Benjamin Gordon McDonald

Transcription

1 Technical Report 5 National Science Foundation Grant DMR Metals Program Geometry of Wigner-Seitz Cells in Intermetallic Compounds and Application to Site Preferences of Indium Impurity Atoms by Benjamin Gordon McDonald November 2012 Hyperfine Interactions Group Department of Physics and Astronomy Washington State University Pullman, Washington USA

2 Foreword This is a research report by Benjamin McDonald submitted to the College of Arts and Sciences at Washington State University in November It describes the application of a computer program written by Kenneth Dorrance to calculate properties of Wigner-Seitz cells for a variety of crystal structures of interest to my research group. Ben and Ken are currently undergraduate physics majors at WSU. Wigner-Seitz cells are the spaces closest to each lattice site in a solid. They are polyhedra, also know of in mathematics as Voronoi tessellations. For more information, see Seitz_unit_cell. Our interest is in the volumes of cells associated with different sites, the distances between a site and its neighboring sites, and the areas of contact between adjacent cells. Ben used the volumes and contact areas to predict lattice locations taken up by impurity atoms in solids. A site preference to occupy a lattice site is favored when there is a good match between the volume of the impurity atom and a site volume. It is also favored when contact areas are greater between adjacent atoms of elements that bind strongly with each other. The particular impurity selected for study was indium, since many experiments are carried out in the Collins group using indium probe atoms. The measure used for strength of binding in this report was the number of intermetallic compounds formed between indium and the other elements in a phase. These considerations were used here to predict lattice locations taken up by indium atoms in about 15 different crystal structures. The research described herein was supported by the College of Arts and Sciences under a summer research minigrant awarded to Ben McDonald and in part by the National Science Foundation under grant DMR (Metals Program). Gary S. Collins mailto:collins@wsu.edu November 2012

3 Geometry of Wigner-Seitz Cells in Intermetallic Compounds and Application to Site Preferences of Indium Impurity Atoms By Benjamin Gordon McDonald 1

4 Acknowledgements: Ken Dorrance wrote the majority of the program, including all calculation as well as a description of how the program operates for this report. Dr. Gary S. Collins provided direction, patience, and drive to complete this report as well as technical advice and the means to compare the output of the program, WS.exe, to measurement data. The College of Sciences at WSU granted money to work on this project with Dr. Collins. This work was supported in part by the College of Arts and Sciences at WSU through a summer research minigrant awarded in 2012 and by the National Science Foundation under grant NSF DMR (Metals Program). 2

5 Table of Contents Introduction...pg. 4-5 Method of Calculation...pg. 5-6 Input and Output Information...pg. 6-7 Intermetallic Compound Tables...pg. 7-9 Results for 35 phases... pg. 10 AlNi...pg LaPd 3...pg LuPd 3...pg AlNb 3...pg AlPd...pg βmn...pg Al 12 W...pg Ga 7 Pd 3...pg αmn...pg AuIn 2...pg Al 2 Gd...pg HoCoGa 5...pg LaCoIn 5...pg FeGa 3...pg RhIn 3...pg Al 3 Ti...pg Al 4 Ba...pg Al 2 Cu...pg Al 3 Zr...pg Ga 2 Hf...pg Ga 2 Pr...pg AuSn...pg Al 3 Ni 2...pg Ni 2 In...pg NiIn...pg BaAg 5...pg CePt 5...pg GdPd 5...pg LaNi 5...pg SmCo 5...pg SrAu 5...pg TbCo 5...pg YCo 5...pg Ni 3 Sn...pg Al 3 Ni...pg Discussion...pg Conclusion...pg Works Cited...pg

6 Abstract: This report uses a computer program written by Ken Dorrance, with minor edits by myself to calculate site volumes and contact areas of Wigner-Seitz cells in compounds. Wigner-Seitz cells are geometrical constructions where planes are drawn that bisect the distance from a site of interest to the nearest neighbors and next nearest neighbors in the lattice. These planes then create polyhedra out of which volumes and surface areas can be calculated. The values produced by the program are then used to predict site preferences of indium impurity atoms in compounds. Where appropriate the prediction is contrasted with measurement. Introduction: Locations of impurity atoms in the crystal lattice of a compound affect many physical properties, such as mechanical strength, magnetism, specific heats, and melting temperature. Measurements of lattice locations have been made at WSU using PAC (Perturbed Angular Correlation of gamma rays) spectroscopy, mostly using indium as the impurity atom. This method allows characterization of sites based off of internal lattice symmetries. For instance, in the compound GdAl 2, the gadolinium site is cubic, while the aluminum site is non-cubic and those two signal types are readily distinguishable. Determination of the specific site is not always straight forward, as some lattices have geometrically similar, yet distinct sites that are harder to characterize. Potential sites may have characteristics such as, volumes which most closely match the impurity atom, good contact area with neighboring atoms of favorable chemistry with the impurity, or a characteristic shape matching (such as an impurity that prefers cubic sites over others). This report will focus on volume matching and optimization of favorable contact areas as well as specifically intermetallics with indium as the impurity atom. The number of intermetallic compounds (IC) indium makes with 4

