheroid fragments were mounted on glass fibers for diffraction. Data were processed using the SAINT and SADABS programs.53 Space group assignment was accomplished by XPREP, and refinement of the structure was performed using SHELXTL. 54 During structure refinement, assignment of rare earth and iron sites is typically straightforward, with most of these atoms being located using direct methods (in the SHELXTL XS program). Lighter element sites can also be found using direct methods, or in some cases by locating the peaks in the residual electron density map (found by difference Fourier calculations). Assignment of lighter elements is difficult if these elements have similar electron numbers; allowing the occupancies of these sites to vary is often not informative (because of very similar X-ray scattering factors, Mg, Al, or Si appear identical). Therefore, assignments are modified

10 based on bond length considerations and elemental analysis. In the final refinement cycles, occupancies of all sites are allowed to vary. Powder X-ray diffraction data were collected on a PANalytical X'Pert PRO diffractometer equipped with a Cu Kα radiation source. For the samples that are air sensitive, samples were ground and loaded into an air-tight holder inside a glove box to prevent oxidation.

2.3.2 Single Crystal Neutron Diffraction

Phases containing Mg, Al, and Si were studied by neutron diffraction at the HB-3A four-circle single crystal diffractometer at the High Flux Isotope Reactor at Oak Ridge National Laboratory (see Chapter three and four). The data were collected at 300 K with neutron wavelength 1.5424 Å from a bent perfect Si-220 monochromator.55 The structure refinement was based on ~ 400 reflections and completed using the program FULLPROF. 56 To limit the number of refinable parameters, the atomic positions were fixed to those obtained from the single crystal X-ray diffraction study of these phases and only the thermal displacement and occupancy parameters were refined. Thermal parameters of light elements (Al, Si and Mg) were constrained to be equivalent. In order to eliminate the effect of large discrepancy between the length and the diameter, the absorption correction was conducted based on the single crystal's size parameters.

2.4 Solid State 27Al and 29Si NMR Magic-angle spinning (MAS) solid state NMR can provide a lot of information about the crystal structure including the site occupancies as well as the coordination. Due to the polarization of conduction electrons, a large Knight shift will be observed for the resonances of nuclei in intermetallic compounds; this will give information about whether a sample is metallic or semiconducting. Most of the compounds concerned in this work contain Al and Si, so 27Al and 29Si MAS NMR spectra were collected for several samples. Data were collected on a Varian/Inova 500WB spectrometer (11.7T) with resonance frequencies of 130.46 and 99.40 MHz respectively. The 27Al and 29Si shifts were referenced to

1M Al(NO3)3 and TMS. Because the conduction electrons can generate eddy currents in a sample when placed in a magnetic field (which hinders spinning of the sample), crystals were finely ground with NaCl in a 1:1 ratio by volume in a glove box and the powder was packed into a 4 mm zirconia rotor sealed with airtight screw caps. The 29Si MAS spectra were obtained with

11 a spinning speed of 13 kHz and a recycle delay of 60s. For the 27Al MAS experiment, single pulse acquisition was applied with a short RF pulse less than 15o. The spinning speed was 12 kHz and the recycle delay was 0.3s.

2.5 Thermal Analysis Thermogravimetric analysis (TGA) and Differential Scanning Calorimetry (DSC) measurements can determine whether there is a phase transition or at what temperature crystals start to melt (the stability of products at high temperatures), and check that the products melt congruently or incongruently. The measurements were performed on a SDT-Q600 (TA Instruments). Crystals were ground into powder to increase the contact area with the alumina sample holder. The sample was heated to 1000 °C (or 1200° C ) in 10 °C/min and then cooled to room temperature in Argon atmosphere (100 ml/min). Thereafter, ex-situ powder XRD data would be collected on the thermally treated sample. If there are some unusual transitions observed in the TGA or DSC data, powder XRD measurements can be done before or after the transition temperature.

2.6 Magnetic Susceptibility The presence of rare earth elements and transition metals in the products of Mg/Al flux reactions may lead to interesting magnetic behavior. The 4f electrons on rare earth (RE) ions are usually localized and are usually simply paramagnetic at high temperatures, but can be magnetically coupled by RKKY interactions and may exhibit ferromagnetic, antiferromagnetic or more complex ordering at low temperatures. Depending on the RE-RE distances and their relative positions, multi-level spin reorientations can be observed. The magnetic properties of transition metals are also interesting (the transition metal used in this work is Fe); coupling of the d-electrons can result in magnetic ordering. Structures containing both rare earth elements and transition metals may exhibit very complex magnetic behavior. Superconducting Quantum Interference Device (SQUID) is commonly used for the magnetic measurement. Temperature-dependent magnetic susceptibility and field-dependent magnetization measurements were undertaken on a Quantum Design SQUID Magnetic Property Measurement System (MPMS). This technique is highly sensitive, so crystals grown in Nb crucibles should be used to avoid the possibility of incorporation of trace paramagnetic

12 contaminants from steel crucibles. Crystals were selected and held between two 4 cm long strips of kapton tape to eliminate background effects; this was placed in a straw attached to the sample holder. Temperature-dependent susceptibility data were collected between 1.8 K and 300 K at variable fields respectively. Field-dependent magnetization data were collected at 1.8 K using applied fields up to 7 T. For well-formed, facetted crystals which grow along clearly distinct axes (for instance, as rods or needles, or plates), magnetic anisotropy was studied by orienting the crystal with a specific axis either parallel or perpendicular to the applied field. The field dependence of AC magnetic susceptibility was performed with 1 Hz frequency and 3×10-4 T amplitude of the AC field under a DC bias field up to 7 T.

2.7 Electrical Resistivity Rare earth intermetallics should exhibit metallic behavior, which can be reflected in the temperature dependence of the electrical resistivity. For metallic materials, resistivity is expected to rise as temperature is increased, due to increased scattering of charge carriers by lattice vibrations (phonons). In addition, for some rare earth elements (such as Eu) that have 4f band close to the Fermi level, the resistivity can be affected by the spins under a magnetic field, resulting in magnetoresistance, as indicated by EuMgTt (Tt = Sn, Pb) in chapter 6. Electrical resistivity measurements were conducted with a conventional four-probe method on a Physical Property Measurement System (PPMS) by Quantum Design. A large enough single crystal was put on a sample holder puck and four 25 micron diameter gold wires were adhered to the crystal surface with silver paste. Resistivity data were taken from 1.9 - 300 K at 0 T and 2.5 T with an applied excitation current of 0.5 mA. Field dependence of resistivity data were obtained at 4.2 K in the field range of 0 - 7 T. The magnetoresistance ratio (MR) at an applied field B was calculated using the equation MR = {[(B) – (0 T))] / (0 T)} × 100.

2.8 Heat Capacity

The PPMS was also used to measure the heat capacity (Cp) of the Gd5(Mg/Al)5Fe4(Al/Si)18 as a function of temperature from 1.9 to 30 K. The calorimeter on this instrument is based on the principle of thermal relaxation, with heat pulses being applied through eight wires that support a sample platform. The sample is thermally coupled to the platform with Apiezon N-grease, which is initially measured and subsequently subtracted from the total Cp. Data was obtained through

13 the application of large heat pulse (maximum 30% temperature rise) and long measurement times (both two and three tau). Upon analysis of the raw data, a large number of points could then be acquired through application of the dual-slope analysis technique within QDs MultiVu software.57

2.9 Electronic Structure Calculations Density of states (DOS) and crystal orbital Hamilton population (COHP) calculations were carried out with the tight binding - linear muffin tin orbitals - atomic sphere approximation (TB-LMTO-ASA) program package.58 To avoid complications from partially filled shells and site mixing, model compounds were used (for instance, Gd3+ ions are modeled as Y3+ ions, and Eu2+ ions are modeled as Sr2+). Integration over the Brillouin zone was performed by the tetrahedron method.59 The detailed calculation for each structure will be described in each chapter.

CHAPTER THREE

SYNTHESIS AND PROPERTIES OF NEW MULTINARY SILICIDES R5(Mg/Al)5Fe4(Al/Si)18 (R=Gd, Dy, Y) GROWN IN Mg/Al FLUX

3.1 Introduction Metal flux chemistry allows for dissolution of refractory elements, lower reaction temperatures, and crystal growth. The flux synthesis technique has enabled the discovery of new phases Eu2AuGe3 and Li2B12Si2 (from reactions in indium and tin fluxes respectively) and more 60-62 complete characterization of known phases such as Ba8Al16Si30 (grown in Al flux). Using a mixture of two metals as a flux can further this technique by lowering the solvent melting point through eutectic formation and increasing the range of elements soluble in the flux. In recent years we have explored La/Ni eutectics for growth of magnetic phases such as La21Fe8Sn7C12 and La6Fe10Al3Sb, and Ca/Li mixtures for growth of new carbides and hydrides such as 63-65 LiCa2C3H and LiCa7Ge3H3. We have also found that Mg/Al mixtures are particularly good solvents for the formation of silicides, allowing for growth of large crystals of CaMgSi and other phases.51 Reactions of silicon, iron, and R = Gd, Dy, or Y in this 1:1 mixture of Mg/Al flux produce crystals of R5(Mg/Al)5Fe4(Al/Si)18. These phases have a complex structure stemming from the presence of several elements which prefer very different coordination environments. The rare earth elements occupy two distinct crystallographic sites and determine the magnetic properties of the compound. As a new structure type, all three crystallize in the tetragonal space group P4/mmm. One typical characteristic of the structure is trigonal prismatic building blocks with Fe centers surrounded by Al and Si atoms. It is difficult to identify Mg, Al and Si sites based on the X-ray diffraction method since these elements have similar scattering factors. Neutron diffraction has a distinct advantage to X-ray diffraction because of the independence of neutron scattering cross section on atomic numbers. This makes it easier to probe the neighboring elements in the periodic table if they are present simultaneously in a structure.66-75 Some examples are 67 68 BaHg2Tl2, REMGa3Ge and RE3Ni3Ga8Ge3 (M = Ni, Co; RE = rare earth element), 72 74 La1-xCexIn3, Y4Mn1-xGa12-yGey, etc. A limitation is that a large polycrystalline sample or big

15 single crystals are usually required due to the low brilliance of the neutron source. A variety of compounds containing Al and Si have been probed with either powder or single crystal neutron diffraction, and the Al/Si occupancies were better understood.76-81 To further clarify the

Mg/Al/Si occupancies in the R5(Mg/Al)5Fe4(Al/Si)18 structure, we performed neutron diffraction measurement on a single crystal of the Dy analog. The neutron scattering lengths are quite different for Al, Si and Mg, at 3.449 fm, 4.149 fm and 5.375 fm respectively. Therefore, the occupancy for Mg, Al and Si should be better distinguished via neutron diffraction. These phases were studied by single crystal X-ray and neutron diffraction, solid state NMR, and the antiferromagnetic ordering observed in the Dy and Gd analogs were characterized with susceptibility measurements. Electronic structure calculation, electrical resistivity and heat capacity measurements were also performed.

3.2 Experimental Procedure

3.2.1 Synthesis

Mg and Al metal slugs (99.95%) and Fe powder (99+%) were obtained from Alfa Aesar. Si (99+%) and Y(99.9%) powders were obtained from Strem Chemicals. Gd and Dy powders (99.9%) were obtained from Metall. The elements Mg/Al/Si/Fe/(Gd, Dy, or Y) were initially weighed out in a 15/15/2/1/1 mmol ratio and loaded into stainless steel crucibles in a dry box. The steel crucibles were welded shut in an argon-filled glovebox and then sealed into fused silica tubes under vacuum. All reaction ampoules were placed in a muffle furnace and heated from room temperature to 950°C in 10 h, held at 950°C for 5 h, cooled to 750°C in 80 h, and held at 750°C for 24 h, at which point the reaction ampoules were quickly removed from the furnace, flipped and centrifuged to let the excess Mg/Al molten flux decant off the product crystals which adhered to the crucible walls. Several reactions were run to determine the optimal reactant ratios; after these were determined, crystals were grown with the optimal mmol ratio of elements in niobium crucibles to eliminate incorporation of impurities.

3.2.2 Elemental Analysis

SEM-EDS analysis was performed using a JEOL 5900 scanning electron microscope (30 kV acceleration voltage) equipped with PGT Prism energy dispersion spectroscopy software.

Selected crystals were arranged on double-sided carbon tape adhered to an aluminum sample puck. Each crystal was cleaved to expose inner portions to acquire more accurate elemental analysis of the bulk sample and avoid erroneous readings due to residual flux coating on the surface. Several spots on each crystal were analyzed for 60 s at each location; results are shown in Table 3.1. Aluminum and silicon pieces were used as external standards to improve the quantification of these elements.

Table 3.1 Result of SEM-EDS analysis of Al and Si (against external Al and Si standards) in R5(Mg/Al)5Fe4(Al/Si)18 products.

Reaction ratio Atomic percent Al Si

Mg/Al/Si/Fe/Y

15/15/2/1/1 38.0 18.0

15/15/3/1/2 36.5 19.5

15/15/4/1/2 37.0 19.0

15/18/4/1/1 35.6 20.4

15/21/4/1/2 37.0 19.0

Mg/Al/Si/Fe/Gd

15/15/2/1/2 38.9 17.1

15/15/3/1/2 36.8 19.2

15/15/4/1/2 37.1 18.9

15/12/2/1/1 37.0 19.0

15/12/3/1/2 38.2 17.8

Mg/Al/Si/Fe/Dy

15/15/2/0.5/1 38.6 17.4

15/15/3/1/2 37.8 18.2

15/15/4/1/2 36.4 19.6

3.2.3 Powder and Single Crystal X-ray Diffraction

Single crystal diffraction data were collected for each analog at room temperature on a Bruker APEX2 single crystal diffractometer with a Mo Kα radiation source. Selected crystal samples were broken into suitable size and small spheroid fragments were mounted on glass fibers for diffraction. Data was processed using the program SAINT and corrected with the SADABS program.53 Space group assignment was accomplished by XPREP, and refinement of the structure was performed by SHELXTL.54 The structures were solved in tetragonal space group P4/mmm; crystallographic data and collection parameters are shown in Tables 3.2 -3.5. During the refinement, assignment of rare earth and iron sites were straightforward; all lighter element sites (Mg, Al, Si) were initially assigned as aluminum, but assignments were modified based on bond length considerations, elemental analysis, and NMR data (see discussion). In the final refinement cycles all occupancies were allowed to vary, but all appeared fully occupied. Powder X-ray diffraction data were collected for each analog on a Rigaku Ultima III Powder X-ray diffractometer with a Cu K radiation source and a CCD detector. Samples were ground and mixed with a silicon internal standard (Strem Chemicals, 99+%).

3.2.4 Single Crystal Neutron Diffraction

To gain more insight into the occupancies of the Mg, Al, and Si sites, a single crystal of

Dy5Mg2.92Fe4Al9.72Si10.36 (0.34×0.26×1.6 mm) was studied using neutron diffraction at the HB-3A four-circle single crystal diffractometer at the High Flux Isotope Reactor at Oak Ridge National Laboratory. The data were collected at 300 K with a neutron wavelength of 1.5424 Å from a bent perfect Si-220 monochromator,55 and structure refinement was based on ~ 400 reflections and completed in the program FULLPROF.56 To reduce the number of refinable parameters, the atomic positions were fixed to those obtained from the single crystal X-ray diffraction (see Table 3.5), while only the thermal displacement and occupancy parameters were refined. In order to eliminate the effect of large discrepancy between the length and the diameter of the crystal, the absorption correction was conducted based on the single crystal's size parameters. The resulting data from the neutron diffraction study are shown accordingly in Table 3.6 and Table 3.7.

Table 3.2 Crystallographic data and collection parameters for R5(Mg/Al)5Fe4(Al/Si)18 phases.

Gd5(Mg/Al)5Fe4(Al/Si)18 Dy5(Mg/Al)5Fe4(Al/Si)18 YR5(Mg/Al)5Fe4(Al/Si)18

Crystal system Tetragonal

Space group P4/mmm

Cell parameters, a = 11.707(4) a = 11.655(2) a = 11.703(11) Å c = 4.087(1) c = 4.0668(8) c = 4.074(4)

V, Å3 560.2(4) 552.5(2) 558.0(9)

Z 1

Calc. Density 4.813 4.959 3.815 (g/cm3)

2Theta (max) 56.26 56.10 56.25

Radiation Mo K

Temperature (K) 290

Reflections 6313 6204 5362

Unique 450 428 446 reflections

Data/parameters 450 / 35 428 / 35 446 / 35

Mu (mm-1) 18.01 20.16 16.29

R(int) 0.0292 0.0289 0.0336

a R1/wR2 0.0138 / 0.0333 0.0155 / 0.0385 0.0229 / 0.0563 (I>2(I))

R1/wR2 (all data) 0.0148 / 0.0335 0.0158 / 0.0386 0.0244 / 0.0567 Largest diff peak 0.643 / -0.756 1.487 / -0.867 1.176 / -0.715 and hole (e·Å-3)

a 2 2 2 2 2 1/2 R1=(|Fo|- |Fc|) /|Fo|; wR2=[[w(Fo - Fc ) ]/(w|Fo| ) ] .

Table 3.3 Atom positions and isotropic thermal parameters for Y5Mg5Fe4Al12Si6.

Wyckoff a x y z Ueq Site

Y1 4n 0.26606(5) 1/2 0 0.0069(2)

Y2 1a 0 0 0 0.0127(3)

Mg1 4j 0.2027(1) 0.2027(1) 0 0.0076(4)

Mg2 1d 1/2 1/2 1/2 0.0106(8)

Fe1 4l 0.29677(7) 0 0 0.0093(2)

Al1 8q 0.1155(1) 0.3704(1) 1/2 0.0073(3)

Al2 4k 0.33101(9) 0.33101(9) 1/2 0.0017(3)

Si1 4m 0.1805(1) 0 1/2 0.0113(3)

Si2 2f 0 1/2 0 0.0123(5)

a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

Table 3.4 Atom positions and isotropic thermal parameters for Gd5Mg5Fe4Al12Si6

Wyckoff a x y z Ueq Site

Gd1 4n 0.26458(2) 1/2 0 0.0081(1)

Gd2 1a 0 0 0 0.0136(1)

Mg1 4j 0.2026(1) 0.2026(1) 0 0.0096(3)

Mg2 1d 1/2 1/2 1/2 0.0128(8)

Fe1 4l 0.29747(7) 0 0 0.0117(1)

Al1 8q 0.1151(1) 0.3700(1) 1/2 0.0097(3)

Al2 4k 0.33026(9) 0.33026(9) 1/2 0.0041(3)

Si1 4m 0.1807(1) 0 1/2 0.0138(3)

Si2 2f 0 1/2 0 0.0145(4)

a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

Table 3.5 Atom positions and isotropic thermal parameters for Dy5Mg5Fe4Al12Si6, determined by X-ray diffraction data collection.

a Wyckoff Site x y z Ueq Dy1 4n 0.26556(2) 1/2 0 0.0073(1) Dy2 1a 0 0 0 0.0130(2) Mg1 4j 0.2022(1) 0.2022(1) 0 0.0086(4) Mg2 1d 1/2 1/2 1/2 0.0111(9) Fe1 4l 0.29640(9) 0 0 0.0103(2) Al1 8q 0.1157(1) 0.3703(1) 1/2 0.0085(3) Al2 4k 0.3315(1) 0.3315(1) 1/2 0.0030(4) Si1 4m 0.1793(1) 0 1/2 0.0118(4) Si2 2f 0 1/2 0 0.0128(5)

a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

Table 3.6 Single crystal neutron crystallographic data and collection parameters for Dy5Mg2.92Fe4Al9.72Si10.36 phase.

Neutron data

Crystal system Tetragonal

Space group P4/mmm a = 11.655(2) Cell parameters, Å c = 4.0668(8) V, Å3 552.5(2) Z 1 Calc. Density (g/cm3) 4.991 2Theta (max) 80 Radiation 1.5424 Å3 Temperature (K) 290 Reflections 323 Unique reflections 163

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

Table 3.7 Atom positions and isotropic thermal parameters for Dy5Mg2.92Fe4Al9.72Si10.3; occupancy determined from neutron diffraction data.

Wyckoff a x y z Occ. Ueq Site

Dy1 4n 0.26556(2) 1/2 0 1 0.0073(1)

Dy2 1a 0 0 0 1 0.0130(2)

Mg1/Al1 4j 0.2022(1) 0.2022(1) 0 0.47(8)/0.52(6) 0.0086(4)

Mg2 1d 1/2 1/2 1/2 1 0.0111(9)

Fe1 4l 0.29640(9) 0 0 1 0.0103(2)

Al2/Si2 4m 0.1793(1) 0 1/2 0.60(1)/0.40(1) 0.0118(4)

Al3/Si3 2f 0 1/2 0 0.70(5)/0.29(7) 0.0128(5)

Al4/Si4 8q 0.1157(1) 0.3703(1) 1/2 0.57(1)/0.43(1) 0.0085(3)

Al5/Si5 4k 0.3315(1) 0.3315(1) 1/2 0.90(4)/0.09(6) 0.0030(4)

a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

3.2.5 Electronic Structure Calculations

Density of states (DOS) and crystal orbital Hamilton population (COHP) were calculated with tight binding - linear muffin tin orbitals - atomic sphere approximation (TB-LMTO-ASA) 58 program package. The calculation was based on the Y5Mg5Fe4(Al/Si)18 parameters determined by single X-ray diffraction data. Eight empty Wigner-Seitz spheres were added to fill the empty space in the structure. In addition, since all the Al and Si sites were mixed occupied and LMTO program cannot deal with the partially occupied sites, these four sites were treated solely as Al or Si. Calculations were carried out on several models with the sites containing either Al or Si. The following radii of atomic spheres were used: r(Y) = 3.49/3.64 Å, r(Fe) = 2.58 Å, r(Mg) = 3.09 Å, r(Al)/r(Si) = 2.78-2.84 Å, r(empty) = 1.04-1.67 Å. The basis set consists of Y(5s, 4p), Fe (4s, 3d, 4p) Mg(3s, 3p) and Al/Si (3s, 3p), with Y(4d, 5p), Mg(3d) and Al/Si (3d) being downfolded. The calculation was made for 195 κ points in the irreducible Brillouin zone, and integration over the Brillouin zone was performed by the tetrahedron method.59

3.2.6 Magnetic Susceptibility

Magnetic susceptibility measurements were carried out on a Quantum Design SQUID Magnetic Property Measurement System. Crystals grown in Nb crucibles were selected and held between two strips of kapton tape. Temperature-dependent susceptibility data were collected between 1.8K and 300K at 100 G for the dysprosium phase and 100 G to 30000 G for the gadolinium and yttrium analogs. Field-dependent data were collected at 1.8 K using fields up to 7 T; crystals were oriented with c-axis parallel to the applied field.

3.2.7 Solid State NMR Characterization

27Al and 29Si MAS NMR spectra were collected on a Varian/Inova 500WB spectrometer (11.7T) with resonance frequencies of 130.46 and 99.40 MHz respectively. The 27Al and 29Si shifts were referenced to 1M Al(NO3)3 and TMS. Crystals of Y5Mg5Fe4Al12Si6 were ground with NaCl in a 1:1 ratio by volume in a glove box and the powder was packed into a 4 mm zirconia rotor sealed with airtight screw caps. The 29Si MAS spectra were obtained with a spinning speed of 13 kHz and a recycle delay of 60s. For the 27Al MAS experiment, single pulse acquisition was applied with a short RF pulse less than 15o. The spinning speed was 12 kHz and the recycle delay was 0.3s.

3.2.8 Electrical Resistivity

Electrical resistivity measurements were conducted with a conventional four-probe method on a Physical Property Measurement System (PPMS) by Quantum Design. A single crystal (5 mm × 0.6 mm × 0.5 mm) was put on a sample holder puck and four 25 micron diameter gold wires were adhered to the crystal surface with silver paste. Resistivity data were taken from 1.9 - 300 K at 0 T with an applied excitation current of 0.5 mA.

3.2.9 Heat Capacity

The PPMS was also used to measure the heat capacity (Cp) of the Gd5(Mg/Al)5Fe4(Al/Si)18 as a function of temperature from 1.9 to 30 K. QDs calorimeter is based on the principle of thermal relaxation, with heat pulses being applied through eight wires that support a sample platform. The sample is thermally coupled to the platform with Apiezon N-grease, which is

23 initially measured and subsequently subtracted from the total Cp. Specifically, 3.04 mg of clean single crystals with uniform morphology and size were mounted onto the platform. Data was obtained through the application of large heat pulsed (maximum 30% temperature rise) and long measurement times (both two and three tau). Upon analysis of the raw data, a dense number of points could then be acquired through application of the dual-slope analysis technique within QDs MultiVu software.57

3.3 Results and Discussion 3.3.1 Synthesis

The R5(Mg/Al)5Fe4(Al/Si)18 phases were synthesized in excess Mg/Al flux in steel crucibles. The optimal Mg/Al/Si/Fe/R reactant ratio is 15:15:3:1:2 for R = Gd, 15:15:2:0.5:1 for R = Dy, and 15:15:4:1:2 for R = Y (in each case the yield was 90% or higher based on Fe). Products formed as silver needles up to 4 mm in length and 1 mm in diameter are shown in Figure 3.1.

Figure 3.1 SEM image of a crystal of Gd5(Mg/Al)5Fe4(Al/Si)18.

Small amounts of silver/grey powder were also present. Visual inspection and powder diffraction data (see Figure 3.2) do not indicate the presence of significant amounts of byproducts. Some crystals had traces of flux residue on their surfaces. Semi-quantitative elemental analysis by SEM-EDS did not indicate incorporation of contaminant elements from the 24 steel crucible, although traces of contamination cannot be ruled out (magnetic measurements were carried out on products grown in niobium crucibles). The products are stable to air and water but dissolve slowly in 5 M HNO3. This structure forms with R = Gd, Dy, Y; attempts to synthesize analogs with early rare earths (La-Eu) or late rare earths (Er-Lu) led to different phases, as did attempts to replace Si with Ge. It is notable that the combination of this many elements yields only the quinary title compounds instead of known ternaries such as REFe4Al8

(RE = Gd, Dy) and RE2Al3Si2 (RE = Tb-Lu, Y) or quaternary phases such as REFe4Al9Si6 (RE = 76, 82-85 Tb, Er) and Al9FeMg3Si5. The presence of a large amount of magnesium in the flux likely eliminates formation of most of these potential byproducts.

Exp Y phase

Exp Dy phase

Exp Gd phase

Calculated Y phase Calculated Gd phase

Intensity ** * * * * *

10 20 30 40 50 60 70 80 2 theta

3.3.2 Structure

R5(Mg/Al)5Fe4(Al/Si)18 exhibits a complex new structure type in tetragonal space group P4/mmm, shown in Figure 3.3. A major building block is the ribbon running in the c-direction comprised of iron in a monocapped trigonal prismatic coordination of Al and Si atoms, linked by

25 the monocapping silicon atom along the a- or b-direction, and by sharing trigonal faces along the c-axis. The coordination of the iron site can also be viewed as a tricapped trigonal prism if the two neighboring Mg atoms are taken into account (Figure 3.4a). Similar tricapped trigonal prismatic coordination of iron can be seen in the -phase Al9FeMg3Si5 and in RFe2Al8 (R = Ce, Eu), with the latter also featuring chains of prisms sharing trigonal faces running along one 82, 84, 85 crystallographic axis. The bond lengths from the iron site in R5(Mg/Al)5Fe4(Al/Si)18 to the surrounding Al and Si atoms are all within the range of 2.37 to 2.59Å; bonds to the Mg sites are 2.600(1)Å (see Table 3.8). The iron sites are fairly isolated from each other, which may be the reason for their lack of magnetic moment (vide infra); the iron-iron distance along the c-axis is the length of the c-axis parameter (4.0668(8) Å for the Dy analog) and 4.75Å across the bridging silicon atom in the a-b plane.

The structure has two rare earth sites; one is located at the corner of the unit cell (1a Wyckoff site), and the other occupies a lower symmetry site (4n Wyckoff site) toward the center of the unit cell. As shown in Figure 3.4b, the 1a rare earth site is surrounded by 8 silicon atoms 26 in a cubic coordination environment at a distance of 2.916(1)Å (for Dy phase). Four magnesium atoms are located a further distance away (3.333(2)Å). The 1a sites are separated from adjacent 1a sites by the length of the c-axis, producing a chain of rare earth atoms with R3+ - R3+ distances of around 4Å (4.0668(8)Å for the Dy analog). The 4n rare earth sites are also separated from neighboring 4n sites by this same distance along c, but additional symmetry equivalents are found at shorter distances in the ab-plane (3.864Å for the Dy analog; see Figure 3.4c) which may lead to complex magnetic behavior. This rare earth site is coordinated by 9 Al or Si atoms at distances from 2.93 - 3.10Å; magnesium and iron atoms are found further away.

Table 3.8 Bond lengths in Dy5Mg5Fe4Al12Si6.

