Structural Phase Transitions in PtIn2 at High Pressure: A Theoretical

Nov 16, 2017 - Here we investigated the high-pressure structural behavior of PtIn2 using crystal structure search calculations, which efficiently comb...
0 downloads 17 Views 5MB Size
Download PDF
Article Cite This: Inorg. Chem. XXXX, XXX, XXX-XXX

pubs.acs.org/IC

Structural Phase Transitions in PtIn2 at High Pressure: A Theoretical Investigation P. Modak* and Ashok K. Verma High Pressure and Synchrotron Radiation Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India ABSTRACT: A study of the bonding and electronic properties of intermetallics under pressure is crucial in the design and development of novel materials for useful applications. These properties are largely controlled by the underlying crystal structures. Here we investigated the high-pressure structural behavior of PtIn2 using crystal structure search calculations, which efficiently combine evolutionary algorithms and state-of-the-art density functional theory. Three new crystal structures, namely, Fe2B-type (I4/mcm, Z = 2), cotunnite-type (Pnma, Z = 4), and monoclinic (C2/m, Z = 2), are proposed at about 9.4, 13.5, and 47.5 GPa, respectively. With pressure, the covalent character of the Pt−In pair interaction is found to increase because of enhancement of spd hybridization, and structural transitions are rationalized in terms of the covalency increase.

■

structure in AuIn2 near 10 GPa.18 An electronic topological transition (ETT) was thought to be responsible for this structural transition. Pt has one less valence electron than Au, and according to the Hume−Rothery rule,3 the average valence electron density (average valence electron/atom) plays an important role for the phase stability of alloys and intermetallics. Hence, it will be interesting to study the structural properties of PtIn2 and its high-pressure behavior to see whether it follows the same structural sequence as AuIn2. If it shows the same structural sequence, then it will be interesting to explore the underlying mechanism because our earlier electronic band-structure calculations did not show an ETT in PtIn2.19 The highest occupied band that was responsible for the ETT in AuIn2 is expected to become unoccupied in PtIn2. So, this work could reveal reasons for the stabilization of PtIn2 and AuIn2 in the CaF2-type phase. In this work, we carried out extensive crystal structure searches for this compound to see whether there is any lower-enthalpy crystal structure other than CaF2- and cotunnite-type structures near 10 GPa. This is important because in our earlier work19 we used a limited set of structures to study its structural stability, and a structural transition from CaF2- to cotunnite-type structure near 10 GPa was proposed. In our earlier studies, we showed that evolutionary structure searches combined with first-principles relaxation are an efficient way of determining crystal structures under high pressure.18,20 We found that PtIn2 undergoes a structural transition from CaF2-type structure to Fe2B-type tetragonal structure near 9.4 GPa similar to AuIn2. Hence, its low-pressure structural behavior is similar to that of AuIn2, although there is no ETT or phonon softening or destruction of giant Kohn anomaly near this transition. In addition, we

INTRODUCTION Intermetallic compounds are probably the oldest manmade materials and have occupied the center stage in modern material research.1,2 They are receiving constant attention from physicists, chemists, and material scientists mainly because of their attractive physical and mechanical properties.3−9 The intermetallics of two or more metallic elements comprise ordered metallic phases of fixed composition. In general, they possess high melting point, low density, high strength, high oxidation resistance, etc.10−12 The most important factor that determines the properties of a material is its crystal structure, which is determined by the chemical bonding among its constituent elements. In binary intermetallics, two major factors, namely, the size difference and the electronegativity difference of the constituent elements, determine their crystal structure.13 The electronegativity difference causes charge transfer from the less electronegative element to the more electronegative element. Hence, the chemical bonding for these types of systems contains partial ionic/covalent bonding in addition to metallic bonding. The interplay between different types of bonding under the application of high pressure or temperature may lead to structural phase transitions, which, in turn, can exhibit some useful material properties. Therefore, studies on the structural properties of intermetallic compounds, under high pressure, have enormous importance for the understanding and design/ development of intermetallics for specific applications. Here we studied the high-pressure structural properties of PtIn2, which crystallizes in the CaF2-type structure and has many important industrial applications.14−17 It is observed that, in CaF2-type structure intermetallics, the constituent elements have nearly identical atomic sizes, and, hence, charge transfer, due to the electronegativity difference, plays an important role in their structural stability.13 Recently, we predicted a structural transition from CaF2-type structure to Fe2B-type tetragonal © XXXX American Chemical Society

