Rhombohedral Distortion of the Cubic MgCu2-Type Structure in Ca2Pt3Ga and Ca2Pd3Ga

Two new fully ordered ternary Laves phase compounds, Ca2Pt3Ga and Ca2Pd3Ga, have been synthesized and characterized by powder and single-crystal X-ray diffraction along with electronic structure calculations. Ca2Pd3Ga was synthesized as a pure phase whereas Ca2Pt3Ga was found as a diphasic product with Ca2Pt2Ga. Electronic structure calculations were performed to try and understand why CaPt2 and CaPd2, which crystalize in the cubic MgCu2-type Laves phase structure, distort to the ordered rhombohedral variant, first observed in the magneto-restricted TbFe2 compound, with the substitution of twenty-five percent of the Pt/Pd with Ga. Electronic stability was investigated by changing the valence electron count from 22e−/f.u. in CaPd2 and CaPt2 (2x) to 37e−/f.u. in Ca2Pd3Ga and Ca2Pt3Ga, which causes the Fermi level to shift to a more energetically favorable location in the DOS. The coloring problem was studied by placing a single Ga atom in each of four tetrahedra of the cubic unit cell of the MgCu2-type structure, with nine symmetrically inequivalent models being investigated. Non-optimized and optimized total energy analyses of structural characteristics, along with electronic properties, will be discussed.


Introduction
Platinum exhibits the second largest relativistic contraction of the 6s orbitals, second only to Au [1], and has interesting catalytic properties, thus making it an interesting metal to study, especially in reduced environments.Exploration of the Ca-Pt-X (X = Ga, In) system revealed a new ternary compound, Ca 2 Pt 3 Ga, which turned out to be an ordered rhombohedral distortion of the MgCu 2 -type Laves phase CaPt 2 .After Ca 2 Pt 3 Ga was synthesized, the Pd analog was targeted and successfully prepared as an isostructural compound.
Laves phases are the largest class of intermetallic compounds with the general formula AB 2 .Binary Laves phases primarily crystalize in one of three crystal structures: MgCu 2 , MgZn 2 , or MgNi 2 [2].These structure types, which appear in a vast number of intermetallic systems, contain topologically closed-packed Frank-Kasper polyhedra and have been intensely studied for magnetic and magnetocaloric properties, hydrogen storage, and catalytic behavior [3][4][5][6][7][8][9].The stability of Laves phases has been described by using geometrical and electronic structure factors.Geometrical factors include packing densities and atomic size ratios of A/B whereas electronic factors include valence electron count (vec) and difference in electronegativities between A and B [10,11].
To tune the properties and structures of Laves phases, an addition via substitution of a third element into the structure can be explored.The resulting ternary compounds can have mixing on the A and B sites but retain the parent Laves phase structure or the structures can change into a fully ordered ternary Laves phase that is a variant of the parent structure.The first ordered ternary Laves phase with the direct rhombohedral distortion of the MgCu 2 -type, first evidenced in the binary TbFe 2 phase, which distorts via magnetostriction, was reported to be Mg 2 Ni 3 Si [11,12].Recently, many examples of this rhombohedral distortion, with varying vec, have been reported: RE 2 Rh 3 Si (RE = Pr, Er), U 2 Ru 3 Si, Ce 2 Rh 3+x Si 1−x , RE 2 Rh 3 Ge, Ca 2 Pd 3 Ge, Sm 2 Rh 3 Ge, U 2 Ru 3 Ge, Mg 2 Ni 3 Ge [2], Mg 2 Ni 3 P, and the heretofore only known gallides RE 2 Rh 3 Ga (RE = Y, La-Nd, Sm, Gd-Er).
The maximal translationengleiche subgroup of the Fd-3m space group that allows for the ordered 3:1 ratio of M:Ga atoms is R-3m [2,3,11].Reported herein is the first extensive computational study of the "coloring problem" [13] for this rhombohedral distortion of the cubic cell.Formation energies and electronic structure calculations were performed on the binary and ternary Laves phases CaM 2 and Ca 2 M 3 Ga (M = Pt, Pd) along with total energy calculations of various "coloring models" with the same composition but different atomic arrangements or "colorings".