Bond Bond distance, Ǻ

Dy(1) - Al(1) × 4 3.078(1) Dy(1) - Al(2) × 4 2.9296(7) Dy(1) - Mg(1) 3.548(2) Dy(1) - Mg(2) × 2 3.4060(5) Dy(2) - Si(1) ×8 2.916(1) Dy(2) - Mg(1) ×4 3.333(2) Dy(2) - Fe(1) 3.455(1) Fe(1) - Al(1) ×4 2.587(1) Fe(1) - Si(1) ×2 2.449(1) Fe(1) - Si(2) 2.373(1) Fe(1) - Mg(1) ×2 2.600(1) Mg(1) - Al(1) ×4 2.998(1) Mg(1) - Si(1) ×4 3.125(1) Mg(1) - Al(2) ×2 2.945(2) Mg(2) - Al(2) ×4 2.778(2) Al(1) - Al(1) 2.696(3) Al(1) - Si(1) 2.602(2) Al(1) - Al(2) ×2 2.556(2) Al(1) - Si(2) ×2 2.870(1)

a) b) 2f

4m 8j

The major difficulty in determining the structure of this phase by X-ray diffraction is the similar numbers of electrons in Mg, Al, and Si and their resulting similar X-ray scattering factors. Magnesium sites can be located by consideration of bond lengths; Mg coordination tends to feature distinctly longer bond lengths than Al or Si. With this guideline, comparison to bondlengths reported in literature, and correlation with EDS analysis, the 4j and 1d sites were assigned as magnesium. Distinguishing between aluminum and silicon is less straightforward, as their average bondlength ranges overlap; for instance, Fe-Si bonds in intermetallics generally range between 2.27 to 2.55Å, and Fe-Al bonds between 2.42 and 2.88Å.86 However, bond length analysis has been used for determination of Al and Si siting in phases such as -Al9FeMg3Si5 and -AlFeSi.85,86 The elemental analyses of the title phases consistently indicate a 2:1 mole ratio of aluminum to silicon, supporting a stoichiometry of R5Mg5Fe4Al12Si6. Considering the Dy analog as an example, a short bond (2.373(1)Å) between iron and a light atom on a 2f Wyckoff site 28 indicates that silicon is most likely to occupy this location (Si(2) is the monocapping atom that bridges two iron-centered monocapped trigonal prisms). The distances from the iron atoms to the adjacent 4m site are also short (2.450(1)Å). While this distance is in the overlapping region of the Fe-Si and Fe-Al bondlength ranges, it is notable that this 4m site is 2.916(1)Å from a Dy3+ ion. The smaller, more electronegative silicon is therefore more likely to occupy this site than aluminum, and it is therefore assigned as Si(1). The 8q Wyckoff site is occupied by a light atom exhibiting longer bonds to iron (2.5874(9)Å), Mg (2.999(1)Å) and Dy (3.078(1)Å) and was therefore assigned as aluminum Al(1). Assignment of the remaining light atom site (on a 4k site) is less clear-cut. The bond lengths to neighboring atoms are somewhat short (2.9296(6)Å to Dy3+, 2.778(2)Å to Mg2+, 2.556(2) Å to Al(1)), and this site is predominantly surrounded by highly electropositive species (Dy3+ and Mg2+); both these factors would support assignment of this site as silicon which would lead to an overall stoichiometry of Dy5Mg5Fe4Al8Si10. However, the elemental analysis data indicates that this compound is more aluminum-rich, so this 4k site was assigned as Al(2). It is notable that the thermal parameters of the 8q and 4k sites (both assigned as aluminum) are similar to each other and differ slightly from the thermal parameters of the 4m and 2f sites assigned as silicon (table 3.5). However, these assignments cannot be resolved or verified by X-ray diffraction (all occupancies were allowed to refine but did not vary from unity, and interchanging Al and Si assignments has no effect on the refinement R-values) and the possibility of site mixing can also not be ignored. 27Al and 29Si solid state NMR studies were carried out to clarify the issue of possible Al/Si mixing, and also to gain insight on the electronic properties of these phases.

Y5Mg5Fe4Al12Si6 was used for these experiments to avoid any additional shifts caused by localized f-electrons in Gd or Dy. Nuclear resonances in metallic compounds are affected by the presence of conduction electrons; these produce an additional field on the nucleus and result in a Knight shift, the size of which depends on the contribution of the atom of interest to the density 3+ of states at Ef. Referenced to Al(H2O)6 at 0 ppm, pure aluminum metal exhibits a resonance at 1640 ppm, and aluminum in alloys and intermetallics typically have resonances in the 600 -1700 87-89 ppm range (for instance, 1486 ppm for CuAl2, and 880 ppm for AlB2). The “semiconducting region” for aluminum is around 100 - 500 ppm; aluminum in charge-balanced Zintl phases and

III-V semiconductors have resonances in that range (for instance, the Zintl phase Ba7Al10 has resonances at 490 and 660 ppm; AlAs and AlP at 130 ppm and 142 ppm respectively; and Al4C3

29 at 120 ppm).90-92 The “insulating region” for aluminum in oxides or aqueous solutions is 0 - 100 ppm, with AlO4 tetrahedral units having resonances around 60 ppm and octahedral AlO6 species having resonances near 0 ppm.93 27 The Al MAS NMR spectrum of Y5Mg5Fe4Al12Si6 (Figure 3.5) features a narrow peak at 200 ppm and a broader peak at 1300 ppm (small peaks in the 0 - 100 ppm region are due to surface oxidation). This indicates the presence of at least two aluminum sites, supporting the assignment of 8q and 4k sites as aluminum. The peak at 1300 ppm in the 27Al spectrum of

Y5Mg5Fe4Al12Si6 is likely due to the 8q site. The broadness of this peak was not changed by faster spinning speeds. This may indicate that all the sites contain mixtures of Al and Si, so in some unit cells the 8q site is bonded to 2Al and 1Si, in other unit cells it is bonded to 1Al and 2Si, yielding a distribution of local environments which cannot be narrowed by magic angle spinning. Aluminum atoms mixing on the 4m and 2f sites may also contribute to this broad peak; these sites are bound to iron and other Al/Si sites would likely have similar resonances as the 8q site Al atoms. The 200 ppm resonance is in the semiconducting region and will be due to aluminum atoms with a large degree of ionic character, which corresponds to the 4k site. This site is surrounded by highly electropositive elements (Mg and Y), and atoms in this location should have similar electronic characteristics to those in charge-balanced Zintl phases. 27Al MAS-NMR studies reported for the clathrate Ba8Al16Si30 show a resonance in the metallic region (1600 ppm) and a couple in the semiconducting region (500 ppm).80 This compound is metallic, but it is close to being a charge-balanced semiconductor since its structure can be viewed by Zintl phase analysis 2+ - 0 as (Ba )8(Al )16(Si )30. The germanium analog of this clathrate, Ba8Al16Ge30, is even closer to being a semiconductor and its 27Al resonances are in the 200 ppm region (and they exhibit broad peaks due to disorder in the Al/Ge framework).94 The very low 27Al Knight shift of 200 ppm for the 4k site may indicate that this compound is a poor metal. This is also supported by the 29Si MAS-NMR data shown in Figure 3.5. While the resonances are unfortunately extremely broad and signal-to-noise is low, two broad peaks are seen at -50 ppm and -150 ppm with respect to TMS at 0 ppm. Silicon Knight shifts in metallic compounds are typically found in the 200 to 1000 ppm range (as observed for the silicon sites in 95 metallic clathrates such as Na24Si136). The negative resonances seen for Y5Mg5Fe4Al12Si6 are in the range characteristic of elemental semiconducting silicon (-81 ppm) and of anionic silicon in

95-96 27 semiconductors such as the Zintl phases LiSi (-107 ppm) and Rb4Si4 (-290 ppm). The Al 29 and Si NMR spectra indicate that while Y5Mg5Fe4Al12Si6 is likely a poor metal with a small density of states at Ef (with states contributed by the 8q Al site), the other Al and Si sites in the structure are somewhat anionic, contributing to bands well below Ef and resulting in chemical shifts for these sites that are typical of these elements in semiconducting Zintl phases.

27Al

1600 1200 800 400 0 -400 ppm

29 Si

600 400 200 0 -200 -400 -600 ppm 27 29 Figure 3.5 Al and Si MAS NMR spectra of Y5Mg5Fe4Al12Si6.

The possibility of extensive site mixing was confirmed by a neutron diffraction study on a single crystal of the Dy analog at 300 K. The results indicate that all the four Al/Si sites (2f, 4m, 8q and 4k) were of mixed occupancy; see Table 3.7. The 2f and 4m sites were mainly occupied by Al (70% and 60%) while silicon atoms were predominant on the 8q and 4k sites (60% and 90%). The new assignments are of stark contrast with our X-ray diffraction data (shown in Table 3.5). It is notable that the 2f site along with the iron sites (4l) form an Fe-Al/Si-Fe chain, and the observed bond length of 2.373(1) Å is in the range of Fe-Al (2.346-2.794 Å) and Fe-Si

(2.298-2.809 Å). For the two Mg sites (1d and 4j), the full occupancy at the body center (1d) by magnesium was confirmed by the neutron diffraction, but the 4j site contains partial aluminum content instead (~53%). As a result, the stoichiometry for the Dy analog based on the neutron diffraction data is Dy5Mg2.92Fe4Al9.72Si10.36. It is likely that the site mixing observed for the Dy analog also extends to the Gd and Y analogs since all three phases were synthesized following the same procedure. If we consider the structure from the perspective of synthesis, these phases can only be produced when aluminum and silicon are simultaneously present.

3.3.3 Electronic Structure Calculations

The electronic structure calculations on these phases were performed with TB-LMTO-ASA program. Since mixed occupancies cannot be analyzed in this program, calculations were carried out on four model compounds developed by varying the assignments on the mixed Al/Si sites (4m, 2f, 8q and 4k). If all of these sites are occupied by aluminum, this gives rise to the formula R5Mg5Fe4Al18 with a valence electron count (VEC) of 111 electrons/unit cell. If all of these sites are filled with silicon, the formula R5Mg5Fe4Si18 results, with VEC of 129. However, the neutron diffraction studies indicate that aluminum is predominant on the 4m and 2f sites, while silicon is predominant on the 8q and 4k sites. Modelling the Mg/Al mixed 4j site as fully occupied by magnesium, a stoichiometry of

R5Mg5Fe4Al6Si12 results, which has a valence electron count of 123. The alternative assignments for Al and Si (i.e. Al on 8q and 4k sites and Si on 4m, 2f sites) will lead to a formula of

R5Mg5Fe4Al12Si6, which has a VEC of 117. Figure 3.6 presents the partial and total density of states (DOS) of the four model phases

Y5Mg5Fe4Si18, Y5Mg5Fe4Al6Si12, Y5Mg5Fe4Al12Si6 and Y5Mg5Fe4Al18 as a function of energy

(eV). The electropositive Y ions dominate the states above the Fermi level (EF), with Fe mainly contributing to the states in the range of -3 to 2 eV. The states for both mainly originate from the d electrons as indicated by the partial DOS of Y and Fe atoms in Figure 3.7. Mg, Al and Si derived bands exist in the entire energy range with a low number of states. As a result, the state distribution of all the elements leaves a small pseudo gap near the EF (solid line); this pseudogap is highlighted by the dashed line on each graph. A pseudogap close to EF is characteristic of polar intermetallic compounds. In addition, when the Al/Si ratios change from Y5Mg5Fe4Si18 to

Y5Mg5Fe4Al18, the valence electron counts decreases from 129 to 111. This makes the highest occupied level (i.e. EF) shift towards a lower energy, and hence the pseudo gap is observed to the left of the EF for Y5Mg5Fe4Si18 (Figure 3.6a) while on the right side of the EF for Y5Mg5Fe4Al18 (Figure 3.6d). The presence of Al/Si mixing modifies the VEC so that the Fermi level optimally coinsides with the pseudogap. Considering the VEC of ~123, Dy5Mg2.92Fe4Al9.72Si10.36 is expected to share a similar electronic structure with Dy5Mg5Fe4Al6Si12, which has around 15.8 states at the EF and a pseudo gap at -0.5 eV.

total Y Mg Fe Si (vec=129) Y 30 5 5 4 18 Mg Fe 20 Si

0 -10 -8 -6 -4 -2 0 2 4 6 total 8 10 Y Mg Fe Al Si (VEC=123) 5 5 4 6 12 Y 30 Mg Fe 20 Al Si 10

40-10 -8 -6 -4 -2 0 2 4 6 8 total10 Y Mg Fe Al Si (vec=117) 5 5 4 12 6 Y 30 Mg Fe 20 Al Si

states/cell eV 10

Density of states, 0 -10 -8 -6 -4 -2 0 2 4 6 8 total 10 Y Mg Fe Al (vec=111) Y 30 5 5 4 18 Mg Fe 20 Al

0 -10 -8 -6 -4 -2 0 2 4 6 8 10 Energy, eV

Figure 3.6 Partial and total density of states with variable Al/Si ratios for Y phase.

Y Mg Fe Al Si 5 5 4 6 12 10

Y_total s p 5 d f

0 Density of states, states/cell eV states/cell Density of states, -10 -8 -6 -4 -2 0 2 4 6 8 10 Energy, eV

Y Mg Fe Al Si Fe_total 20 5 5 4 6 12 s p d

0 Density of states, states/cell eV states/cell Density of states, -10 -8 -6 -4 -2 0 2 4 6 8 10 Energy, eV

Figure 3.7 Partial density of states of Y and Fe in Y5Mg5Fe4Al6Si12.

Figure 3.8 displays the total and partial DOS of Gd5Mg5Fe4Al6Si12. The 4f electrons of Gd were treated as core electrons. The states of both analogs show similar variation as

Y5Mg5Fe4Al6Si12 in Figure 3.6, demonstrating ~15.7 states at EF. In reality, Al/Si mixing might 3+ shift EF slightly, and the localized 4f electrons on Gd may interact with conduction electrons near EF, further impacting the electrical properties, as shown in the following section.

Electronic calculations can also shed light on the stability of bonds within the Fe(Al/Si)6 clusters, which contain three types of Fe-Al/Si bonds corresponding to the 2f, 4m and 8q Al/Si sites. In order to compare the impact of Al/Si variable assignments on the bonding energies with Fe (4l site), crystal orbital Hamilton populations (-COHP) were performed and the results are shown in Figure 3.9. The -COHP bands for all the bond types, mainly from the Fe 3d and Al (or

Si) 3p states, exhibit a filled bonding interaction below the EF. The empty anti-bonding area is mainly present at least 10 eV above the EF. The only exception is notably seen for

Y5Mg5Fe4Al6Si12 corresponding to the Fe-Al/Si (8q) bond, which shows a widely dispersed anti-bonding area right below the EF. Its energy integration up to the EF (-ICOHP), as shown in Table 3.9, is apparently higher than other three model phases, reflecting the bond stabilization. Considering the total number of Fe-Al/Si bonds for 2f, 4m and 8q (1:1:2) in the structure, Fe-Al/Si (8q) is playing the most important role with respect to the structural stabilization.

total Gd Mg Fe Al Si Gd 5 5 4 6 12 30 Mg E Al Si 20

10 DOS, states/cells eV DOS, states/cells

0 -10 -8 -6 -4 -2 0 2 4 6 8 10 Energy, eV

Figure 3.8 Total and partial density of states of Gd5Mg5Fe4Al6Si12.

Fe-Al/Si(2f) Fe-Al/Si(4m) Fe-Al/Si (8q) 1 Y Mg Fe Al 1 5 5 4 18 Y Mg Fe Al 1 Y Mg Fe Al EF EF 5 5 4 18 EF 5 5 4 18 0 0 0

-1 -1 -1 1 -10 0 10 20 30 -10 0 10 20 30 -10 0 10 20 30 Y Mg Fe Al Si 5 5 4 6 12 1 Y Mg Fe Al Si Y Mg Fe Al Si 5 5 4 6 12 1 5 5 4 6 12 0 0 0 -1 -1 -1 -COHP, 1 -10 0 10 20 30 -10 0 10 20 30 -10 0 10 20 30 Y Mg Fe Al Si Y Mg Fe Al Si 5 5 4 12 6 1 5 5 4 12 6 1 Y Mg Fe Al Si 5 5 4 12 6 0 0 0

-1 -1 -1 1 -10 0 10 20 30 -10 0 10 20 30 -10 0 10 20 30 Y Mg Fe Si 5 5 4 18 Y Mg Fe Si Y Mg Fe Si 1 5 5 4 18 1 5 5 4 18 0 0 0 -1 -1 -1 -10 0 10 20 30 -10 0 10 20 30 -10 0 10 20 30 Energy, eV Energy, eV Energy, eV Figure 3.9 COHP (eV/bond mol) of Fe-Al/Si bonds for the imaginary Y phases.

Table 3.9 -ICOHP components (eV) in the four imaginary Y5Mg5Fe4(Al/Si)18 phases

Fe-Al/Si (2f) Fe-Al/Si (4m) Fe-Al/Si (8q)

Y5Mg5Fe4Al18 2.12 4.21 5.69

Y5Mg5Fe4Al6Si12 2.05 3.93 6.40

Y5Mg5Fe4Al12Si6 2.42 4.79 5.30

Y5Mg5Fe4Si18 2.24 4.54 5.89

3.3.4 Magnetic Behavior

The magnetic characterization of these phases was hindered by incorporation of ferromagnetic impurities. The possibility of impurities from the steel crucible was eliminated by using only samples synthesized in niobium ampoules for magnetic measurements. However, residual iron powder reactant or traces of ferromagnetic byproducts may also act as contaminants. Susceptibility data for both the Y and Gd analogs showed a broad ferromagnetic transition at around 100 K. However, data taken at higher fields to saturate impurities eliminated this peak.

The resulting high field susceptibility data for Y5Mg5Fe4Al12Si6 (Figure 3.10) is very close to temperature independent, indicating that this compound is Pauli paramagnetic, with χp of approximately 0.01 emu/mol (or 5 x 10-6 emu/g, a value of the magnitude expected for metals).97 Therefore, the iron in this compound does not appear to have a magnetic moment.

2.0

0.20 0.01 T 0.1 T 1.5 0.16 1 T 3 T 0.12

1.0 0.08

0.04

0.5 0.00 , emu/mol Y phase

m 0 50 100 150 200 250 300 X

0.0

0 50 100 150 200 250 300 Temperature, K

Figure 3.10 Temperature dependence of magnetic susceptibility of Y5(Mg/Al)5Fe4(Al/Si)18 at different magnetic fields.

The magnetic susceptibility data for the Gd and Dy analogs indicates that the iron in these phases is also diamagnetic, with all of the magnetic moment and ordering due to the rare earth ions. After correcting for a small amount of ferromagnetic impurity, the high temperature data for the Gd5Mg5Fe4Al12Si6 phase (see Figure 3.11) can be fit to the Curie-Weiss law, resulting in 3+ 97 an effective moment per Gd ion of 8.5 B, similar to the theoretical value of 7.94 B. The Weiss constant θ is -40 K, indicative of antiferromagnetic coupling forces between the Gd ions.

This is in agreement with the observed antiferromagnetic ordering transition observed at TN = 11 K. Field-dependent magnetization data taken at several temperatures (Figure 3.12) shows paramagnetic behavior above 100 K, and metamagnetic behavior below the Neel temperature. A reorientation of the spins occurs at fields above 20000 G, although saturation is not achieved.

0.40 50

0.35 40 0.30

0.25 30 0.20 ZFC at 100 Oe FC at 100 Oe 0.15 ZFC at 1000 Oe FC at 1000 Oe 20 , mol Gd/emu , emu/mol Gd ZFC at 1 T m m 0.10 FC at 1 T X ZFC at 3 T 1/X 0.05 FC at 3 T 10

0.00 0 0 50 100 150 200 250 300 Temperature, K

Figure 3.11 Temperature dependence of magnetic susceptibility of Gd5(Mg/Al)5Fe4(Al/Si)18 at different magnetic fields.

Dy5Mg5Fe4Al12Si6 exhibits a sharp antiferromagnetic transition at 6.9 K (figure 3.13). In the paramagnetic regime above this temperature, the magnetic susceptibility data can be fit to the 3+ Curie-Weiss law, indicating an effective moment per Dy ion of 10.55 B (close to the expected 47 value of 10.63 B) and a Weiss constant of 9.9 K. The positive sign of the Weiss constant is indicative of ferromagnetic coupling at high temperatures. The presence of this coupling at high temperatures and the antiferromagnetic transition at low temperature indicates competing magnetic forces, likely due to the presence of two rare earth sublattices in the unit cell. This is

37 further evidenced by the complexity of the magnetization data below the ordering temperature, which shows several metamagnetic transitions (see Figure 3.14). A small amount of hysteresis is observed at low fields, possibly indicating that the initial ordering is ferrimagnetic or canted; as the applied field increases, spin reorientations occur at 10000 G, 20000 G, and 40000 G, achieving saturated ferromagnetic ordering above 40000 G.

2.0

1.5 1.8 K 115 K 1.0 135 K /Gd

B 0.5

0.0 0.03 -0.5 0.02 1.8 K 0.01 -1.0 0.00 -0.01 Magnetization, u -0.02 -1.5 -0.03 -1000 -500 0 500 1000 -2.0 -60000 -40000 -20000 0 20000 40000 60000 Field, Oe

Figure 3.12 Field dependence of magnetization for Gd5(Mg/Al)5Fe4(Al/Si)18 at different temperatures.

1.8 20 1.6 1.4 16 1.2 1.0 12 0.8 8 0.6 ZFC , mol Dy/emu m , emu/mol Dy

m FC 1/X X 0.4 4 0.2 0 0.0

0 50 100 150 200 250 300 Temperature, K

Figure 3.13 Temperature dependence of magnetic susceptibility of Dy5(Mg/Al)5Fe4(Al/Si)18 at 100 Oe.

10 8.618 u 8 B 6 4

/mol Dy 2 B 0 2

-2 1

-4 0

-6 -1 Magnetization, u

-8 -2 -10000 -5000 0 5000 10000 -10 -80000 -40000 0 40000 80000 Field, Oe

Figure 3.14 Field dependence of magnetization for Dy5(Mg/Al)5Fe4(Al/Si)18 at 1.8 K.

3.3.5 Electrical Resistivity

According to Matthiessen's rule,98-100 the electrical resistivity (ρ) of magnetic materials can be written as three parts: residual resistivity (ρ0), electron-phonon (lattice) scattering resistivity

(ρf), and electron-spin wave scattering resistivity (ρm). Depending on the lattice differences and ordering of magnetic spins, ρf and ρm will contribute to the total resistivity (ρ) differently.

2.75 3.54 Dy 2.70 Y 3.53 2.65 5 3.52 2.60 3.51 Dy 2.55 ), 0 5 10 15 20 25 0 10 20 30 40  2.58 Gd 2.52 4 2.46 m Y 0 10 20 30 

-7 10 3 Gd Electrical resistivity (

2 0 50 100 150 200 250 300 Temperature, K Figure 3.15 Electrical resistivity of R5(Mg/Al)5Fe4(Al/Si)18 (R = Gd, Y, Dy)

Electrical resistivity measurements along the c-direction for the three analogs were performed as a function of temperature between 1.8 - 300 K. The data is shown in Figure 3.15. All three compounds exhibit linear metallic behavior at temperatures above ~ 50 K. At room temperature, the resistivity for Gd, Y and Dy phases are respectively 3.29×10-7, 4.28×10-7 and

5.17×10-7 Ωm, similar in magnitude and entirely in the metallic range.101 The low temperature data are more interesting, as seen in the insets of Figure 3.15. The Y phase approaches its -7 residual resistivity (~2.64×10 Ωm) below 30 K. In comparison, Dy(Mg/Al)5Fe4(Al/Si)18 exhibits a resistivity upturn transition at ~12 K. This is slightly above the Neel temperature of 6.9 K; this resistivity increase may be due to scattering from the development of small magnetically ordered clusters in the compound. More complex behavior is observed for

Gd(Mg/Al)5Fe4(Al/Si)18. When the temperature decreases, the resistivity increases from ~25 K

(above TN of 11 K, but still likely due to nascent magnetically ordered regions) and then undergoes a sudden drop leaving an obvious peak at ~3.7 K. This peak is not correlated to anything in the magnetic susceptibility data; Figure 3.11 does not indicate any ordering or spin reorientation at that temperature.

6 10.8 K -2 K -1

Jg 4

0.06 -3

2 /T, 10 /T, -1 p C K

-1 0 0 5 10 15 20 0.04 T, K

4.3 K

0.02 Specific heat, Jg

0.00 0 5 10 15 20 Temperature, K

Figure 3.16 Heat capacity of Gd5(Mg/Al)5Fe4(Al/Si)18

This low temperature transition in Gd5(Mg/Al)5Fe4(Al/Si)18 is confirmed by heat capacity measurements, which show two kinks in the temperature dependence as shown in Figure 3.16.

The sharp peak at 10.8 K corresponds with the antiferromagnetic ordering, while the small kink at ~ 4.3 K corresponds to that seen in the resistivity data. The Cp/T ~ T fitting (inset in Figure 6) highlights the two peaks at 4.3 K and 10.8 K respectively. While the phase transition at 10.8 K is an antiferromagnetic ordering, the nature of the lower temperature transition is not clear, and more studies are needed.

3.4 Conclusion Reactions of Si, Fe, and R=Gd, Dy, and Y in mixed Mg/Al flux have yielded quinary phases R5Mg5Fe4Al12Si6 with a new structure type. Single crystal neutron diffraction study on

Dy5(Mg/Al)5Fe4(Al/Si)18 indicates that five sites in the structure are mixed-occupied sites: one by Mg and Al (4j), and four by Al and Si (4m, 2f, 8q and 4k), giving rising to a stoichiometric formula of Dy5Mg2.92Fe4Al9.72Si10.36. The R5Mg5Fe4Al12Si6 phases are polar intermetallics; there is significant charge transfer from the strongly electropositive elements (rare earths and magnesium) to the more electronegative Fe, Al, and Si atoms. Further electronic structure calculations based on several ordered model phases of Y5(Mg/Al)5Fe4(Al/Si)18 reveal that a pseudo gap tends to form around the Fermi level in order for the stabilization of the polar intermetallic structure, and the Al/Si mixing may act to position EF at the pseudogap. The compounds are quite metallic, as evidenced by the temperature-variable electrical resistivity of the three phases. Finally, low temperature resistivity data for Dy and Gd phases exhibit anomalies that do not correlate to their antiferromagnetic orderings completely, indicating that while the magnetic ordering does impact the resistivity, additional phenomena may be occurring in the Gd phase. More electrical studies will be needed. The strongly reducing Mg/Al flux appears to be a rich source of phases that are close to the metal/semiconducting Zintl phase border.

CHAPTER FOUR

COMPETING PHASES, COMPLEX STRUCTURE, AND COMPLEMENTARY DIFFRACTION STUDIES OF R3FeAl4-xMgxTt2 INTERMETALLICS (R = Y, Dy, Er, Yb; Tt = Si or Ge; x < 0.5)

4.1 Introduction Exploratory synthesis in molten metal solvents has resulted in the discovery of a large number of new intermetallic silicides and germanides, a class of materials of interest for their wide ranging applications.102-105 Low melting metals most commonly used as reaction media include Al, Ga, In, Sn, and Pb.43 Aluminum flux has been proven to be a particularly productive growth medium; complex silicide phases synthesized in molten aluminum include 106 107 80 Gd1.33Pt3Al7Si, R(AuAl2)nAl2(AuxSi1-x)2 (R = La - Gd, Yb), Ba8Al14Si31, 78 76 R8Ru12Al49Si9(AlxSi12-x) (R = Pr, Sm; x ≈ 4), and RFe4Al9Si6 (R = Tb, Er) . The crystals can be isolated readily by soaking the product in a strong basic solution to etch away the flux after the reaction. Heavier group III elements gallium and indium are also good flux synthesis media.

Gallium often incorporates into products to yield gallides such as RE4FeGa12-xGex (RE = Y, Ce,

Sm, Gd or Tb), RE3Ga9Ge (RE = Y, Ce or Gd), RE3Ni3Ga8Ge3 (RE = Sm, Gd) and 108-111 Yb3Ga4Ge6. In comparison to the usually reactive fluxes Al and Ga, molten indium is often an inert solvent; for instance, germanides -RENiGe2 (RE = Dy, Er, Yb or Lu) and -CaGe2 can be isolated from excess indium flux.112,113 Flux reactivity is of particular interest if mixed metal fluxes are used; out group has recently explored syntheses in mixtures such as RE/Ni, RE/Co (RE= La, Ce, Nd, etc), Mg/Al, and Ca/Li. Some metal combinations form low-melting eutectics at specific elemental ratios. For instance, a 24/76 mole ratio of Ce and Co melts at 424°C; a 12/88 ratio of Al and Si melts at 577°C; and a 81/19 ratio of Au and Si, while too expensive to be used as a flux, exhibits a low eutectic melting point of 363°C.17 Eutectic formation allows for lowered reaction temperatures, which favor the formation of kinetically stabilized phases. However, flux mixtures introduce the additional complication of one or both flux metals potentially being incorporated into the final products. The Mg-Al phase diagram reveals a broad low temperature range (~ 470 ° C ) with 40 - 60% Mg content.114 The reaction of Ca and Si in a 1:1 mole ratio Mg/Al flux yields CaMgSi; in this case, 42

64 Mg is a reactive flux component and Al is inert. In chapter 3, the growth of R5Mg5Fe4Al12Si6 (R = Y, Gd, Dy) in the same flux was reported; both magnesium and aluminum were incorporated into the product.115 The present chapter demonstrates the usefulness of complementary diffraction techniques in the analysis of the complex structure of new quinary phases grown in Mg/Al flux. Both flux elements are incorporated when reacted with iron, late rare earths, and either silicon or germanium. The product silicides (R3-δFeAl4-xMgxSi2 with R = Yb or Dy) and germanides

(R3-δFeAl4-xMgxGe2 with R = Er or Y) crystallize in a new tetragonal structure type. Accurate determination of the Mg, Al, and Si site occupancies required a combination of single crystal neutron and X-ray diffraction studies, which also enabled the observation of Mg/Al mixed occupancy on one site. Observing and understanding the mixing behavior of these elements is of great interest for optimizing the properties of lightweight alloys and adventitious precipitates that form therein, such as the “pi phase” Al9FeMg3Si5, a compound with a structure which has proven difficult to characterize.116 Electronic structure calculations on model compounds

Y3FeAl3.5Mg0.5Ge2 and Y3FeAl4Ge2 indicate that the change in valence electron count resulting from Mg incorporation may induce vacancies on one or both rare earth sites. The title phases form in the midst of a rich phase space, with the large excess of flux allowing the syntheses to forgo formation of many known binary and ternary phases. Indeed, the major competing phase is another quinary phase featuring similar iron-centered building blocks, the previously reported 115 R5Mg5Fe4Al12Si6 (R = Y, Gd, Dy). The formation of R3-δFeAl4-xMgxSi2 instead of

R5Mg5Fe4Al12Si6 can be promoted by adjusting the R:Tt ratio in the synthesis; the title phases also incorporate a much smaller amount of Mg into their structure.