Received: September 29, 2017

A

DOI: 10.1021/acs.inorgchem.7b02507 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry predicted two additional structural transitions for PtIn2, namely, (i) Fe2B-type tetragonal to cotunnite-type orthorhombic structure (Pnma) near 13.5 GPa and (ii) cotunnite-type orthorhombic (Pnma) to monoclinic (C2/m) structure near 47.5 GPa.

■

METHOD OF CALCULATIONS

Probable crystal structures at various pressures are determined using the USPEX code, which efficiently combines the evolutionary algorithm and first-principles structural relaxation.21−23 Structural relaxation is carried out using density functional theory, as implemented in the VASP code.24−27 The exchange correlations are treated within the local density approximation (LDA).28 Ambient properties are also calculated with the generalized gradient approximation (GGA).29 Structural searches are carried out at 0, 10, 20, 30, and 50 GPa. The initial structures are always generated with random structure generators with a starting cell having four formula units. The initial population is taken as 30, and the population for subsequent generations is kept fixed at 20. In each generation, structures are generated by heredity (50%), soft mutation (20%), lattice mutation (20%), and a certain percentage by random structure generation (10%). The best structures of the previous generations are also kept in the population. We found that a structural evolution of up to 20 generations is sufficient for getting the most probable structures at a given pressure. After completion of all generations, the most probable structures are reoptimized and symmetry-analyzed to determine the final structure. Because the results are sensitive to the initial size of the unit cell, we also studied structural evolutions with eight formula units in the starting cell for 10 GPa. The projector-augmented-wave (PAW) potentials with the valence configurations 5d96s1 and 4d105s25p1 for Pt and In, respectively, are used for structural relaxation and total energy calculations. The plane-wave basis functions are expanded with a 500 eV cutoff energy, and the Brillouin zone (BZ) integration is carried out using Γ-centered uniform k-mesh with a resolution of 2π × 0.01 Å−1. In the total energy calculations, we used the tetrahedron method with Blöchl corrections30 for BZ integration, whereas for relaxation and force calculations, we used the first-order Methfessel−Paxton smearing scheme31 with a smearing parameter of 0.1 eV. The noncollinear mode implementation of spin− orbit (SO) interactions, where the relativistic Hamiltonian is expressed as a 2 × 2 matrix in spin space, as implemented in the VASP code,32,33 is used to study the SO effects. In this implementation, the Hamiltonian is a function of the 2 × 2 density matrix, which can be written as a linear combination of the 2 × 2 unit matrix and the vector of the Pauli spin matrices. The trace of the density matrix gives the electron density. To determine pressure−volume equation of states (EOS) for a given structure, we calculated the total energy for different volumes and then fitted the energy-volume data to a polynomial. Calculating the first-order derivative of the polynomial, we determined the pressure at different volumes and, hence, the pressure−volume relationship of a particular structure. Phonon calculations are carried out using the smalldisplacement supercell approach, as implemented in the PHON code.34 In these phonon calculations, we took a 4 × 4 × 4 supercell for the CaF2-type structure, a 2 × 2 × 2 supercell for the Fe2B-type structure, a 2 × 3 × 2 supercell for the orthorhombic (Pnma) structure, and a 3 × 3 × 3 supercell for the monoclinic (C2/m) structure. The number of displacements required to generate the full phonon spectra are determined by the program itself. The amplitude of the atomic displacement is chosen as 0.04 Å for all cases. The elastic constants for all of the structures are determined using the strain−energy relationhip (for details, see ref 35).