Electronic Structure Calculations
Electronic structure calculations to obtain DOS and COHP curves for bonding analysis were performed on CaM 2 and Ca 2 M 3 Ga (M = Pd, Pt) using the Stuttgart Tight-Binding, Linear-Muffin-Tin Orbital program with the Atomic Sphere Approximation (TB-LMTO-ASA) [14].This approximation uses overlapping Wigner-Seitz (WS) spheres surrounding each atom so that spherical basis functions, i.e., atomic orbital (AO)-like wavefunctions, are used to fill space.The WS sphere radii used for the various atoms are: Ca 3.403-3.509Å, Pt 2.800-2.844Å, Pd 2.864-2.865Å, and Ga 2.800-2.951Å.The total overlap volume was 6.44% for the cubic Laves phase structures and 7.25% and 7.11%, respectively, for Ca 2 Pt 3 Ga and Ca 2 Pd 3 Ga.No empty spheres were required to attain 100% space filling of the unit cells.The exchange-correlation potential was treated with the von Barth-Hedin formulation within the local density approximation (LDA) [15].All relativistic effects except spin-orbit coupling were taken into account using a scalar relativistic approximation [16].The basis sets included 4s/(4p)/3d for Ca, 6s/6p/5d/(5f) for Pt, 5s/5p/4d/(4f) for Pd, and 4s/4p/(4d) for Ga (down-folded orbitals are shown in parentheses).Reciprocal space integrations were performed using k-point meshes of 1313 points for rhombohedral Ca 2 Pt 3 Ga and Ca 2 Pd 3 Ga and 145 points for cubic CaPt 2 and CaPd 2 in the corresponding irreducible wedges of the first Brillouin zones.
Structure optimization and total energy calculations were performed using the Vienna ab Initio Simulation Package (VASP) [17,18], which uses projector augmented-wave (PAW) [19] pseudopotentials that were treated with the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) [20].Reciprocal space integrations were accomplished over a 13 × 13 × 13 Monkhorst-Pack k-point mesh [21] by the linear tetrahedron method [22] with the energy cutoff for the plane wave calculations set at 500.00 eV.

Synthesis
All ternary compounds were obtained by melting mixtures of Ca pieces (99.99%,Sigma-Aldrich, St. Louis, MO, USA), Pt spheres (99.98%,Ames Laboratory, Ames, IA, USA) or Pd pieces (99.999%,Ames Laboratory), Ga ingots (99.99%,Alfa Aesar, Haverhill, MA, USA), and, in some cases, including Ag powder (99.9% Alfa Aesar).Samples of total weight ca.300 mg were weighed out in a N 2 -filled glovebox with <0.1 ppm moisture and sealed in tantalum tubes by arc-melting under an argon atmosphere.To prevent the tantalum tubes from oxidizing during the heating process, they were enclosed in evacuated silica jackets.The silica ampoules were placed in programmable furnaces and heated at a rate of 150 • C per hour to 1050 • C, held there for 3 h, then cooled at 50 • C per hour to 850 • C and annealed for 5 days.The samples were then cooled at 50 • C per hour to room temperature.Ca 2 Pt 3 Ga crystals were obtained from a loading of "Ca 2 Pt 3 Ga 0.85 Ag 0.15 ", whereas Ca 2 Pd 3 Ga crystals were obtained from stoichiometric mixtures of these elements.

Powder X-ray Diffraction
All samples were characterized by powder X-ray diffraction on a STOE WinXPOW powder diffractometer using Cu Kα radiation (λ = 1.540598Å).Each sample was ground using an agate mortar and pestle and then sifted through a US standard sieve with hole sizes of 150 microns.All powder specimens were fixed on a transparent acetate film using a thin layer of vacuum grease, covered by a second acetate film, placed in a holder and mounted in the X-ray diffractometer.Scattered intensities were recorded using a scintillation detector with a step size of 0.03 • in 2Θ using a step scan mode ranging from 0 • to 130 • .Phase analysis was performed using the program PowderCell [23] by overlaying theoretical powder patterns determined from single crystal X-ray diffraction over the powder patterns determined experimentally.