7 different elements will be a rough measure of it's propensity to bond with that element. The program, WS.exe, used to calculate the volumes and surface areas was written by Ken Dorrance and uses the Wigner-Seitz approximation. The Wigner-Seitz approximation finds the nearest neighbors and the next nearest neighbors to the sites of interest, draws vectors from the site to the neighbors, and these vectors are then bisected by planes. The planes are chosen to uniquely characterize the site, and volume and surface area calculation are done from there. This means that site locations are determined by the geometry of the lattice site, not the size of the atom occupying it. Some crystal structures were shown to have competing forces between the volume matching elemental indium and contact area with favorable atoms. In most cases the volume matching was chosen over contact area. Method of Calculation: The following description of the method of calculation was written by Kenneth Dorrance: The program is designed to take as input a minimum set of parameters describing a crystal structure. It is written in C++ and optionally can be linked with the OpenGL graphics library for visualization of results. An input file describes a basis and atom positions in that basis. A larger model of the crystal structure is then constructed in memory from the small input set. Within the larger crystal structure model the first atom from each unique site is used to construct a Wigner-Seitz cell. For each unique site, neighboring atoms are first identified and then surfaces are calculated from neighboring atom positions. The following happens for each unique site after neighboring atoms have been identified. For every combination of three unique neighboring atoms a point is calculated, if it exists, representing the intersection of planes located at half the distance and normal to the three unique neighboring atoms. 5

8 Intersection points calculated for unique neighboring atoms that are themselves neighbors are recorded as a vertex of the surface associated with the first neighbor. After all the vertices have been identified they are sorted spatially in memory to allow volumes and surfaces to be calculated logically and allow direct use by a graphics library. Finally, the volumes and the surface areas are calculated from vectors originating at the surface point halfway between neighboring atoms and extending to each vertex on the surface. The cross product of adjacent vectors equals twice the surface area of the triangle section of the surface described. That cross product then dotted with a vector of same origin extending to the center atom gives the volume of the parallelepiped described by the three vectors. This volume is six times the volume of the section of the Wigner-Seitz cell described by the three vectors. Surface area and volumes are calculated for each section of the cell. Input and output file information: Basis vector input should be relative to the translation vectors. Currently, the program outputs to a text file called Output.txt. Modification of this file will not affect the program in any way, as the program simply creates an Output.txt if there isn't one and overwrites it if there already is one. To save outputs, simply rename Output.txt as some other name. No spaces should be used when naming input files, as the console cannot interpret that, as well as the extention.txt should be appended when writing in the file to read from, as otherwise Windows will not find the file. Errors in the input files, mostly pertaining to the wrong numbers used for origins for basis, atoms per cell, or number of sites, as well as too many basis vectors (potentially upwards of 500, untested) will cause the program to crash. If a crash occurs simply fix the error and run the program again. Depending upon how the input file was constructed, more than one origin for 6

9 basis may be needed. In a couple of cases in this report, such as Ga 7 Pd 3 and Al 4 Ba, the full cubic translation vectors were used, thus they needed more than one origin for a basis. Nearly all other phases used primitive translation vectors and thus did not need multiple origins for basis. The primitive vectors are what are reported on the NRL websites. Table of intermetallic compounds formed with indium The next two figures show the binary alloy tables that were used for the IC count in the reports below to give a suggestion about indium bonding preference. The first figure shows the key, while the second figure shows the values for the relevant element, indium. From ref. [4]. 7

10 Figure 1: This figure shows how the other tables within Atlas for Binary Alloys [4] are read, as well as information on the element lithium. 8

11 Figure 2: This figure shows the Atlas for Binary Alloys information pertaining to indium, which was used in the report. 9

12 Site preferences of indium impurity atoms in 35 intermetallic Crystal Structures: For all structures below with an NRL website listed, the prototype of the structure, Structurbereicht designation, Pearson symbol, space group, representative picture, and basis vectors were obtained from the NRL website, whose form is where the asterisks denote the specific website for that structure. Also most structures got their parameters from source [1]. All IC numbers are gotten from Atlas for Binary Alloys. [4] All elemental atomic volumes are gotten from Introduction to Solid State Phys. [3] For the ones that do not have an NRL website listed, here are the sources that were used for the specific structures: Ga 7 Pd 3 used structure and averaged parameters from phases in similar structure from source [18]. LaCoIn 5 used parameters from a currently misplaced source. FeGa 3 and RuGa 3 used source [2]. RhIn 3 used source [16]. Al 3 Ni used source [17] for picture and parameters. The value labeled Summed atomic volume is the sum of the volumes the program gives for the individual sites, while the value labeled Unit cell volume is the size of the unit cell as determined by the volume defined by the translation vectors. The ratio given immediately afterward is Unit cell volume over Summed atomic volume, given as such because for the first few structures done that was the larger value. 10

13 Prototype Structurbereicht Pearson Space Group CsCl B2 cp2 Pm3m #221 NRL link: Phase a (nm) b (nm) c (nm) AlNi N/A N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector AlNi cp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Al Area 2 Ni Atomic vols 1 Al Ni Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 2.17 Ratio of volumes for site 2: 2.17 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Indium has greater bonding with nickel than aluminum. (5 IC with Ni, 0 with Al. In and Al liquids are immiscible.) The Al-site has the largest surface area with nickel atoms, by a relatively significant portion. Both sites have equivalent volume. 11

14 Conclusion: Due to both volumes being equal, the only predictor of site preference is contact area with preferential atoms. This happens to be on the aluminum site, which has the largest contact area with nickel atoms of either site. 12

15 Prototype Structurbereicht Pearson Space Group Cu 3 Au L1 2 cp4 Pm3m #221 NRL link: Phase a (nm) b (nm) c (nm) LaPd N/A N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector LaPd3 cp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Area 2 Atomic vols La Pd 1 La Pd Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.39 Ratio of volumes for site 2: 1.39 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Bonding: 13