Figure 1. Different crystal structures of PtIn2. Here, the golden balls represent Pt atoms, and the violet balls represent In atoms.

ambient-pressure phase. The calculated equilibrium volume and bulk modulus for the ambient-pressure phase are compared with the available experimental and theoretical results in Table 1.19,36 Table 1. Ground-State Properties of PtIn2

present calculations

others (GGA)36 pseudopotential FP-LAPW experiment19

LDA LDA + SO GGA

volume (Å3/ f.u.)

bulk modulus (GPa)

63.05 63.17 67.94

122.50 113.80 97.00

64.34 64.41 64.40

68.64 88.54 130.00

The present results are in good agreement with those of the experiment. We also found that LDA describes the ambientpressure volume and bulk modulus better than GGA. The large difference in the bulk modulus particularly between the earlier pseudopotential GGA36 and the present PAW−GGA calculations may be attributed to the difference in the computational parameters. In earlier work,36 the authors used ultrasoft pseudopotential, which generally needs larger plane-wave cutoff energy compared to the PAW potentials. However, they used a lower plane-wave energy cutoff (400 eV) compared to the present PAW calculations (500 eV). Also, they used the Perdew−Wang-91 GGA functional,28 whereas in the present calculations, we used the PBE−GGA functional.29 It is to be noted that their bulk modulus computed with FP-LAPW-GGA (∼88 GPa) is comparable to our PAW−GGA value (97 GPa). SO interactions have a minor effect on the ground-state properties (ambient-pressure lattice constant, bulk modulus, etc.). Hence, the SO effects are not included for the high-pressure properties and electronic structures. Elastic constants are also estimated at the LDA level and without SO corrections; the results are presented in Table 2. Details of the structural

■

RESULTS AND DISCUSSION The energetically most favorable crystal structures, obtained from crystal structure searches under pressure, are CaF2-type (space group Fm3̅m, No. 225), Fe2B-type (space group I4/mcm, No. 140), cotunnite-type (space group Pnma, No. 62), and monoclinic (space group C2/m, No. 12) (Figure 1). Our crystal structure searches correctly reproduce the CaF2-type structure as B

DOI: 10.1021/acs.inorgchem.7b02507 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

C44 − P > 0, C66 − P > 0, C11 − P > |C12 + P|, [(C33 − P)(C11 + C12) − 2(C13 + P)2] > 0

C11 − P > 0, C44 − P > 0; C55 − P > 0, C66 − P > 0; (C11 − P)(C22 − P) > (C12 + P)2; [(C11 − P)(C22 − P)(C33 − P) + 2(C12 + P)(C13 + P)(C23 + P) − (C11 − P) (C23 + P)2− (C22 − P) (C13 + P)2 − (C33 − P) (C12 + P)2] > 0

eigenvalues of the elastic stiffness matrix C will be all positive

at P = 10 GPa; C11 = 219.12, C12 = 148.15; C13 = 106.19, C33 = 295.89; C44 = 60.44, C66 = 43.82

at P = 16 GPa, C11 = 261.20, C12 = 205.96, C13 = 154.74, C22 = 294.67, C23 = 179.92, C33 = 338.18, C44 = 73.30, C55 = 99.84, C66 = 50.27

at P = 49 GPa, C11 = 558.22, C12 = 251.49, C13 = 212.26, C22 = 602.34, C23 = 220.78, C33 = 515.04, C44 = 150.05, C55 = 140.26, C66 = 50.07, C16 = −5.49, C26 = −5.74, C36 = −14.60, C45 = 1.90

C11 + 2C12 + P > 0, C44 − P > 0, C11 − C12 − 2P > 0 at P = 10 GPa, C11 = 199.57, C12 = 137.97, C44 = 34.71, B = (C11 + 2 C12)/3 = 158.50 at P = 0 GPa, C11 = 100.07, C12 = 52.93, C44 = 20.74, B = (C11 + 2C12)/3 = 68.64

information on the predicted high-pressure phases are presented in Table 3. The energy−volume and enthalpy−pressure Table 3. Structural Information of the High-Pressure Phases lattice parameters (Å) Fe2B-type (space group I4/ mcm), P = 10 GPa

cotunnite-type (space group Pnma), P = 15 GPa

monoclinic (space group C2/m), P = 50 GPa

orthorhombic (space group Pnma) monoclinic (space group C2/m)