4.2 Experimental Methods

4.2.1 Synthesis

Reactants were used as received: Mg and Al metal slugs (99.95%), Fe (99+%) and Ge (99.999%) powders from Alfa Aesar; Si (99+%), Yb, Er and Y (99.9%) powders from Strem Chemicals; Yb slugs and Dy powder (99.9%) from Metall. The elements were initially weighed out in Mg/Al/Tt/Fe/R ratios of 15/15/2/1/1 mmol and loaded into stainless steel crucibles in an Ar-filled glove box. The steel crucibles were welded shut under argon and then sealed into fused

43 silica tubes under vacuum (30 mTorr). All reaction ampoules were placed in a muffle furnace and heated from room temperature to 950 °C in 10 h, held at 950 °C for 5 h, cooled to 750 °C in 80 h, and then held at 750 °C. While at this temperature, the reaction ampoules were quickly removed from the furnace, flipped and centrifuged to decant excess Mg/Al molten flux off the product crystals which adhere to the crucible walls. Reactions with varying reactant ratios were attempted to optimize yield and crystal size. After the optimal ratios were determined, reactions were carried out using the same preparation method in niobium crucibles, to avoid possible contamination from the elements found in steel crucibles.

Two additional phases were prepared in this work, using aluminum flux. Yb5Fe4Al17Si6 was produced from reactions carried out to explore the effect of eliminating Mg from the flux.

Crystals of Yb5Fe4Al17Si6 were obtained from reacting Al/Si/Fe/Yb (30/2/1/1 mmol) in steel crucibles with the same heating and centrifuge procedure described for the title phases. The known ternary phase YbAl2Si2 was then synthesized to be used as a standard to determine accurate Al/Si ratios in SEM-EDS measurements (vide infra).117 To grow crystals of this phase, Al, Si and Yb were loaded into an alumina crucible with a mmol ratio of 20/2/1. The alumina crucible was then sealed in a fused silica tube and the reaction was carried out using a different heating profile: the ampoule was heated to 950 °C in 10 h, held at 950 °C for 5 h, then cooled to room temperature in 80 h. Once the reaction was finished, the alumina crucible was soaked overnight in a 5 M NaOH solution to remove the flux from the product YbAl2Si2 crystals.

4.2.2 Elemental Analysis

SEM-EDS analysis was performed using a JEOL 5900 scanning electron microscope (30 kV acceleration voltage) equipped with PGT Prism energy dispersion spectroscopy software. Selected crystals were arranged on double-sided carbon tape adhered to an aluminum sample puck. Each crystal was cleaved to expose inner portions to acquire more accurate elemental analysis of the bulk sample and avoid erroneous readings due to residual flux coating on the surface. Several spots on each crystal were analyzed for 60 s at each location. Magnesium analysis was hindered by the very small amount of this element present in the R3-δFeAl4-xMgxTt2 phases (x < 0.5) and some overlap of the Mg Kα peak was observed for the Y3-δFeAl4-xMgxGe2 analog, but not for the others. The flux-grown

YbAl2Si2 crystals were used as an external reference to enable more accuracy in analysis of Si

44 and Al contents of the silicide phases. For instance, the EDS data for YbAl2Si2 exhibit an Al/Si atomic ratio of 44.2%/26.0% versus 42.9%/13.1% for Yb3-δFeAl4-xMgxSi2. This indicates that the

Al:Si ratio in Yb3-δFeAl4-xMgxSi2 should be 2:1 considering the similar backscatter coefficients of aluminum and silicon in EDS measurement.52

4.2.3 X-ray Diffraction

For all phases studied in this work, powder X-ray diffraction data were collected on a PANalytical X’Pert PRO with a Cu Kα radiation source, and single crystal diffraction data were radiation source. Selected crystal samples were broken into suitable size and small spheroid fragments were mounted on glass fibers for diffraction. Data were processed using the SAINT and SADABS programs. 53 Space group assignment was accomplished by XPREP, and refinement of the structure was performed using SHELXTL.54 The structures of the four

R3-δFeAl4-xMgxTt2 title phases were solved in tetragonal space group P4/mbm; Yb5Fe4Al17Si6 was solved in tetragonal space group P4/mmm. Crystallographic data and collection parameters for all five phases are shown in Table 4.1; Table 4.2 and 4.3 show atom positions and isotropic thermal parameters for Yb2.77FeAl3.72Mg0.28Si2 and Yb5Fe4Al17Si6 respectively. Further data for the other three R3-δFeAl4-xMgxTt2 analogs can be found inTables 4.4 to 4.7. During the refinement of the silicide structures, assignments of rare earth and iron sites were straightforward; all lighter element sites were initially assigned as aluminum. Allowing the occupancies of these sites to vary was not informative (because of very similar X-ray scattering factors, the sites appeared fully occupied whether assigned as Mg, Al, or Si). Assignments were modified based on bond length considerations and elemental analysis. In the final refinement cycles, occupancies of all sites were allowed to vary. All appeared fully occupied (100 +/- 1%), with the exception of one or both of the rare earth sites in the R3-δFeAl4-xMgxTt2 compounds. The occupancies of both the 8j and 4h sites in Yb3-δFeAl4-xMgxSi2 were significantly lower than 100% (89% and 97% respectively); for the other analogs, the 4h sites were fully occupied but the 8j site consistently dropped to 97-99%. Although the variation from 100% was small and occupancy values can be affected by other factors such as absorption effects, allowing the occupancy to refine consistently yielded more appropriate thermal parameters for the 8j rare earth site.

Table 4.1 Crystallographic data and collection parameters for Yb2.77FeAl3.72Mg0.28Si2, Dy3-δFeAl4-xMgxSi2, Y3-δFeAl4-xMgxGe2, Er3-δFeAl4-xMgxGe2 and Yb5Fe4Al17Si6 phases.

Yb2.77FeAl3.7 Yb2.77FeAl3. Dy3-δFeAl4-x Y3-δFeAl4-xM Er3-δFeAl4-xM 2Mg0.28Si2, 72Mg0.28Si2, Yb5Fe4Al17Si6 MgxSi2 gxGe2 gxGe2 XRD data neutron data Crystal Tetragonal system Space P4/mbm P4/mbm P4/mbm P4/mbm P4/mbm P4/mmm group Cell edges a = 13.3479(9)b a = 13.527(4) a = 13.680(1) a = 13.562(4) a = 11.433(8) (Å) c = 4.0996(3)b c = 4.142(1) c = 4.1507(3) c = 4.120(1) c = 4.040(3) V, Å3 730.41(9) 730.41(9) 758.0(4) 776.8(1) 757.8(4) 528.2(7) Z 4 4 4 4 4 1 3) 6.35 6.92 6.19 4.91 7.09 5.40 2 Theta 56.55° 80° 56.03° 56.40° 56.52° 56.52° (max) Radiation 1.5424 Å Temperatur 290 e (K) Reflections 7778 404 8116 8382 8148 5908 Unique 533 138 550 566 557 424 reflections Data/param 533 / 39 550/40 566 / 38 557 / 38 424 / 35 eters Mu (mm-1) 37.78 31.77 31.94 42.88 25.60 R(int) 0.0384 0.0313 0.0366 0.0572 0.0346 0.0385 a R1/wR2 0.0172 / 0.0131 / 0.0187 / 0.0152 / 0.0170 / 0.0475 (I>2(I)) 0.0385 0.0220 0.0393 0.0292 0.0378

R1/wR2 (all 0.0182 / 0.0155 / 0.0231 / 0.0156 / 0.0190 / 0.08160 data) 0.0388 0.223 0.0405 0.0293 0.0383 Largest diff peak and 1.36 / -0.90 0.98 / -0.72 0.61 / -0.72 1.22 / -0.99 0.83 / -0.90 hole (e·Å-3) a 2 2 2 2 2 1/2 R1=(|Fo|-|Fc|)/|Fo|; wR2=[[w(Fo - Fc ) ]/(w|Fo| ) ] . b Unit cell parameters for Yb2.77FeAl3.72Mg0.28Si2 determined by X-ray diffraction data.

Table 4.2 Atom positions and isotropic thermal parameters for Yb2.77FeAl3.72Mg0.28Si2.

Wyckoff a a x y z Occ Uiso Site

Yb1 8j 0.17837(2) 0.05979(2) 0.5 0.92(2) 0.0167(18)

Yb2 4h 0.66751(2) 0.16751(2) 0.5 0.93(6) 0.020(3)

Fe1 4h 0.12263(7) 0.62263(7) 0.5 1 0.022(3)

Si1 8i 0.0971(1) 0.1872(1) 0 1 0.024(3)

Al1/Mg1 2a 0 0 0 0.44(9)/0.56(9) 0.024(3)

Al2 8i 0.3493(1) 0.0064(1) 0 1 0.024(3)

Al3 4g 0.2038(1) 0.7038(1) 0 1 0.024(3)

Al4 2c 0 0.5 0.5 1 0.024(3) a The occupancy and isotropic thermal parameters were determined from the refinement of single crystal neutron diffraction data. Atom positions were determined from the refinement of single crystal X-ray diffraction data.

Table 4.3 Atom positions and isotropic thermal parameters for Yb5Fe4Al17Si6.

a Wyckoff Site x y Z Ueq

Yb1 4n 0.26972(3) 1/2 0 0.0087(1)

Yb2 1a 0 0 0 0.0123(1)

Fe1 4l 0.2904(1) 0 0 0.0081(2)

Al1 4j 0.2027(1) 0.2027(1) 0 0.0121(4)

Al2 1d 1/2 1/2 1/2 0.013(1)

Al3 8q 0.1169(1) 0.3701(1) 1/2 0.0093(3)

Al4 4k 0.3321(1) 0.3321(1) 1/2 0.0041(4)

Si1 4m 0.1755(2) 0 1/2 0.0114(4)

Si2 2f 0 1/2 0 0.0132(6) a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

Table 4.4 Atom positions and isotropic thermal parameters for Dy3-δFeAl4-xMgxSi2 phase.

a Wyckoff Site x y z Ueq

Dy1b 8j 0.18010(2) 0.06193(2) 0.5 0.00706(8)

Dy2 4h 0.66397(2) 0.16397(2) 0.5 0.0073(1)

Fe1 4h 0.12102(5) 0.62102(2) 0.5 0.0068(2)

Si1 8i 0.0975(1) 0.19056(9) 0 0.0077(2)

Al1/Mg1 2a 0 0 0 0.014(1)

Al2 8i 0.3505(1) 0.0083(1) 0 0.0082(3)

Al3 4g 0.2036(1) 0.7036(1) 0 0.0084(4)

Al4 2c 0 0.5 0.5 0.0092(6) a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor. b Dy1 occupancy = 0.989(2)

Table 4.5 Atom positions and isotropic thermal parameters for Er3-δFeAl4-xMgxGe2 phase. a Wyckoff Site x y z Ueq

Er1b 8j 0.18230(2) 0.06233(2) 0.5 0.0059(1)

Er2 4h 0.66393(2) 0.16393(2) 0.5 0.0068(1)

Fe1 4h 0.12112(5) 0.62112(5) 0.5 0.0051(2)

Ge1 8i 0.09721(4) 0.18935(4) 0 0.0064(1)

Al1/Mg1 2a 0 0 0 0.0118(7)

Al2 8i 0.3518(1) 0.0079(1) 0 0.0074(3)

Al3 4g 0.2016(1) 0.7016(1) 0 0.0067(4)

Al4 2c 0 0.5 0.5 0.0073(5) a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor. b Er1 occupancy = 0.982(1)

Table 4.6 Atom positions and isotropic thermal parameters for Y3-δFeAl4-xMgxGe2 phase.

a Wyckoff Site x y z Ueq

Y1b 8j 0.18205(3) 0.06245(3) 0.5 0.0072(1)

Y2 4h 0.66340(3) 0.16340(3) 0.5 0.0080(1)

Fe1 4h 0.12055(4) 0.62055(4) 0.5 0.0065(2)

Ge1 8i 0.09718(3) 0.19006(3) 0 0.0076(1)

Al1/Mg1 2a 0 0 0 0.0142(6)

Al2 8i 0.35192(9) 0.00854(9) 0 0.0089(3)

Al3 4g 0.20116(9) 0.70116(9) 0 0.0077(3)

Al4 2c 0 0.5 0.5 0.0087(5) a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor. b Y1 occupancy = 0.989(1)

4.2.4 Neutron Diffraction

To gain more insight into the occupancies of the Mg, Al, and Si sites, a large single crystal

(1 × 1 × 4 mm) of Yb3-δFeAl4-xMgxSi2 was studied by neutron diffraction at the HB-3A four-circle single crystal diffractometer at the High Flux Isotope Reactor at Oak Ridge National Laboratory. The data were collected at 300 K with neutron wavelength 1.5424 Å from a bent perfect Si-220 monochromator.55 The structure refinement was based on ~ 400 reflections and completed using the program FULLPROF.56 To limit the number of refinable parameters, the atomic positions were fixed to those obtained from the single crystal X-ray diffraction study of this phase and only the thermal displacement and occupancy parameters were refined. Thermal parameters of light elements (Al, Si and Mg) were constrained to be equivalent. The neutron diffraction data collection conditions and refined structural parameters are shown in Table 4.1 and Table 4.2.

Table 4.7 Bond lengths in R3-δFeAl4-xMgxTt2 phases.

Bond Dy3-δFeAl4-xMgxSi2 Er3-δFeAl4-xMgxGe2 Y3-δFeAl4-xMgxGe2

R(1) - Fe(1) 2.806(1) 2.783(1) 2.8146(7)

R(1) - Tt(1) ×4 2.925(1)/2.995(2) 2.989(1)/2.922(1) 3.0148(5)/2.9503(5)

R(1) - Al(1) ×2 3.3057(7) 3.3276(8) 3.3528(4)

R(1) - Al(2) ×2 3.182(2) 3.175(3) 3.201(1)

R(1) - Al(3) ×4 3.2304(8) 3.2076(9) 3.2341(4)

R(1) - R(1) 3.643(1) 3.696(1) 3.7239(7)

R(2) - Tt(1) ×4 2.995(1) 3.004(1) 3.0240(4)

R(2) - Al(2) ×4 3.123(2) 3.116(2) 3.144(1)

R(2) - Al(3) ×2 3.272(3) 3.298(4) 3.343(2)

R(2) - Al(4) ×2 3.136(1) 3.143(1) 3.1606(7)

R(2) - R(1) 3.713(1) 3.710(1) 3.7433(6)

Fe(1) - Al(2) ×4 2.600(2) 2.595(2) 2.6064(9)

Fe(1) - Al (3) ×2 2.606(2) 2.578(3) 2.596(2)

Fe(1) - Al(4) ×2 2.314(1) 2.321(2) 2.332(1)

Al(1) - Tt(1) ×4 2.896(2) 2.886(2) 2.9207(6)

Al(2) - Tt(1) 2.594(3) 2.625(3) 2.645(1)

Al(2) - Al(2) ×2 3.020(2)/2.704(4) 2.989(6)/2.691(6) 3.033(3)/2.698(3)

Al(2) - Al(3) 2.742(4) 2.729(5) 2.732(2)

Al(2) - Al(4) ×8 2.898(1) 2.879(2) 2.903(1)

Al(3) - Tt(1) ×2 2.694(3) 2.731(3) 2.762(2)

4.2.5 X-ray Photoelectron Spectroscopy (XPS)

X-ray photoelectron spectra for Yb2.77FeAl3.72Mg0.28Si2 were obtained on a Physical Electronics PHI 5100 series XPS with a non-monochromated dual anode (Mg and Al) source

50 equipped with a single channel hemispherical energy analyzer. The Al Kα X-ray source (15 kV and 30 mA) was used. Single crystals were placed on carbon tape adhered to a XPS stage puck. To avoid the effect of impurities on the surface, the XPS spectra were collected after sputtering with Ar ions (5 kV) for 30 minutes.

4.2.6 Electronic Structure Calculations

Density of states (DOS) and crystal orbital Hamilton population (COHP) calculations were carried out with the tight binding-linear muffin tin orbitals-atomic sphere approximation (TB-LMTO-ASA) program package.58 To avoid complications from partially filled shells and site mixing, model compounds were used. Yb3-δFeAl4-xMgxSi2 was modeled as Y3FeAl4Si2

(atomic positions determined by single crystal X-ray diffraction of Yb3-δFeAl4-xMgxSi2 were used, 3+ 3+ with x = 0 and Yb replaced with Y at 100% occupancy). Er3-δFeAl4-xMgxGe2 was modeled 3+ 3+ either as Y3FeAl4Ge2 (atomic positions for Er3-δFeAl4-xMgxGe2 used, with Er replaced with Y , and x = 0) or Y3FeAl3.5Mg0.5Ge2 (with x = 0.5, corresponding to 100% Mg occupancy on the 2a site). No empty Wigner-Seitz spheres were needed to fill the empty space in the structure. The following radii of atomic spheres were used: r(Y) = 3.54/3.70 Å, r(Fe) = 2.55 Å, r(Mg) = 3.48 Å, r(Al) = 2.55/2.87/3.11 Å, r(Si) = 2.82 Å, r(Ge) = 2.92 Å. The basis set contains Y(5s, 4p), Fe(4s, 3d, 4p), Mg(3s, 3p), Al(3s, 3p), Si(3s, 3p), and Ge(4s, 4p), with Y(4d, 5p), Mg(3d), Al(3d), Si(3d), and Ge(4d) being downfolded. The calculation was made for 195 k points in the irreducible Brillouin zone. Integration over the Brillouin zone was performed by the tetrahedron method.59

4.2.7 Magnetic Properties

Magnetic measurements were carried out on a Quantum Design SQUID Magnetic Property Measurement System. Large single crystals were selected and held between two strips of kapton tape, oriented with c-axis parallel to the applied field. Magnetic susceptibility temperature dependence data were collected between 1.8 K and 300 K at 100 G. Field-dependent magnetization data were collected at 1.8 K in fields up to 7 T. Field dependence studies of AC magnetization for Er3-δFeAl4-xMgxGe2 and Dy3-δFeAl4-xMgxSi2 were performed with 1 Hz frequency and 3×10-4 amplitude of the AC field under a DC bias field up to 3 T.

4.3 Results and Discussion

4.3.1 Synthesis

R3-δFeAl4-xMgxTt2 compounds were grown from reactions of iron with either silicon or germanium and R = Y, Dy, Er, or Yb in Mg/Al flux in stainless steel crucibles. The phases form as air-stable silver rectangular crystals up to 5 mm in length; Figure 4.1a shows the SEM image of a Yb2.77FeAl3.72Mg0.28Si2 crystal. Visual inspection indicates that very little flux residue is left on the crystal surface after centrifugation. The yield of this phase is optimized with a reactant ratio of Mg/Al/Si/Fe/Yb = 15/12/3/1/2 (yield ~ 40%). Varying the ratio lowers the yield and leads to formation of competing byproducts such as YbAl2, Fe5Si3 and Mg2Si. Attempts to carry out the reaction in Nb crucibles produced a Yb/Fe/Al/Si quaternary phase instead (P-31c, a = 8.50(1) Å, c = 18.41(2) Å), the detailed structure of which is not yet solved. Its SEM image (Figure 4.1b) indicates that the crystals form in a twisted rod shape and are likely twinned.

Failure to reproduce the synthesis of Yb3-δFeAl4-xMgxSi2 in Nb crucibles may indicate that incorporation of trace impurities from the steel is needed to form this compound (although the Dy analog can be grown in Nb crucibles). Nevertheless, single phase products were obtained in steel crucibles, as indicated by the powder X-ray diffraction data in Figure 4.2. No incorporation of impurities from the steel was observed in the EDS analysis, although due to the low sensitivity of this technique, trace contamination cannot be ruled out. a) b)

Figure 4.1 SEM images of a) a representative Yb2.77FeAl3.72Mg0.28Si2 crystal and b) a typical crystal produced from reaction (Mg/Al/Si/Fe/Yb = 15/12/3/1/2) in Nb crucibles.

impurity

Experimental Y phase

Experimental Er phase

Experimental Dy phase

Intensity Experimental Yb phase

Calculated Yb phase

10 20 30 40 50 60 70 80

2,degree

Attempts to synthesize R3-δFeAl4-xMgxSi2 analogs with other rare earth metals confirm that the structure is only stable for smaller rare earth ions. Reactions with early rare earths (R = 118 La-Sm) produce RFe2Al8-xMgx (x≤1), quaternary variants of the RFe2Al8 structure; studies of their properties are in progress. Syntheses with R = Gd and Y produce the previously reported

R5Mg5Fe4Al12Si6 compounds in chapter three. It is notable that RFe2Al8-xMgx, R5Mg5Fe4Al12Si6, and the title phases R3-δFeAl4-xMgxSi2 all contain an identical structural building block: a chain of face-sharing FeAl6 trigonal prisms, highlighted in Figure 4.3. Reactions with dysprosium involve a competition between two possible products: Dy3-δFeAl4-xMgxSi2 and

Dy5Mg5Fe4Al12Si6. Having a Si:Dy ratio above 1 makes dysprosium the limiting reactant and

53 favors Dy5Mg5Fe4Al12Si6; if this ratio is 1 or lower, Dy3FeAl4-xMgxSi2 is produced. This presents an example of control over the synthesis of compositionally and structurally related phases by careful adjusting of the reactant ratio. The Dy3-δFeAl4-xMgxSi2 analog can be grown in steel or niobium crucibles, with the yield optimized at a reactant ratio of Mg/Al/Si/Fe/Dy = 15/15/2/1/2 (~40% yield).

Germanium analogs of the R3-δFeAl4-xMgxSi2 phases were sought to aid in structural analysis; Al and Si have very similar X-ray scattering factors, but Al and Ge can easily be distinguished in a structural refinement. Attempts to synthesize Yb3-δFeAl4-xMgxGe2 from the reaction of Yb/Fe/Ge in Mg/Al flux yielded the known ternary phase YbMgGe instead.119 The analogous Dy/Fe/Ge reaction in Mg/Al flux produces DyFe4Al8-xMgx, a substituted variant of 120 DyFe4Al8. On the other hand, substitution of Yb by Y or Er (reactions of Y/Fe/Ge or Er/Fe/Ge in Mg/Al flux) generated Y3-δFeAl3.5Mg0.5Ge2 and Er3-δFeAl4-xMgxGe2; the optimal reactant ratio for both is Mg/Al/Ge/Fe/R = 15/15/1/1/2 (producing ~ 70% and 45% yields respectively). The powder patterns of the products indicated the presence of trace amounts of ErFe4Al8, YFe6Ge6 and YAlGe3 byproducts. These rare earths do not form the silicide R3-δFeAl4-xMgxSi2; reactions 121 of Er/Fe/Si in Mg/Al flux lead to Er2Fe3Al9-xSix, a quaternary analogue of Nd2Co3Al9. The extent of magnesium incorporation in the title phases was difficult to determine. EDS analysis typically indicated little to no Mg in the samples, and the slight overlap between the Al Kα and Mg Kα peaks (as well as the possibility of residual flux on the samples) puts the accuracy of the analysis into question. Neutron diffraction data does support the presence of Mg on one site in the Yb analog (see structure description). However, the question remains whether magnesium is actually needed for the synthesis of this phase. To test this, a reaction of silicon, iron and ytterbium in aluminum flux was prepared. Aluminum has a melting point of 660 °C, and crystalline products were isolated from the flux by centrifugation at 750 °C though the yield was quite poor. Single crystal diffraction analysis reveals that the reaction leads to a different phase, Yb5Fe4Al17Si6, isostructural to R5Mg5Fe4Al12Si6 (R = Dy, Gd, Y). Hence, the presence of magnesium is necessary to promote the formation of the R3-δFeAl4-xMgxSi2 phases; it is incorporated in small amounts (x = 0.5 or less) on a particular site to stabilize the structure. Attempts to synthesize the title phases from stoichiometric mixtures of the elements led to binary and ternary aluminide phases instead, likely due to loss of the volatile magnesium during the reaction.

4.3.2 Structure

The R3-δFeAl4-xMgxTt2 title phases crystallize with a new structure type in tetragonal space group P4/mbm, shown in Figure 4.3a. The unit cell sizes scale as expected with the sizes of the 3+ R cations and the incorporation of silicon versus germanium; Yb2.77FeAl3.72Mg0.28Si2 has the smallest unit cell and Y3-δFeAl4-xMgxGe2 the largest (see table 1). Yb5Fe4Al17Si6 has the same structure as R5Mg5Fe4Al12Si6 (R = Gd, Dy, Y), which forms in space group P4/mmm and is shown in Figure 4.3b. Magnesium is not incorporated in Yb5Fe4Al17Si6; all the Mg sites in the structure (4j and 1d Wyckoff sites) are instead occupied by Al atoms.

A common building block in the R3-δFeAl4-xMgxTt2, R5Mg5Fe4Al12Si6, and RFe2Al8-xMgx structures is the chain of iron-centered aluminum trigonal prisms (shown as red polyhedra in Figures 4.3 and 4.4), linked by sharing trigonal faces along the c-axis. Accordingly, the c-axis unit cell parameter for all three structure types is around 4 Å, defined by the length of the FeAl6 prism. The trigonal prisms are also connected to form dimers or chains within the ab plane by monocapping Al or Si atoms. In Yb5Fe4Al17Si6 this linkage forms dimers along the a- or b-axes; in R3-δFeAl4-xMgxTt2, the dimers are at an angle to these axes. While the iron atoms in

Yb5Fe4Al17Si6 are coordinated by a mixture of Al and Si atoms, the iron site in the

R3-δFeAl4-xMgxTt2 structure is surrounded only by Al (8i, 4g, and 2c Wyckoff sites, see Figure

4.4a). In Yb2.77FeAl3.72Mg0.28Si2, the bond lengths between Fe and surrounding sites range from 2.31-2.60 Å (see Table 4.8); this falls in the Fe-Al bond range of 2.3-2.8 Å observed in other 122,123 intermetallic phases such as EuFe2Al8 and Al2FeSi. The iron-iron distance along the c-axis is the length of the c-axis parameter (about 4Å in both structures and all analogs), and longer than that across the bridge of the dimers.

The determination of Al and Si siting in R3-δFeAl4-xMgxSi2 (R = Yb or Dy) was aided by the synthesis of the germanide analogs R3-δFeAl4-xMgxGe2 (R = Er or Y). In the structural refinements of the germanides, Ge was clearly located on the 8i site, with the lighter Al atoms on 2a, 8i, 4g, and 2c sites; all atomic sites display occupancies close to 1. The tetrel atom is bonded to three nearby Al (or Al/Mg) sites in trigonal planar coordination; it is also surrounded by a trigonal prism of rare earth atoms along the same trigonal axis. The bonds to the 8i site in

Yb2.77FeAl3.72Mg0.28Si2 are shorter than would be expected for an Al atom (for instance, the bonds to neighboring Yb ions range from 2.87 – 2.97Å, compared to the Yb-Al bonds in the structure which are all longer than 3.1Å; see table 4.7), supporting the assignment of silicon to 55 this site. Silicon (or germanium) is also the most electronegative element in the compound and will be stabilized by the surrounding trigonal prism of rare earth cations.

(a) R3-FeAl4-xMgxSi2 (b) R5Fe4Al17-xMgxSi6

Al Si

Mg/Al Si Yb Al Fe Fe

Mg/Al

Al Mg/Al

The assignments described above lead to a stoichiometry of R3-δFeAl4Tt2 and leave open the question of the amount and location of magnesium substitution in the structure. Due to similarities in size and electronegativity, Mg will be likely to substitute onto aluminum sites in

56 the structure, rather than on tetrel or rare earth positions. The 2a site at the center and corners of the unit cell is the most likely position for Mg incorporation. This site is surrounded by a cube of eight rare earth atoms and also coordinated to four tetrel atoms. The coordination environment is similar to that of the 1d site in the R5Mg5Fe4Al12Si6 structure, which was also assigned as a Mg site. It features longer bond lengths to neighboring atoms than seen for the other aluminum sites, and is therefore suited to incorporate the larger magnesium atoms. Refining this position as occupied by Mg instead of Al does not affect the overall R-factor since these elements have very similar X-ray scattering factors. However, for all four R3-δFeAl4-xMgxTt2 analogs, the thermal parameters for this position are higher than expected if assigned as Al, but drop to values more in line with the other light elements in the structure when refined as a Mg site. If this site has 100%

Mg occupancy, the resulting stoichiometry is R3-δFeAl3.5Mg0.5Tt2 and the phase is better denoted by its empirical formula R6-2δFe2Al7MgTt4 (Z = 2). However, due to the likelihood of mixed

Mg/Al occupancy (see below), it is instead written as R3-δFeAl4-xMgxTt2 (Z = 4) to maintain resemblance to the simpler R3-δFeAl4Tt2 formula.

Neutron diffraction studies were carried out on a large crystal of Yb3-δFeAl4-xMgxSi2 to confirm atom siting and occupancies and determine the extent of substitution. While Mg, Al, and Si have nearly identical X-ray scattering coefficients, their neutron scattering coefficients are different enough to enable distinction of these elements (coherent neutron scattering length is smallest for Al at 3.449 fm, then Si at 4.149 fm, and largest for Mg at 5.375 fm).124 This feature was used to analyze Al and Si siting and mixed occupancies in Ba8Al14Si31 and 78, 80 Pr8Ru12Al49Si9(AlxSi12-x). The R3-δFeAl4-xMgxSi2 structure has 5 light-element sites and 3 possible elements filling them. Refinement of the neutron diffraction data indicates that the 2a site has a neutron scattering factor in between that of Al and Mg. The site is not likely to contain silicon (due to bond length considerations and comparison to the germanide analogs) and while it could be refined as a partially occupied Mg site, the X-ray data refinement does not support this. Therefore, it was refined as a mixed site, containing a mixture of 56% Mg and 44% Al (see table

4.2); this would lead to a stoichiometry of Yb3-δFeAl3.72Mg0.28Si2. The possibility of mixtures on the other light element sites in the structure was also investigated. Of particular interest were the 8i silicon site (which was confirmed to be 100% silicon) and the 2c aluminum site. The latter position is the bridging site across the iron centered dimers, centering the Fe-Al-Fe linkage. The observed Fe-Al bond length of 2.315(1)Å is on the short end of the expected Fe-Al bond

57 lengths in intermetallics; this could indicate that this 2c position is actually filled by smaller silicon atoms (as it is in the corresponding dimers in the R5Mg5Fe4Al12Si6 structure). However, assigning this site as silicon resulted in poorer refinement parameters and 50% larger thermal displacements, indicating aluminum is more likely to occupy this site.

Al2 (8i) Al3 (4g)

Fe Al4 (2c) Mg/Al Si

(a) (b) (c)

8j (d)

(f) (e)

Table 4.8 Bond lengths in Yb2.77FeAl3.72Mg0.28Si2 and Yb5Fe4Al17Si6.