16 Indium has a greater bond with lanthanum than palladium. (6 IC with La, 5 IC with Pd.) The Pd-site has a large contact area with neighboring La atoms. The Pd-site has a larger contact area with neighboring Pd atoms. The La-site has the largest contact area with neighboring Pd atoms. Both sites have equivalent volume. Conclusion: The lanthanum and palladium site volumes are equal, however bonding with lanthanum is preferable and the palladium site has the largest contact area with lanthanum. The lanthanum site also has good contact area with a preferred element. According to this model, indium should go to the palladium site, but the prediction is weak. 14

17 Prototype Structurbereicht Pearson Space Group Cu 3 Au L1 2 cp4 Pm3m #221 NRL link: Phase a (nm) b (nm) c (nm) LuPd N/A N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector LuPd3 cp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Area 2 Atomic vols Lu Pd 1 Lu Pd Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.59 Ratio of volumes for site 2: 1.59 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Bonding: 15

18 Indium has a greater bond with palladium than lutetium. (5 IC with Pd, 1 IC with Lu.) The Lu-site has the largest contact area with neighboring Pd atoms. The Pd-site has a large contact area with neighboring Pd atoms. Both sites have equivalent volume. Conclusion: The lutetium and palladium site volumes are equal, however bonding with palladium is preferable and the lutetium site has the largest contact area with palladium. According to this model, indium should go to the lutetium site. 16

19 Prototype Structurbereicht Pearson Space Group Cr 3 Si A15 cp8 Pm3n #223 NRL link: Phase a (nm) [1] b (nm) c (nm) Nb 3 Al N/A N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Nb3Al cp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Al Area 2 Nb Atomic vols 1 Al Nb Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.54 Ratio of volumes for site 2: 1.49 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: 17

20 Indium has greater bonding with niobium than with aluminum. (1 IC with Nb, 0 with Al. In and Al liquids are immiscible.) The Al-site has a much larger contact area with neighboring Nb atoms and has no contact area with other Al atoms. The Nb-site has a slightly larger volume, closer matching the atomic indium volume. 18

21 Prototype Structurbereicht Pearson Space Group FeSi B20 cp8 P2 1 3 #198 NRL link: Phase a (nm) b (nm) c (nm) x1 x2 AlPd N/A N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector AlPd cp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Al Area 2 Pd Atomic vols 1 Al Pd Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.82 Ratio of volumes for site 2: 2.00 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: 1.05 Site preference for indium solutes: 19

22 Bonding: Indium has greater bonding with palladium than with aluminum. (5 IC with Pd, 0 with Al. In and Al liquids are immiscible.) The Al-site has a much larger contact area with neighboring Pd atoms and has the least contact area with neighboring Al atoms. The Al-site has a larger volume, closer matching the atomic indium volume. Conclusion: The significantly larger contact area of the Al-site with the Pd-site along with very little contact area with the Al-site, with which indium is immiscible, and a larger volume, seems to suggest that In will prefer the Al-site. 20

23 Prototype Structurbereicht Pearson Space Group βmn A13 cp20 P #213 NRL link: Phase a (nm) b (nm) c (nm) x1 x2 βmn N/A N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Mn cp

24 Type Site Vol(Å 3 ) Area 1 (Å 2 ) Mn 8 Area 2 Mn 12 Atomic vols 1 Mn Mn Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 2.23 Ratio of volumes for site 2: 1.96 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Bonding: Indium bonds equally well to Mn than to Mn. (1 IC with Mn.) The Mn 12 -site has a larger surface area with neighboring Mn atoms. The Mn 12 -site has a larger volume, closer matching the atomic indium volume. Conclusion: Both volume and surface area data suggest that indium prefers the Mn 12 - site over the Mn 8 -site. 22

25 Prototype Structurbereicht Pearson Space Group Al 12 W N/A ci26 Im3 #204 NRL link: Phase a (nm) b (nm) c (nm) y z Al 12 W N/A N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Al12W ci Type Site Vol(Å 3 ) Area 1 (Å 2 ) Area 2 Atomic vols W Al 1 W Al Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.86 Ratio of volumes for site 2:

26 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Bonding: Indium has greater bonding with tungsten than with aluminum. (0 IC with Pd, 0 with Al. In and Al liquids are immiscible.) The Al-site has a contact area with neighboring W atoms but has the more contact area with neighboring Al atoms than does the W- site. The Al-site has a larger volume, closer matching the atomic indium volume. Conclusion: The slightly larger size and the slightly larger contact area with tungsten suggests that an indium might rest on an aluminum site, but the aluminum site also has contact with aluminum and I don't know how that will affect the site preference. The indium will most likely rest on the Al-site. 24

27 Prototype Structurbereicht Pearson Space Group Ga 7 Ir 3 D8 f ci40 Im3m NRL link: N/A Phase a (nm) b (nm) c (nm) x1 x2 Ga 7 Pd N/A N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Ga7Pd

28 Type Site Vol(Å 3 ) Area 1 (Å 2 ) Pd 3 Area 2 Ga 3 Area 3 Ga 4 Area 2+3 Atomic vols 1 Pd Ga Ga Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.92 Ratio of volumes for site 2: 1.34 Ratio of volumes for site 3: 1.52 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Indium has a greater bonding with palladium than with gallium. (5 IC with Pd, 0 with Ga.) The Ga 3 site has the largest surface area with neighboring Pd atoms. The Ga 3 site has the greatest volume, closest matching the elemental volume of indium. Conclusion: The gallium-3 site has the largest volume, which is the closest to the volume of indium. The gallium-3 site also has the largest surface area to palladium, which has good binding with indium. According to this model indium should go to the gallium-3 site. 26