Fe2B-type

Wyckoff positions

a = 6.3917, b = 6.3917, and c Pt 4a: 0.0000, = 5.3679 0.0000, 0.2500 In 8h: 0.1573, 0.6573, 0.0000 a = 6.5757, b = 3.8131, and c Pt 4c: 0.2481, = 8.4265 0.2500, 0.6457 In1 4c: 0.0475, 0.2500, 0.3359 In2 4c: 0.1459, 0.2500, 0.9442 a = 4.7348, b = 8.0160, and c Pt 4i: 0.7973, = 4.7156; β = 88.85° 0.0000, 0.7443 In 8j: 0.2048, 0.3379, 0.2480

relationships are given in Figure 2. In the energy−volume relationship, we compared the energy per formula unit for different structures, and the structural sequence ‘cubic CaF2 → tetragonal Fe2B → orthorhombic Pnma → monoclinic C2/m’ as a function of the compression is clear from the energy−volume curves. In the enthalpy−pressure relationships, we plotted the enthalpies of different high-pressure phases with respect to that of the ambient-pressure phase (CaF2-type) as a function of the pressure. It is evident from the figure that the ambient-condition fluorite structure transforms to a Fe2B-type body-centered tetragonal structure at ∼9.4 GPa, which transforms to a cotunnite-type structure (Pnma) at ∼13.5 GPa. Upon further compression, the cotunnite-type structure transforms to the monoclinic C2/m structure at ∼47.5 GPa. The value of the transition pressure corresponding to first phase transition agrees very well with the experimental value of ∼10 GPa.19 No experimental data exist beyond 13.4 GPa. It is to be noted that in our earlier calculations19 we did not carry out a structure search but calculated the total energies for ambient CaF2-type and cotunnite-type orthorhombic (Pnma) structures and predicted a structural transition from the CaF2-type to cotunnite-type structure near 10.5 GPa. In the present calculations, we found that the tetragonal Fe2B-type and orthorhombic cotunnite-type Pnma are very close in energy, but the Fe2B-type structure is energetically more favorable. It is also evident from Figure 2 that near 10 GPa the enthalpy of the orthorhombic Pnma structure becomes lower compared to the ambient CaF2-type structure but remains higher compared to the Fe2B-type structure and, hence, is consistent with our earlier calculations. Note that AuIn2 also adopts the Fe2B-type structure at ∼10 GPa.18 Figure 3 shows the calculated pressure−volume relationships of these structures. The volume drops (ΔV) during the first, second, and third phase transitions, as mentioned above, are 6.8%, 0.9%, and 1.5%, respectively. The large volume drop in the CaF2-type → Fe2B-type (6.8%) transition is related to the coordination number increases of Pt (8 → 10) and In (4 → 5). However, in the Fe2B-type → cotunnite-type transition (ΔV ∼ 0.9%), the coordination number of Pt decreases (10 → 9) and that of In increases (In1, 5 → 7; In2, 5 → 8). The cotunnite phase has three types of Pt−In bonds, whose lengths are distributed around the Pt−In bond length of the Fe2B-type and CaF2-type phase. In the cotunnite-type → C2/m transition (ΔV ∼ 1.5%), the coordination numbers of Pt and In become 10 and all Pt−In

other theory (GGA)36 present calculations (LDA) present calculations (LDA) present calculations (LDA

C11 + 2C12 > 0, C44 > 0, C11 − C12 > 0 at P = 0 GPa, C11 = 160.79, C12 = 103.42, C44 = 33.75, B = (C11 + 2 C12)/3 = 122.54 present calculations (LDA) CaF2-type

structure

Table 2. Elastic Constants of PtIn2

elastic constant (GPa)

stability condition37,38

Inorganic Chemistry

C

DOI: 10.1021/acs.inorgchem.7b02507 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 2. Calculated energy−volume and enthalpy−pressure relationships of different phases of PtIn2. Here, the enthalpy of each phase is plotted with respect to that of the ambient phase; i.e., ΔH = H − HCaF2. Here, energy/enthalpy is given per formula unit of PtIn2.