Single Crystal X-ray Diffraction
Single crystals were extracted from samples and mounted on the tips of thin glass fibers.Intensity data were collected at room temperature on a Bruker SMART APEX II diffractometer with a CCD area detector, distance set at 6.0 cm, using graphite monochromated Mo Kα radiation (λ= 0.71073 Å).The data collection strategies were obtained both by a pre-saved set of runs as well as from an algorithm in the program COSMO in the APEX II software package [24].Indexing and integration of data were performed with the program SAINT in the APEX II package [24,25].SADABS was used to apply empirical absorption corrections [24].Crystal structures were solved by direct methods and refined by full-matrix least squares on F 2 using SHELXL [26].The final refinements were performed using anisotropic displacement parameters on all atoms.All crystal structure figures were produced using the program Diamond [27].

Phase Analysis
Ca 2 Pt 3 Ga has been synthesized, but not as a pure phase.Using high temperature reactions, this compound can only be synthesized with the addition of a small quantity of silver in the loaded reaction mixture.Without adding silver the binary cubic Laves phase CaPt 2 forms as the major product as well as a small amount of some unidentified phase(s) according to X-ray powder diffraction.At reaction and annealing temperatures, Ga, Ca, and Ag are molten and their respective binary phase diagrams indicate miscibility.As Pt dissolves into the liquid, we hypothesize that the presence of Ag slows the reaction rate between Ca and Pt to form CaPt 2 and allows Pt and Ga to achieve sufficient mixing in the liquid before crystallizing into Ca 2 Pt 3 Ga.However, even when synthesized with the addition of silver and at 1050 • C, Ca 2 Pt 3 Ga does coexists with Ca 2 Pt 2 Ga and the binary CaPt 2 .Figure 1 shows the powder pattern for the sample loaded as "Ca 2 Pt 3 Ga 0.85 Ag 0.15 " along with the theoretical patterns for the Ca 2 Pt 3 Ga and Ca 2 Pt 2 Ga.Peak fitting analysis performed with Jana [28] can be found in Figure S1 along with relative contributions of the three phases.
Three samples with varying silver content, viz., 2.50, 8.33, and 14.29 mole percent Ag, were examined.According to the XPD patterns (see Figure S3 in Supporting Information), as the silver content increased, the yield of Ca 2 Pt 2 Ga increased.The outcome was also successfully reproducible for the loading "Ca 2 Pt 3 Ga 0.85 Ag 0.15 " (see Figure S4).
On the other hand, Ca 2 Pd 3 Ga can be prepared without the addition of silver.Since Ag and Pd have similar X-ray scattering factors, using Ag for the synthesis of Ca 2 Pd 3 Ga would present distinct challenges for subsequent characterization.Fortunately, a stoichiometric loading yielded Ca 2 Pd 3 Ga essentially as a pure phase product, with two non-indexed peaks at 2θ values of 20.0 • and 32.8 • most likely coming from a slight impurity of Ca 3 Pd 2 Ga 2 (see Figure 2).Figure S2 shows the Rietveld refinement of Ca 2 Pt 3 Ga.Both compounds Ca 2 Pt 3 Ga and Ca 2 Pd 3 Ga degrade in air after approximately two weeks.