29 Prototype Structurbereicht Pearson Space Group α-mn A12 ci58 I43m #217 NRL link: Phase a (nm) b c x2 (nm) x3 (nm) z3 (nm) x4 (nm) z4 (nm) α-mn N/A N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Mn ci

30 Area 3 Area 4 Type Site Vol(Å 3 ) Area 1 (Å 2 ) Area 2 Atomic vols Mn 1 Mn 4 Mn 12a Mn 12b 1 Mn Mn Mn 12a Mn 12b Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.95 Ratio of volumes for site 2: 1.99 Ratio of volumes for site 3: 2.09 Ratio of volumes for site 4: 2.26 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Bonding: Indium bonds equally well to Mn than to Mn. (1 IC with Mn.) The Mn 1 -site has a larger surface area with neighboring Mn atoms. The Mn 1 -site has a larger volume, closer matching the atomic indium volume. Conclusion: Indium will most likely deposit itself on the Mn 1 site. 28

31 Prototype Structurbereicht Pearson Space Group CaF 2 C1 cf12 Fm3m #225 NRL link: Phase a (nm) b (nm) c (nm) AuIn N/A N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector AuIn Type Site Vol(Å 3 ) Area 1 (Å 2 ) Au Area 2 In Atomic vols 1 Au In Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.35 Ratio of volumes for site 2: 1.05 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Indium forms 7+ IC with gold. Conclusion: Gold has no contact with neighboring gold atoms. Indium has about twice as much contact with neighboring gold atoms than other indium 29

32 atoms, suggesting that per atom the surface areas are about the same. 30

33 Prototype Structurbereicht Pearson Space Group Cu 2 Mg C15 cf24 Fd3m #227 NRL link: Phase a (nm) b (nm) c (nm) Al 2 Gd N/A N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector GdAl2 cf Type Site Vol(Å 3 ) Area 1 (Å 2 ) Gd Area 2 Al Atomic vols 1 Gd Al Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.11 Ratio of volumes for site 2: 1.37 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Bonding: 31

34 Indium has a greater bonding with gadolinium than to aluminum. (5 IC with Gd, 0 with Al. In and Al liquids are immiscible). The Al-site has a larger contact area with neighboring Gd atoms than the Gd-site has with neighboring Gd atoms. The Gd-site has a larger volume, closer matching the atomic indium volume. Conclusion: Volumetrically the indium would rather go to the gadolinium site, but larger contact area with gadolinium on the aluminum site suggests better bonding from that site. The less contact with aluminum is also on the aluminum site, but the volume of the gadolinium site is so much closer to elemental indium. Due to volume being the most reliable predictor, according to this model indium should go to the gadolinium site. 32

35 Prototype Structurbereicht Pearson Space Group HoCoGa 5 N/A tp7 P4/mmm #123 NRL link: Phase a (nm) b (nm) c (nm) z (nm) HoCoGa N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector HoCoGa5 tp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Ho Area 2 Area 3 Area 4 Area 3+4 Atomic vols Co Ga 1 Ga 4 1 Ho Co Ga Ga Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.41 Ratio of volumes for site 2: 2.04 Ratio of volumes for site 3: 1.39 Ratio of volumes for site 4:

36 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Bonding: Indium has the greatest bonding with cobalt, followed by holmium, then finally by gallium. (3 IC with Co, 1 with Ho, 0 with Ga.) The Ga 4 site has the largest contact with neighboring Co atoms, but only 7.34 Å 2, which is comparatively small. The Ga 1 site has the largest contact with neighboring Ho atoms. The Ga 1 site has the largest volume, closer matching the atomic indium volume. Conclusion: Indium most strongly bonds with cobalt, but there is no site with a good volume and surface area match to favor this site. As an ignorant guess, I would assume that indium would favor the gallium-1 site for its relatively high surface area to a somewhat favorable element and largest volume. 34

37 Prototype Structurbereicht Pearson Space Group HoCoGa 5 N/A tp7 P4/mmm #123 NRL link: Phase a (nm) b (nm) c (nm) z (nm) LaCoIn N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector LaCoIn5 tp Type Site Vol(Å 3 ) Area 1 (Å 2 ) La Area 2 Area 3 Area 4 Atomic vols Co In 1 In 4 1 La Co In In Ratio of volumes (In / site): Ratio of volumes for site 1: 1.03 Ratio of volumes for site 2: 1.50 Ratio of volumes for site 3: 1.03 Ratio of volumes for site 4: 1.09 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) 35

38 Ratio: Site preference for indium solutes: Bonding: Indium has a greater bonding with lanthanum than to cobalt. (6 IC with La, 3 IC with Co.) The Co site has greater contact area with neighboring La atoms than the La site does. The La site has the largest volume of the non-indium sites, closest matching the atomic indium volume. Conclusion: The La site has the larger site volume, and the site volume is about the size of the atomic atom. This suggests that excess In would prefer the La site over the Co site. 36

39 Prototype Structurbereicht Pearson Space Group CoGa 3 N/A tp16 P4n2 NRL link: N/A Phase a (nm) b (nm) c (nm) x1 x2 z FeGa N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector FeGa3 tp