dispersion relationships (Figure 4). The calculated elastic constants satisfy the stability conditions37,38 for all the structures near the transition. For the monoclinic structure, the elastic stability is verified by calculating the eigenvalues of the elastic stiffness matrix, which has 13 independent elements. All of the eigenvalues of this stiffness matrix are positive, indicating the elastic stability of this structure. From Figure 4, it is evident that the absence of imaginary frequencies in phonon dispersions and density of states (DOSs) definitely establishes the dynamic stabilities of the high-pressure phases. It is also evident that the phonon (Figure 4, 0 and 12 GPa) in PtIn2 shows usual pressure hardening, ruling out any possibility of the phonon softening in the ambient-pressure phase. Contrary to this, phonon softening was predicted in the CaF2-type phase of AuIn2 close to the transition.18 The electronic properties of different phases are analyzed by calculating the band structure, DOSs, and electron-localization functions (ELFs; Figures 5 and 6). The overall band structure of the CaF2-type PtIn2 is very similar to that of AuIn2.18 Because Pt has one electron less than Au, the Fermi level moves down, leaving one band partially empty in PtIn2. It is clear that Pt d states are nearly full and are located 3−6 eV below the Fermi level. The top of the d band mixes with sp-hybridized bands, whereas the bottom of the d band mixes with s-type bands. The flat band just (∼1 eV) above the Fermi level along the Γ−X direction is the In s antibonding state. The flatness of the band indicates that it is an unhybridized band. The same band was partially occupied in AuIn2 and under pressure became empty, causing ETT. From this, it is expected that PtIn2 will not show ETT under pressure. The SO coupling effects are weaker in PtIn2, as is evident from the electronic band structure. The SO only splits the d−t2g band, which is located 4.5 eV below the Fermi level, and negligible changes are in those bands that pass through the Fermi level. Hence, SO effects are not included in the electronic structure of the high-pressure phases. Under pressure (∼10 GPa), the d band moves down, whereas sphybridized band moves up relative to the Fermi level. This opposite movement reduces the overall spd hybridization in the vicinity of the Fermi level. No ETT was seen in this compound under pressure. Although the Fermi level in the Fe2B-type phase lies in a local minimum of the electronic DOS, the total DOS at the Fermi level is slightly higher than that of the CaF2-type structure. The Fe2B-type phase has highly dispersive bands near the Fermi level (shown in Figure 5 near 10 GPa) due to larger sp hybridization near the Fermi level than the ambient phase. Note that, for solid In, the face-centered-cubic structure distorts to the body-centered-tetragonal structure to maximize the sp hybrid-

Figure 3. Pressure−volume EOSs for different structures of PtIn2. The vertical lines connecting two pressure−volume curves represent structural transitions from the upper one to the lower one. Here, the volume is given per formula unit of PtIn2.

bond lengths are nearly equal. Details of the coordination environments for different structures are given in Table 4. The elastic and dynamic stabilities of all of the phases are investigated by estimating the elastic constants (Table 2) and phonon Table 4. Atomic Coordination in Different Structures structure CaF2-type (Fm3̅m), P = 0 GPa CaF2-type (Fm3m ̅ ), P = 10 GPa Fe2B-type (I4/ mcm), P = 10 GPa cotunnite-type (Pnma), P = 15 GPa

coordination number

2.74 (8, In)

In: 4 Pt: 8

2.74 (4, Pt) 2.67 (8, In)

In: 4 Pt: 10

2.67 (4, Pt) 2.68 (2, Pt), 2.76 (8, In)

In: 5 Pt: 9

2.76 (4, Pt), 2.86 (1, In) 2.61 (1, In), 2.65 (2, In), 2.73 (3, In), 2.83 (2, In), 2.93 (1, In)

In1:7

2.73 (2, Pt), 2.83 (2, Pt), 2.93 (1, Pt), 2.92 (2, In2) 2.61 (1, Pt), 2.65 (2, Pt), 2.73 (1, Pt), 2.87 (2, In2), 2.92 (2, In1) 2.69 (2, In), 2.71 (4, In), 2.72 (2, In) 2.73 (2, In) 2.60 (1, In), 2.69 (1, Pt), 2.71 (2, Pt), 2.72 (1, Pt), 2.73 (1, Pt), 2.76 (3, In), 2.80 (1, In)

In2:8 monoclinic (C2/ m), P = 50 GPa

neighbor distances (Å) (number, type)

Pt: 8

Pt: 10 In: 10

D

DOI: 10.1021/acs.inorgchem.7b02507 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 4. Phonon dispersions and DOSs for all of the phases of PtIn2. Phonon dispersions are along the high-symmetry directions of the respective BZ.