Structure Determination
Several single crystals were selected from the loaded samples and tested on a Bruker SMART APEX II single crystal diffractometer for quality.Among those, the best 3 samples for Ca2Pt3Ga and Ca2Pd3Ga were examined.The results of single crystal X-ray diffraction on these crystals are found in Table 1 and Table S3.Ca2M3Ga (M = Pt, Pd) crystallize in the Y2Rh3Ge structure type [29], which is a rhombohedral distortion of the cubic Laves phase MgCu2-type structure, as discussed by Doverbratt et al. [3] and Siggelkow et al. [2].The M atoms occupy 9e Wyckoff positions which buildup 3.6.3.6 Kagomé nets orthogonal to the c-axis [2].The Ga atoms cap alternate triangular faces of the

Structure Determination
Several single crystals were selected from the loaded samples and tested on a Bruker SMART APEX II single crystal diffractometer for quality.Among those, the best 3 samples for Ca2Pt3Ga and Ca2Pd3Ga were examined.The results of single crystal X-ray diffraction on these crystals are found in Table 1 and Table S3.Ca2M3Ga (M = Pt, Pd) crystallize in the Y2Rh3Ge structure type [29], which is a rhombohedral distortion of the cubic Laves phase MgCu2-type structure, as discussed by Doverbratt et al. [3] and Siggelkow et al. [2].The M atoms occupy 9e Wyckoff positions which buildup 3.6.3.6 Kagomé nets orthogonal to the c-axis [2].The Ga atoms cap alternate triangular faces of the

Structure Determination
Several single crystals were selected from the loaded samples and tested on a Bruker SMART APEX II single crystal diffractometer for quality.Among those, the best 3 samples for Ca 2 Pt 3 Ga and Ca 2 Pd 3 Ga were examined.The results of single crystal X-ray diffraction on these crystals are found in Table 1 and Table S3.Ca 2 M 3 Ga (M = Pt, Pd) crystallize in the Y 2 Rh 3 Ge structure type [29], which is a rhombohedral distortion of the cubic Laves phase MgCu 2 -type structure, as discussed by Doverbratt et al. [3] and Siggelkow et al. [2].The M atoms occupy 9e Wyckoff positions which buildup 3.6.3.6 Kagomé nets orthogonal to the c-axis [2].The Ga atoms cap alternate triangular faces of the Kagomé net and themselves form hexagonal nets.The Ga and M atoms are each coordinated by 6 Ga or M atoms.Nine M and three Ga atoms surround each Ca atom in a slightly distorted Frank-Kasper polyhedral environment.The rhombohedral structure of Ca 2 M 3 Ga has no Ga-Ga nearest neighbor interactions, with distances (6×/6×) of 5.2361(9)/5.576(1)Å and 5.2331(6)/5.6326(8)Å for the Pt and Pd cases, respectively [3].For the binary compounds CaM 2 , each type of nearest neighbor interaction, i.e., Ca-Ca, Ca-M, and M-M, has a single length.When the structure distorts rhombohedrally to incorporate Ga atoms, the Ca-Ca and Ca-M contacts each split into two different distances: there are three shorter and one longer Ca-Ca interactions; whereas six Ca-M interactions that are longer and three shorter.Atomic positions and anisotropic displacement parameters for both compounds can be found in Tables S1  and S2.