Yb2.77FeAl3.72Mg0.28Si2 Yb5Fe4Al17Si6

Bond Bond distance, Ǻ Bond Bond distance, Ǻ

Yb(1) - Fe(1) 2.7856(7) Yb(1) - Al(1) 3.485(3)

Yb(1) - Si(1) ×4 2.932(1)/2.876(1) Yb(1) - Al(2) ×2 3.319(1)

Yb(1) - Mg(1) ×2 3.2414(3) Yb(1) - Al(3) ×4 3.056(2)

Yb(1) - Al(2) ×2 3.149(1) Yb(1) - Al(4) ×4 2.876(1)

Yb(1) - Al(3) ×4 3.220(4) Yb(1) - Si(2) 3.084(2)

Yb(1) - Yb(1) 3.5510(5) Yb(2) - Al(1) ×4 3.277(3)

Yb(2) - Si(1) ×4 2.974(1) Yb (2) - Si(1) ×8 2.848(2)

Yb(2) - Al(2) ×4 3.104(1) Yb(2) - Fe(1) 3.320(2)

Yb(2) - Al(3) ×2 3.179(2) Fe(1) - Al(1) ×2 2.525(2)

Yb(2) - Al(4) ×2 3.1620(5) Fe(1) - Al(3) ×4 2.588(1)

Yb(2) - Yb(1) 3.6429(5) Fe(1) - Si(1) ×2 2.410(2)

Fe(1) - Al(2) ×4 2.599(1) Fe(1) - Si(2) 2.396(2)

Fe(1) - Al(3) ×2 2.559(1) Al(1) - Al(3) ×4 2.951(2)

Fe(1) - Al(4) ×2 2.315(1) Al(1) - Al(4) ×2 2.910(2)

Mg(1) - Si(1) ×4 2.815(1) Al(2) - Al(4) ×4 2.714(2)

Al(2) - Si(1) 2.565(2) Al(3) - Al(3) × 2 2.971(3)/2.674(3)

Al(2) - Al(2) ×2 2.965(4)/2.726(4) Al(3) - Al(4) 2.499(2)

Al(2) - Al(3) 2.729(3) Al(3) - Si(1) 2.595(3)

Al(2) - Al(4) ×8 2.874(1) Al(3) - Si(2) ×2 2.842(2)

Al(3) - Si(1) ×2 2.668(2) Si(1) - Si(1) ×2 2.838(4)

The neutron diffraction data also confirm partial occupancy of the rare earth sites in

Yb3-δFeAl3.72Mg0.28Si2. Rare earth atoms occupy two sites in the structure (8j and 4h Wyckoff sites). Figure 4.4d shows the coordination of the 4h rare earth site, which is coordinated by 4 Al,

3+ 2 Mg/Al, 4 Si and 1 Fe atom. Each 4h site in R3-δFeAl4-xMgxTt2 also has 4 neighboring R ions in the ab-plane at distances of 3.6429(5) Å for the Yb analog, with 2 more at a longer distance of 4.0996(3)Å along the c-axis (not shown). The 8j sites are coordinated by 7 Al, 4 Si and 3 Fe atoms, with 4 neighboring R3+ ions at distances of 3.6429(5)Å and 3.5510(5)Å, as seen in Figure 4.4e. The short R3+-R3+ distances in the ab-plane, and the fact that the positions form triangular motifs (shown in Figure 4.4f) may have implications for their magnetic behavior (vide infra). Refinement of the neutron diffraction data indicates that the 8j and 4h sites are 92% and 93% occupied, respectively, leading to an overall stoichiometry of Yb2.77FeAl3.72Mg0.28Si2. Since slight partial occupancy (97-99%) of the 8j site was consistently observed in refinements of the

X-ray data for all the analogs, a general formula of R3-δFeAl4-xMgxTt2 for these phases is indicated, with δ < 0.3.

4.3.3 Electronic Structure Calculations

To investigate the electronic effects of Mg substitution on the 2a site, total and partial density-of-states (DOS) data were calculated for model compounds Y3FeAl4Si2, Y3FeAl4Ge2

(both with 100% Al on the 2a site), and Y3FeAl3.5Mg0.5Ge2 (with 100% Mg occupancy on the 2a site). To avoid complications from partially occupied f-shells, Yb and Er ions are substituted with Y, reasonable considering their similar ionic radii and same oxidation number of +3. The DOS diagrams are shown in Figure 4.5. All three model compounds exhibit similar DOS characteristics over the whole energy range. The rare earth cations have the main contribution to the states above the EF, while orbitals from Fe, Al and Si (or Ge) are dominant below the EF, leaving a pseudo gap at or near the EF. This is expected for stable polar intermetallic structures. - Y3FeAl4Si2 and Y3FeAl4Ge2 both have a valence electron count (VEC, per formula unit) of 37 e ; replacing the aluminum on the 2a site with magnesium results in a VEC of 36.5 e- for

Y3FeMg0.5Al3.5Ge2, which shifts the Fermi level of this phase out of the pseudogap. The resulting

DOS at EF for Y3FeAl4Si2, Y3FeAl4Ge2, and Y3FeAl3.5Mg0.5Ge2 are 5.2, 6.2, and 15.8 states/eV·cell, respectively. This indicates that incorporation of Mg has a slight electronic destabilizing effect. This may induce the vacancies that are consistently observed on the adjacent 8j rare earth sites (see figure 3c); these vacancies and associated local distortions may act to stabilize the structure. Similar behavior has been observed in intermetallics such as Nb1-δB2, 125-127 LaZn1-δAs2, and La21-δMn8Te7C12.

60 E Y FeAl Si F total 3 4 2 Y 40 Fe Al 20 Si

0 60-10 -5 0 5 10 15 Y FeAl Ge total 3 4 2 Y

40 Fe Al Ge 20

DOS, states/eV cells 0 60 total Mg Y Al

40 Fe Ge Y FeAl Mg Ge 3 3.5 0.5 2 20

0 -10 -5 0 5 10 15 Energy, eV

The partial DOS data for each element in Y3FeMg0.5Al3.5Ge2 are compared in Figure 4.6a-e. The region just below the Fermi level is dominated by bands derived from iron 3d orbitals, with smaller contributions from aluminum 3p and yttrium 4d states. The chains of iron-centered trigonal prisms of aluminum may therefore make the dominant contribution to the conductivity of this phase, which is likely to be highly anisotropic. Transport measurements along each axis are needed to confirm this, but are hindered by the rod-shaped crystals. The fact that the Fe d-orbitals are below Ef and essentially filled is in agreement with the diamagnetic behavior of iron in these compounds. Some hybridization is observed between states derived from Mg p-orbitals and states from Y d-orbitals, further supporting a link between the presence of Mg and vacancies on the adjacent RE sites.

s 20 Y EF p 10 d f 0 30 Fe 20 10 0 3 Mg 2

DOS 1 0 12 Al 8

4 0 40-10 -8 -6 -4 -2 0 2 4 6 8 10 12 Ge 20

0 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 Energy, eV Figure 4.6 The partial density of states data for Y, Fe, Mg, Al and Ge in Y3FeAl3.5Mg0.5Ge2. Note the different DOS scales for various elements.

To further investigate the bonding within the iron/aluminum chains, orbital interactions between the iron and each of the three surrounding aluminum sites were analyzed by calculation of crystal orbital Hamilton populations (COHP) for model compounds Y3FeAl4Si2 and

Y3FeAl4Ge2 (based on Yb3-δFeAl4-xMgxSi2 and Er3-δFeAl4-xMgxGe2 respectively, with x=0). The COHP data for the silicide and germanide are very similar, as shown in Figure 4.7. As discussed previously, the iron atom is coordinated by a trigonal prism of aluminum (8i and 4g Al sites); these prisms are linked in the ab-plane by a bridging Al atom (2c site), which forms an Fe-Al-Fe chain with unusually short bond lengths in the range of 2.313(7) - 2.332(2) Å. Of the three unique Fe-Al bonds, those between the iron and the aluminum in the 4g sites appear to be most optimized, changing from bonding to antibonding at the Fermi level. The Fe-Al bonds involving the 2c and 8i aluminum sites are predominantly non-bonding in the vicinity of EF, with the bond

62 to the 2c aluminum atoms exhibiting slight antibonding character just below EF. Despite the short bond length, this Fe-Al bond is not as stable as the other two. It is derived predominantly from interactions between Fe 3d and Al 3p orbitals, indicated by the narrow range of bonding states from -1 to -1.5 eV (corresponding to the Fe d-orbital states). The interactions with the other two Al sites involve the Fe 3p orbitals, and are bonding over a broader and lower energy range. This indicates that the iron-aluminum interactions running in the c-axis direction (along the chains of face-sharing prisms) are stronger than the linkage between the prisms in the ab-plane.

1.5 EF Fe-Al (2c site) 1.0

0.5 0.0 -0.5 1.5 -5 -4 -3 -2 -1 0 1 2 3 4 5 1.0 Fe-Al (4g site)

0.5

0.0 -COHP -0.5

-1.0 -5 -4 -3 -2 -1 0 1 2 3 4 5 3 Fe-Al (8i site) 2

1 0 Yb analog -1 Er analog -5 -4 -3 -2 -1 0 1 2 3 4 5 Energy, eV Figure 4.7 Calculated COHP data for the three Fe-Al bonds in Yb3FeAl4-xMgxSi2 and Er3FeAl4-xMgxGe2 phases.

4.3.4 Magnetic Properties

Figure 4.4f highlights the co-planar positioning of the two rare earth sites in the

R3-δFeAl4-xMgxTt2 structure; the rare earth ions form a tiling pattern comprised of squares,

63 triangles, and distorted octagons. The presence of triangles of ions (featuring short R3+-R3+ distances) is of particular interest, since positioning of paramagnetic ions in triangular patterns leads to competing magnetic coupling forces and is a key feature in many geometrically frustrated magnetic systems such as pyrochlores.128 The temperature-dependent magnetic susceptibility and inverse magnetic susceptibility data for Yb2.77FeAl3.72Mg0.28Si2,

Er3-δFeAl4-xMgxGe2 and Dy3-δFeAl4-xMgxSi2 are presented in Figure 4.8.

0.5 120 25 2.1 ZFC 2.0 FC 100 1.8 0.4 1/ 20 

80 , mol Yb/emu 1.5 1.5 0.3 (a) (b) 15  1 2 3 4 5 6 ,mol Er /emu 60 1.0 0.2 10 40 , emu/mol Yb ,emu/mol Er 

 ZFC 0.1 0.5 20 FC 5

0.0 0 0.0 0

0 50 100 150 200 250 300 0 50 100 150 200 250 300 Temperature, K Temperature, K 25 0.08 0.8 0.8 (c) 2 Ge 0.7 20 0.6 0.5 0.06  Mg

15 ,mol Dy/emu

0.6 3.5 2 4 6 8 10 0.4 0.04 FeAl 10 3 ZFC

,emu/mol Dy 0.2 FC  0.02 ZFC 5 (d) FC emu/mol Y ,

0.0  0 0.00 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Temperature, K Temperature, K Figure 4.8 Temperature dependence of magnetic susceptibilities (filled symbols) and inverse magnetic susceptibilities (unfilled symbols) for (a) Yb2.77FeAl3.72Mg0.28Si2, (b) Er3-δFeAl4-xMgxGe2 and (c) Dy3-δFeAl4-xMgxSi2 at 100 G. Insets show low temperature magnetic susceptibility behavior. (d) ZFC and FC temperature dependence of magnetic susceptibility for Y3-δFeAl4-xMgxGe2 at 100 G

Yb2.77FeAl3.72Mg0.28Si2 exhibits paramagnetic behavior over the entire measured temperature range; no magnetic ordering was observed, and no splitting between field-cooled and zero-field cooled data. The inverse susceptibility versus temperature follows the Curie-Weiss

64 law well; the fit yields a magnetic moment of 4.64(2) B per ytterbium ion and a Weiss constant θ = -4.8(1) K. The observed ytterbium moment is in good agreement with the theoretical value of 3+ 4.5 B for Yb ions; a +3 oxidation state is also supported by XPS data (see Figure 4.9). This indicates that the iron electrons are delocalized and do not contribute to the magnetic moment of these phases. This is further evidenced by susceptibility data for Y3-δFeAl4-xMgxGe2, which exhibits temperature independent Pauli paramagnetism as expected for an intermetallic phase with no magnetic ions (see Figure 4.8d).

4p 3/2

4p 1/2 Intensity, cts Intensity,

400 380 360 340 320 Binding energy, eV

Figure 4.8b and 4.8c show the magnetic susceptibility data for Er3-δFeAl4-xMgxGe2 and

Dy3-δFeAl4-xMgxSi2. Both phases exhibit Curie-Weiss behavior at high temperature and antiferromagnetic ordering at low temperature, with Neel temperatures (TN) of 2.8 K and 3.8 K respectively. The very low ordering temperatures of Er and Dy phases (and the lack of ordering in the Yb phase) are somewhat surprising given the short distances between the rare earth ions.

Fitting the inverse susceptibilities (above 150 K) of Er and Dy phases to the Curie-Weiss law 3+ yields effective magnetic moments of 9.57(3) B per Er ion (and θ = 17.3(λ) K), and 10.63(1) 3+ B per Dy ion (and θ = -15.0(7) K). The magnetic moments are in agreement with the 3+ 3+ theoretical values for Er ions (λ.6 B) and Dy ions (10.6 B). The Weiss constants are significantly higher than the observed ordering temperatures for these phases. This, and the triangular arrangements of the rare earth ions, indicates the possibility of competing magnetic interactions or geometric frustration (as does the fact that Er3-δFeAl4-xMgxGe2 orders antiferromagnetically but has a positive Weiss constant, which usually indicates ferromagnetic coupling forces). However, the ratio of θ to TN is not as high as would be expected for a spin 128 glass (θ / TN is usually 10 or higher for spin glasses; observed ratios are 6.2 and 3.9 for the Er and Dy phases studied here). Also, magnetically frustrated systems often exhibit differences in their field-cooled vs zero field-cooled susceptibilities; little to no FC/ZFC splitting is seen in the data for the R3-δFeAl4-xMgxTt2 phases.

a) b) 50 6 4 Er phase 2 40 Dy phase 4 0 -2

B/mol 2 -4 30  -1.0 -0.5 0.0 0.5 1.0 0 20 -2 M', emu/mol 10 Yb phase -4

Magnetization, Er phase Dy phase 0 -6

-8 -6 -4 -2 0 2 4 6 8 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Field, T Field, T Figure 4.10 a) Field dependence of magnetization for Yb2.77FeAl3.72Mg0.28Si2, Dy3-δFeAl4-xMgxSi2 and Er3-δFeAl4-xMgxGe2 at 1.8 K. b) AC magnetization of Er3-δFeAl4-xMgxGe2 and Dy3-δFeAl4-xMgxSi2 in the applied DC magnetic field at 1.8 K.

Field dependence of magnetization data collected at 1.8 K for the Yb, Er and Dy phases are shown in Figure 4.10a. At low applied fields, Yb2.77FeAl3.72Mg0.28Si2 exhibits the linear field dependence typical of a paramagnet, although fields above 1.5 T appear sufficient to induce some spin alignment and saturation. The antiferromagnetically ordered Dy3-δFeAl4-xMgxSi2 exhibits similar behavior, saturating above 2 T. However, the magnetization at this field is well

66 below that expected for Dy3+ moments, indicating a metamagnetic transition might occur at higher fields than are available in this study. Er3-δFeAl4-xMgxGe2 exhibits more complex magnetization data. A metamagnetic transition is observed for the Er analog at ~ 4400 G. The antiferromagnetically ordered spins undergo an evident reorientation, possibly to a canted ferromagnetic state, which slowly saturates with increasing field. The spin reorientation for

Er3-δFeAl4-xMgxGe2 is further confirmed by a sharp peak at ~ 4400 G in the field-dependent AC magnetization curve at 1.8 K, while the data for Dy3-δFeAl4-xMgxSi2 do not show evidence of any distinct transition up to 3 T (see Figure 4.10b). The triangular positioning and short distances between the magnetic ions in the R3-δFeAl4-xMgxTt2 phases may produce several nearly degenerate magnetic ground states, but their energies are different enough so that one state is favored over another at sufficiently low temperature or high field.

4.4 Conclusion Reactions in metal flux mixtures promote formation of complex multinary phases instead of potential binary and ternary intermetallic products. This has been demonstrated by the formation of four new quinary phases Yb2.77FeAl3.72Mg0.28Si2, Dy3-δFeAl4-xMgxSi2, Er3-δFeAl4-xMgxGe2, and Y3-δFeAl4-xMgxGe2 from reactions of Si or Ge with Fe and late rare earth elements (Yb, Er, Dy or Y) in mixed Mg/Al flux. Single crystal neutron diffraction studies were vital in determining the siting of the Mg, Al, and Si atoms in the structure, even enabling the determination of the Mg/Al ratio on a mixed site. While the magnesium content of these phases is low (x < 0.5), it is needed to stabilize the structure; in the absence of Mg, other compounds such as Yb5Fe4Al17Si6 will form. The R3-δFeAl4-xMgxTt2 structure is highlighted by a chain of face-sharing iron-centered trigonal prisms of aluminum, a feature also seen in a flux-grown phases R5Mg5Fe4Al12Si6 and RFe2Al8-xMgx, which form when different rare earths are used in the synthesis. The size of the rare earth ion determines how these chains of FeAl6 prisms pack together to form the overall structure. The stability of this structural building block was confirmed by DOS and COHP calculations. This FeAl6 trigonal prism does not appear in other multinary phases grown from Al flux such as RFe4Al9Si6 (R = Tb, Er) and R4Fe2+xAl7-xSi8 (R = Ce-Sm), likely because those syntheses had a higher concentration of silicon in the flux.76,131

CHAPTER FIVE

Mg/Al FLUX GROWTH AND PROPERTIES OF M5+xMg18-xTt13 PHASES (M = Eu, Ba/Sr; Tt = Si, Ge)

5.1 Introduction Intermetallic silicides are of interest for a wide variety of applications. Complex multinary 132 silicides often feature fascinating silicon bonding motifs, from tetrahedral clusters in Na4Si4 to 133 planar rings analogous to benzene in La10Si8O and the 3-D silicon networks in clathrate phases 36 such as K8Si44. Main group silicides span the border between charge-balanced Zintl phases 134 135 136 (Na4Si4, CaSi2 ) and metallic conductors (BaSn5, Ba8Al16Si30 ). We have been exploring synthesis of new intermetallics and Zintl phases in metal flux mixtures such as La/Ni, Ca/Li, and Mg/Al. The Mg-Al phase diagram contains a broad low-melting range (mp 450ºC) from 30% to 70% Mg. A 1:1 mole ratio of Mg and Al is an excellent solvent for silicon, allowing for crystal growth of both known (CaMgSi 51) and new 115 (Dy5(Mg/Al)5Fe4(Al/Si)18 ) silicides. While this flux is a rich medium for exploratory synthesis of lightweight intermetallics, several questions still need to be resolved regarding its reactivity. It is never an inert solvent; phases crystallizing out of Mg/Al melts always contain at least one of its components. We are exploring the conditions under which both flux components are reactive, or only one. In this chapter, reactions of alkaline earth or europium metals with silicon in Mg/Al flux were carried out. Large crystals of Eu8Mg15Si13 and Ba3.4Sr4.5Mg15.1Si12.9 were grown; substituting Ge for the silicon reactant yields a germanium analog Eu7.1Mg15.9Ge13. These phases are all isostructural with the A5+xMg18-xTt13 phases (A = Ba or Sr, Tt = Si, Ge) previously reported by Nesper. 137 This structure type has a number of interesting features, including variable A/Mg site mixing and a Si4 unit with a geometry and charge which varies from a 8- 10- trigonal planar configuration (Si4 ) to a slightly pyramidal configuration (Si4 ). These phases behave as heavily doped semiconductors or semimetals, and show promise as potential thermoelectric materials. Synthesis of additional analogs of this structure allows for improved understanding of the relationship between structural aspects and the electronic properties of this class of Zintl phases.

5.2 Experimental Procedure

5.2.1 Synthesis

The Eu7.5Mg15.5Si13 and Eu7.1Mg15.9Ge13 phases were synthesized from a mixture of Mg/Al/Si (or Ge)/Eu at a 15:15:2:1 mmol ratio in welded stainless steel crucibles which were encased in quartz ampoules. The Ba3.4Sr4.5Mg15.1Si12.9 phase was grown from the reaction of Mg/Al/Si/Ba/Sr = 15:15:2:1:1. While it is a cost effective crucible material, reactions in steel can leach carbon and paramagnetic impurities from the crucible walls. Therefore, after optimization of reaction conditions, reactions were repeated in niobium crucibles. The reaction vessels were heated to 950 °C in 5 hours, held for 5 hours, cooled to 750 °C in 80 hours and held at 750 °C for 24 hours then centrifuged.

5.2.2 Elemental Analysis

Crystals from each reaction were adhered to an SEM sample puck using double-sided carbon tape. Each crystal was cleaved to expose inner portions to acquire more accurate elemental analysis and avoid erroneous readings due to residual flux coating on the surface. SEM-EDS analysis was performed using a JEOL 5900 scanning electron microscope (30 kV acceleration voltage) equipped with PGT Prism energy dispersion spectroscopy software. Several spots on each crystal were analyzed for 60 s.

5.2.3 TGA-DSC Measurement

Thermal analysis was performed on a SDT-Q600 thermal analyzer (TA Instruments).

Eu7.5Mg15.5Si13 crystals were ground into powder to increase the contact area with the alumina sample holder. The sample was heated to 1200 ° C in 10 ° C /min and then cooled to room temperature in Argon atmosphere (100 ml/min). Powder X-ray diffraction data were collected on the thermally treated sample.

5.2.4 X-ray Diffraction

Single crystal diffraction data were collected at room temperature on a Bruker APEX2 single crystal diffractometer with a Mo Kα radiation source. Selected crystal samples were broken into suitable size and small spheroid fragments were mounted on glass fibers for the data 69 collection. Data was processed using the program SAINT and corrected with the SADABS program.53 Space group assignment was accomplished by XPREP, and refinement of the structure was performed by SHELXTL.54 The structures were solved in hexagonal space group P-62m. This is a non-centrosymmetric space group, which is susceptible to racemic twinning. The absolute structure was determined during the refinement by using the TWIN instruction with the default matrix R = (-1 0 0, 0 -1 0, 0 0 -1) and addition of the BASF absolute structure parameter. Crystallographic data and collection parameters are shown in Tables 5.1. The detailed structure parameters of Eu7.5Mg15.5Si13, Eu7.1Mg15.9Ge13 and Ba3.4Sr4.5Mg15.1Si12.9 are indicated in Tables 5.2, 5.3 and 5.4 respectively. Table 5.5 lists all the bond lengths in three analogs.

Table 5.1 Crystallographic data for Eu7.5Mg15.5Si13, Eu7.1Mg15.9Ge13 and Ba3.4Sr4.5Mg15.1Si12.9.

Compound Eu7.5Mg15.5Si13 Eu7.1Mg15.9Ge13 Ba3.4Sr4.5Mg15.1Si12.9 Space group P-62m (no. 189) Data collection temperature, K 296 150 296 a = 14.668(5) a = 14.715(2) a = 14.862(9) Cell parameters, Å c = 4.428(1) c = 4.425(3) c = 4.521(2) V, Å3 824.9(7) 829.8(6) 864.7(9) Z 1 Density (calc.), g cm–3 3.788 4.826 3.225 , mm–1 15.72 25.09 10.91 Data collection range, deg. 1.60<  < 28.19 1.60<  < 28.31 1.58<  < 22.16 Reflections collected 9221 9415 6533

Independent reflections 787[Rint = 0.0252] 802[Rint = 0.0372] 453[Rint = 0.0639] Parameters refined 46 46 43 Absolute structure parameter 0.83(1) 0.04(5) 0.63(1) a) b) R1 , wR2 [Fo > 4Fo] 0.0110, 0.0239 0.0279, 0.0918 0.0382, 0.0963

R1, wR2 (all data) 0.0110, 0.0239 0.0282, 0.0923 0.0395, 0.0974 Largest diff. peak and hole 0.698 and –1.044 6.478 and -2.687 0.930 and -0.730 [e/Å3] Goodness-of-fit 1.118 0.873 1.046 a) R1 = ║Fo│–│Fc║/  │Fo║. b) 2 2 2 2 2 1/2 2 2 2 –1 2 2 wR2 = [Σ w(Fo – Fc ) / Σ w(Fo ) ] , w = [ (Fo ) + (A·p) + B·p] ; p = (Fo + 2Fc )/3; A = 0.0067, B = 0.

Table 5.2 Wyckoff sites, atomic coordinates, equivalent isotropic displacement parameters [Å2] and occupancies of Eu7.5Mg15.5Si13.

Wyckoff Site Atomic Coordinates Ueq Occupancy Eu1 2c 1/3, 2/3, 0 0.0135(1) 1

Eu2 3g 0.82151(2), 0, 1/2 0.0144(1) 1

Eu3/Mg3 3f 0.43750(2), 0, 0 0.0094(1) 0.841(2)/0.159(2)

Mg1 3g 0.2751(1), 0, 1/2 0.0111(4) 1

Mg2 6j 0.18085(8), 0.37284(9), 0 0.0122(2) 1

Mg4 6k 0.35664(2), 0.48057(5), 1/2 0.0118(3) 1

Si1 1a 0, 0, 0 0.081(3) 1

Si2 3f1 0.17277(4), 0, 0 0.0128(3) 1

Si3 3f2 0.64071(7), 0, 0 0.0110(3) 1

Si4 6k 0.17109(9), 0.48028(5), 1/2 0.0102(2) 1

Table 5.3 Wyckoff sites, atomic coordinates, equivalent isotropic displacement parameters [Å2] and occupancies of Eu7.1Mg15.9Ge13.

Wyckoff Site Atomic Coordinates Ueq Occupancy Eu1 2c 1/3, 2/3, 0 0.0068(8) 1

Eu2 3g 0.82035(3), 0, 1/2 0.0077(1) 1

Eu3/Mg3 3f 0.43835(3), 0, 0 0.0064(3) 0.705(4)/0.294(2)

Mg1 3g 0.27613(2), 0, 0.5 0.0061(5) 1

Mg2 6j 0.17996(9), 0.37295(1), 0 0.0078(3) 1

Mg4 6k 0.35473(1), 0.47977(7), 1/2 0.0097(1) 1

Ge1 1a 0, 0, 0 0.1743(7) 1

Ge2 3f1 0.17319(6), 0, 0 0.0074(9) 1

Ge3 3f2 0.64150(1), 0, 0 0.0049(1) 1

Ge4 6k 0.17138(6), 0.48159(1), 1/2 0.0055(5) 1

Table 5.4 Wyckoff sites, atomic coordinates, equivalent isotropic displacement parameters [Å2] and occupancies of Ba3.4Sr4.5Mg15.1Si12.9.

Wyckoff Site Atomic Coordinates Ueq Occupancy Ba1 2c 1/3, 2/3, 0 0.0156(6) 0.910(1)

Ba2 3g 0.81774(2), 0, 1/2 0.0160(9) 0.877(3)

Sr1 3f 0.43299(1), 0, 0 0.0082(5) 0.982(5)

Mg1 3g 0.27407(2), 0, 1/2 0.0019(5) 1

Mg2 6j 0.18266(2), 0.37321(4), 0 0.0113(5) 1

Mg4 6k 0.35806(3), 0.48176(6), 1/2 0.0109(7) 1

Si1 1a 0, 0, 0 0.0142(4) 1

Si2 3f1 0.17751(6), 0, 0 0.0038(3) 1

Si3 3f2 0.63743(7), 0, 0 0.0023(7) 1 Si4 6k 0.17186(2), 0.47572(7), 1/2 0.0055(6) 1

5.2.5 Magnetic Susceptibility

Magnetic susceptibility measurements were undertaken on a Quantum Design SQUID Magnetic Property Measurement System. Crystals grown in Nb crucibles were selected and held between two strips of kapton tape. Temperature-dependent susceptibility data were collected between 1.8 K and 300 K at applied fields of 100 G, 500 G, and 1000 G. For each run, the sample was cooled to 1.8 K without a field and then the field turned on and data collected as the temperature was raised to collect zero-field cooled (ZFC) data; data was then collected as the temperature was lowered back down to 1.8 K to collect the corresponding field-cooled data (FC). Field-dependent magnetization data were collected at 4.2 K using applied fields up to 7 T. Magnetic anisotropy was studied by orienting the c-axis of the crystal parallel and perpendicular to the applied field.