Bader charge analysis was carried out to understand the role of the electronegativity difference and charge transfer in structural stability at varied conditions.40 There is around 0.60e charge transfer from In to Pt at ambient pressure, indicating a significant role of ionic interactions in the bonding of this compound. This could be a factor for CaF2-type phase formation in this intermetallic, which is a well-known structure for ionic insulators. The charge transfer slightly increases with the pressure, reaching 0.62e at the transition to the Fe2B-type phase. A similar analysis for high-pressure phases shows a lesser charge transfer from the In atom to the Pt atom. In the Fe2B-type phase, each In atom transfers only ∼0.47e to Pt near ∼9.4 GPa. So, this phase is less ionic. In Pnma phase, the average charge transfer from each In atom is ∼0.55e and that for the C2/m phase is ∼0.50e. Both are calculated near their respective phase transitions. Finally, to understand the role of the band structure and electrostatic interactions for the stability of the Fe2B-type structure over the fluorite structure, we separated the band structure energy from the total energy and plotted both parts as a function of the volume (Figure 7). The band energy, which represents the sum of the occupied states, is important for understanding the energy gain due to band rearrangements or electronic transitions. The rest of the total energy, which consists of electrostatic and exchange-correlation parts, is important for understanding the change in the electrostatic interactions because the exchange correlations are expected to be similar in both phases because the sp types of electrons are mostly responsible for bonding. It is clear that the ambient structure is favored by the band-structure energy, whereas the high-pressure Fe2B-type structure is favored by the electrostatic energy. Under

ization, which helps to push the s-type antibonding states above the Fermi level.39 The Pnma phase also has highly dispersive bands close to the Fermi level due to increased spd hybridization (shown in Figure 5 near 20 GPa). The total electronic DOS at the Fermi level is slightly smaller than that in the Fe2B-type structure, indicating a slight gain in the band energy. The spd hybridization is further enhanced in the monoclinic phase, as is evident from the band structure and DOS function (shown in Figure 5 near 50 GPa). This phase has a well developed pseudogap in the DOS function close to the Fermi level. It is also seen that at 50 GPa a pseudogap also develops in the DOS function for the Pnma phase, but the Fermi level lies slightly away from the pseudogap and as a result the total DOS at the Fermi level in the Pnma phase is higher than that of the monoclinic C2/ m structure. Figure 6 shows the ELFs for different phases. It is clear that at ambient pressure the Pt d electrons are localized around Pt and the higher localization arises along the nonbonding direction. At high pressures, the d electron localization along the nonbonding direction increases; i.e., spd hybridization decreases. However, in the Fe2B-type structure, some of the d electrons get delocalized and the occurrence of higher localization near the bond center indicates enhanced covalent interaction. Hence, enhanced covalent interaction at high pressures plays an important role in the stability of the Fe2B-type phase. It is evident that, as the pressure increases, the Pt−In bonding acquires more and more covalent character or, in other words, spd hybridization increases. Therefore, to increase spd hybridization, the system adopts a lower-symmetry structure under pressure. E

DOI: 10.1021/acs.inorgchem.7b02507 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 5. Electronic properties of different phases of PtIn2. Here, the DOS is given in units of states per electronvolts per formula unit.

■

compression, the gain due to electrostatic interactions for the Fe2B-type structure approaches the gain due to the bandstructure part in the CaF2-type structure and finally overtakes it near 9.4 GPa. Hence, this structural transition occurred because of the higher electrostatic energy cost of the ambient phase compared to that of daughter phase. A similar analysis for AuIn2 also leads to the same conclusion, indicating an electrostatic origin for the CaF2-to-Fe2B-type structural transition under pressure. Similarly, we can say that in PtIn2 the second transition, i.e., Fe2B-type to Pnma, occurred because of the band-structure rearrangement because Pnma has a lower band-structure energy than the Fe2B-type structure. This is also evident from the electronic DOS discussed above.