Coloring Models and Electronic Structure Calculations
To elucidate the driving force that leads to the rhombohedral arrangement of Pt/Pd and Ga atoms in the majority atom positions of the cubic Laves phase, Burnside's lemma [30] was used to construct nine distinct structural models for the unit cells formulated as Ca 8 [M 3 Ga] 4 [31].These models are illustrated in Figure S5 along with their respective space groups.The total energy of each model, listed in Table 2, was calculated using VASP without optimization.These results show that the rhombohedral model (α) is the lowest in energy.There are three models that have no nearest neighbor Ga-Ga interactions, these include the rhombohedral coloring, a cubic coloring (µ), and an orthorhombic coloring (γ).The rhombohedral and cubic models are the two lowest in energy before optimization, whereas the orthorhombic coloring is the second highest in energy.All models were then optimized using VASP by allowing all structural parameters, including volume, cell shape, and atomic coordinates, to relax.The energies of the optimized structures can also be found in Table 2. Details of the optimized structures can be found in Tables S5-S13.After optimization, the rhombohedral model remains the lowest energy with the orthorhombic and cubic models coming in second and third lowest energy.The orthorhombic (γ) model optimized to a monoclinic unit cell, a = b = c and only β = 90 • , while the other two models retained their symmetry through the optimization.As the energies increase for the various optimized structures, the number of nearest neighbor Ga-Ga interactions increases and the corresponding Ga-Ga distances decrease.Table 2 lists the energies after optimization as well as the resulting nearest Ga-Ga distance showing the correlation between total energy and Ga-Ga interactions.
Calculations have shown that the rhombohedral model is the lowest energy both before and after optimization.This leads to the question of how does the rhombohedral structure arise from the "cubic" arranged starting point?The "cubic" starting point, for Ca 2 Pt 3 Ga, has a lattice parameter of 7.598 Å and a body diagonal distance of 13.160 Å.The primitive rhombohedral unit cell, within the face-centered cubic cell, has angles equal to 60 • before optimization.After optimization these angles are 57.825• and 57.515 • for Ca 2 Pt 3 Ga and Ca 2 Pd 3 Ga respectively.This collapsing of the angles, comprising the primitive unit cell, causes the expansion of the body diagonal.Optimization expands the lattice parameter by 1.43% to 7.708 Å.However, during optimization, the body diagonals do not expand congruently.Three body diagonals are congruent with a length of 13.627 Å while the fourth body diagonal shrinks to 12.482 Å.In the Pd case the three equivalent body diagonals are 13.754Å while the fourth body diagonal shrinks to 12.412 Å.The shorter body diagonal is parallel to the direction that the Ga atoms are located in each of the four tetrahedra in the unit cell (see Figure 3).Calculated ICOHP values for the "cubic" starting point indicate that the Pt-Ga bonds (ICOHP = −1.857eV) would become shorter as compared with the Pt-Pt bonds (ICOHP = −0.775eV).These ICOHP values shed light on the driving force behind the corresponding distortion of the cubic unit cell to the rhombohedral structure by substituting Ga for Pd/Pt: shorter Pt-Ga contacts will contract one body-diagonal of the cubic cell.Calculations have shown that the rhombohedral model is the lowest energy both before and after optimization.This leads to the question of how does the rhombohedral structure arise from the "cubic" arranged starting point?The "cubic" starting point, for Ca2Pt3Ga, has a lattice parameter of 7.598 Å and a body diagonal distance of 13.160 Å.The primitive rhombohedral unit cell, within the face-centered cubic cell, has angles equal to 60° before optimization.After optimization these angles are 57.825° and 57.515° for Ca2Pt3Ga and Ca2Pd3Ga respectively.This collapsing of the angles, comprising the primitive unit cell, causes the expansion of the body diagonal.Optimization expands the lattice parameter by 1.43% to 7.708 Å.However, during optimization, the body diagonals do not expand congruently.Three body diagonals are congruent with a length of 13.627 Å while the fourth body diagonal shrinks to 12.482 Å.In the Pd case the three equivalent body diagonals are 13.754Å while the fourth body diagonal shrinks to 12.412 Å.The shorter body diagonal is parallel to the direction that the Ga atoms are located in each of the four tetrahedra in the unit cell (see Figure 3).Calculated ICOHP values for the "cubic" starting point indicate that the Pt-Ga bonds (ICOHP = −1.857eV) would become shorter as compared with the Pt-Pt bonds (ICOHP = −0.775eV).These ICOHP values shed light on the driving force behind the corresponding distortion of the cubic unit cell to the rhombohedral structure by substituting Ga for Pd/Pt: shorter Pt-Ga contacts will contract one bodydiagonal of the cubic cell.All "coloring" calculations performed above were evaluated for the case of vec = 37e − /f.u.Models were also created for the Ca 2 Pd 3 Ge to determine if there were any differences by changing the vec to 38 e − /f.u.The energies of the non-optimized and optimized colorings can be found in Table S4, and the results show the same trends as those for Ca 2 M 3 Ga (M = Pd, Pt): the lowest energy model shows rhombohedral coloring and the largest Ge-Ge nearest neighbor distance.