5.2.6 Electronic Structure Calculations

Density of states (DOS) was calculated with tight binding - linear muffin tin orbitals - atomic sphere approximation (TB-LMTO-ASA) program package.58 The calculation was based on the Eu7.5Mg15.5Si13 parameters determined by single X-ray diffraction data. Fourteen empty

Wigner-Seitz spheres were added to fill the empty space in the structure. In addition, since the 3f site is mixed occupied by Eu3/Mg3 and LMTO program cannot deal with the partially occupied sites, this site was treated solely as Eu. For all three Eu sites, the 4f electrons were treated as core. The following radii of atomic spheres were used: r(Eu) = 4.25/4.15/3.36 Å, r(Mg) = 2.87/3.0 Å, r(Si) = 2.76/3.0 Å, r(empty) = 1.01-1.65 Å. The basis set consists of Eu(6s, 5p), Mg(3s, 3p) and Si (3s, 3p), with Eu(6p), Mg(3d) and Si (3d) being downfolded. The calculation was made for 40 κ points in the irreducible Brillouin zone, and integration over the Brillouin zone was performed by the tetrahedron method.59

Table 5.5 Bond lengths in Eu7.5Mg15.5Si13, Eu7.1Mg15.9Ge13 and Ba3.4Sr4.5Mg15.1Si12.9. Bond distance, Bond distance, Bond Bond Bond Bond Ǻ Ǻ distance, Ǻ Eu(1)-Mg(3)×6 3.660(3) Eu(1)-Mg(3)×6 3.664(5) Ba(1)-Mg(3)×6 3.715(6) Eu(1)-Si(4)×6 3.395(3) Eu(1)-Si(4)×6 3.391(1) Ba(1) - Si(4)×6 3.480(4) Eu(2)-Mg(1)×2 3.539(5) Eu(2)-Mg(1)×2 3. 571(6) Ba(2)-Mg(1)×2 3.591(7) Eu(2)-Mg(2)×2 3.596(4) Eu(2)-Mg(2)×2 3.602(6) Ba(2)-Mg(2)×2 3.626(6) Eu(2)-Si(1)×2 3.428(1) Eu(2)-Ge(1)×2 3.447(1) Ba(2)-Si(1)×2 3.527(2) Eu(2)-Si(2)×4 3.397(2) Eu(2)-Ge(2)×4 3.412(1) Ba(2)-Si(2)×4 3.501(3) Eu(2)-Si(3)× 2 3.454(4) Eu(2)-Ge(3)×2 3.438(2) Ba(2)-Si(3)×2 3.505(7) Eu(3)-Mg(1)×2 3.257(5) Eu(3)-Mg(1)×2 3.255(6) Sr(1)-Mg(1)×2 3.269(7) Eu(3)-Mg(2)×2 3.233(5) Eu(3)-Mg(2)×2 3.238(6) Sr(1)-Mg(2)×2 3.251(9) Eu(3)-Mg(3)×3 3.440(3) Eu(3)-Mg(3)×3 3.457(5) Sr(1)-Mg(3)×3 3.524(6) Eu(3)-Si(3) 2.981(5) Eu(3)-Ge(3) 2.989(3) Sr(1)-Si(3) 3.038(9) Eu(3)-Si(4)×4 3.165(3) Eu(3)-Ge(4)×4 3.171(1) Sr(1)-Si(4)×4 3.227(4) Mg(1)-Mg(2)×4 3.192(3) Mg(1)-Mg(2)×4 3.188(4) Mg(1)-Mg(2)×4 3.263(5) Mg(1)-Si(2)×2 2.670(5) Mg(1)-Ge(2)×2 2.677(7) Mg(1) - Si(2)×2 2.677(7) Mg(1)-Si(4)×2 2.798(6) Mg(1)-Ge(4)×2 2.806(6) Mg(1)-Si(4)×2 2.802(8) Mg(2)-Mg(3)× 2 3.157(5) Mg(2)-Mg(3)× 2 3.152(6) Mg(2)-Mg(3)× 2 3.209(8) Mg(2)-Si(2) 2.804(5) Mg(2)-Ge(2) 2.805(2) Mg(2)-Si(2) 2.816(8) Mg(2)-Si(3) 2.722(5) Mg(2)-Ge(3) 2.739(6) Mg(2)-Si(3) 2.756(8) Mg(2)-Si(4)×2 2.762(4) Mg(2)-Ge(4)×2 2.769(4) Mg(2)-Si(4)×2 2.775(6) Mg(3)-Si(3)×2 2.852(3) Mg(3)-Ge(3)×2 2.860(4) Mg(3)-Si(3)×2 2.893(6) Mg(3)-Si(4)×2 2.719(6)/2.802(6) Mg(3)-Ge(4)×2 2.711(7)/2.812(6) Mg(3)-Si(4)×2 2.72(1)/2.89(1) Si(1)-Si(2)×3 2.534(5) Ge(1)-Ge(2)×3 2.548(2) Si(1)-Si(2)×3 2.638(8)

5.2.7 Solid State NMR Characterization

29Si MAS NMR spectrum was collected on a Varian/Inova 500WB spectrometer (11.7T) 29 with resonance frequencies of 99.40 MHz. The Si shifts were referenced to 1M Al(NO3)3 and

TMS. Crystals of Ba3.4Sr4.5Mg15.1Si12.9 were ground with NaCl in a 1:1 ratio by volume in a glove box and the powder was packed into a 4 mm zirconia rotor sealed with airtight screw caps. The 29Si MAS spectra were obtained with a spinning speed of 13 kHz and a recycle delay of 60s.

5.2.8 Electrical Resistivity

Electrical resistivity measurements were conducted with a conventional four-probe method on a Physical Property Measurement System (PPMS) by Quantum Design. A single crystal (5 mm × 2 mm × 2 mm) was put on a sample holder puck and four 25 micron diameter gold wires were adhered to the crystal surface with silver paste. Resistivity data were taken from 1.9 - 300 K at 0 T with an applied excitation current of 0.5 mA.

5.2.9 Seebeck Measurement

A large number of single crystal samples of this phase were were ground and pressed into two pellets using spark plasma sintering (SPS). A high pressure is applied during the SPS process; it allows for formation of highly dense, sintered pellets suitable for transport and Seebeck measurements. Two samples were pressed at 620°C and 650°C respectively (below the decomposition temperature indicated in Figure 3).

5.3 Results and Discussion

5.3.1 Synthesis and Thermal Analysis

Mg/Al flux has proven to be an excellent solvent for silicon and other elements, and a very useful medium for crystallization of silicides. A preliminary reaction of Si/Fe/Eu in molten

Mg/Al resulted in a mixture of two ternary phases: EuFe2Al8 in thin needle shape and

Eu7.5Mg15.5Si13 in thick rod shape. These two phases can be separated easily by adjusting the reactants. Reactions of Mg/Al/Fe/Eu will produce the EuFe2Al8 phase. Reactions of calcium and silicon in molten Mg/Al yield large crystals of CaMgSi. 51 Attempts at replacing calcium with

74 europium in this synthesis (to form EuMgSi) instead lead to the phase Eu7.5Mg15.5Si13. In addition, Mg/Al flux reactions of europium or alkaline earth metals with tetrelides have yielded two further analogs: Eu7.1Mg15.9Ge12.4, and Ba3.4Sr4.5Mg15.1Si12.9.

Eu7.5Mg15.5Si13 forms as large facetted rod-shaped silver crystals up to 3 mm in diameter and 6 mm in length. The microscopic image of an Eu7.5Mg15.5Si13 single crystal is shown in Figure 5.1. The best yield is approximately 84% based on Eu. Comparison of the experimental and calculated PXRD data (see Figure 5.2) indicates that the product is predominantly pure except some extra peaks for Mg17Al12 and Fe5Si3. This phase is air stable but reacts with water and dilute acids. Thermal analysis under argon indicates it decomposes above 900°C with an associated weight loss likely due to evaporation of magnesium metal; see Figure 5.3. Powder diffraction data taken on the remaining sample are shown in Figure 5.4 and support a decomposition of the compound at high temperature, resulting in the formation of binary EuSi2 phase. The germanide analog Eu7.1Mg15.9Ge13 is slightly air sensitive and should be kept under Ar atomosphere. The highest yield is around 80% with Mg/Al/Ge/Eu mmol ratio = 15/15/3/1.

Figure 5.1 The microscopic image of an Eu7.5Mg15.5Si13 single crystal (1mm×1mm grid)

5.3.2 Structure

137 Eu7.5Mg15.5Si13 crystallizes with the Ba5Mg18Si13 structure type in hexagonal space group P-62m, shown in Figure 5.5a. The previous report on this structure type detailed four analogs of

A5+xMg18-xTt13, with A = Sr and Ba and Tt = Si and Ge, all synthesized using traditional

75 stoichiometric high temperature method. Recently, Nesper's group has reported the structure and 138 139 physical properties of Eu5+xMg18-xGe13 (x=0.1), Eu8Mg16Ge12 and Eu5+xMg18-xSi13 (x=2.2) , all of which were also synthesized with traditional stoichiometric method. Here we synthesized the Eu7.5Mg15.5Si13, Eu7.1Mg15.9Ge13 and Ba3.4Sr4.5Mg15.1Si12.9 with Mg/Al flux. The benefit of the flux method is to enable the growth of metastable compounds as large single crystals, but it is more difficult to control the elemental composition of flux grown products. Indeed, the elemental ratios of our products vary slightly from those of the compounds reported by Nesper's group.

Experimental

Calculated

10 20 30 40 50 60 70 80 2

Figure 5.2 Powder X-ray diffraction data on the products of Eu7.5Mg15.5Si13 synthesis in Mg/Al flux, compared to the pattern calculated based on the single crystal structure.

The anionic tetrelide building blocks in this structure type include isolated E4- anions m- surrounded by cations, and intriguing pseudo trigonal planar [E4] units (see Figure 5.5b.) Previously reported electronic calculations indicate that the charge on this unit depends on 8- 10- whether it is completely planar ([Si4] ) or if it is slightly pyramidal ([Si4] ). Charge-balancing of these phases according to Zintl-Klemm rules requires a -10 charge on this 2+ 2+ 4- 10- unit, yielding a charge distribution of (A or Mg )23(E )9([E4] ). In the previously reported

A5+xMg18-xSi13 (A = Ba and Sr) analogs, highly anisotropic thermal parameters for the central silicon atom in this unit (on the 1a site) indicated that the Si4 unit is pyramidal, with static disorder in the orientation of the pyramid leading to apparent planarity in the averaged structure.

The pyramidal nature of this unit, with an associated charge of -10, leads to an overall charge-balanced stoichiometry. Deviation from planarity is even more pronounced in the germanium analogs; the 1a site is split into two partially occupied 2e sites along the c-axis.

36 20

35 0

34 -20 temperature up 33 temperature down -40

32 -60 Weight, mg

31 -80 Heat flow, mW/mg

30 -100

29 -120 0 200 400 600 800 1000 1200

o Temperature, C

Figure 5.3 Thermal analysis data for a sample of Eu7.5Mg15.5Si13. Decomposition with associated loss of Mg is indicated above 900 °C.

after TGA

before TGA

10 20 30 40 50 60 70 80 2 

Figure 5.4 PXRD patterns of Eu7.5Mg15.5Si13 taken before and after heating to 1200 °C.

m- The [E4] units in the analogs studied here demonstrate a variety of deviations from planarity. In Eu7.5Mg15.5Si13, the Si-Si bond distance in this unit is 2.532(2)Å. The central silicon atom exhibits a large thermal parameter along the c-axis, but it is not extensive enough to be 10- considered a split site. This indicates a pyramidal [Si4] unit with static disorder in orientation, similar to that reported for the A5+xMg18-xSi13 (A = Ba and Sr) analogs. The germanide analog,

Eu7.1Mg15.9Ge13, has a Ge-Ge bond of 2.5498(9) Å in this E4 unit. The central Ge atom exhibits a large thermal parameter along the c-axis and also exhibits partial (36%) occupancy. Whether this is a true partial occupancy or possibly mixed occupation with a lighter element is not clear. EDS analysis did not indicate incorporation of aluminum, but magnesium mixing on this site is a possibility. However, the bond lengths to the surrounding three Ge sites are much shorter than would be expected for a Mg atom at this site (Mg-Ge bonds are typically 2.7 - 2.8Å or longer).

Similar partial occupancy is seen for the Ba3.4Sr4.5Mg15.1Si12.9 analog; the Si site in the center of the Si4 unit is 89% occupied. Again, this could indicate incorporation of Mg at this location. The observed bond length of 2.636(4)Å is slightly long for Si-Si (compared to the

2.532(2)Å seen in the Eu7.5Mg15.5Si13 phase, and the 2.4 - 2.5 Å range typically observed in 140 141 silicides such as FeSi2 and EuZn2Si2 ). Incorporation of Mg on this site would lead to charge-balancing if one assigns it as Mg2+ and the surrounding tetrelides as E4- anions, leading to 4- 2+ 10- a cluster of [(Si )3(Mg )] . It is notable that the thermal parameter along the c-axis in this phase is very large, as is it is in the other phases studied in this work.

The six cation positions in the Eu5+xMg18-xTt13 phases exhibit occupation behavior similar to that seen for the previously reported barium and strontium analogs. Europium consistently occupies the 2c and 3g sites fully; Mg fully occupies the 3g, 6k1, and 6k2 sites. In particular, six Eu atoms on 3g site form a tricapped trigonal prism, with the three-fold rotational axis along the m- c axis across the center atom of [E4] units (see Figure 5.5c and 5.5d). The 3f site is occupied by a mixture of Eu and Mg, predominantly Eu (84% Eu in the silicide; 71% Eu in the germanide).

In the previously reported Sr5+xMg18-xSi13 analog, this site was 55% Sr/45% Mg; in the barium analogs, it was fully occupied by Mg. The lack of barium on this site indicates that Ba2+ is evidently too large to fit on this site. Sr2+ can fit to some extent. Divalent europium is slightly smaller than Sr2+, so a higher proportion of Eu2+ fits on this site.

a) b)

c) d)

5.3.3 Magnetic Properties

The magnetic behavior of the Eu5+xMg18-xTt13 phases may be complicated by the possibility of mixed valence for europium (Eu2+/Eu3+), although the need for charge balancing suggests that the europium should be divalent. This is supported by magnetic susceptibility measurements on Eu7.5Mg15.5Si13. This compound exhibits Curie-Weiss behavior at high temperature, with ferromagnetic ordering at 10 K as shown in Figure 5.6. Fitting of the high temperature data to the Curie-Weiss law indicates a magnetic moment per europium ion of eff = 2+ 8.0 B, close to the theoretical eff = 7.94 B expected for Eu . The calculated Weiss constant (θ

= 8 K) agrees well with the observed Curie temperature (Tc = 10 K) and thus the compound orders with negligible frustration. Eu7.5Mg15.5Si13 behaves as a soft ferromagnet below Tc, with spins preferentially aligned along the c-axis. The field dependence data (Figure 5.7) shows very

79 small hysteresis when the c-axis is parallel to the field, and none when it is perpendicular to the field. Close to complete saturation is seen above applied field of 5 T.

a) b) 8 8 40 c axis parallel to the field 3 80 7 6 35 2 80 Xm/Eu(ZFC),100G 6 4 Xm/Eu(FC),100G 30 2 1 60 Xm/Eu(ZFC),500G 60 5 Xm/Eu(FC),500G 0 0 25 0 5 10 15 20 25 30 Xm/Eu(ZFC),1000G 4 Xm/Eu(FC),1000G 20 40 40 3 ZFC FC 15

20 Eu/emu mol , , emu/mol Eu emu/mol , m per Eu, emu/mol Eu, per m 2 m 10 20 X 1/X X 0 1 c axis perpendicular to the field (100 G) 5 0 10 20 30 0 0 0 -1 -5 0 50 100 150 200 250 300 0 50 100 150 200 250 300

Temperature (K) Temperature, K

6 2

1 4 0 -1 2 -2 parallel (ll) -3 perpendicular (=)

-6000 -4000 -2000 0 2000 4000 6000 0 6 4 -2 2 -4 0 -2

-6 -4 Magnetic susceptibility, uB/mol Eu uB/mol susceptibility, Magnetic

-6 -6000 -4000 -2000 0 2000 4000 6000 -8 -80000 -60000 -40000 -20000 0 20000 40000 60000 80000 Field, Oe

Figure 5.7 Field dependence of magnetization for Eu7.5Mg15.5Si13 at 4 K. Insets show data at low fields.

The magnetic susceptibility and magnetization data of Eu7.1Mg15.9Ge13 are shown in Figure

5.8a and 5.8b respectively. Eu7.1Mg15.9Ge13 exhibits an antiferromagnetic transition with the Néel temperature TN = 5.9 K. This antiferromagnetic ordering is somewhat surprising, considering the ferromagnetic ordering (at Tc=10 K) observed for the silicide analog Eu7.5Mg15.5Si13. The linear inverse susceptibility versus temperature above 10 K can be fitted to the Curie-Weiss law,

80 leading to a theoretical magnetic moment of 6.2 B, which is quite off the calculated value of 2+ Eu (7.94 B). The fitted Weiss constant is 11.6(8) K, indicating ferromagnetic coupling forces between the europium cations. Ferromagnetic coupling may be the default for this structure type, but the nature of the the ordering may be affected by the concentration of europium in the compound. As the amount of europium is decreased (due to substitution by Mg2+ on the Eu2+ sites), the effective average distance between Eu2+ cations increases. The magnetic ordering of ions in intermetallics is facilitated by RKKY coupling of the magnetic centers by the conduction electrons; the nature of the RKKY coupling oscillates between ferromagnetic and antiferromagnetic as a function of the distance between the magnetic ions. The europium content of the germanide is lower than that of the silicide; this may be sufficient to cause the switch from ferromagnetic to antiferromagnetic ordering. Similar behavior was reported for Eu5.1Mg17.9Ge13 and Eu8Mg16Ge12 ; the former exhibited antiferromagnetic coupling, and the latter exhibited ferromagnetic coupling. Figure 5.8b shows the field dependence of the magnetization of

Eu7.5Mg15.5Si13. Approximately linear dependence is observed at low field (below 2 T) and the magnetization approaches saturation at high field up to 7 T.

2.0 8 a) 60 6 1.6 ZFC b) 50 2+ FC 4 1.2 40 2 B/mol Eu

 0 30 0.8 -2 , emu/mol Eu 100 G m 20 , mol Eu/emu X 0.4 m -4

10 1/X

Magnetization, -6 0.0 0 -8 -8 -6 -4 -2 0 2 4 6 8 0 50 100 150 200 250 300 Field, T Temperature, K

Figure 5.8 Magnetic data for Eu7.1Mg15.9Ge13: a) temperature dependence of magnetic susceptibility in 100 G; b) field dependence of magnetization at 1.8 K.

5.3.4 Solid State 29Si MAS NMR

29 The Si MAS NMR spectrum collected at room temperature for Ba3.4Sr4.5Mg15.1Si12.9 is shown in Figure 5.9, and shifts are reported with respect to TMS at 0 ppm. Measurement for

Eu7.5Mg15.5Si13 and Eu7.1Mg15.9Ge13 was not carried out due to the presence of localized f-electrons on Eu2+ ions, which likely affects the chemical shift of nearby Si nuclei. The structure contains four silicon sites in a 1:3:3:6 ratio of multiplicities, so four individual resonances are expected, with a 1:3:3:6 integrated resonance intensity ratio. The observed resonance is broad and features shoulders; it can be fit to the sum of four individual peaks as shown in the calculated 4- pattern. In the structure, the 6k (Si4) and 3f2 (Si3) sites both correspond to isolated Si ions in very similar environments (coordinated by tricapped trigonal prisms of M2+ cations). These silicon nuclei should have similar chemical shifts, and are likely represented by the pink and 10- green curves in the fitted spectrum. The Si4 anions are comprised of the 1a Si site in the middle, bonded to three Si2 atoms on 3f1 sites. These atoms correspond to the small resonance at 60 ppm and the larger one at -100 ppm, respectively.

Experimental

Total simulated Si 1 Si 3 Si 4 Si 2

400 200 0 -200 -400 ppm 29 Figure 5.9 Si MAS NMR data for Ba3.4Sr4.5Mg15.1Si12.9

All four resonances fall in the range between -100 to 100 ppm. Similar chemical shifts are 142 seen for semiconducting silicon phases such as low sodium clathrates (NaxSi136). The silicon resonances of more metallic silicides typically exhibit large Knight shifts, due to the effects of conduction electrons on the effective magnetic field at the nucleus. For instance, metallic 143 144 clathrates such as Na8Si46 and Na16Rb8Si136 have resonances between 200 - 1000 ppm. 51 145 The silicides CaMgSi and Ba3Si4 --both of which are also ostensibly Zintl phases but show

82 metallic behavior--have resonances of 160 and 281 ppm, respectively. More traditional Zintl phases such as the M4Si4 family (M=Na, K, Rb, Cs; these phases are semiconducting, containing 4- Si4 anions) have resonances in the -280 to -360 ppm region. The observed range of chemical shifts of the silicon atoms in Eu7.5Mg15.5Si13 indicate that this phase is behaving as a semiconductor doped into semimetallic behavior.

5.3.5 Transport Properties

The resistivity data for a single crystal sample of Eu7.5Mg15.5Si13 is shown in Figure 5.10. At room temperature, this compound has a resistivity of 1.45 mΩ·cm, which is lower than would be expected for an ostensibly semiconducting Zintl phase. The temperature dependence of the resistivity is also characteristic of a metallic compound. Metallic behavior was also observed for the A5+xMg18-xSi13 (A = Ba and Sr) analogs, which exhibited room temperature resistivities of a similar order of magnitude to Eu7.5Mg15.5Si13. The calculated density of states of Eu7.5Mg15.5Si13 (shown in Figure 5.11) shows a pseudogap at the Fermi level, but still indicates the phase should be metallic. It must be noted that these calculations were carried out on the idealized model 2+ structure Eu8Mg15Si13 which contains an ordered distribution of M cations and and the 8- crystallographically averaged--and therefore planar--Si4 unit, instead of the actual dynamically 10- disordered Si4 unit. This may introduce errors in the resulting DOS data, a possibility that was recently addressed in a recent report by the Nesper group. Conversion of a charge-balanced Zintl phase into a metallic compound may be induced by the numerous possible defects introduced by 10- 2+ the non-planarity of the Si4 unit, partial occupancy of Si1, possible Mg mixing on this site, and possibility of Eu2+/3+ mixed valency. The resistivity data shows a minimum at around 30 K, followed by an increase at lower temperatures. This may be caused by magnetic scattering as the sample approaches its Curie temperature, or by an opening of a pseudogap at Ef at low temperature, resulting in a metal to semiconductor transition. A similar resistivity minimum at low temperature was observed for CaMgSi, which should also be a Zintl phase but behaves as a metal at high temperature. (No data below 50 K was reported for the A5+xMg18-xSi13 (A = Ba and Sr) analogs.) It is notable that a resistivity maximum was observed at around 9 K for the pressed 11 polycrystalline pellet of Eu5+xMg18-xSi13 (x = 2.2) according to the literature. However, in our case, the maximum is seen at approximately 4 K. This is likely due to the different amount of Eu ions in both compounds Eu5+xMg18-xSi13 (x = 2.2 vs. 2.5). The magnetic spins will be affected by

83 the conduction electrons through the RKKY interaction, and conversely the electrical resistivity will also be impacted by the magnetic spins, as indicated by the magnetoresistance behavior for 139 Eu5+xMg18-xSi13 (x = 2.2).

1.5

1.274 cm cm  1.4 1.272 1.270 cm  Resistivity, m Resistivity, 1.268 1 2 3 4 5 6 7 1.3 Temperature, K

Resistivity, m 1.2 Temp up Temp down

1.1 0 50 100 150 200 250 300 Temperature, K

Figure 5.10 Temperature dependence of resistivity of Eu7.5Mg15.5Si13.

40 E total F 35 Eu Mg Si 30

DOS, states/eV cell 10

0 -8 -6 -4 -2 0 2 4 6 8 10 Energy, eV

Figure 5.11 Density of states data calculated for Eu8Mg15Si13

Heavily doped small band gap semiconductors or semimetals are of great interest as potential thermoelectric materials. It was therefore of interest to measure the Seebeck coefficient of Eu7.5Mg15.5Si13. Powder diffraction data taken before and after the SPS process (Figure 5.12) indicate the phase maintained its structure in both samples.

Figure 5.12 PXRD of Eu7.5Mg15.5Si13 samples pressed into two sample pellets, before (above) and after (below) the spark plasma sintering process to make the pellets.

Despite the high temperature of the SPS process, it appears that the samples were not fully sintered, and the grain boundaries in the pellets have a significant effect on the resistivity. The Sample 1 pellet (pressed at the lower temperature) also appeared to have a small crack in it. As seen in Figure 5.13, both pelletized samples have resistivity an order of magnitude higher than that measured on a single crystal of Eu7.5Mg15.5Si13, and hysteresis is seen upon heating and cooling, consistent with the theory that the particles are not completely sintered. The Seebeck coefficient measurement is not as dependent on complete sintering, and the data (Figure 5.14) are reproducible between the two samples. The negative Seebeck coefficient indicates this phase is an n-type semiconductor or semimetal. The magnitude of the Seebeck coefficient increases from -20 uV/K at room temperature to -100 uV/K at 600°C. This is decidedly larger than most 16 147 148 intermetallic phases such as YbAl3, YMB4 (M = Cr, Mo, W), CeNi2Sn2, etc, indicating again that Eu7.5Mg15.5Si13 is a semiconductor or semimetal.

Comparing the properties of Eu7.5Mg15.5Si13 to other benchmark Zintl phase thermoelectrics indicates it is a promising system for further exploration. The thermoelectric figure of merit ZT = S2T/, shows that materials with higher Seebeck coefficient S, lower resistivity , and lower 149 thermal conductivity  will have better performance. At 600 °C, Yb14MnSb11 has a higher magnitude Seebeck coefficient (150 uV/K) than Eu7.5Mg15.5Si13 (-100 uV/K), but its resistivity is also higher (4 mOhm cm, compared to the value of 2 mOhm cm obtained from extrapolating

Figure 7 to 600 °C). Measurement of the thermal conductivity of Eu7.5Mg15.5Si13 is still needed. However, one can postulate that the complex structure of this phase, featuring a large unit cell

85 and heavy atoms which are loosely bound and susceptible to rattling (as well as mixing of Mg and Eu on one site), will lead to scattering of phonons and a very low lattice thermal conductivity, as is the case with Yb14MnSb11.

Figure 5.13 Temperature dependence of resistivity on two spark plasma sintered pellet samples of Eu7.5Mg15.5Si13.

Figure 5.14 Temperature-dependent Seebeck coefficients on two spark plasma sintered pellet samples of Eu7.5Mg15.5Si13.

The flexibility of the Eu7.5Mg15.5Si13 structure should allow for further optimization of thermoelectric properties. Substitution of germanium for silicon may lower the resistivity of this

86 phase. Mixing of Ba2+ and/or Sr2+ on several of the cation sites will cause increased scattering of phonons, lowering the thermal conductivity. The ability to grow large crystals of these phases from Mg/Al flux will facilitate accurate measurements of transport properties.

5.4 Conclusion

Large single crystals of Eu7.5Mg15.5Si13, Eu7.1Mg15.9Ge13, and Ba3.4Sr4.5Mg15.1Si12.9 have been successfully grown in Mg/Al flux. These three phases crystallize in the A5+xMg18-xTt13 (A = Sr 10- 10- and Ba; Tt = Si and Ge) structure type. The structure features a [Si4] or [Ge4] trigonal planar unit at each corner of the hexagonal unit cell, leading to a charge balanced Zintl phase as (A2+ or 2+ 4- 10- Mg )23(E )9([E4] ) for these three compounds. Magnetic study indicates that the Eu ions are divalent and Eu7.5Mg15.5Si13 shows a ferromagnetic ordering with Tc =10 K. The electrical resistivity of Eu7.5Mg15.5Si13 exhibits a linear metallic dependence on the temperature, consistent with the presence of a pseudo gap at the Fermi level. Eu7.5Mg15.5Si13 exhibits sharp thermoelectric power increase from -20 V/K at room temperature to -100 V/K at 600 K.

Considering the low electrical resistivity and complex structure, Eu7.5Mg15.5Si13 is likely a good high temperature thermoelectric candidate.

CHAPTER SIX

FLUX GROWTH AND MAGNETORESISTANCE BEHAVIOR OF RARE EARTH ZINTL PHASES EuMgTt (Tt=Sn, Pb)

6.1 Introduction Intermetallic compounds are traditionally synthesized by arc melting reactant elements with subsequent annealing at high temperatures. Unfortunately, arc melting allows very little control during the rapid heating and cooling of samples and polycrystalline phases or tiny single crystals are often produced. The molten flux technique is an appealing tool for exploratory synthesis of new single crystal phases.43,150 Dissolution of solid reactants in a molten solvent (e.g. metals, salts, metal oxides, etc ) helps to circumvent diffusion barriers and avoid the formation of thermodynamically stable products, and slow cooling often leads to growth of large single crystals of products.45-47 Using mixed fluxes composed of two elements in large amounts can lower the melting point by eutectic formation, although it introduces additional complexity since one or both of the flux metals may act as reactants and be incorporated into the products. Previous research in our group has explored the use of several Mg-based molten Mg-X fluxes (X = Ni, Zn, Cu, Ga, Al) for the growth of new phases, with Mg/Al mixtures being of particular interest. The Mg/Al phase diagram exhibits a wide low melting range (40-60 atom% 50 Mg, ~450 °C) between the only two binary phases Mg2Al3 and Mg17Al12. Mg/Al mixtures have proven to be good solvents for the synthesis of silicides such as CaMgSi and R5Mg5Fe4Al12Si6 (R=Gd, Dy, Y).51, 115 However, it is difficult to distinguish Al and Si sites in the silicides containing aluminum because of their similar X-ray scattering cross-sections. Therefore, it is interesting to explore the replacement of silicon with its heavier congener tin in Mg/Al flux reactions. Stannides are more often sought using tin flux; some examples of phases grown in 151,152 153 154 molten tin are Ti2Sn3, Os4Sn17, REMn6Sn6 (RE = Tb, Ho, Er, Tm, Lu) and 155 La4.87Ni12Sn24. In this chapter, large EuMgTt (Tt= Sn, Pb) single crystals were successfully grown in Mg/Al (and also Mg/Ag) flux. Although EuMgTt (Tt= Sn, Pb) polycrystalline samples have previously been produced with traditional high temperature synthesis, the small crystal size limited the characterization of the phase and only powder X-ray diffraction data were reported.156 Europium intermetallic compounds have been widely studied due to the half-filled 4f shell of Eu2+ (Eu3+ are very rare for intermetallics). Complex behavior is observed even in well-known

88 and relatively simple structure types, as demonstrated by a review of the properties and partially polarized chemical bonding in 72 equiatomic EuTX compounds (T = transition metal; X = elements of groups 13, 14, or 15).157 Europium is also being explored as a substitute for alkaline earth metals in Zintl phases; in compounds such as Eu(Zn1-xGex)2 and EuGaSi, europium partially transfers valence electrons to the electronegative components, leading to a pseudo gap at the Fermi level.158-160 Such phases are of interest because changes in the magnetization of the rare earth ions may impact other physical properties such as the resistivity, potentially leading to magnetoresistance. For magnetoresistant materials, the electrical resistivity exhibits dramatic changes upon application of a magnetic field. EuMgSn appears to be close to a metal-insulator transition, as seen in the isostructural compound CaMgSi, which exhibits a metal to semimetal transition at ~50 K.51 Its resistivity is therefore very sensitive to perturbations caused by the magnetic ordering transition of the Eu2+ ions at 10 K. Introducing a magnetic ion into intermetallic phases which lie on the border between metallic and semiconducting behaviors appears to be a promising way of promoting magnetoresistivity.