40 Type Site Vol(Å 3 ) Area 1 (Å 2 ) Fe Area 2 Ga 1 Area 3 Ga 2 Atomic vols 1 Fe Ga Ga Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 2.10 Ratio of volumes for site 2: 1.50 Ratio of volumes for site 3: 1.38 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: 0.95 Site preference for indium solutes: Indium does not appear to have greater bonding with iron or gallium. (0 IC with Fe, 0 with Ga.) Due to the small solubility of either iron or gallium, the surface areas do not seem to matter much. The Ga 2 -site has the greatest volume, closest matching the atomic volume of indium. Ga 1 -site has a large surface area with the Ga 2 -site, while the Ga 2 -site has almost equal surface areas with Ga 2 and Ga 1 -sites. This suggests that indium atoms will diffuse from Ga 1 -sites to Ga 2 -sites. Conclusion: Due to indium's chemical inertness with both iron and gallium, the volume matching and the diffusional jumping should determine what site indium solutes prefer. The gallium-2 site has the largest volume and greatest surface area, thus the gallium-2 site seems to be the most preferred. 38

41 Prototype Structurbereicht Pearson Space Group CoGa 3 N/A tp16 P4n2 NRL link: N/A Phase a (nm) b (nm) c (nm) x1 x2 z RhIn N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector RhIn3 tp

42 Type Site Vol(Å 3 ) Area 1 (Å 2 ) Rh Area 2 In 1 Area 3 In 2 Atomic vols 1 Rh In In Ratio of volumes (In / site): Ratio of volumes for site 1: 1.63 Ratio of volumes for site 2: 1.15 Ratio of volumes for site 3: 1.09 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: For low indium solutes, indium will probably prefer the indium-2 site. For high indium solutes, indium will only be able to populate the rhodium site. Conclusion: For low indium solutes, the In 2 site will be preferred. 40

43 Prototype Structurbereicht Pearson Space Group Al 3 Ti D0 22 ti8 I4/mmm #139 NRL link: Phase a (nm) b (nm) c (nm) Al 3 Ti N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector DO22 Al3Ti c= a= Type Site Vol(Å 3 ) Area 1 (Å 2 ) Ti Area 2 Al 1 Area 3 Al 2 Atomic vols 1 Ti Al Al Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.64 Ratio of volumes for site 2: 1.64 Ratio of volumes for site 3: 1.64 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Indium has a greater bonding with titanium than aluminum. (2 IC with Ti, 0 with Al. In and Al liquids are immiscible.) [4] 41

44 The Al 1 -site has the largest contact area with neighboring titanium atoms. All sites have equal volume. Conclusion: The titanium and aluminum site volumes are equal, however bonding with titanium is preferable and the aluminum-1 site has the largest contact area with titanium. According to this model, indium should go to the aluminum-1 site. This conclusion is known to be false. 42

45 Prototype Structurbereicht Pearson Space Group Al 4 Ba D1 3 ti10 I4/mmm NRL link: Phase a (nm) b (nm) c (nm) z Al 4 Ba N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Al4Ba ti Type Site Vol(Å 3 ) Area 1 (Å 2 ) Ba Area 2 Al a Area 3 Al b Atomic vols 1 Ba Al a Al b Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: Ratio of volumes for site 2: 1.22 Ratio of volumes for site 3: 1.24 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) 43

46 Ratio: 0.98 Site preference for indium solutes: Indium has greater bonding with barium than with aluminum. (1 IC with Ba, 0 with Al. In and Al liquids are immiscible.) [4] The Al-b site has the largest contact area with neighboring Ba atoms and has the smallest contact area with neighboring Al atoms. The Al-a site has slightly smaller contact area with neighboring Ba atoms, but has a slightly larger volume. The Ba site has the largest volume and is also the closest matching to the atomic indium volume, but the other sites are almost as close to the atomic indium volume. Conclusion: The barium and aluminum site volumes are almost equally proportional to the atomic indium volume. Bonding with barium is preferable and the Al-b site has the largest contact area. This model would predict the Al-b site. 44

47 Prototype Structurbereicht Pearson Space Group Al 2 Cu C16 ti12 I4/mcm #140 NRL link: Phase a (nm) b (nm) c (nm) x y Al 2 Cu N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Al2Cu Type Site Vol(Å 3 ) Area 1 (Å 2 ) Cu Area 2 Al Atomic vols 1 Cu Al Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.79 Ratio of volumes for site 2: 1.73 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: 45

48 Bonding: Indium has greater bonding with copper than to aluminum. (3 IC with Cu, 0 IC with Al. In and Al liquids are immiscible.) The Al site has the largest contact area with neighboring Cu atoms, suggesting stronger bonding there. The Al site has a larger volume, closer matching the atomic volume of indium. Conclusion: Indium will strongly prefer site 2 (Al) because it has a slightly larger volume than the Cu-site. More importantly, it has three times greater contact area with Cu atoms than does the Cu-site. 46

49 Prototype Structurbereicht Pearson Space Group Al 3 Zr D0 23 ti16 I4/mmm #139 NRL link: Phase a (nm) b (nm) c (nm) z1 z2 Al 3 Zr N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Al3Zr ti Type Site Vol(Å 3 ) Area 1 (Å 2 ) Area 2 Area 3 Area Area 4 Atomic Al a Al b Al c Zr vols 1 Al a Al b Al c Zr Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.45 Ratio of volumes for site 2: 1.57 Ratio of volumes for site 3: 1.50 Ratio of volumes for site 4:

50 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Indium has greater bonding with zirconium than aluminum. (5+ IC with Ni, 0 with Al. In and Al liquids are immiscible.) The Al c -site has the largest surface area with zirconium atoms. The Al a -site has the greatest volume, closest matching the elemental volume of indium. Comparatively, Al a has 4% larger volume, while Al c has 14% larger contact with zirconium atoms. Conclusion: A larger volume is probably the best predictor of site preference through this model. This suggests that while the prediction is a weak one due to competition between contact area with a preferable atom and volume, the Al a -site is the most probable site for an indium solute. 48

51 Prototype Structurbereicht Pearson Space Group Ga 2 Hf N/A ti24 I4 1 /amd #141 NRL link: Phase a (nm) b (nm) c (nm) z1 z2 z3 Ga 2 Hf N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Ga2Hf ti Type Site Vol(Å 3 ) Area 1 (Å 2 ) Ga a Area 2 Ga b Area 1+2 Area 3 Hf Atomic vols 1 Ga a Ga b Hf

52 Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.60 Ratio of volumes for site 2: 1.46 Ratio of volumes for site 3: 1.48 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Bonding: Indium has greater bonding with hafnium than to gallium. (1 IC with Hf, 0 IC with Ga.) The Ga b site has the largest contact area with neighboring Hf atoms, suggesting stronger bonding there. The Ga b site has a larger volume, closer matching the atomic volume of indium. Conclusion: The larger contact area of neighboring Hf atoms with the Ga b site and a larger volume of the Ga b site, seem to suggest that In will prefer the Ga b site. Notes: This crystal seems oddly squished in terms of site sizes. It probably stems from imprecision in the z parameters, causing errors to propagate. 50

53 Prototype Structurbereicht Pearson Space Group AlB 2 C32 hp3 P6/mmm #191 NRL link: Phase a (nm) b (nm) c (nm) Ga 2 Pr N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Ga2Pr hp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Pr Area 2 Ga Atomic vols 1 Pr Ga Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: Ratio of volumes for site 2: 1.26 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Bonding: Indium has greater bonding with praseodymium than to gallium. (5 IC with Pr, 0 IC with Ga.) The Ga site has the largest contact area with neighboring Pr atoms, suggesting stronger bonding there. 51

54 The Pr site has a larger volume, closer matching the atomic volume of indium. Conclusion: There is a conflict between contact area preference and atomic volume matching with this compound. It most probably will go to the larger volume site, but indium vastly prefers praseodymium over gallium. This prediction is unclear. 52

55 Prototype Structurbereicht Pearson Space Group NiAs B8 1 hp4 P6 3 /mmc #194 NRL link: Phase a (nm) b (nm) c (nm) AuSn N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector AuSn B8~ Type Site Vol(Å 3 ) Area 1 (Å 2 ) Au Area 2 Sn Atomic vols 1 Au Sn Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.30 Ratio of volumes for site 2: 1.05 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Bonding: Indium has greater bonding with gold than with tin. (7 IC with Au, 1 IC with Sn.) 53

56 The Sn site has the largest contact areas with neighboring Au atoms. The Sn-site has the largest volume, closest to the atomic volume of indium. Conclusion: Both values suggest that indium prefers the tin site over the gold site. Notes: The excessively high amount of significant figures used in the input file is to ensure that round-off errors are reduced. This is shown by the extremely close to unity value of the ratio. 54

57 Prototype Structurbereicht Pearson Space Group Al 3 Ni 2 D5 19 hp5 P3m1 #164 NRL link: Phase a (nm) b (nm) c (nm) z1 z2 Al 3 Ni N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Al3Ni2 hp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Area 2 Area 3 Atomic vols Al 1 Al 2 Ni 2 1 Al Al Ni Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.85 Ratio of volumes for site 2: 1.70 Ratio of volumes for site 3: 2.15 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: 55

58 Indium has greater bonding with nickel than aluminum. (5 IC with Ni, 0 with Al. In and Al liquids are immiscible.) The Al 1 site has the largest contact area with neighboring nickel atoms, by a relatively significant portion. The Al 2 site has the greatest volume, closest matching the atomic volume of indium. Going beyond basic volume and bonding arguments, lattice relaxation about the oversized In-solute is probably greater for asymmetric Al 2 -site, possibly allowing an increased volume and perhaps also increasing contact with Ni-atoms. Al 1 -site is less symmetric and less lattice relaxation may be possible. Conclusion: A larger volume is probably the best predictor of site preference through this model. This suggests that while the prediction is a weak one due to competition between contact area with a preferable atom and volume, the Al 2 -site is the most probable site for an indium solute. 56

59 Prototype Structurbereich Pearson Space Group InNi 2 B8 2 hp6 P6 3 /mmc #194 NRL link: Phase a (nm) b (nm) c (nm) InNi N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector InNi2 B8~ Type Site Vol(Å 3 ) Area 1 (Å 2 ) Ni 1 Area 2 In Area 3 Ni 2 Atomic vols 1 Ni In Ni Ratio of volumes (In / site): Ratio of volumes for site 1: 1.97 Ratio of volumes for site 2: 2.05 Ratio of volumes for site 3: 2.05 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: 57

60 Bonding: The Ni 1 site has a larger contact area to neighboring Ni atoms. The Ni 1 site has the largest volume, closer matching the atomic volume of indium. Conclusion: Both values suggest that excess indium prefers the nickel-1 site over the nickel-2 site. Notes: The high amount of significant figures used in the input file is to ensure that round-off errors are reduced. This is shown by the extremely close to unity value of the ratio. 58