To shed light on the nature of the distortion of the cubic Laves phase structure of CaM 2 (M = Pd, Pt) upon the substitution of Ga for M and their stability, various total energies as well as the density of states (DOS) and crystal orbital Hamilton population (COHP) curves were determined for the binaries CaM 2 and ternaries Ca 2 M 3 Ga (M = Pd,Pt).With respect to the elemental solids, the binaries CaM 2 and ternaries Ca 2 M 3 Ga are favored.For the experimental structures, CaPt 2 has an especially high formation energy compared to CaPd 2 ; the experimental volume of CaPt 2 is ca. 10 Å 3 /formula unit smaller than that of CaPd 2 , although Pt is slightly larger than Pd (the 12-coordinate metallic radii are 1.39 (Pt) and 1.37 (Pd) [32].This outcome may be an indication of relativistic effects on the valence orbitals of Pt, effects which can enhance empty d-filled d Ca-Pt 3d-5d interactions as compared to Ca-Pd 3d-4d interactions.
Total energy calculations for the "reactions" 2CaPt 2 + Ga → Ca 2 Pt 3 Ga + Pt and 2CaPd 2 + Ga → Ca 2 Pd 3 Ga + Pd illuminate significant aspects of the relative stability and formation of the ternaries.Both "reactions" yield favorable ∆E values, respectively, of −0.297 and −0.599 eV, and they can be separated into the sum of three hypothetical but revealing steps: (1) elemental substitution of Ga for M with no metric changes (volume, unit cell shape) in the cubic Laves phase structure; (2) volume change for the ternary without change in unit cell shape; and (3) distortion of the unit cell shape of the ternary at constant cell volume.Table 3 summarizes these results.The difference in overall total energies essentially arises from the energetic difference for step (1) between Pt and Pd cases: replacing Pt with Ga is energetically unfavorable whereas Pd for Ga is favorable.Since Ga (metallic radius of 1.50 Å [32]) is larger than either Pt or Pd, these energy differences reflect, in part, volume effects, but also are influenced by the relative Mulliken electronegativities [33], which increase Ga (3.2 eV) to Pd (4.45 eV) to Pt (5.6 eV).In the second step, both structures favorably expand by over 3% (based on unit cell volume) with slight energetic lowering.In the third step, both lattice distortions provide similar energetic stabilizations.Table 3. Relative total energies (eV) for conversion of binary cubic Laves phases CaM 2 into ternary rhombohedral derivatives Ca 2 M 3 Ga (M = Pd, Pt).* = cubic unit cell metric with volume matching the corresponding binary compound; ** = cubic unit cell metric with volume matching the corresponding rhombohedral ternary compound.Specific total energies (eV/formula unit) for each component are listed in Supporting Information.We now consider some specific aspects of the electronic structures of the binary CaM 2 and ternary Ca 2 M 3 Ga.The DOS and COHP for CaPt 2 are shown in Figure 4; the DOS shows a significant sharp peak at the Fermi level which suggests a potential electronic instability.The precise reason for this peak and the possible instability has not been forthcoming to date and an electronic structure investigation was performed.Analysis of the band structure at the Fermi level, specifically at the W point, because there are bands with nearly zero slope near this point, shows that the Pt 5d atomic orbitals are major contributors to this peak.For each Pt atom the orbital contribution is split approximately as 80 percent 5d and 20 percent 6p, and the primary interatomic orbital interactions are 5d-5d π* interactions.Spin-orbit coupling was added to the Hamiltonian operator of CaPt2 to see if the peak at the Fermi level would be affected.Figure S6 shows the DOS curve and band structure for these calculations.The degeneracies in the band structure at the high symmetry k-points are removed by the spin-orbit coupling; however, the peak at EF is not affected.Furthermore, the application of spin-orbit coupling would only converge with a unit cell expanded by ~1.1 Å.A second hypothesis was to consider that vacancies might be playing a role to stabilize the structure.DOS calculations were subsequently performed using VASP on "Ca8Pt15" and "Ca8Pt12" models to see the effect of vacancies on the peak at EF; these results can be seen in Figure S7.The peak is no longer present in the "Ca8Pt12" model only when all 4 vacancies are adjacent to each other so that the resulting defect Laves phase structure is missing an entire tetrahedron per unit cell.Lastly, DOS curves calculated for AEM2 (AE = Ca, Sr, Ba; M = Ni, Pd, Pt), shown in Figure S8, indicate that as the size of the alkaline earth metal increases, the peak in the DOS moves away from EF.These calculations have not identified the reason behind the potential electronic instability in CaM2 and now the possibility of superconductivity is being investigated.