6.2 Experimental Procedure

6.2.1 Synthesis

The elemental reactants were used as received: Mg and Al metal slugs (99.95%, Alfa Aesar), Ag crystalline powder (99.99%, Alfa Aesar), Sn metal slugs (99.9%, Cerac Inc.) Pb metal slugs (99.9%, Cerac Inc.)and Eu slugs (99.9% Metall Rare Earth Ltd.). The elements Mg/Al/Tt/Eu (Tt=Sn, Pb) were initially weighed out in a 15/15/1/1 mmol ratio and loaded into a stainless steel crucible in an Ar-filled glove box. The steel crucible was welded shut under argon and then sealed into a fused silica tube under vacuum (30 mTorr). The reaction ampoule was placed in a muffle furnace and heated from room temperature to 950°C in 10 h, held at 950°C for 5 h, cooled to 750°C in 80 h, and held at 750 °C for 24 h, at which point the reaction ampoule was quickly removed from the furnace, flipped and centrifuged to let the excess Mg/Al molten flux decant off the product crystals which were adhered to the crucible wall. Reactions with different reactant ratios were compared in order to determine the highest yield, which was obtained at a Mg/Al/Tt/Eu ratio of 15:15:2:1. After the reaction ratio was optimized, the reaction was carried out in a niobium crucible to avoid the possibility of iron

89 contamination; pure EuMgSn and EuMgPb crystals could be grown by the same preparation method as stated above. In addition to Mg/Al flux, Mg/Ag and tin fluxes were also explored as reaction media. The Mg/Ag eutectic (at 85/15 atomic% ratio) has a melting point of 450 ° C , and reactions of the elements Mg/Ag/Sn/Eu in a mmol ratio of 17/3/2/1 were prepared using the same procedure described for Mg/Al flux. Tin has a very low melting point (232 ° C ) and reactions of Mg/Eu/Sn in a mmol ratio of 2/1/20 were prepared in alumina crucibles, sealed in quartz tubes, and heated to 850 ° C , held at 850°C for 5 h, cooled to 600°C in 80 h, and held at 600 °C for 24 h, at which point the reaction ampoule was quickly removed from the furnace, flipped and centrifuged.

6.2.2 Elemental Analysis

6.2.3 X-ray Diffraction

Single crystal diffraction data were collected at room temperature on a Bruker APEX2 single crystal diffractometer with a Mo Kα radiation source. Selected crystal samples were broken into suitable size and small spheroid fragments were mounted on glass fibers for the data collection. Data was processed using the program SAINT and corrected with the SADABS program.53 Space group assignment was accomplished by XPREP, and refinement of the 54 structure was performed using SHELXTL. The structure of EuMgSn and EuMgPb was solved in orthorhombic space group Pnma. In the final refinement cycles, occupancies of all sites were allowed to vary, but all appeared fully occupied (100 +/- 1%). Crystallographic data and collection parameters are shown in Table 6.1 and important interatomic distances in Table 6.2; further data can be found in the CIF file in Supporting Information. Powder X-ray diffraction data for crystals grown in Mg/Al and Mg/Ag fluxes were collected on a PANalytical X'Pert PRO

90 diffractometer equipped with a Cu Kα radiation source. To prevent oxidation, samples were ground and loaded into an air-tight holder inside a glove box.

Table 6.1 Crystallographic data and collection parameters for EuMgSn and EuMgPb.

EuMgSn EuMgPb

Crystal system orthorhombic orthorhombic

Space group Pnma Pnma

a = 8.0849(7) a = 8.126(4) Cell parameters, Å b = 4.8517(4) b = 4.872(3) c = 8.7504(8) c = 8.892(5) Eu (0.01241(4), 1/4, Eu (0.01061(3), 1/4, 0.69129(2)); 0.68981(3)); Mg (0.14966(4), Atom positions Mg (0.1523(1), 1/4, 0.0695(1)); 1/4, 0.06670(7)); Sn (0.27654(3), 1/4, 0.39392(3)) Pb (0.27366(7), 1/4, 0.39168(3))

V, Å3 343.24(5) 352.1(4)

Z 4 4 Calc. Density (g/cm3) 5.71 7.24 Max. 2Theta (°) 56.56 56.46 Radiation Mo Kα Mo Kα Temperature (K) 290 290 Reflections 3587 3986 Unique reflections 458 465 Data/parameters 458 / 20 465 / 20 Mu (mm-1) 25.26 65.29 R(int) 0.0232 0.0327 a R1/wR2 (I>2(I)) 0.0137 / 0.0290 0.0153 / 0.0317

R1/wR2 (all data) 0.0142 / 0.0291 0.0160/ 0.0318 Largest diff peak and hole (e·Å-3) 0.830 / -1.128 1.360 / -0.832 a 2 2 2 2 2 1/2 R1=(|Fo|- |Fc|) /|Fo|; wR2=[[w(Fo - Fc ) ]/(w|Fo| ) ] .

Table 6.2 Interatomic distances in EuMgSn.

Bond Bond distances, Ǻ

Eu - Sn 3.3754(4), 3.4395(3), 3.4627(3) Eu - Mg 3.464(1), 3.502(1), 3.687(1), 3.801(1) Eu - Eu 4.1378(3), 4.1710(5), 4.8517(4) Sn - Mg 2.9284(9), 3.011(1), 3.055(1)

Table 6.3 Interatomic distances in EuMgPb.

Bond Bond distances, Ǻ

Eu - Pb 3.3963(15), 3.4444(14), 3.489(13) Eu - Mg 3.5152 (23), 3.5320(32), 3.7273(31), 3.8306(25) Eu - Eu 4.1677(19), 4.20(2), 4.87(2) Pb - Mg 2.9571(19), 3.0603(30), 3.0779(32)

6.2.4 TGA-DSC Measurement

Thermal analysis was performed on a SDT-Q600 (TA Instruments). EuMgSn crystals were ground into powder to increase the contact area with the alumina sample holder. The sample was heated to 1000 ° C in 10 ° C /min and then cooled to room temperature in Argon atmosphere (100 ml/min). Powder X-ray diffraction data were collected on the thermally treated sample. Since a small endothermic peak was observed at around 430 ° C , another EuMgSn sample was heated to just above that temperature (500 ° C ) in 10 ° C /min and cooled down, and powder XRD data collected on the sample residue.

6.2.5 Electronic Structure Calculations

Density of states data for EuMgSn and EuMgPb were calculated with the tight binding - linear muffin tin orbitals - atomic sphere approximation (TB-LMTO-ASA) program package.58 The calculation was based on the EuMgTt (Tt = Sn, Pb) structure parameters determined by single X-ray diffraction data. Eu 4f shell was treated as the "core". Four types of empty Wigner-Seitz spheres in the radii range of 1.26 -1.39 Å were added to fill the empty space in the structure. The following radii of atomic spheres were used: R(Eu) = 3.88 Å, R(Mg) = 2.98 Å,

R(Sn) = 3.35 Å, R(Pb) = 3.40 Å.. The basis set contains Eu (6s, 5p), Mg(3s, 3p) and Sn (5s, 5p), Pb (6s, 6p) with Eu(6p), Mg(3d), Sn (5d, 4f) and Pb (6d, 5f) being downfolded. The calculation was made for 585 κ points in the irreducible Brillouin zone. Integration over the Brillouin zone was performed by the tetrahedron method.59

6.2.6 Magnetic Susceptibility

Magnetic susceptibility measurements were undertaken on a Quantum Design SQUID Magnetic Property Measurement System. Crystals grown in Nb crucibles were selected and held between two 4 cm long strips of kapton tape to eliminate background effects; this was placed in a straw attached to the sample holder. For EuMgSn, temperature-dependent susceptibility data of were collected between 1.8 K and 300 K at 100 G, 1000 G, 1.5 T, 2 T and 2.5 T respectively. Field-dependent magnetization data were collected at 4.2 K using applied fields up to 7 T. Magnetic anisotropy was studied by orienting the crystal with its b axis either parallel or perpendicular to the applied field. The field dependence of AC magnetic susceptibility was performed with 1 Hz frequency and 3×10-4 T amplitude of the AC field under a DC bias field up to 7 T. For EuMgPb, temperature dependence of magnetic susceptibility data were collected between 1.8 K and 300 K at 100 G. Field-dependent magnetization data were collected at 1.8 K in the field range to 7 T; crystals were oriented with c-axis parallel to the applied field. The field dependence of AC magnetization for EuMgPb was performed with 1 Hz frequency and 3×10-4 amplitude of the AC field under a DC bias field up to 3 T.

6.2.7 Electrical Resistivity

Electrical resistivity measurements were conducted with a conventional four-probe method on a Physical Property Measurement System (PPMS) by Quantum Design. An EuMgSn single crystal (5 mm × 0.6 mm × 0.5 mm) was put on a sample holder puck and four 25 micron diameter gold wires were adhered to the crystal surface with silver paste. Resistivity data were taken from 1.9 - 300 K at 0 T and 2.5 T with an applied excitation current of 0.5 mA. Field dependence of resistivity data were obtained at 4.2 K in the field range of 0 - 7 T. For EuMgPb, two single crystals (5 mm × 0.5 mm × 0.7 mm and 5 mm × 0.6 mm × 0.6 mm) were put on the sample holder puck, one being placed with b axis parallel to the field and the other perpendicular to the field. Resistivity data were taken from 1.9 - 300 K at 0 T and 4 T with an applied

93 excitation current of 0.5 mA. In particular, resistivity data were also taken from 1.9 - 30 K at 0.5, 1, 2 and 3 T. The magnetoresistance ratio (MR) at an applied field B was calculated using the equation MR = {[(B) – (0 T))] / (0 T)} × 100.

6.3 Results and Discussion

6.3.1 Synthesis

Single crystals of EuMgTt (Tt = Sn, Pb) in rod-like shape (up to 1 mm in diameter and 5 mm in length) were successfully grown in Mg/Al flux. The SEM image of a selected EuMgSn crystal is shown in Figure 6.1. The crystal surface appears clean, indicating that most of the flux residue has been removed from the crystal by centrifugation at high temperature (750 ° C ). If lower centrifugation temperatures are used, the flux is more viscous and difficult to remove. The EuMgSn or EuMgPb compound is air-sensitive and will darken if exposed to air for more than a day. The optimal Mg/Al/Tt/Eu reaction ratio is 15/15/2/1, leading to a 60% yield based on Eu. Aluminum was not incorporated into the structure and acts only as a flux component to enhance reactant solubility and diffusion. Attempts to make EuMgTt analogs with lighter tetrelides (via reactions such as Mg/Al/Tt/Eu where Tt = Si or Ge) lead instead to large crystals of the 138 Eu5+xMg18-xTt13 phases recently reported by Slabon and Nesper et al, which has been discussed in Chapter 5.

Figure 6.1 SEM image of a single crystal of EuMgSn grown from Mg/Al flux.

EuMgSn can also be synthesized in Mg/Ag flux through the reaction of Mg/Ag/Sn/Eu (mmol ratio: 17/3/1/1), although the yield is lower and the crystals smaller than those grown in Mg/Al flux. Powder X-ray diffraction data collected on products from Mg/Al and Mg/Ag fluxes are shown in Figure 6.2a. No obvious impurity peaks are observed when compared with the calculated pattern. Attempts to form EuMgSn from reactions of europium and magnesium in tin flux produced the binary phase EuSn3, which was likely favored by the presence of the large amount of tin.

a) b)

EuMgSn from Mg/Ag flux Original

EuMgSn from Mg/Al flux TGA - DSC up to 500 C

Intensity, a.u.

Calculated  TGA - DSC up to 1000 C

10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80

2deg 2deg Figure 6.2 a) Powder X-ray diffraction patterns of EuMgSn samples from Mg/Al and Mg/Ag fluxes, compared to calculated pattern based on single crystal structure; b) Powder X-ray diffraction of EuMgSn after thermal treatment

In order to determine whether EuMgSn melts congruently, TGA-DSC analysis was performed; the data are shown in Figure 6.3. An endothermic peak appears at 910 ° C during the heating process. The recrystallization of the sample occurs upon cooling to 800 ° C , indicated by an exothermic peak. However, powder X-ray data (see Figure 6.2b) reveals that the sample has converted to mainly EuSn (small amounts of EuSn3 and Sn were also present) after the thermal treatment. The ~6.5% weight loss above 910°C is likely caused by the decomposition of the sample and associated vaporization of magnesium content (magnesium has a high vapor pressure and accounts for ~8% mass of EuMgSn). A tiny endothermic peak is also present at about 430 ° C , which is likely attributed to melting of a small amount of Mg/Al flux on the crystal surface. The powder X-ray data of another EuMgSn sample heated only to 500 ° C does not exhibit any difference from the original powder pattern, as shown in Figure 6.2b, indicating this tiny peak does not correspond to a phase change.

60 80 40

60 20 Heat flow, mW 0

40 -20 Weight, mg Weight,

20 -40

-60 0 0 200 400 600 800 1000  Temperature, C

Figure 6.3 TGA and DSC of EuMgSn

6.3.2 Structure

EuMgTt (Tt = Sn, Pb) crystallizes with the common TiNiSi structure type (orthorhombic space group Pnma), isostructural to EuZnSn,161, 162 EuPdSn, and EuPtSn.163, 164 Atom positions are listed in Table 1. The structure of EuMgTt (Tt = Sn, Pb) is shown in Figure 6.4 (viewed down the b-axis). Each type of atom occupies only one site in the structure. Magnesium and tin atoms alternate and are connected to form puckered hexagonal layers along the bc-plane, and neighboring layers are connected by rhombic Mg2Sn2 units (as highlighted in blue) along the a-axis. Magnesium and tin atoms are each coordinated by a distorted tin or magnesium tetrahedron respectively. A comparison of atom positioning in the anionic frameworks of the stannides EuMgSn, EuZnSn, EuPdSn, and EuPtSn shows different sitings for the tin atoms. The

Sn sites in the Mg/Sn and Zn/Sn frameworks correspond to Pd (or Pt) sites in the Pd/Sn (or Pt/Sn) frameworks. This phenomenon results from the higher electronegativity of Sn than Mg or Zn, in contrast to Sn having lower electronegativity than Pd (or Pt).156 The Mg-Sn intralayer distances of 2.9284(9) Å and 3.011(1) Å in the Mg3Sn3 hexagons are slightly shorter than the Mg-Sn bond distance of 3.055(1) Å between the layers. Considering the sum of the metallic single bond radii of 2.79 Å for magnesium and tin,165 the Mg-Sn intralayer bonds are more covalent than the Mg-Sn interlayer bonds. While magnesium is an alkaline earth metal, it behaves more like a transition metal in EuMgSn, similar to zinc in EuZnSn.

Figure 6.4 Structure of EuMgTt (Tt = Sn, Pb) viewed down the b-axis; europium, magnesium and tin (or Pb) atoms are pink, yellow and cyan respectively.

Europium ions, the most electropositive species in the structure, reside between the puckered

Mg/Tt layers. Each europium atom is sandwiched by two puckered Mg3Tt3 hexagons, leading to a coordination of Eu by 6 magnesium atoms and 5 tin atoms within the range of 3.3754(4) Å to 3.801(1) Å. One tin atom is located farther (4.096 Å) from the europium and hence is excluded. Inspection of the distances between europium ions in EuMgSn indicates that each is adjacent to six other Eu ions, with two of them located along the b-direction at a distance of 4.1378(3) Å and two more further out at 4.8517(4) Å; the other two are at a distance of 4.1710(5) Å along the a-direction. In the case of EuMgPb, the Eu-Eu distances are 4.1677(19), 4.20(2), 4.87(2) Å, respectively. The two sets of neighboring europium ions at distances of 4.1378(3) and 4.1710(5) Å for EuMgSn (or 4.1677(19), 4.20(2) Å for EuMgPb) are expected to cause competing magnetic interactions, which will be discussed in magnetic studies.

6.3.3 Electronic Structure Calculations

Figure 6.5a and 6.5b exhibit the calculated total and partial density of states (DOS) diagram for EuMgSn and EuMgPb respectively. The change in electronegative ions (Sn or Pb) does cause an apparently different DOS curves. Not surprisingly, the DOS data for EuMgSn resembles that 51 -1 reported for CaMgSi. A pseudogap (~1.3 states eV per unit cell) at the Fermi level (EF)

97 reveals that EuMgTt (Tt = Sn, Pb) are still metallic, and not semiconducting as would be expected for a charge-balanced Zintl phase (Eu2+Mg2+Sn4- or Eu2+Mg2+Pb4-). The DOS analysis agrees well with the electrical resistivity of EuMgSn and EuMgPb, which show behavior typical of a metal (vide infra). Electropositive europium has the main contribution to the states above the

EF, while tin or lead states are predominant below the EF. Magnesium states are highly disperse in a wide range across the EF, indicating strong hybridization with Eu and Sn (or Pb) states. Eu,

Mg and Sn (or Pb) elements all contribute to the states near EF, indicating a significant cation-anion orbital overlap. While modeling of Eu2+ f-states was not possible, they are known to be located near the Fermi level in intermetallics, facilitating phenomena such as valence fluctuation and 4f-5d hybridization.166 This allows the partially delocalized valence electrons of europium to impact the electrical conductivity when a magnetic field is applied, as is discussed in the resistivity section.

a) 30 b) 40 E F total E F total 25 Eu Eu Sn Mg Mg 30 Pb 20

15 20 10 states/eV cell states/eV DOS, states/eV cell 10 Density of states, Density of states, 5

0 0 -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 Energy, eV Energy, eV Figure 6.5 Partial and total density of states data calculated for a) EuMgSn and b) EuMgPb

6.3.4 Magnetic Properties

Magnetic measurements were performed on EuMgSn and EuMgPb single crystals prepared in a Nb crucible, with their b-axis oriented either parallel or perpendicular to the magnetic field. The parallel magnetic susceptibilities versus temperature of EuMgSn (ZFC and FC) at 100 G, 1000 G, 1.5 T, 2 T and 2.5 T are shown in Figure 6.6a. All curves indicate antiferromagnetic transitions with decreasing Néel temperature (TN) as higher field is applied. As seen from Figure 6.6a, EuMgSn has a TN = 10.9 K at 100 G and a TN of 7.8 K at 2.0 T. When the

field increased to 2.5 T, the susceptibility below 6 K was almost saturated and TN is difficult to see. The shifts of Néel temperature towards low temperature is attributed to the nature of the antiferromagnetic transition.167 An applied magnetic field parallel to the easy axis of a structure (b-axis for EuMgSn) tends to cause the spin flop anisotropically, resulting in the destabilization of the structure. For EuMgSn, a higher magnetic field will induce the europium moments to potentially align with it, overwhelming the antiferromagnetic coupling forces and promoting ferromagnetic ordering if the magnetic field is high enough. Thus, to stabilize the antiferromagnetic ordering, a lower temperature is required.

1.5 1.0 40 40 0.8 30 30 20 1.0 20 0.6 10 10 mol Eu ions/emu Eu mol , mol Eu ions/emu Eu mol 0  ,

 0 0.4 1/

1/ 0 50 100 150 200 250 300 0.5 0 50 100 150 200 250 300 Temperature, K emu/mol Eu ions Temperature, K emu/mol Eu ions 

 0.2 (a) (b) 0.0 0.0 0 20 40 60 80 100 0 20 40 60 80 100 Temperature, K Temperature, K

This field-induced spin reorientation can also be seen in field-dependent magnetization measurements performed at 4.2 K with the b-axis of the crystal aligned both parallel and perpendicular to the field (see Figure 6.7). When the field is applied parallel to the b-axis, the magnetization versus field displays linear behavior up to 2 T, at which point a metamagnetic

transition occurs. This transition is also evidenced by the χ' peak at Hcr = ~2 T in the AC magnetization as a function of the applied DC field (Figure 6.8). A second peak is present at ~2.6 T, revealing the spin reorientation is almost complete at that field. Figure 6.7 also displays the

99 magnetization data for the crystal with b-axis perpendicular to the applied field, and the magnetization increases linearly with increasing field over the entire field range to 7 T. The magnetization in both orientations starts to saturate at 7 T.

6 5 /mol B  4

2 Magnetization, H b axis 1 H  b axis

0 0 1 2 3 4 5 6 7 Field, T Figure 6.7 Field dependence of magnetization at 4.2 K for EuMgSn crystal oriented with b-axis either parallel or perpendicular to the field.

The inverse magnetic susceptibility versus temperature curves of EuMgSn (see the insets of Figure 6.6) can be fit to the Curie-Weiss law above 50 K, resulting in effective magnetic 2+ 3+ moments per europium ion of 7.9 ~ 8.4 B. The theoretical magnetic moments of Eu and Eu are 7.9 and 3.4 B respectively. Hence, europium ions in EuMgSn have a +2 oxidation state. The positive sign of the Weiss constant (θ = 3 K) indicates that ferromagnetic coupling forces are present at high temperatures, which contradicts the observed antiferromagnetic ordering. There are evidently two competing mechanisms for ordering, which is also supported by the observation of the spin reorientation in Figures 6.7 and 6.8. As shown in Figure 6.4, each Eu2+ ion has six neighboring Eu2+ ions at distances of 4.1378(3) Å, 4.1710(5) Å and 4.8517(4) Å along the a, b and c axes respectively, which will lead to competing coupling forces. To study the magnetic anisotropy of EuMgSn, magnetic susceptibility measurements were also undertaken with the b-axis of the crystal oriented perpendicular to the applied 1000 G magnetic field and the result is shown in Figure 6.6b. For the convenience of comparison, the parallel magnetic susceptibility at 1000 G is also included. Although the two curves are very

100 similar, the parallel susceptibility shows a higher Néel temperature (10.9 K) compared to the perpendicular one (7.9 K), indicative of the b-axis as the easy axis. The straight 1/χ versus T curve at above TN follows Curie-Weiss law very well, and the calculated effective magnetic moment (7.9 B) is similar to that found for the parallel orientation.

2.5

2.0

1.5

1.0 ', emu/mol

 0.5

0.0 0 1 2 3 4 5 6 7 Field, T Figure 6.8 Field dependence of AC magnetization of EuMgSn at 4.2 K (AC frequency 1 Hz).

The magnetic susceptibility versus temperature data for EuMgPb (ZFC and FC) at 100 G are shown in Figure 6.9. When the b axis is parallel to the field, EuMgPb exhibits an antiferromagnetic ordering with TN = 13.9 K. In comparison, the Néel temperature is 8.9 K when the b axis is perpendicular to the field. This result indicates that b axis is the easy axis, similar to EuMgSn. Fitting the inverse susceptibilities at temperature above 30 K results in the effective 2+ magnetic moment of 8.0 B, consistent with the calculated moment of Eu (7.9 B). The positive sign of the Weiss constant (θ = 1.8 K) indicates the presence of ferromagnetic coupling forces at high temperatures, which is believed to arise from the competing interactions of Eu ions which are close to each other. Figure 6.10 shows the anisotropy of the field dependence of magnetization of EuMgPb at 1.8 K with the crystal (b axis) oriented parallel and perpendicular to the field. When the crystal is positioned parallel to the field, a sharp spin reorientation at 3 T is observed. However, the spins are reoriented at 2 T if the b axis is perpendicular to H. This spin orientation anisotropy is likely

101 attributed to the different Eu-Eu distance along the b axis (4.1677(19) Å) versus perpendicular to the b axis (4.20(2) Å). The spin reorientations can be further evidenced by the AC field dependence of magnetization (see Figure 6.11), which shows two sharp peaks at 2 T and 3 T respectively.

0.8 0.8 40 0.6 0.6 0.4 30 0.2 0 10 20 30 40 50 0.4 20 ZFC, H// b FC, H// b ZFC, H b , emu/mol Eu 0.2  FC, H b 10

0.0 0 0 50 100 150 200 250 300 Temperature, K Figure 6.9 Temperature dependence of magnetic susceptibility (χ) for EuMgPb.

2 B/mol Eu  0

-2

H // b axis -4 H  b axis

Magnetization, Magnetization, -6

-8 -6 -4 -2 0 2 4 6 8 Field, T Figure 6.10 Field dependence of magnetization at 1.8 K for EuMgPb

102

6 H // b H  b

4 1.8 K, 1Hz M', emu/mol 2

0 1 2 3 4 5 6 Field, T Figure 6.11 Field dependence of AC magnetization of EuMgPb at 1.8 K (AC frequency 1 Hz).

6.3.5 Resistivity and Magnetoresistance

Standard four-probe resistivity measurements were undertaken in the temperature range 1.9 - 300 K. To study the magnetoresistance of EuMgSn, the measurements were also carried out at an applied field of 2.5 T. These data are shown in Figure 6.12. At temperatures above ~100 K, the difference between zero-field resistivity and that at 2.5 T is negligible, and the resistivity decreases almost linearly with decreasing temperature, typically indicative of metallic behavior. The resistivity of EuMgSn at 300 K (3.8×10-6 Ω·m) lies in the metallic range (10-7-10-1 Ω·m),168 and it is several orders of magnitude smaller than that of CaMgSi (1.95×10-2 Ω·m),51 consistent with the expected trend of metallicity increasing as Ca is replaced by Eu and as Si is replaced by Sn. At temperatures below ~100 K, a divergence between the sample resistivity at 2.5 T and at zero field can be observed (that is, magnetoresistance). Under an applied field, resistivity drops in a sharper slope until the magnetic ordering temperature of ~9.3 K, at which point the resistivity falls rapidly to 9.2×10-7 Ω·m at 1.9 K. In the zero field case, the resistivity decreases at a constant rate until a slope change appears at the ordering temperature of ~10.2 K. Traditionally, compounds with metallic conductivity do not show significant magnetoresistance; metals usually have a magnetoresistance ratio (MR) of less than 2%.169 However, colossal magnetoresistance is often associated with materials that exhibit competing

103 magnetic interactions with associated metamagnetic transitions, or compounds that are close to a metal-insulator transition. EuMgSn exhibits both these characteristics; the structure has two slightly different and competing Eu-Eu interactions, and an ostensibly semiconducting stoichiometry with a pseudo gap at the Fermi level. This results in a large MR of -29.5% at 12 K and an applied field of 2.5 T. The effect of similar competing magnetic interactions is evidenced in EuMgAu and EuMgAg phases (also with the TiNiSi structure), which also exhibit magnetoresistance.170 This effect will be heightened in EuMgSn by the presence of the pseudogap at Ef, putting the phase close to a metal-insulator transition (which was observed for isostructural and isoelectronic CaMgSi).7 For rare earth Zintl phases with a pseudo gap, the few electronic states at the Fermi level provide sufficient mobile electrons to produce metallic conductivity. However, if the localized magnetic moments of the Eu2+ cations are strongly coupled with the conduction electrons, magnetoresistance can occur when the 4f moments order. Accordingly, colossal magnetoresistance has been observed in several rare earth Zintl phases, such as EuIn2M2 (M = As, P), EuGa2M2 (M = As, P), and EuxCa1-xB6, with EuIn2P2 exhibiting a negative MR of -298% at a temperature of 24 K and applied field of 5 T.171-173

H = 0 T H = 2.5 T

3 m 

-6 2.0 2 1.6

Resistivity,10 1.2

1 0.8 0 4 8 12 16 20

0 50 100 150 200 250 300

Temperature, K

Figure 6.12 Temperature dependence of the electrical resistivity of EuMgSn crystal at both 0 T and 2.5 T applied fields. Inset: low temperature data.

104

The temperature dependence of the magnetoresistance of EuMgSn was calculated from the resistivity versus temperature data at zero field and 2.5 T, and is shown in Figure 6.13. The magnitude of the magnetoresistance ratio increases drastically as the temperature falls below 100 K, with a maximum of -29.5% at 12 - 16 K. This is consistent with the report that the highest MR value is often observed near the magnetic ordering temperature.171, 174 The field dependence of resistivity at 4.2 K (see Figure 6.14) further indicates how resistivity is affected by the varying field. A valley with the minimal resistivity (1.16×10-6 Ω·m) is observed in the field range of 2.0 - 2.9 T; this is the range at which a metamagnetic transition is indicated by the DC and AC magnetization data shown in Figures 6.7 and 6.8. The peak magnetoresistance for EuMgSn is found at the combination of temperature and field that promotes a metamagnetic transition from an antiferromagnetic to ferromagnetic ordered state. The induced ferromagnetic ordering of europium spins reduces the effect of spin scattering on the conduction electrons, minimizing resistivity.

-5

-10 -26 -15

-20 -28

-25 Magnetoresistance ratio, % -30 0 4 8 12 16 20 -30

0 50 100 150 200 250 300 Temperature (K)

Figure 6.13 Temperature dependence of magnetoresistance ratio (MR) for EuMgSn at an applied field of 2.5 T. Inset: low temperature data.

The temperature-dependent resistivity data of EuMgPb at zero field and 4 T are shown in Figure 6.15. Similar to the behavior of EuMgSn, the high temperature resistivity (above 50 K) rises with temperature, indicating the metallic character of EuMgPb. The resistivity at 300 K is

105

2.2×10-6 Ω·m, which is lower than that of EuMgSn (3.8×10-6 Ω·m). EuMgPb also shows magnetoresistance at low temperatures (below 50 K) and the maximum MR value of ~24% is achieved at 13.9 K, at which temperature the antiferromagnetic ordering occurs (see Figure 6.16).

1.5

1.4 m 

-6 1.3

Resistivity,10 1.2 4.2 K

1.1 0 20000 40000 60000 Field, G Figure 6.14 Field dependence of resistivity for EuMgSn at 4.2 K.

2.4

2.0

cm 1.6   

, 1.2 0 T  4 T 0.8

0.4 0 50 100 150 200 250 300

Temperature, K

Figure 6.15 Temperature-dependent electrical resistivity of EuMgPb at 0T and 4T

106

-10

-20

% Magnetoresistance,

0 50 100 150 200 250 300 Temperature, K Figure 6.16 Temperature-dependent magnetorisistance of EuMgPb (4T)

In order to obtain more information on the magnetoresistance, the resistivity of EuMgPb crystals between 1.8-30 K was measured with variable fields 0.5 T, 1T, 2T and 3T. The result is shown in Figure 6.17. It is obvious that the MR increases with increasing magnetic field and exhibits the largest values at 4 T. For both orientations, the MR values are very small in the temperature range with the field up to 1 T due to the small magnetization as shown in Figure 6.10. However, when the field is above 2 T and the spin reorientation has finished, the MR values obviously increased.