CONCLUSIONS

In summary, we explored the high-pressure structural properties of PtIn2 using crystal structure searches. Three new phases, namely, Fe2B-type (I4/mcm), cotunnite-type (Pnma), and monoclinic (C2/m), are proposed below 50 GPa. The transition pressures are not very high and are easily achievable in diamondanvil cell experiments, and hence our findings might trigger some high-pressure experiments. The covalent nature of Pt−In bonding increases in successive high-pressure phases. Higher Madelung energy corresponding to higher coordination number or favorable electrostatic interactions stabilizes the Fe2B-type structure. The same effects are also found to be responsible for the structural transition of AuIn2. So, we conclude that the electrostatic interactions play an important role in the F

DOI: 10.1021/acs.inorgchem.7b02507 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 6. ELFs of different phases of PtIn2. Here, green balls represent Pt atoms and pink balls represent In atoms.

Figure 7. Comparison of the band energy (EB) and rest of the total energy (E − EB) as a function of the volume. Here, vertical lines represent the transition points.

stabilization of the Fe2B-type structure in PtIn2 and AuIn2 at high pressure. We also found that with increasing pressure the hybridization pseudogap becomes progressively prominent at the Fermi level, indicating that there may be a metal−insulator transition at further high pressure. It is to be noted that narrowgap intermetallics like RuGa2 are good thermoelectric materials,41 and hence the possibility of thermoelectricity in the postcotunnite-type PtIn2 is an enticing preposition.

■

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We are thankful to Prof. Valentina F. Degtyareva for fruitful discussions.

■

AUTHOR INFORMATION

REFERENCES

(1) Paramasivan, S. Investigations on ancient Indian metallurgy. I. A pre-historic bronze bowl. II. Ancient Indian bronze coins of the 2nd and 11th centuries A.D. Proc. Indian Acad. Sci., Sec. A 1941, 13, 87−93. (2) Srinivasan, S. Iron Age beta (23% tin) bronze: Peninsular Indian bowls of Adichanallur, Nilgiris, and Boregaon. Mater. Manuf. Processes 2017, 32, 807−812.

Corresponding Author

*E-mail: [email protected]. ORCID

P. Modak: 0000-0002-1865-1114 G

DOI: 10.1021/acs.inorgchem.7b02507 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry (3) Hume-Rothery, W. Researches on the nature, properties, and condition of formation of intermetallic compounds. J. Inst. Met. 1926, 35, 319−335. (4) Zintl, E. Intermetallische Verbindungen. Angew. Chem. 1939, 52, 1−6. (5) Laves, F. Kristallographie der Legierungen. Naturwissenschaften 1939, 27, 65−73. (6) Pearson, W. B. The stability of metallic phases and structuresPhases with the AlB2 and related structures. Proc. R. Soc. London, Ser. A 1979, 365, 523−535. (7) Nesper, R. Structure and chemical bonding in zintl-phases containing lithium. Prog. Solid State Chem. 1990, 20, 1−45. (8) Morris, D. G.; Muñoz-Morris, M. A. Intermetallics: past, present and future. Rev. Metal. 2005, 41, 498−501. (9) Fredrickson, D. C. The discovery of FeBi2 could lead to further investigation of other materials unobservable at ambient pressure. ACS Cent. Sci. 2016, 2, 773−774. (10) Okamoto, H. In Binary Alloy Phase Diagrams; Massalski, T. B., Eds.; ASM International: Materials Park, OH, 1990; p 2276. (11) Loria, E. A. Gamma titanium aluminides as prospective structural materials. Intermetallics 2000, 8, 1339−1345. (12) Sikka, V. K.; Deevi, S. C.; Viswanathan, S.; Swindeman, R. W.; Santella, M. L. Advances in processing of Ni3Al-based intermetallics and applications. Intermetallics 2000, 8, 1329−1337. (13) Van Attekum, P. M. Th. M.; Wertheim, G. K.; Crecelius, G.; Wernick, J. H. Electronic properties of some CaF2 -structure intermetallic compounds. Phys. Rev. B: Condens. Matter Mater. Phys. 1980, 22, 3998. (14) Renner, H.; et al. Platinum Group Metals and Compounds. Ullmann’s Encyclopedia of Industrial Chemistry; Wiley-VCH Verlag GmbH & Co. KGaA, 2000. (15) Shiraishi, T.; Hisatsune, K.; Tanaka, Y.; Miura, E.; Takuma, Y. Gold Bulletin 2001, 34, 129−133. (16) Gupta, A.; Sen Gupta, R.; Goswami, K. Electronic structures and optical properties of some fluorite structured intermetallics. J. Phys. I 1994, 4, 1867−1876. (17) Ingerly, D. B.; Chang, Y. A.; Perkins, N. R.; Kuech, T. F. Ohmic contacts to n-GaN using PtIn2. Appl. Phys. Lett. 1997, 70, 108−110. (18) Modak, P.; Verma, A. K. Prediction of a novel 10-fold gold coordinated structure in AuIn2 above 10 GPa. Phys. Chem. Chem. Phys. 2017, 19, 3532−3537. (19) Garg, A. B.; Modak, P.; Vijayakumar, V. Phase stability of intermetallic PtIn2 under pressure: An in-situ transport, structural and first principles investigations. J. Appl. Phys. 2011, 109, 083531. (20) Verma, A. K.; Modak, P.; Sharma; Surinder, M. Structural phase transitions in Li2S, Na2S and K2S under compression. J. Alloys Compd. 2017, 710, 460−467. (21) Oganov, A. R.; Glass, C. W. Crystal structure prediction using ab initio evolutionary techniques: Principles and applications. J. Chem. Phys. 2006, 124, 244704. (22) Lyakhov, A. O.; Oganov, A. R.; Stokes, H. T.; Zhu, Q. New developments in evolutionary structure prediction algorithm USPEX. Comput. Phys. Commun. 2013, 184, 1172−1182. (23) Oganov, A. R.; Lyakhov, A. O.; Valle, M. How Evolutionary Crystal Structure Prediction Worksand Why. Acc. Chem. Res. 2011, 44, 227−237. (24) Kresse, G.; Hafner, J. Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements. J. Phys.: Condens. Matter 1994, 6, 8245. (25) Kresse, G.; Furthmuller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15−50. (26) Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953. (27) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758.