61 Prototype Structurbereicht Pearson Space Group CoSn B35 hp6 P6/mmm #191 NRL link: Phase a (nm) b (nm) c (nm) NiIn N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector InNi B8/ Type Site Vol(Å 3 ) Area 1 Area 2 Area 3 Atomic vols (Å 2 ) In 1 In 2 Ni 3 1 In In * Ni Ratio of volumes (In / site): Ratio of volumes for site 1: 1.34 Ratio of volumes for site 2: 2.29 Ratio of volumes for site 3: 2.48 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio:

62 Site preference for indium solutes: Bonding: The In 1 -site has a larger volume, suggesting that deficient indium would prefer that site. Conclusion: Excess indium would obviously go to the nickel site. Deficient indium would seem to prefer to occupy the indium-1 site. Notes: The high amount of significant figures used in the input file is to ensure that round-off errors are reduced. This is shown by the extremely close to unity value of the ratio. *Volumes of appear to have contributed significantly to the surface area of site 2 in contact to site 3, both having surface area of (nm 2 ), with normals of {0.000, , ±0.856}. No equivalent surface areas occur from site 2. Subtracting these values from the total site 2 to 3 surface area results in the value (nm 2 ), or Å 2. 60

63 Prototype Structurbereicht Pearson Space Group CaCu 5 D2 d hp6 P6/mmm #191 NRL link: Phase a (nm) b (nm) c (nm) BaAg N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector BaAg5 hp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Ba Area 2 Ag 2 Area 3 Ag 3 Area 2+3 Atomic vols 1 Ba Ag Ag Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: Ratio of volumes for site 2: 1.30 Ratio of volumes for site 3: 1.25 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: 61

64 Bonding: Indium has a greater bonding with silver than barium. (4 IC with Ag, 1 IC with Ba.) The Ba site has the largest contact area with neighboring Ag sites. The Ba site has the greatest volume, and is also the closest to the atomic volume of indium. Conclusion: The closer in volumes of the Ba-site and elemental indium along with the largest contact area to the Ag-sites seems to suggest that In will prefer the Ba-site. Note: in the source, the silver and barium sites were flipped and thus must be an error. 62

65 Prototype Structurbereicht Pearson Space Group CaCu 5 D2 d hp6 P6/mmm #191 NRL link: Phase a (nm) b (nm) c (nm) CePt N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector CePt5 hp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Ce Area 2 Pt 1 Area 3 Pt 2 Area 2+3 Atomic vols 1 Ce Pt Pt Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.09 Ratio of volumes for site 2: 1.56 Ratio of volumes for site 3: 1.51 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: 63

66 Bonding: Indium has greater bonding with cerium than to platinum. (5 IC with Ce, 3 IC with Pt.) The Pt 1 -site has the largest contact area with neighboring Ce atoms. The Pt 2 -site has comparable, but slightly less contact area with neighboring Ce atoms, but also has a comparable, but slightly more contact area with other Pt atoms, when compared to the Pt 1 - site. The Ce-site has the largest contact area with neighboring Pt atoms. The Ce-site has the largest volume, closest to the atomic volume of indium. Conclusion: It is hard to say which will be preferable, the Ce-site, or either Ptsite. Larger contact with the Ce-site is preferable, but there is not much contact with it in any case, although it is larger on the Ptsites. The much larger contact areas with the Pt-sites may entice the In to rest on the Ce-site, along with the much closer volume to elemental indium. 64

67 Prototype Structurbereicht Pearson Space Group CaCu 5 D2 d hp6 P6/mmm #191 NRL link: Phase a (nm) b (nm) c (nm) GdRh N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector GdRh5 hp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Gd Area 2 Rh 1 Area 3 Rh 2 Area 2+3 Atomic vols 1 Gd Rh Rh Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.20 Ratio of volumes for site 2: 1.71 Ratio of volumes for site 3: 1.66 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: 65

68 Bonding: Indium has greater bonding with gadolinium than to rhodium. (5 IC with Gd, 2 IC with Rh.) The Rh 1 site has the largest contact area with neighboring Gd atoms, but there is not much total area. The Rh 2 site has somewhat comparable contact area with the Rh 1 - site; it has slightly less contact with neighboring Gd atoms, and slightly more with neighboring Rh atoms. The Gd site has much more contact area than the other sites, but it is mostly with neighboring Rh atoms. The Gd site has the largest volume, closest matching the atomic volume of indium. Conclusion: It is hard to tell which site In will prefer, since it would like to bond to Gd, but there is not much surface area in contact with it. In will bond to Rh so a large contact area with Rh is also preferable. The Gd-site has the largest volume, which is close to the size of elemental indium, so that suggests that it will most likely go for the Gd-site. 66

69 Prototype Structurbereicht Pearson Space Group CaCu 5 D2 d hp6 P6/mmm #191 NRL link: Phase a (nm) b (nm) c (nm) LaNi N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector LaNi5 hp Type Site Vol(Å 3 ) Area 1 (Å 2 ) La Area 2 Ni 1 Area 3 Ni 2 Area 2+3 Atomic vols 1 La Ni Ni Volume of Indium: Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: Bonding: Indium has greater bonding with lanthanum than to nickel. (6 IC with La, 5 IC with Ni.) The La site has the largest contact area with neighboring Ni atoms. 67

70 The Ni 1 site has the largest contact area with neighboring La atoms, although it is comparatively small. The La site has the largest volume, closer matching the atomic volume of indium. Conclusion: Indium will probably rest on the lanthanum site, due to the largest volume at that site and the large contact area with nickel. 68