7 10 H // b H b 9 6 8 cm cm   

 5 0 T

 7 0T ,  0.5 T

 0.5T , 1 T  1T 2 T 6 2T 4 3 T 3T 4 T (b) (a) 5 4T 3 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Temperature, K Temperature, K Figure 6.17 Temperature-dependent electrical resistivity of EuMgPb at different fields below 30 K. (a) H // b; (b) H⊥b.

107

The trend of MR change with the field can be seen more clearly from the calculated temperature variable MR in Figure 6.18. It is noteworthy that the MR changed from negative to positive at around 7.5 K when the samples were cooled down. In addition, the positive MR values were only obtained at below 2 T in the case of H // b and below 3 T in the case of H⊥b. The reason is still unclear but it may be related to the spin ordering at low temperatures.

10 (a)

-10

0.5T -20 1T

Magnetoresistance, % Magnetoresistance, H // b 2T 3T 4T -30 0 5 10 15 20 25 30 Temperature, K

10 (b)

-10

0.5 T -20 1 T 2 T

Magnetoresistance, % Magnetoresistance, H  b 3 T 4 T -30 0 5 10 15 20 25 30 Temperature, K Figure 6.18 Temperature-dependent magnetoresistance of EuMgPb at different fields below 30 K. (a) H // b; (b) H⊥b.

108

6.3.6 Thermoelectric Power of EuMgPb

Figure 6.19 shows the thermoelectric power of EuMgPb as a function of temperature. The closely linear dependence also indicates the metallic character of EuMgPb. At room temperature, the thermoelectric power is about 25 V/K, which is comparable to those of many intermetallic compounds. Considering the relatively simple structure, EuMgPb likely has low thermal resistivity and is not likely to be a good thermoelectric material.

30 Cooling (3k/min) 25 Warming (3K/min) EuMgPb

20 V/K)

 15

S ( 10

0 50 100 150 200 250 300 T (K)

Figure 6.19 Temperature dependence of the thermoelectric power for EuMgPb

6.4 Conclusion Reactions of tin (or lead) and europium in Mg/Al (or Mg/Ag) flux have yielded large EuMgTt (Tt=Sn, Pb) single crystals, which are difficult to obtain from traditional solid state synthesis. Although EuMgTt (Tt=Sn, Pb) can be temptingly considered as rare earth Zintl phases based on the stoichiometry, DOS calculations and transport measurements reveal that both have metallic character with a pseudo gap at the Fermi level. The low number of carriers are likely coupled to the localized Eu2+ moments and strongly scattered by them. Therefore, reducing spin scatter by inducing a ferromagnetic ordering of these moments will have a large effect on the resistivity of the compound. Accordingly, large magnetoresistance is observed at low

109 temperature and applied fields sufficient to force a metamagnetic transition from antiferromagnetic to ferromagnetic ordering.

110

CHAPTER SEVEN

RFe2MgxAl8-x (R = La-Nd and Sm; x≤1): FLUX SYNTHESIS, STRUCTURE, MAGNETIC AND ELECTRICAL PROPERTIES

7.1 Introduction

Intermetallic aluminides CeT2X8 (T = Fe, Co; X = Al, Ga) have been of great recent interest due to the observation of Kondo effects in these phases. CeFe2Al8 crystallizes in an orthorhombic structure with space group Pbam, as first characterized by Yarmoljuk et al.30 57 Neither Ce nor Fe shows magnetic ordering based on magnetic measurements, Fe MÖssbauer 31,32 spectra and neutron diffraction of CeFe2Al8 and LaFe2Al8. Hybridization between Ce 4f electrons and the conduction electrons leads to a metallic Fermi-liquid ground state, as characterized by the electrical resistivity, thermoelectric power and heat capacity. 33-35

Notably, all the CeT2X8 compounds reported so far were synthesized by direct melting of elements in the stoichiometric ratio, and the characterization of some physical properties can be hindered by the lack of single crystal phases. Compared with the traditional solid state synthesis, the metal flux method facilitates the growth of intermetallics as large single crystals. Previously, we reported the synthesis of intermetallic phases containing middle rare earth ions such as

R5(Mg/Al)5Fe4(Al/Si)18 (R=Gd, Dy and Y) and EuMgSn grown in Mg/Al flux (1:1 mol ratio with a melting point of ~470 ° C ). 115,175 The production of large single crystals enabled us to find interesting antiferromagnetic ordering and magnetoresistance behaviors in these structures. In the present work, we synthesized single crystals of CeFe2MgxAl8-x and LaFe2MgxAl8-x in Mg/Al flux. Mg was incorporated into the structure on an original Al site. Furthermore, we successfully expanded the synthesis to Pr, Nd and Sm analogs, which have never been reported previously.

7.2 Experimental Methods

7.2.1 Synthesis

Reactants were used as received: Mg and Al metal slugs (99.95%), Fe powders (99+%) from Alfa Aesar; Si (99+%), powders from Strem Chemicals. The detailed synthesis process can be found in our previous paper.14 The elements Mg/Al/Si/Fe/R (R = La, Ce, Pr, Nd, Sm) were initially weighed out in a mmol ratio of 15/15/2/1/1. Subsequently, the highest product yield was

111 obtained by varying reactant ratios and reactions were then carried out in niobium crucibles to produce relatively pure crystals for further physical characterization.

7.2.2 Elemental Analysis

7.2.3 X-ray Diffraction

Table 7.1; Table 7.2 shows atom positions and isotropic thermal parameters for LaFe2MgxAl8-x. Further data for other four analogs can be found in supporting information (Table 7.3 - 7.7). During the refinement, assignment of rare earth and iron sites were straightforward; all lighter element sites (Mg and Al) were initially assigned as aluminum, but assignments were modified based on bond length considerations and elemental analysis. In the final refinement cycles, occupancies of all sites were allowed to vary, but all appeared fully occupied (100 +/- 1%). Powder X-ray diffraction data were collected on a PANalytical X’Pert PRO with a Cu Kα radiation source in the temperature range of -160° C to room temperature.

112

Table 7.1 Crystallographic data and collection parameters for RFe2MgxAl8-x (R = La-Nd and Sm)

LaFe2MgxAl8-x CeFe2MgxAl8-x PrFe2MgxAl8-x NdFe2MgxAl8-x SmFe2MgxAl8-x

Crystal system Orthorhombic

Space group Pbam

a = 12.6060(6) a = 12.546(2) a =12.5309(8) a = 12.522(2) a = 12.4860(8) Cell parameters, b = 14.4369(7) b = 14.422(2) b =14.3804(9) b = 14.417(2) b = 14.3996(9) Å c = 4.0653(2) c = 4.0551(5) c =4.0430(2) c = 4.0381(6) c = 4.0202(3)

V, Å3 739.85 733.78 728.55 729.04 722.81

Z 4 Calc.Density 4.164 4.209 4.247 4.274 4.367 (g/cm3) 2Theta (max) 56.56 56.30 56.41 56.44 56.39

Radiation Mo Kα

Temperature (K) 290

Reflections 8398 8223 8243 7870 8176 Unique 1006 996 987 995 974 reflections Data/parameters 1006/69 996/ 69 987/69 995/69 974/69

Mu (mm-1) 10.35 10.82 11.34 11.77 12.81

R(int) 0.0283 0.0237 0.0241 0.0326 0.0214

a R1/wR2 0.0152/0.0334 0.0148/0.0338 0.0129/0.0259 0.0192/0.0563 0.0123/ 0.0250 (I>2(I))

R1/wR2 (all data) 0.0180/0.0344 0.0159/0.0342 0.0162/0.0268 0.0216/0.0572 0.0153/0.0258 Largest diff peak 0.781/-0.489 0.730/ -0.619 0.441/ -0.556 1.237/-1.761 0.539/ -0.546 and hole (e·Å-3) a 2 2 2 2 2 1/2 R1=(|Fo|-|Fc|)/|Fo|; wR2=[[w(Fo - Fc ) ]/(w|Fo| ) ]

113

Table 7.2 Atom positions and isotropic thermal parameters for LaFe2MgxAl8-x.

a Wyckoff Site x y z Ueq

La1 4g 0.33957(7) 0.31875(8) 0 0.0122(3)

Fe1 4g 0.14641(5) 0.09900(7) 0 0.0095(6)

Fe2 4g 0.03342(1) 0.40944(3) 0 0.0104(6)

Mg/Al1 4g 0.33404(3) 0.04683(1) 0 0.0097(1)

Al1 2d 0 0.5 0.5 0.0061(3)

Al2 4h 0.33272(3) 0.49371(6) 0.5 0.0089(9)

Al3 2a 0 0 0 0.0078(9)

Al4 4h 0.02555(7) 0.13243(2) 0.5 0.0095(5)

Al5 4h 0.15794(5) 0.38050(2) 0.5 0.0108(3)

Al6 4g 0.09285(5) 0.25461(5) 0 0.0068(8)

Al7 4h 0.23284(6) 0.17217(1) 0.5 0.0113(3)

Al8 4h 0.45151(7) 0.17861(2) 0.5 0.0088(4) a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

Table 7.3 Atom positions and isotropic thermal parameters for CeFe2MgxAl8-x.

a Wyckoff Site x y z Ueq Ce1 4g 0.33980(5) 0.31887(3) 0 0.0116(1) Fe1 4g 0.14698(9) 0.09863(7) 0 0.0083(8) Fe2 4g 0.03389(1) 0.40836(5) 0 0.0084(2) Mg/Al1 4g 0.33483(5) 0.04659(8) 0 0.0087(8) Al1 2d 0 0.5 0.5 0.0045(9) Al2 4h 0.33258(4) 0.49285(4) 0.5 0.0065(1) Al3 2a 0 0 0 0.0046(9) Al4 4h 0.02423(6) 0.13234(5) 0.5 0.0079(6) Al5 4h 0.15910(6) 0.37904(7) 0.5 0.0089(1) Al6 4g 0.09350(5) 0.25411(5) 0 0.0049(4) Al7 4h 0.23319(1) 0.17338(1) 0.5 0.0094(3) Al8 4h 0.45130(4) 0.17944(8) 0.5 0.0077(1)

114

Table 7.4 Atom positions and isotropic thermal parameters for PrFe2MgxAl8-x.

a Wyckoff Site x y z Ueq Pr1 4g 0.33982(9) 0.31905(8) 0 0.0137(8) Fe1 4g 0.14626(6) 0.09887(4) 0 0.0104(1) Fe2 4g 0.03371(8) 0.40838(4) 0 0.0102(3) Mg/Al1 4g 0.33436(7) 0.04673(1) 0 0.0097(4) Al1 2d 0 0.5 0.5 0.0061(4) Al2 4h 0.33272(9) 0.49290(1) 0.5 0.0085(6) Al3 2a 0 0 0 0.0075(2) Al4 4h 0.02392(7) 0.13246(1) 0.5 0.0092(8) Al5 4h 0.15929(9) 0.37918(6) 0.5 0.0108(9) Al6 4g 0.09339(5) 0.25440(1) 0 0.0070(9) Al7 4h 0.23293(9) 0.17360(4) 0.5 0.0099(3) Al8 4h 0.45094(9) 0.17961(7) 0.5 0.0089(1)

Table 7.5 Atom positions and isotropic thermal parameters for NdFe2MgxAl8-x.

a Wyckoff Site x y z Ueq

Nd1 4g 0.34044(8) 0.31897(5) 0 0.0135(1)

Fe1 4g 0.14741(6) 0.09864(5) 0 0.0084(7)

Fe2 4g 0.03375(7) 0.40884(1) 0 0.0091(5)

Mg/Al1 4g 0.33472(8) 0.04665(6) 0 0.0098(7)

Al1 2d 0 0.5 0.5 0.0062(1)

Al2 4h 0.33284(2) 0.49268(8) 0.5 0.0074(3)

Al3 2a 0 0 0 0.0072(4)

Al4 4h 0.02446(5) 0.13239(3) 0.5 0.0084(9)

Al5 4h 0.15982(3) 0.37911(3) 0.5 0.0091(2)

Al6 4g 0.09415(6) 0.25450(7) 0 0.0070(6)

Al7 4h 0.23376(7) 0.17338(5) 0.5 0.0102(1)

Al8 4h 0.45152(3) 0.17984(4) 0.5 0.0085(3)

115

Table 7.6 Atom positions and isotropic thermal parameters for SmFe2MgxAl8-x.

a Wyckoff Site x y z Ueq Sm1 4g 0.34066(8) 0.31906(1) 0 0.0145(1) Fe1 4g 0.14765(1) 0.09857(2) 0 0.0087(9) Fe2 4g 0.03396(3) 0.40863(5) 0 0.0090(4) Mg/Al1 4g 0.33492(8) 0.04668(3) 0 0.0098(8) Al1 2d 0 0.5 0.5 0.0064(9) Al2 4h 0.33257(9) 0.49247(5) 0.5 0.0080(5) Al3 2a 0 0 0 0.0065(4) Al4 4h 0.02424(5) 0.13260(1) 0.5 0.0086(7) Al5 4h 0.16032(1) 0.37877(7) 0.5 0.0100(7) Al6 4g 0.09448(1) 0.25432(2) 0 0.0065(6) Al7 4h 0.23406(9) 0.17379(3) 0.5 0.0101(3) Al8 4h 0.45138(7) 0.18031(3) 0.5 0.0080(9)

Table 7.7 Bond lengths (Ǻ) in RFe2MgxAl8-x (R = Ce -Nd and Sm).

Bond La Ce Pr Nd Sm Fe(1) - Mg(1) 2.483(1) 2.475(1) 2.475(1) 2.464(2) 2.4557(9) Fe(1) - Al(4)×2 2.5858(6) 2.5923(6) 2.5828(6) 2.585(1) 2.5799(6) Fe(1) - Al(6) 2.3454(9) 2.3399(9) 2.3322(9) 2.343(1) 2.3385(8) Fe(1) - Al(7)×2 2.5367(6) 2.5386(6) 2.5341(6) 2.531(1) 2.5256(6) 2.591(1)/ 2.580(1)/ 2.580(1)/ 2.573(2)/ 2.5668(9)/ Fe(2) - Mg(1)×2 2.592(1) 2.584(1) 2.586(1) 2.579(2) 2.5742(9) Fe(2) - Fe(2) 2.7478(9) 2.7778(8) 2.7678(8) 2.762(1) 2.7650(8) Fe(2) - Al(1)×4 2.4534(3) 2.4576(3) 2.4498(2) 2.4462(5) 2.4396(2) Fe(2) - Al(5)×2 2.6019(6) 2.5995(6) 2.5959(6) 2.598(1) 2.5911(6) Fe(2) - Al(6) 2.3577(9) 2.3472(9) 2.3374(9) 2.350(1) 2.3472(8) Fe(2) - Al(8)×2 2.6102(6) 2.6056(6) 2.6007(6) 2.602(1) 2.5968(6) Mg(1) - Al(1)×4 2.9933(7) 2.9749(7) 2.9734(7) 2.968(1) 2.9558(6) Mg(1) - Al(2)×2 3.024(1) 3.0215(9) 3.0123(9) 3.015(1) 3.0044(9) Mg(1) - Al(5) 3.147(1) 3.154(1) 3.1456(1) 3.147(2) 2.9558(6) Mg(1) - Al(7)×2 3.007(1) 3.0151(9) 3.0061(9) 3.004(1) 2.9969(9) Mg(1) - Al(8)×2 3.154(1) 3.1501(9) 3.1422(9) 3.148(1) 3.1399(9)

116

7.2.4 Solid State 27Al NMR

27Al MAS NMR spectra were collected on a Varian/Inova 500WB spectrometer (11.7 T) 27 with resonance frequencies of 130.46 MHz. The Al shifts was referenced to 1M Al(NO3)3.

Crystals of LaFe2MgAl7 were ground with NaCl in a 1:1 ratio by volume in a glove box and the powder was packed into a 4 mm zirconia rotor sealed with airtight screw caps. Single pulse acquisition was applied with a short RF pulse less than 15o. The spinning speed was 12 kHz and the recycle delay was 0.3 s.

7.2.5 Electronic Structure Calculations

Density of state (DOS) calculations on LaFe2MgxAl8-x and LaFe2Al8 were performed with tight binding - linear muffin tin orbitals - atomic sphere approximation (TB-LMTO-ASA) 58 program package. The calculation was based on the LaFe2MgxAl8-x structure parameters determined by single X-ray diffraction data. Six empty Wigner-Seitz spheres were needed to fill the empty space in the structure. The following radii of atomic spheres were used: r(La) = 3.88 Å, r(Fe) = 2.56/2.59 Å, r(Mg) = 2.88 Å, r(Al) = 2.56-3.02 Å, r(E) = 1.28-1.68 Å. The basis set contains La (6s, 5p, 4f), Fe (4s, 4p, 3d), Mg(3s, 3p) and Al (3s, 3p) with La (6p), Mg(3d) and Al (3d) being downfolded. The calculation was made for 160 κ points in the irreducible Brillouin zone. Integration over the Brillouin zone was performed by the tetrahedron method.59

7.2.6 Magnetic Properties

Magnetic measurements were carried out on a Quantum Design SQUID Magnetic Property Measurement System. Clean crystals were selected and held between two strips of kapton tape. Temperature dependence of magnetic susceptibility data were collected between 1.8 K and 300

K. A magnetic field of 1000 G was applied for PrFe2MgxAl8-x and NdFe2MgxAl8-x, and 1 T for

LaFe2MgxAl8-x, CeFe2MgxAl8-x and SmFe2MgxAl8-x. The magnetic susceptibility of

LaFe2MgxAl8-x was utilized to be the background susceptibility due to the non-magnetic character of La ions. The susceptibility of LaFe2MgxAl8-x was accordingly substracted from those of other four analogs to fit the Curie-Weiss law. Field-dependent magnetization data were collected at 1.8 K in the field range to 7 T; crystals were oriented with c-axis parallel to the applied field.

117

7.2.7 Electrical Resistivity

Electrical resistivity measurements were conducted with a conventional four-probe method on a Physical Property Measurement System (PPMS) by Quantum Design. Single crystals were put on a sample holder puck and four 25 micron diameter gold wires were adhered to the crystal surface with silver paste. Resistivity data were taken from 2 - 300 K with an applied excitation current of 5 mA.

7.3 Results and Discussion

7.3.1 Synthesis

Figure 7.1 SEM image of a single crystal for NdFe2MgxAl8-x

RFe2MgxAl8-x (R = La-Nd and Sm) needle-shape single crystals were grown in excess

Mg/Al flux. The SEM image of a crystal of NdFe2MgxAl8-x phase is shown in Figure 7.1. The neat surface indicates that products can be separated from the flux above the melting point of Mg/Al flux. No apparent impurity peaks were observed from the powder X-ray diffraction pattern of NdFe2MgxAl8-x in the temperature range of -160° C to room temperature (see Figure 7.2). The presence of silicon as reactant was found to increase the yield though silicon was not incorporated into the structure. Reactions of Mg/Al/Fe/R can also form the title phases. The optimal Mg/Al/Si/Fe/R ratios are 15/15/2/1/2 for R=La and Ce, and 15/15/2/0.5/1 for R=Pr, Nd

118 and Sm. Subsequently, reactions with the optimal ratios were accomplished in Nb crucibles and higher purity samples were obtained for further magnetic and electrical measurements.

NdFe MgAl 2 7 Exp, -160 C

Exp, -120 C

Exp, -80 C

Exp, -40 C Intensity

Exp, 20 C

Calculated

10 20 30 40 50 60 70 2 degree

Figure 7.2 Variable-temperature powder X-ray diffraction pattern of NdFe2MgxAl8-x

7.3.2 Structure

RFe2MgxAl8-x (R = La-Nd and Sm) crystallize in the CaCo2Al8 structure type with space group Pbam. Previous reports on CeFe2Al8 and LaFe2Al8 involved synthesis of polycrystalline samples synthesized by traditional stoichiometric reactions for the study of heavy fermion properties. Here we successfully incorporated magnesium to the 4g Wyckoff site (yellow atoms in Figure 7.3), which is originally occupied by aluminum in LaFe2Al8 and CeFe2Al8. In addition, we also expanded the structure to other early rare earth analogs (Pr, Nd and Sm). If viewed from b direction, the layers of rare earth and magnesium atoms are separated by aluminum layers.

As shown in Figure 7.3, RFe2MgxAl8-x (R = La-Nd and Sm) features FeAl6 polyhedra, which are highlighted in red. All the FeAl6 clusters contain centered iron atoms in a trigonal prismatic coordination of aluminum atoms, monocapped by an aluminum atom on one side and share Al trigonal faces in the a-b plane, forming chains running along the c direction. This is 115 similar to the chains of FeAl6 clusters seen in R5(MgAl)5Fe4(Al/Si)18 (R=Gd, Dy and Y) and

119

R3Fe(Mg/Al)4Si2 (see Chapters 3 and 4). The bond lengths in the Fe-Al-Fe chain are comparable for these structures (for instance, 2.3345(5) Å for LaFe2MgxAl8-x vs. 2.373(1) Å for

Dy5(MgAl)5Fe4(Al/Si)18).

Figure 7.4 displays the coordination of the electropositive rare earth and magnesium atoms. The rare earth atom is drum coordinated by 13 electronegative aluminum atoms at a distance of

120

3.1820(9) to 3.3070(2) Å, as shown in Figure 3a. Magnesium also sits in a drum coordination environment composed of ten aluminum atoms on the top and bottom surfaces of the drum and three iron atoms forming the drum shoulder. The distance between Mg and Al is in the range of 2.9942(8) - 3.153(1) Å, in agreement with the literature Mg-Al bond lengths (2.77 - 3.44 Å).176-179 Refining this position as occupied by Mg instead of Al does apparently decrease the thermal parameter (Ueq) from 0.01619 for Al occupancy to 0.0097 for Mg occupancy in

LaFe2MgAl7. Parameters for other analogs were summarized in Table 7.8. The large distance between rare earth and magnesium (3.927 Å at minimum) also favors the site assignment of Mg and answers the question why magnesium only occupies the particular 4g sites instead of other aluminum sites. However, considering the close X-ray scattering factors of magnesium and aluminum, it cannot be ruled out that this 4g site is likely mixed occupied by Mg and Al, so a general stoichiometry LaFe2MgxAl8-x is used. a) b)

Figure 7.4 Coordination environments of a) rare earth atoms and b) Mg in the RFe2MgxAl8-x (R = La-Nd or Sm) structure.

Table 7.8 Thermal parameters for the Mg/Al 4g Wyckoff site occupied by Mg or Al separately

LaMgFe2Al7 CeMgFe2Al7 PrMgFe2Al7 NdMgFe2Al7 SmMgFe2Al7

Site occupancy 0.998 0.991 1.014 1.01 0.956

Ueq(Mg)/R1(Mg) 0.00971/0.0194 0.00917/0.0233 0.00944/0.0154 0.00988/0.0237 0.00811/0.0417

Ueq(Al)/R1(Al) 0.01619/0.0200 0.01564/0.0238 0.01600/0.0160 0.001629/0.0242 0.01465/0.0423

121

7.3.3 Electronic Structure Calculations

The total and partial density of states (DOS) of LaFe2MgAl7 and LaFe2Al8 calculated with

TB-LMTO-ASA is shown in Figure 7.5. LaFe2MgAl7 contains one less valence electron than

LaFe2Al8 due to the presence of Mg, which shifts the DOS of LaFe2MgAl7 slightly towards higher energy and more states can be observed at the Fermi level (EF) compared to LaFe2Al8. A sharp peak at ~4 eV corresponds to the states of electropositive lanthanum ions. Iron states lie in the energy range between -3 and 0.7 eV across the Fermi level (EF), leaving ~23 states per eV cells at the EF for LaFe2MgAl7 (~20 states per eV cells for LaFe2Al8). The high number of states at EF contributes to the hybridization between R-4f and Fe-3d electrons, which will affect the magnetization of the structure. Aluminum derived states are widely located below and above the

EF and the contribution of Mg is negligible. The presence of pseudo gaps at ~0.7 eV for

LaFe2MgAl7 and ~0.5 eV for LaFe2Al8 are indicative of polar intermetallic compounds due to the partial polarities of the electropositive and electronegative ions.

90 LaFe MgAl 2 7 La Fe 60 Mg Al

0 90 -4 -2 0 2 4 LaFe Al 2 8 DOS, La Fe states/eV cells 60 Al

-4 -2 0 2 4 Energy, eV

Figure 7.5 Total and partial density of states of LaFe2MgAl7 and LaFe2Al8

122

7.3.4 Solid State 27Al NMR

27 The solid state Al MAS NMR of LaFe2MgxAl8-x is shown in Figure 7.6. Measurements on other rare earth analogs were not performed due to the presence of 4f electrons. Powder X-ray diffraction reveals the high purity of LaFe2MgxAl8-x sample (Figure 7.7). A metallic broad peak at ~1200 ppm is observed in Figure 5, corresponding to all the aluminum content in

LaFe2MgxAl8-x. The eight aluminum sites in the structure have similar coordination environment and hence are difficult to differentiate in the NMR data. The aluminum mixing on the Mg/Al 4g Wyckoff site will also contribute to this broad peak. Many reported intermetallic compounds 180 show Knight peaks in the range of 1100-1300 ppm like Al85Ni11Y4 and Y5(MgAl)5Fe4AlxSi18-x 115 . This Knight shift is also in accordance with the metallic character of LaFe2MgxAl8-x as shown by the DOS at the EF. (see Figure 7.5).

1800 1600 1400 1200 1000 800 600 ppm 27 Figure 7.6 Solid state Al NMR of LaFe2MgxAl8-x

LaFe MgAl 2 7

Experimental Intensity

Calculated

10 20 30 40 50 60 70 80 2degree

Figure 7.7 Powder X-ray diffraction pattern of LaFe2MgxAl8-x 123

7.3.5 Magnetic Properties

Fe ions are not magnetic in this structure, as indicated by the temperature-independent Pauli paramagnetism of LaFe2MgxAl8-x shown in Figure 7.8. This is consistent with the magnetic study 31,32 for LaFe2Al8 and CeFe2Al8 in the literature. Accordingly, the magnetic susceptibility of

LaFe2MgxAl8-x was subtracted from that of RFe2MgxAl8-x (R=Ce, Pr, Nd or Sm) in order to fit each to the Curie-Weiss law, and the resulting temperature-dependent magnetic susceptibilities of these four compounds are exhibited in Figure 7.9.

0.0006

0.0005

0.0004 emu/mol  0.0003

0.0002 0 50 100 150 200 250 300 Temperature, K

Figure 7.8 Temperature-dependent magnetic susceptibility of LaFe2MgxAl8-x

The temperature-dependent magnetic susceptibility for CeFe2MgxAl8-x is shown in Figure 7.9a. The Zero-field-cooled (ZFC) and field-cooled (FC) curves overlap well when a magnetic field of 1T was applied. The linear temperature dependence of inverse susceptibility obeys the

Curie-Weiss law above 150 K with the calculated magnetic moment of ~2.4 B, close to the 3+ theoretical effective value of Ce (2.5 B). The temperature variable magnetic susceptibilies of Pr, Nd or Sm analogs are shown in Figure 7.9b, 7.9c and 7.9d respectively. All three phases exhibit antiferromagnetic transition and the Néel temperatures are 2.8 K (PrFe2MgxAl8-x), 7.8 K (NdFe2MgxAl8-x) and 12 K

(SmFe2MgxAl8-x). The inverse susceptibility data for PrFe2MgxAl8-x and NdFe2MgxAl8-x can be well fitted to the Curie-Weiss law at temperatures above 100 K and the calculated magnetic

124 moments (~3.7 B for PrFe2MgxAl8-x and ~3.5 B for NdFe2MgxAl8-x) are close to their theoretical value (3.6 B). The positive Weiss constants of 44 K for PrFe2MgxAl8-x and 47 K for

NdFe2MgxAl8-x is likely due to the competing magnetic interaction at high temperature. The magnetic susceptibility data for SmFe2MgxAl8-x does not show Curie-Weiss behavior at high temperatures. This is often the case for samarium containing phases, due to mixing of the ground state with low-lying excited states for the Sm3+ ion (van vleck behavior).

0.012 0.6 160 600 a b 120 1/ 1/

 0.4  , mol Ce ions/emu Ce mol , 0.008 ions/emu Pr mol , 400 80 X(ZFC) 0.2 X(ZFC) X(FC) X(FC) 40 0.004

200 , emu/mol Pr ions  , emu/mol Ce ions  0.0 0

0.000 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Temperature, K Temperature, K

0.15 800 0.005 160 d

c 1/ 0.004 0.10 1/ 120  600 , mol Nd ions/emu Nd mol ,  , mol Sm ions/emu Sm mol ,

0.003 X(ZFC) ZFC 80 X(FC) 0.05 400 FC 0.002 40 , emu/mol Sm ions , emu/mol Nd ions   0.00 200 0.001 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Temperature, K Temperature, K

Figure 7.9 Temperature dependence of magnetic susceptibilities of (a) CeFe2MgxAl8-x, (b) PrFe2MgxAl8-x, (c) NdFe2MgxAl8-x and (d) SmFe2MgxAl8-x.

Figure 7.10 displays the field dependence of magnetization of RFe2MgxAl8-x (R=Ce, Pr,

Nd and Sm) at 1.8 K. CeFe2MgxAl8-x and SmFe2MgxAl8-x present linear magnetization with the field, leaving magnetization values of 0.22 B and 0.06 B respectively at 7 T, which are still quite far from being saturated. The low magnetic response for CeFe2MgxAl8-x and

SmFe2MgxAl8-x is also reflected by their low magnetic susceptibilities compared to

NdFe2MgxAl8-x and PrFe2MgxAl8-x, as indicated in Figure 7.9. The low magnetization for Ce

125 phase is likely attributed to the hybridization between 4f electrons and the conduction electrons, which disabled the localized spin moments. NdFe2MgxAl8-x also shows linear magnetization at fields below 4 T and then a strong spin reorientation occurs, as indicated by the sharp jump at ~4

T, but the saturation was not achieved at 7 T. PrFe2MgxAl8-x exhibits metamagnetic behavior and the magnetization was almost stable from 4 T but not saturated at 7 T.