The Pt 5d band dominates the overall occupied DOS of CaPt2 and the majority contribution to the overall polar covalent bonding via ICOHP values arises from Pt-Pt interactions, which switch from bonding to antibonding at an energy value corresponding to 12.42 e − /formula unit.At the Fermi level, the Pt-Pt COHP curve shows a small antibonding peak, whereas the Ca-Pt and Ca-Ca COHPs show a small bonding peak.On transitioning to Ca2Pt3Ga, the peak at the Fermi level in the DOS of The precise reason for this peak and the possible instability has not been forthcoming to date and an electronic structure investigation was performed.Analysis of the band structure at the Fermi level, specifically at the W point, because there are bands with nearly zero slope near this point, shows that the Pt 5d atomic orbitals are major contributors to this peak.For each Pt atom the orbital contribution is split approximately as 80 percent 5d and 20 percent 6p, and the primary interatomic orbital interactions are 5d-5d π* interactions.Spin-orbit coupling was added to the Hamiltonian operator of CaPt 2 to see if the peak at the Fermi level would be affected.Figure S6 shows the DOS curve and band structure for these calculations.The degeneracies in the band structure at the high symmetry k-points are removed by the spin-orbit coupling; however, the peak at E F is not affected.Furthermore, the application of spin-orbit coupling would only converge with a unit cell expanded by ~1.1 Å.A second hypothesis was to consider that vacancies might be playing a role to stabilize the structure.DOS calculations were subsequently performed using VASP on "Ca 8 Pt 15 " and "Ca 8 Pt 12 " models to see the effect of vacancies on the peak at E F ; these results can be seen in Figure S7.The peak is no longer present in the "Ca 8 Pt 12 " model only when all 4 vacancies are adjacent to each other so that the resulting defect Laves phase structure is missing an entire tetrahedron per unit cell.Lastly, DOS curves calculated for AEM 2 (AE = Ca, Sr, Ba; M = Ni, Pd, Pt), shown in Figure S8, indicate that as the size of the alkaline earth metal increases, the peak in the DOS moves away from E F .These calculations have not identified the reason behind the potential electronic instability in CaM 2 and now the possibility of superconductivity is being investigated.
The Pt 5d band dominates the overall occupied DOS of CaPt 2 and the majority contribution to the overall polar covalent bonding via ICOHP values arises from Pt-Pt interactions, which switch from bonding to antibonding at an energy value corresponding to 12.42 e − /formula unit.At the Fermi level, the Pt-Pt COHP curve shows a small antibonding peak, whereas the Ca-Pt and Ca-Ca COHPs show a small bonding peak.On transitioning to Ca 2 Pt 3 Ga, the peak at the Fermi level in the DOS of CaPt 2 has all but disappeared in the DOS curve of Ca 2 Pt 3 Ga (see Figure 5).There is a large range from ca. −1.5 to +1 eV over which the DOS of Ca 2 Pt 3 Ga remains flat.The COHP curves have also changed in that the Pt-Pt interactions still transition to antibonding at −2.60 eV, although around the Fermi level they are mostly nonbonding rather than antibonding.Overall, at the Fermi level there are now no small peaks but mostly constant intensities of nonbonding or slightly bonding interactions with the Ca-Pt interactions still contributing the most to overall bonding.
CaPt2 has all but disappeared in the DOS curve of Ca2Pt3Ga (see Figure 5).There is a large range from ca. −1.5 to +1 eV over which the DOS of Ca2Pt3Ga remains flat.The COHP curves have also changed in that the Pt-Pt interactions still transition to antibonding at −2.60 eV, although around the Fermi level they are mostly nonbonding rather than antibonding.Overall, at the Fermi level there are now no small peaks but mostly constant intensities of nonbonding or slightly bonding interactions with the Ca-Pt interactions still contributing the most to overall bonding.The DOS and COHP curves for CaPd2 (see Figure 6) and Ca2Pd3Ga (see Figure 7) look similar overall to those described above for the Pt counterparts, although there are a few distinct differences.The peak at the Fermi level in the DOS for CaPd2 as well as the antibonding Pd-Pd peak in the COHP are not as intense nor as sharp as those observed for CaPt2.The Pd-Pd interactions transition from bonding to antibonding at an energy which corresponds to 15.36 eV/formula unit.There is a similar minimum in the Pd 4d states at −1.40 eV which corresponds to 7.5 4d electrons/Pd.The DOS and COHP for Ca2Pd3Ga are similar to those for Ca2Pt3Ga.There is again a large energy range from ca. −1.8-1.8 eV over which the DOS remains flat.The DOS and COHP curves for CaPd 2 (see Figure 6) and Ca 2 Pd 3 Ga (see Figure 7) look similar overall to those described above for the Pt counterparts, although there are a few distinct differences.The peak at the Fermi level in the DOS for CaPd 2 as well as the antibonding Pd-Pd peak in the COHP are not as intense nor as sharp as those observed for CaPt 2 .The Pd-Pd interactions transition from bonding to antibonding at an energy which corresponds to 15.36 eV/formula unit.There is a similar minimum in the Pd 4d states at −1.40 eV which corresponds to 7.5 4d electrons/Pd.The DOS and COHP for Ca 2 Pd 3 Ga are similar to those for Ca 2 Pt 3 Ga.There is again a large energy range from ca. −1.8-1.8 eV over which the DOS remains flat.Tables S14-S17 contain the percent contributions of each type of interaction to the overall integrated COHP (ICOHP) values.These can be used as an indication to determine the bond energy   Tables S14-S17 contain the percent contributions of each type of interaction to the overall integrated COHP (ICOHP) values.These can be used as an indication to determine the bond energy