71 Prototype Structurbereicht Pearson Space Group CaCu 5 D2 d hp6 P6/mmm #191 NRL link: Phase a (nm) b (nm) c (nm) SmCo N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector SmCo5 hp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Sm Area 2 Co 1 Area 3 Co 2 Area 2+3 Atomic vols 1 Sm Co Co Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.37 Ratio of volumes for site 2: 2.00 Ratio of volumes for site 3: 1.92 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio:

72 Site preference for indium solutes: Bonding: Indium has greater bonding with cobalt than to samarium. (3 IC with Co, 1 IC with Sm.) The Sm site has the largest contact area with neighboring Co atoms. The Sm site has the largest volume, closest matching the atomic volume of indium. Conclusion: Indium will most likely rest on a Sm-site, considering a more preferable volume match and more contact area with cobalt, which it prefers over samarium. 70

73 Prototype Structurbereicht Pearson Space Group CaCu 5 D2 d hp6 P6/mmm #191 NRL link: Phase a (nm) b (nm) c (nm) SrAu N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector SrAu5 hp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Sr Area 2 Au 1 Area 3 Au 2 Area 2+3 Atomic vols 1 Sr Au Au Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: Ratio of volumes for site 2: 1.35 Ratio of volumes for site 3: 1.30 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: Site preference for indium solutes: 71

74 Bonding: Indium has greater bonding with gold than to strontium. (7+ IC with Au, 1 IC with Sr.) The Sr-site also has the largest contact area with neighboring Au atoms. The Sr-site has the largest volume, and is also the closest to the atomic volume of indium. Conclusion: The similarity in volumes of the Sr-site and elemental indium along with the largest contact area to the Au-sites seems to suggest that In will prefer the Sr-site. 72

75 Prototype Structurbereicht Pearson Space Group CaCu 5 D2 d hp6 P6/mmm #191 NRL link: Phase a (nm) b (nm) c (nm) TbCo N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector TbCo5 hp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Tb Area 2 Co 1 Area 3 Co 2 Area 2+3 Atomic vols 1 Tb Co Co Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.40 Ratio of volumes for site 2: 2.03 Ratio of volumes for site 3: 1.96 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio:

76 Site preference for indium solutes: Bonding: Indium has greater bonding with cobalt than to terbium. (3 IC with Co, 2 IC with Tb.) The Tb site has the largest contact area with neighboring Co atoms. The Tb site has the largest volume, closer matching the atomic volume of indium. Conclusion: Indium will most likely rest on a Tb-site, considering a more preferable volume match and more contact area with cobalt, which it prefers over terbium. 74

77 Prototype Structurbereicht Pearson Space Group CaCu 5 D2 d hp6 P6/mmm #191 NRL link: Phase a (nm) b (nm) c (nm) YCo N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector YCo5 hp Type Site Vol(Å 3 ) Area 1 (Å 2 ) Y Area 2 Co 1 Area 3 Co 2 Area 2+3 Atomic vols 1 Y Co Co Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 1.41 Ratio of volumes for site 2: 2.04 Ratio of volumes for site 3: 1.97 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio:

78 Site preference for indium solutes: Bonding: Indium has greater bonding with cobalt than to yttrium. (3 IC with Co, 1 IC with Y.) The Y site has the largest contact area with neighboring Co atoms. The Y site has the largest volume, closer matching the atomic volume of indium. Conclusion: Indium will most likely rest on a Y-site, considering a more preferable volume match and more contact area with cobalt, which it prefers over yttrium. 76

79 Prototype Structurbereicht Pearson Space Group Ni 3 Sn D0 19 hp8 P6 3 /mmc #194 NRL link: Phase a (nm) b (nm) c (nm) x Ni 3 Sn N/A Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Ni3Sn D0~ Type Site Vol(Å 3 ) Area 1 (Å 2 ) Sn Area 2 Ni Atomic vols 1 Sn Ni Volume of Indium: Ratio of volumes (In / site): Ratio of volumes for site 1: 2.37 Ratio of volumes for site 2: 2.04 Summed atomic volume: (nm 3 ) Unit cell volume: (nm 3 ) Ratio: 1.2 Site preference for indium solutes: 77

80 Bonding: Indium has greater bonding with nickel than to tin. (5 IC with Ni, 1 IC with Sn.) The Sn site has a larger contact area with neighboring nickel atoms. The Sn site has a larger volume, closer to the atomic volume of indium. Conclusion: Both values suggest that indium prefers the tin site over the nickel site. Notes: The disagreement between summed atomic volume and unit cell volume seems to stem from the inaccuracy of the x1 parameter, which affects the placement of the Ni atoms. This suggests that the volume of the Ni-site should be larger than reported. Replacing x with (closer to 5/6, as suggested by the NRL site) brings the summed atomic volume to (nm 3 ), thus the precision to 1.1. This also brings the volume of the Ni-site to 11.04, but the other values are only affected by their least significant digit. In general, having a high precision for the translation vectors improves the ratio value of the program by a significant amount. 78

81 Prototype Structurbereicht Pearson Space Group Al 3 Ni D0 22 op16 Pnma #62 NRL link: N/A Phase a (nm) b (nm) c (nm) x1 x2 x3 y z1 z2 z3 Al 3 Ni Input file: Label Translation vectors (nm) Number of origins for basis Atoms per cell, number of sites Site, atomic number, basis vector Al3Ni