1 B/mol R  0

-1 CeFe MgAl 2 7 PrFe MgAl -2 2 7 NdFe MgAl 2 7 Magnetization, SmFe MgAl -3 2 7

-8 -6 -4 -2 0 2 4 6 8 Field, T

Figure 7.10 Field dependence of magnetization for RFe2MgxAl8-x (R = Ce, Pr, Nd or Sm)

7.3.6 Electrical Resistivity

Figure 7.11 shows the temperature-dependent electrical resistivity of RFe2MgxAl8-x (R= La - Nd, Sm) in the temperature range of 2-300 K and the detailed low temperature data (2-60 K) are displayed in Figure 7.11b-f respectively. All five phases exhibit metallic behavior at temperatures above 50 K, with resistivity rising linearly along the temperature. No anomaly was observed for CeFe2MgxAl8-x and NdFe2MgxAl8-x, similar to the resistivity data reported for 11 CeFe2Al8. Notably, LaFe2MgxAl8-x shows a minimum at ~20 K, which has never been mentioned by the literature on LaFe2Al8. It is unclear whether this ρmin is attributed to the magnesium incorporation or the poor crystal quality, as reflected by its low residual resistivity ratio (RRR) =ρ300K/ρmin = 1.6. It is worth noting that an irregular phononic behavior was 33 observed at ~25 K from the temperature-variable specific heat for LaFe2Al8 and likely

126 correlates to the ρmin of LaFe2MgxAl8-x. The resistivity upturn for PrFe2MgxAl8-x is almost negligible, probably caused by the weak antiferromagnetic ordering at 2.8 K. In comparison,

SmFe2MgxAl8-x exhibits a correlation between the magnetic ordering and electrical conduction. ρ experienced a sharp increase at ~11 K, consistent with its antiferromagnetic ordering at 12 K.

6 Pr 3.90 Pr a cm



-4 3.85 , 10 b  5 0 10 20 30 40 Temperature, K 2.45 Sm

cm cm Sm  2.40

-4 

4 -4

, 10

 2.35 c 0 10 20 30 40

), 10 Temperature, K 

2.08 3 cm Ce 

Ce -4

, 10 2.04  d

0 10 20 30 40 Nd Temperature, K 2 1.00 Nd cm 

Electrical resistivity ( 0.95 -4

, 10 e  La 0.90 1 0 10 20 30 40 Temperature, K 0.70 La cm 

0.69 -4

, 10

0  f 0 50 100 150 200 250 300 0.68 0 10 20 30 40 Temperature, K Temperature, K

Figure 7.11 Temperature variation of electrical resistivity for RFe2MgxAl8-x (R= La-Nd, Sm)

7.4 Conclusion

Polycrystalline CeFe2Al8 and LaFe2Al8 have been widely studied due to the strong hybridization of 4f and conduction electrons arising from the intermediate valence of Ce ions. Here magnesium was successfully incorporated to one aluminum site in the structure through the reaction of R/Fe/Si in Mg/Al flux, leading to CeFe2MgxAl8-x. Three analogs containing Pr, Nd and Sm were also synthesized. The presence of magnesium was found to tune the DOS at Fermi

127 level based on the result of electronic structure calculation. These five phases exhibit apparently different magnetic properties: La and Ce phases are paramagnetic while Pr, Nd and Sm show antiferromagnetic ordering. Typically, PrFe2MgxAl8-x exhibits field-dependent metamagnetic transition and spins of NdFe2MgxAl8-x undergoes a sharp reorientation at ~ 4T. The electrical resistivity transition of SmFe2MgxAl8-x at ~11 K was correlated to its antiferromagnetic ordering, indicating the apparent effect of localized spins on conduction electrons.

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CHAPTER EIGHT

FUTURE WORK

8.1 Introduction The Mg/Al flux is very productive with respect to the synthesis of rare earth aluminides and silicides, as indicated by the products described in chapter 3 to chapter 7. In addition, many other phases have been synthesized in the Mg/Al flux, which needs to be fully characterized in the future. Beside the reactions in the Mg/Al flux, some preliminary synthesis in other Mg-based binary fluxes such as Mg/Ca and Mg/Ag were also explored. This chapter will give a brief introduction on the phases that require further investigation.

8.2 Er2Fe3Al8Si (Z=4)

8.2.1 Experimental

Er2Fe3Al8Si was produced in the reaction of Mg/Al/Si/Fe/Er with a mmol ratio of 15/15/2/1/1. Reactants were used as received: Mg and Al metal slugs (99.95%), Fe powders (99+%) from Alfa Aesar; Si (99+%), Er powders from Strem Chemicals. The detailed synthesis process was described in chapter 3. Mg is not incorporated into the structure as an efficient diffusion media. A number of reactions with different reactant ratios have been inspected, and single crystals up to 1mm in length and 0.5 mm in diameter were obtained with the optimal reactant ratio Mg/Al/Si/Fe/Er = 15/15/4/1/2. Er2Fe3Al8Si sample is very stable to the ambient environment. Attempts to replace Si with Ge lead to another quaternary phase Er3FeAl4Si2. SEM-EDS analysis was performed using a JEOL 5900 scanning electron microscope (30 kV acceleration voltage) equipped with PGT Prism energy dispersion spectroscopy software. Figure

8.1 shows the SEM image of one Er2Fe3Al6+xSi3-x single crystal, which was cut off and left the internal surface exposed. The EDS result indicates that the atomic ratio of Er/Fe/Mg/Al/Si is 37/43/0/17/3%. Trace amount of flux is likely attached on the crystal surface although most have been successfully removed through centrifugation at temperature above the melting point of Mg/Al flux.

129

Figure 8.1 SEM image of one selected Er2Fe3Al8Si single crystal.

Single crystal diffraction data were collected at room temperature on a Bruker APEX2 single crystal diffractometer with a Mo Kα radiation source. The structure was solved in orthorhombic space group Cmcm; crystallographic data and collection parameters are shown in

Table 8.1; Table 8.2 shows atom positions and isotropic thermal parameters for Er2Fe3Al8Si. Table 8.3 shows the bond lengths in the structure. Density of states (DOS) were calculated with tight binding-linear muffin tin orbitals-atomic sphere approximation (TB-LMTO-ASA) program package.58 The calculation was based on the

Er2Fe3Al6Si3 structure parameters determined by single X-ray diffraction data. Two empty Wigner-Seitz spheres were needed to fill the empty space in the structure. The following radii of atomic spheres were used: r(Er) = 3.58 Å, r(Fe) = 2.68 Å, r(Mg) = 3.48 Å, r(Al) = 2.69/2.76 Å, r(Si) = 2.74/2.80 Å. The basis set contains Er(6s, 5p), Fe(4s, 3d, 4p), Al(3s, 3p) and Si(3s, 3p), with Er (6p), Al (3d), and Si (3d) being downfolded. The calculation was made for 365 κ points in the irreducible Brillouin zone. Integration over the Brillouin zone was performed by the tetrahedron method.59 Magnetic measurements were carried out on a Quantum Design SQUID Magnetic Property Measurement System. Temperature dependence of magnetic susceptibility data were collected between 1.8 K and 300 K at 100 G. Field-dependent magnetization data were collected at 1.8 K in the field range to 7 T; crystals were oriented with c-axis parallel to the applied field.

130

Table 8.1 Crystallographic data and collection parameters for Er2Fe3Al8Si.

Er2Fe3Al8Si Crystal system Orthorhombic Space group Cmcm a = 12.6034 Cell parameters, Å b = 7.3262 c = 9.2594 V, Å3 854.97 Z 4 Calc.Density (g/cm3) 5.813 2Theta (max) 56.60 Radiation Mo Kα Temperature (K) 290 Reflections 4857 Unique reflections 578 Data/parameters 578/41 Mu (mm-1) 25.35 R(int) 0.0341 a R1/wR2 (I>2(I)) 0.0323/0.0792

R1/wR2 (all data) 0.0342/ Largest diff peak and hole (e·Å-3) 1.267/-6.140 a 2 2 2 2 2 1/2 R1=(|Fo|-|Fc|)/|Fo|; wR2=[[w(Fo - Fc ) ]/(w|Fo| ) ] .

Table 8.2 Atom positions and isotropic thermal parameters for Er2Fe3Al8Si.

Wyckoff a x Y z Occ. Ueq Site Er1 8g 0.335161 0.334127 1/4 0.991 0.01192 Fe1 4a 0 0 0 1.001 0.00681 Fe2 8e 0.326659 0 0 1.003 0.00916 Al1 16h 0.166607 0.167992 0.068769 1.000 0.00712 Al2 8f 0 0.333002 0.551141 0.989 0.00832 Al3 8g 0.106711 0.444095 1/4 0.987 0.00550 Si1 4c 0 0.120796 1/4 0.960 0.01460 a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

131

Table 8.3 Bond lengths in Er2Fe3Al8Si.

Bond Bond distance, Ǻ

Er(1) - Fe(1)×4 3.3394 Er(1) - Fe(2)×4 3.3153/3.3708 Er(1) - Al(1)×6 2.9655 Er(1) - Al(2)×2 3.0329 Er(1) - Al(3)×2 2.9508/2.9898 Er(1) - Si(1) 2.9517 Fe(1) - Al(1)×4 2.5160 Fe(1) - Al(2)×2 2.4857 Fe(1) - Si(1)×2 2.4770 Fe(2) - Al(1)×4 2.4479/2.5159 Fe(2) - Al(2)×2 2.5493 Fe(2) - Al(3)×2 2.4968 Al(1) - Al(1)×2 2.7382/2.7739 Al(1) - Al(2)×2 2.6663 Al(1) - Al(3) 2.7324 Al(1) - Si(1) 2.7090 Al(2) - Al(2) 2.6251 Al(2) - Al(3)×2 2.8035 Al(3) - Al(3) 2.6893 Al(3) - Si(1)×2 2.7260

8.2.2 Structure and Magnetic Property

Er2Fe3Al8Si crystallizes in the orthorhombic Nd2Co3Al9 structure type with a space group Cmcm.181 Viewed down the b axis as shown in Figure 8.2, the structure can be separated into two layers along the ab plane. The iron and aluminum atoms form one layer while erbium, aluminum and silicon atoms form a neighboring layer. In the Fe/Al layer, each Fe atom is coordinated by one zigzaged Al hexgon with a Fe-Al bond lengths in the range of 2.447(9)-2.549(3) Ǻ. In the Er/Al/Si layer, two aluminum atoms and a silicon atom form a trigonal planar cluster, which is then surrounded by six erbium atoms. Though it is difficult to distinguish aluminum from silicon

132 with X-ray diffraction technique, their identification was still attempted. Comparing the thermal parameters of the four Al/Si sites reveals that the three aluminum sites show similar Ueq values

(0.00550-0.00712), while the silicon site corresponds to an Ueq value of 0.01460, which indicates its special thermal stability from other three Al sites. The occupancies of these four Al and Si sites are close to 1, indicating the reasonable assignment.

Figure 8.2 Structure of Er2Fe3Al8Si viewed down the b-axis. Erbium, iron, aluminum and silicon atoms are green, brown, cyan and blue respectively.

The total and partial DOS diagram of Er2Fe3Al8Si is shown in Figure 8.3 and the 4f electrons of erbium ions were treated as the core. The structure exhibits typical characteristics of a polar intermetallic compound. The Er3+ cations have the main contribution to the states above the EF, while 3d orbital of Fe is dominant below the EF, leaving a pseudo gap at or near the EF.

The orbitals from Al and Si are dispersed in the over the whole energy range. Er2Fe3Al8Si has a valence electron count (VEC, per formula unit) of 58. The DOS at the EF for is 12.39 states/eV·cell. The temperature-dependent magnetic susceptibility and inverse magnetic susceptibility data for Er2Fe3Al8Si is presented in Figure 8.4. Paramagnetic behavior over the entire measured temperature range was observed; no magnetic ordering was seen, and there is no splitting between field-cooled (FC) and zero-field cooled (ZFC) data. The FC inverse susceptibility

133 versus temperature follows the Curie-Weiss law well; the fit yields a magnetic moment of 4.64(2)

B per ytterbium ion and a Weiss constant θ = -4.8(1) K. The observed ytterbium moment is in good agreement with the theoretical value of 10.12 B, close to the calculated magnetic moment 3+ Er ions ( 10.6 B). This indicates that the iron electrons are delocalized and do not contribute to the magnetic moment of these phases. Indeed, the Fe atoms are isolated in the Er2Fe3Al8Si structure and the closed Fe-Fe distance is Ǻ, which is too far to induce magnetic ordering.

50 E F total Er 40 Fe Al 30 Si

Density of states, 10

0 -10 -8 -6 -4 -2 0 2 4 6 8 10 Energy, eV

Figure 8.3 Total and partial density of states for Er2Fe3Al8Si

4 25 (a) 8 (b) 3 X/mol Er(ZFC) 20 4 X/mol Er(FC) B  2 15 0

10 emu/mol Er  =9.63 or 10.12  1 eff B -4 Magnetization, Field down

Magnetic susceptibility, 5 Field up -8 0 0

0 50 100 150 200 250 300 -8 -6 -4 -2 0 2 4 6 8 Field, T Temperature, K

Figure 8.4 Magnetic data for Er2Fe3Al8Si. (a) Temperature dependence of magnetic susceptibility and inverse magnetic susceptibility at 100 G. (b) Field dependence of magnetization 1.8 K.

134

8.2.3 Further Discussion

Although Er2Fe3Al8Si is considered as the stoichiometric formula based on the X-ray diffraction data, more synthesis and characterization method are still needed to further confirm the Al/Si ratio. For instance, since no magnesium is present in the structure, some more reactions without magnesium can be tried to see if magnesium is necessary to the formation of Er2Fe3Al8Si such as some reaction of Er/Fe/Si in aluminum flux. In addition, if Er2Fe3Al9 can be synthesized, the bond lengths regarding Al and Si will be compared to those in Er2Fe3Al8Si, which might help understand the occupancies of Al and Si. The synthesis of Er2Fe3Al9 can probably be realized through some reactions like Mg/Al/Fe/Er (Mg/Al as the flux) or Al/Fe/Er (Al as the flux). It is no doubt that neutron diffraction will be a direct way to unveil the Al/Si occupancies just like the neutron analysis for Dy5Mg2.92Fe4Al9.72Si10.36 and Yb2.77FeAl3.72Mg0.28Si2 as discussed in the previous chapters.

8.3 Sm3CaFeC6 (Z=2)

8.3.1 Experimental

Sm3CaFeC6 was produced in the reaction of Mg/Ca/C/CaH2/Sm with a mmol ratio of 5.4/14.6/1/1/1 when some hydride compounds was targeted and Fe is incorporated from the steel crucible. Reactants were used as received: Mg and Al metal slugs (99.95%) from Alfa Aesar, acetylene carbon black (99.99%) from Strem Chemicals, Sm granules (<1 mm, 99.99%) from ARRIS International Corp. The detailed synthesis process is similar as described for reactions in the Mg/Al flux. Mg is not incorporated into the structure as an efficient diffusion media.

Sm3CaFeC6 is very air-sensitive to the ambient environment. The EDS result indicate that the atomic ratio of Sm/Ca/Fe is 72/14/14 atom % and carbon is too light to be seen. SEM-EDS analysis was performed using a JEOL 5900 scanning electron microscope (30 kV acceleration voltage) equipped with PGT Prism energy dispersion spectroscopy software.

Figure 8.5 shows the SEM image of one Sm3CaFeC6 single crystal, which was cut off and left the internal surface exposed. The EDS result indicates that the atomic ratio of Sm/Ca/Fe is 73/13/14%. and carbon cannot be seen due to the light atomic weight. Trace amount of flux is likely attached on the crystal surface although most have been successfully removed through centrifugation at temperature above the melting point of Mg/Ca flux. 135

Figure 8.5 SEM image of one selected Sm3CaFeC6 single crystal.

Single crystal diffraction data were collected for each analog at room temperature on a Bruker APEX2 single crystal diffractometer with a Mo Kα radiation source. The structures were solved in hexagonal space group p6(3); crystallographic data and collection parameters for all the four phases are shown in Table 8.4; Table 8.5 shows atom positions and isotropic thermal parameters for Sm3CaFeC6. Table 8.6 shows the bond lengths in the structure.

8.3.2 Structure Discussion

Sm3CaFeC6 crystallizes in the hexagonal structure with a space group P6(3). Attempt to refine the structure to a space group (P6(3)/m) with higher symmetry leads to the increase of refinement parameters. Figure 8.6a and b shows the structure viewed along c axis and [110] direction respectively. Calcium atoms occupy the corner of the unit cell, forming Ca chains along the c axis. The Ca-Ca distance is only 2.5707(8) Ǻ, which is much shorter compared to the literature bond distances of Ca-Ca (3.4 - 4.4 Ǻ). So the calcium site is only partially occupied by Ca (about 88%) and this explains the instability of the structure when a mirror symmetry perpendicular to the c axis was set. Viewed from the side direction (Figure 8.6b), Samarium, iron and carbon atoms form layers on the ab plane with calcium intercalated among them.

136

Table 8.4 Crystallographic data and collection parameters for Sm3CaFeC6.

Sm3CaFeC6

Crystal system Hexagonal

Space group P6(3) a = 8.518(3) Cell parameters, Å c = 5.141(2) V, Å3 323.14 Z 2 Calc.Density (g/cm3) 6.856 2Theta (max) 56.30 Radiation Mo Kα Temperature (K) 150 Reflections 3649 Unique reflections 518 Data/parameters 518/22 Mu (mm-1) 17.85 R(int) 0.0257 a R1/wR2 (I>2(I)) 0.0176/0.0383

R1/wR2 (all data) 0.0201/ Largest diff peak and hole (e·Å-3) 2.393/-1.467

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

Table 8.5 Atom positions and isotropic thermal parameters for Sm3CaFeC6.

Wyckoff a x Y z Occ. Ueq Site

Sm1 6c 0.664262 0.058986 0.029621 1.00131 0.00788

Ca1 6c 1 0 0.355271 0.87889 0.00561

Fe2 2b 2/3 1/3 0.527927 1.02442 0.00725

C1 6c 0.437405 0.293642 0.517479 1.08189 0.00845

C2 6c 1.269881 0.264032 0.510300 1.07213 0.04702 a Ueq is defined as one-third of the trace of the orthogonalized Uij tensor.

137

Table 8.6 Bond lengths in Sm3CaFeC6.

Bond Bond distance, Ǻ Sm - Sm 3.5551(9) Sm - Fe×9 3.461(6)/3.474(6)/3.114(1) Sm - Ca×4 3.268(1)/3.557(2) Sm - C(1)×4 2.736(6)/2.69(2)/2.681(6)/2.59(2) Sm - C(2)×3 2.64(2)/2.543(7)/2.82(2) Ca - Ca×2 2.5707(8) Ca - C(2)×6 2.41(1)/2.88(1) Fe - C(1)×3 1.809(7) C(1) - C(2) 1.32(1)

Figure 8.6 Structure of Sm3CaFeC6 viewed down the c-axis (a) and [110] direction. Erbium, iron, aluminum and silicon atoms are green, brown, cyan and blue respectively.

138

A typical building block in the structure is FeC3 trigonal planar cluster with Fe atoms at the center, as shown in Figure 8.7a and b. Each Fe-C bond (1.809(7) Å) extends to connect with another carbon atom, giving rise to a Fe-C-C geometry. The bond distances of C-C is 1.32(1) Å, consistent with the C=C bond length (1.33 Å). So it is more suitable to take it as Fe-C=C instead of Fe-C-C. The thermal displacement parameters of the two carbon sites are quite different

(0.00845 vs. 0.04702 Ueq values), attributed to their different coordination environment. Figure 8.3.3c shows the coordination of calcium atoms. Each calcium atom is surrounded by 6 carbon atoms in the bond length range of 2.41(1)/2.88(1) Å and 6 samarium atoms in the bond length range of 3.268(1)/3.557(2) Å. Along the c axis, two other calcium atoms lie on the both sides.

a) b)

Figure 8.7 Fe-C-C cluster viewed down the c-axis (a) and a-axis (b), and the coordination of calcium.

8.3.3 Future Characterization

Sm3CaFeC6 was synthesized from the reaction of C/CaH2/Sm in Mg/Ca flux, which is quite accidental and the role of CaH2 is not very clear. More reactions such as Sm/C/Fe in Mg/Ca flux should be checked. Once the synthesis has been optimized, the physical properties like magnetic

139 behavior might be interesting to investigate. In the structure, Sm ions are close to each other with a bond distance of 3.5551(9) Å, which is likely able to induce some competing magnetic ordering especially considering the Van Vleck bebavior of Sm3+. But Fe ions are quite isolated and are not expected to exhibit interesting magnetic property.

140

CHAPTER NINE

CONCLUSION

The Mg-based binary fluxes exhibit their highly productive character for the synthesis of rare earth intermetallics. This work mainly explored the growth of rare earth silicides and aluminides in Mg/Al (1:1 mmol) flux. Various products can be formed when different rare earth elements are selected. For instance, reactions with the early elements (R = La-Nd, Sm) lead to an orthorhombic structure RFe2MgxAl8-x; Europium and 14 group elements (Si-Pb) in Mg/Al flux can form two rare earth pseudo Zintl phases: hexagonal Eu6Mg17Tt13 (Tt = Si, Ge) and orthorhombic EuMgTt (Tt = Sn, Pb). The reactions concerning the late rare earth elements and yttrium are more complex depending on the selection of silicon or germanium and the reaction ratios, producing three different structural compounds: R5(Mg/Al)5Fe4(Al/Si)18 (R = Gd, Dy, Y),

R3FeAl4-xMgxTt2 (R = Yb, Dy, Er, Y; Tt = Si, Ge) and Er2Fe3Al8Si. Due to the simultaneous presence of Mg/Al/Si, neutron diffraction exhibits its advantage in studying the structures containing these adjacent elements. The single crystal neutron diffraction data of the Dy5(Mg/Al)5Fe4(Al/Si)18 analog distinguished the Mg, Al and Si sites, indicating a stoichiometry of Dy5Mg2.92Fe4Al9.72Si10.36. For Yb3FeAl4-xMgxTt2 phase, neutron diffraction data confirmed the partial incorporation of Mg into one Al site, leading to a formula of

Yb3FeAl3.72Mg0.28Si2. A close study indicates that magnesium can almost always be incorporated into the structure either in a large amount (e.g. R5(Mg/Al)5Fe4(Al/Si)18) or partially occupy some site (e.g.

R3FeAl4-xMgxTt2), so magnesium no only behaves as a flux component but likely contribute to the structure stability. A direct evidence is that similar reactants in both Al flux (frequently studied) and Mg/Al flux usually do not result in similar structures. Study of the magnetic properties of these structures constitutes the main part of the characterization. Due to the close distances of rare earth atoms or the presence of more than one rare earth site, many compounds exhibit competing magnetic ordering with spin reorientations. Unfortunately, the iron ions are usually isolated in most of the structures and do not exhibit magnetic ordering, which let us lose the opportunity to study the interacted magnetic competition between rare earth ions and Fe ions.

141

As polar intermetallics, all of these structures show pseudo gaps either at the Fermi level or close to the Fermi level. The presence of Mg/Al/Si will tend to adjust the pseudo gap to the

Fermi level to stabilize the strcutre as in the case of R5(Mg/Al)5Fe4(Al/Si)18 (R = Gd, Dy, Y). If the 4f orbitals of the rare earth atoms (e.g. Eu) are close to the Fermi level, the conduction electrons will be affect by the localized spins in the presence of an external magnetic field, leading to the magnetoresistance behavior. This was examplified from EuMgTt (Tt = Sn, Pb). Magnetic and electrical studies indicate that both compounds show large magnetoresistance up to -30% and -25% at their Néel temperatures (10.9 K and 13.9 K), respectively.

142

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BIOGRAPHICAL SKETCH

Education Florida State University, Tallahassee, FL, U.S. Solid State Chemistry. 2008- present Dissertation: "Flux growth and physical properties of rare earth aluminides and tetrelides." Advisor: Dr. Susan E. Latturner Tongji University, Shanghai, China, M.S. Power Engineering. Spring, 2007 Dissertation: "Design of Air filters for the fuel cell vehicles." Advisor: Dr. Jianxin Ma Tongji University, Shanghai, China, B.S. Chemistry. Summer, 2004

Dissertation: "Preparation of a hydrophobic SiO2 aerogel." Advisor: Dr. Lihua Gan Field of Interest

Synthesis and characterization of solid state materials with promising properties (e.g. electrical, magnetic, thermoelectric, superconducting, multiferroic, etc.) aiming for clean-energy applications. Research Experience Florida State university, Department of Chemistry & Biochemistry, Aug. 2008 - present Research projects involve growth of new structural single crystals with both flux method and traditional solid state method, structure determination by X-ray and neutron diffraction, characterization of their magnetic and transport properties (mainly electrical resistivity), investigation on the connection between the structure and physical properties. Tongji University, Department of Automotive Engineering, 2004 - 2007 Cooperation project between Canada and China (2004DFB01500) to study the effects of air impurities on the performance of PEMFC; Assembly of fuel cell stacks; Research on modification of porous materials and adsorption efficiency of air impurities; Design and test of new style air filters for fuel cells. Tongji University, Department of Chemistry, 2000 - 2004 Preparation of new type of hydrophobic SiO2 aerogel with supercritical drying method. Technical Experience

 Synthesis: Solid state synthesis (stoichiometric, arc melting, flux growth); modification of activated carbon materials; preparation of SiO2 aerogels with supercritical method.

 Characterization: Single crystal/powder X-ray & neutron diffraction, SQUID, solid state NMR (MAS), transport properties by PPMS, SEM-EDS, X-ray photoelectron spectroscopy (XPS), TGA-DSC, mass spectrometry (MS), gas chromatography (GC), BET

 Analysis: Familiar with electronic structure calculation with TB-LMTO-ASA software

 Practical: Assembly of small fuel cell stacks (250W); Test bench buildup of fuel cell stacks;

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Setup for absorption tests of air impurities; Design and assembly of new structural air filters Social & Campus Experience

 Mentor of 1st Undergraduate School on Magnetic Materials sponsored by FSU. 2012. Direct the nationwide undergraduate participants to synthesize solid state materials with arc melting and perform powder X-ray diffraction measurements.

 Teaching assistant in Department of Chemistry & Biochemistry, FSU. 2008 - 2011 Direct undergraduate students to operate lab experiments (general and organic chemistry) and to review the main points through recitation classes.

 Chemical engineer in Shanghai Fuel Cell Vehicle Powertrain Co.Ltd, China. 2007 - 2008 Evaluate chemical filters for fuel cells from Freudenberg Co.Ltd; pressurize and inject hydrogen for fuel cell vehicles; Supervise hydrogen supply for the test of fuel cell stacks(PEMFC).

 Coordinator in Michelin (china) Investment Co. Ltd, China. 2004 Coordinate worldwide teams for sustainable mobility match during the Michelin Challenge Bibendum 2004 at Shanghai

 Track referee of Formula One (F1) Grand Prix 2004, Shanghai. 2004 Supervise the assigned track area and report the unexpected emergencies, through 5 months' technical training.

 Chair of Student Association in Chemistry Department, Tongji University. 2002 - 2003 Arrange and coordinate with the executive committee a variety of academic and recreational activities in campus. Honors & Awards Dean scholarship, Dept of Chemistry & Biochemistry, FSU. 2008 Infineon scholarship from Infineon (China) Co. Ltd. 2006 Master fellowship, Tongji University. 2005 Excellent Undergraduate student, Tongji University, 2004 Undergraduate fellowship, Tongji University, 2001 - 2003

Publications In preparation & Submitted:

 Ma, X.; Qi, T.; Zeng, B.; Latturner, S.E. "Field-induced spin-reorientation in antiferromagnetic EuMgPb". In preparation.  Ma, X.; Cao, H.; Zeng, B.; Kinyon, J.; Latturner, S.E. "An intensive study of the multinary R5(MgAl)5Fe4(Al/Si)18 (R = Gd, Dy, Y): Neutron diffraction, electronic structure and electrical resistivity". Manuscript available upon request.  Ma, X.; Lochner, E.; Chen, B.; Latturner, S.E. "RFe2MgAl7 (R = La - Nd and Sm): synthesis,

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structure, magnetic and electrical properties". Manuscript available upon request.  Ma, X.; Kauzlarich, S.M.; Nesper, R.; Latturner, S.E. "Mg/Al Flux growth and properties of M5+xMg18-xTt13 phases (M =Eu, Ba/Sr; Tt=Si,Ge) ". Manuscript available upon request. Appeared & Accepted (including patents):

 Ma, X.; Whalen, J.B.; Cao, H.; Latturner, S.E." Competing phases, complex structure, and complementary diffraction studies of R3FeAl4-xMgxTt2 intermetallics (R = Y, Dy, Er, Yb; Tt = Si or Ge; x < 0.5)". Chem. Mater. 2013, 25, 3363-3372  Ma, X.; Lu, J.;Whalen, J.B.; Latturner, S.E."Magnetoresistance behavior of rare earth Zintl phase EuMgSn grown in Mg/Al flux". Inorg. Chem. 2013, 52, 3342-3348.  Ma, X.; Chen, B.; Latturner, S.E."Synthesis and properties of new multinary silicides R5Mg5Fe4Al12Si6 (R = Gd, Dy, Y) grown in Mg/Al flux". Inorg. Chem. 2012, 51, 6089-6095.  Ma, X.; Yang, D.; Ma, J. "Evaluation of activated carbon adsorbent for fuel cell cathode air filtration", J. Power Sources. 2008, 175, 383-389.  Ma, X.; Ma, J."Progress of air purification for fuel cell vehicle". Energy. 2006, 4, 7-10.  Ma, J.; Ma, X."Design of new type of air filter for fuel cell vehicles". CN101079489, 2007  Gan, L.; Ma, X."Preparation of hydrophobic SiO2 aerogel by supercritical drying". CN1636871, 2004. Presentations & Training

"Synthesis and magnetic properties of rare earth silicides and aluminides grown in Mg/Al flux". Poster, North American Solid State Chemistry conference, Oregon State University, Corvallis, June. 2013 "Synthesis and magnetic properties of rare earth silicides and aluminides grown in Mg/Al flux". Poster, 245th ACS National conference, New Orleans. April. 2013 "National school on Neutron & X-ray scattering", Argonne & Oak Ridge National Laboratory. August, 2012 "New multinary rare earth silicides grown in Mg/Al flux". Talk. FAME. Tampa, FL 2011

"Characterization of multiferroic BiFeO3". Inorganic seminar talk, Department of Chemistry, FSU. 2010 "Solid state synthesis from metal flux using traditional heating and microwave dielectric heating". Inorganic seminar talk, Department of Chemistry, FSU. 2009

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