(28) Perdew, J. P.; Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 13244. (29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. (30) Blöchl, P. E.; Jepsen, O.; Andersen, O. K. Improved tetrahedron method for Brillouin-zone integrations. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 16223. (31) Methfessel, M.; Paxton, A. T. High-precision sampling for Brillouin-zone integration in metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1989, 40, 3616. (32) Hobbs, D.; Kresse, G.; Hafner, J. Fully unconstrained noncollinear magnetism within the projector augmented-wave method. Phys. Rev. B: Condens. Matter Mater. Phys. 2000, 62, 11556. (33) Marsman, M.; Hafner, J. Broken symmetries in the crystalline and magnetic structures of γ-iron. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 66, 224409. (34) Alfè, D. PHON: A program to calculate phonons using the small displacement method. Comput. Phys. Commun. 2009, 180, 2622. (35) Modak, P.; Verma, A. K. First-principles investigation of electronic, vibrational, elastic, and structural properties of ThN and UN up to 100 GPa. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 024108. (36) Goumri-Said, S.; Kanoun, M. B. Theoretical investigations of structural, elastic, electronic and thermal properties of Damiaoite PtIn2. Comput. Mater. Sci. 2008, 43, 243−250. (37) Mouhat, F.; Coudert, F.-X. Necessary and sufficient elastic stability conditions in various crystal systems. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 224104. (38) Wallace, D. C. Thermoelasticity of Stressed Materials and Comparison of Various Elastic Constants. Phys. Rev. 1967, 162, 776. (39) Häussermann, U.; Simak, S. I.; Ahuja, R.; Johansson, B.; Lidin, S. The Origin of the Distorted Close-Packed Elemental Structure of Indium. Angew. Chem., Int. Ed. 1999, 38, 2017−2020. (40) Tang, W.; Sanville, E.; Henkelman, G. A grid-based Bader analysis algorithm without lattice bias. J. Phys.: Condens. Matter 2009, 21, 084204. (41) Takagiwa, Y.; Kitahara, K.; Kimura, K. Effect of electron doping on thermoelectric properties for narrow-bandgap intermetallic compound RuGa2. J. Appl. Phys. 2013, 113, 023713.

H

DOI: 10.1021/acs.inorgchem.7b02507 Inorg. Chem. XXXX, XXX, XXX−XXX