Figure 1 .
Figure 1.Powder Patterns for Ca2Pt3Ga showing the existence of Ca2Pt2Ga in the system.

Figure 1 .
Figure 1.Powder Patterns for Ca 2 Pt 3 Ga showing the existence of Ca 2 Pt 2 Ga in the system.

Figure 1 .
Figure 1.Powder Patterns for Ca2Pt3Ga showing the existence of Ca2Pt2Ga in the system.

Figure 3 .
Figure 3. "Cubic" arranged starting point with 4 congruent body diagonals (left) optimized rhombohedral unit cell (right) with 3 body diagonals of 13. 627 Å and 1 body diagonal of 12.482 Å. Red colored bonds shrink during optimization causing the reduction in body diagonal length from 011 to 100.Blue, black, and red atoms are Ca, Pt, and Ga respectively.

Figure 3 .
Figure 3. "Cubic" arranged starting point with 4 congruent body diagonals (left) optimized rhombohedral unit cell (right) with 3 body diagonals of 13.627 Å and 1 body diagonal of 12.482 Å. Red colored bonds shrink during optimization causing the reduction in body diagonal length from 011 to 100.Blue, black, and red atoms are Ca, Pt, and Ga respectively.

Table 1 .
Crystallographic information for Ca 2 Pt 3 Ga and Ca 2 Pd 3 Ga.

Table 2 .
Total energy of non-optimized and optimized coloring models showing optimized Ga-Ga distances.

Table 2 .
Total energy of non-optimized and optimized coloring models showing optimized Ga-Ga distances.