Theoretical calculations of elastic, mechanical and thermal properties of REPt_{3} (RE = Sc, Y and Lu) intermetallic compounds based on DFT
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Abstract
The elastic, mechanical and thermal properties of isostructural and isoelectronic nonmagnetic REPt_{3} (RE = Sc, Y and Lu) intermetallic compounds, which crystallize in AuCu_{3}-type structure, are studied using first principles density functional theory based on full potential linearized augmented plane wave method. The calculations are carried out within PBE-GGA, WC-GGA and PBE-sol GGA for the exchange correlation potential. Our calculated ground state properties such as lattice constant (a_{o}), bulk modulus (B) and its pressure derivative (B′) are in good agreement with the available experimental and other theoretical results. We first time predict the elastic constants for these compounds using GGA approximations. All the compounds are found to be ductile in nature in accordance with Pugh’s criteria. The computed electronic band structures show metallic character of these compounds. The charge density plot and density of states of these compounds reveals that the chemical bond between RE and Pt is mainly ionic. The elastic properties including Poisson’s ratio (σ), Young’s modulus (E), shear modulus (G_{H}) and anisotropy factor (A) are also determined using the Voigt–Reuss–Hill averaging scheme. The average sound velocities (v_{m}), density (ρ) and Debye temperature (θ_{D}) of these REPt_{3} compounds are also estimated from the elastic constants. We first time report the variation of elastic constants, elastic moduli, sound velocities and Debye temperatures of these compounds as a function of pressure.
Keywords
Intermetallic compounds Density functional theory Electronic properties Elastic constants Thermal propertiesPACS Nos
71.20.Lp 71.15Mb 71.20.-b 62.20.de 65.40.-b1 Introduction
In recent years, the intermetallic compounds have attracted considerable attention because of their potential for technological applications at high temperature. Moreover, some of the intermetallics exhibit different valence states in compounds with metallic character, which gives elevate to intriguing structural, electronic and magnetic properties. Many rare earths (RE) and group IIIA or IVA elements (X) form stable REX_{3} compounds which crystallize in the AuCu_{3} structure. REX_{3} compounds with the AuCu_{3}-type cubic structure exhibit a variety of phenomena [1, 2, 3, 4]. Compounds of this family are investigated because of phenomena such as magnetic moment formation, crystal field and Kondo effect or multiaxial magnetic structures, due to their incomplete 4f shell. Platinum and its alloys readily form intermetallics. The platinum group metal based intermetallics are of particular interest due to high temperature material, better oxidation or corrosive resistance than refractory metals. Arikan et al. [5] have reported the structural, electronic and elastic properties of scandium predicated compound ScX_{3} (X = Ir, Pd, Pt and Rh) utilizing ab-initio calculations. Meddar et al. [6] have studied the structure and morphology of Pt_{3}Sc alloy thin film using pulsed laser deposition (PLD). Xing et al. [7] have studied the structural stability and enthalpy of formation of refractory intermetallics TM and TM_{3} (T = Ti, Zr, Hf; M = Ru, Rh, Pd, Os, Ir, Pt). Kumar et al. [8] studied the electronic structure and magneto-optical properties of XPt_{3} (X = V, Cr, Mn, Fe, Co, Ni) compounds. Archarya et al. [9] have reported the structure, electronic and Fermi properties of ScPt_{3} and YPt_{3} compounds. Chen et al. [10] have investigated the structural, elastic, electronic and thermodynamic properties of ScX_{3} (X = Ir, Pd, Pt and Rh) compounds under high pressure by using the ab-initio pseudo potential method implemented in CASTEP code. Giannozzi et al. [11] have been studied the structural and electronic properties of ScRh_{3}. Sundareswari et al. [12] have reported the electronic structure of the Rhodium predicated intermetallic compounds (A_{3}B) such as Rh_{3}Sc, Rh_{3}Y and Rh_{3}La by the Self Consistent Tight Binding Linear Muffin Tin Orbital (TB-LMTO). Goncharuk et al. [13] have investigated the thermodynamic parameters of ScIr_{3} and ScIr_{2}. The high-pressure structural (B1–B2) phase transition and the elastic properties of ScS and ScSe have studied by Maachou et al. [14] using the full-potential augmented plane wave plus local orbitals method (FP-APW+LO) with the generalized-gradient approximation (GGA) exchange–correlation functional. Platinum based compounds REPt_{3} (RE = Sc, Y and Lu) are binary intermetallics compounds with AuCu_{3} structure, which belongs to Pm-3m space group, with the RE atoms occupying the corners of the cube while the Pt atoms occupy the cube faces. It is well known that pressure plays a significant role in physical properties of materials. Hence the deformation behavior of materials under compression has become quite interesting as it can provide deep insight into the nature of solid-state theories and evaluate the values of fundamental parameters [15]. So the study of pressure effects on REPt_{3} (RE = Sc, Y and Lu) is necessary and significant. Hence in the present paper, we have made efforts to shed more light on structural, electronic, elastic, mechanical and thermal behavior of LuPt_{3}, ScPt_{3} and YPt_{3} compounds using three different approaches under generalized gradient approximation (GGA) based on full-potential linear augmented plane-wave (FP-LAPW) method within the density functional theory (DFT), at ambient pressure as well as high pressures.
The paper is organized as follows: Sect. 2 is staunch to the description of our methods of calculation. In Sect. 3, the results are presented including comparison with experimental and theoretical data, followed by discussion. Conclusions are given in Sect. 4.
2 Computational method
3 Results and discussions
3.1 Structural properties
Calculated lattice constant (a_{o}), bulk modulus (B), its pressure derivative (B′) of REPt_{3} (RE = Sc, Y and Lu) compounds at ambient pressure
Solid | Work | Approximation | a_{o} (Å) | B(GPa) | B′ | N(E_{F}) states/eV |
---|---|---|---|---|---|---|
ScPt_{3} | Pre. | PBE-GGA | 4.009 | 216.12 | 4.42 | 3.76 |
WC-GGA | 3.967 | 238.24 | 4.39 | 3.49 | ||
PBE sol-GGA | 3.958 | 239.40 | 4.64 | 3.44 | ||
Expt. | 3.954^{a} | |||||
3.958^{b} | ||||||
3.958^{c} | ||||||
3.953^{d} | ||||||
Oth. | LMTO | 3.959^{e} | ||||
EMTO-LDA | 246.20^{f} | |||||
GGA | 4.024^{g} | 198.36^{g} | 3.87^{g} | 3.11^{g} | ||
GGA | 4.003^{h} | 208.57^{h} | 5.36^{h} | 3.61^{h} | ||
CASTEP | 4.019^{i} | 205.27^{i} | 5.8^{i} | |||
YPt_{3} | Pre. | PBE-GGA | 4.123 | 187.20 | 4.81 | 2.91 |
WC-GGA | 4.079 | 202.73 | 5.13 | 2.98 | ||
PBE sol-GGA | 4.068 | 206.05 | 5.68 | 3.01 | ||
Expt. | 4.069^{a} | |||||
Oth. | GGA | 4.081^{h} | 175.82^{h} | 5.45^{h} | 3.08^{h} | |
LuPt_{3} | Pre. | PBE-GGA | 4.080 | 209.85 | 4.01 | 3.53 |
WC-GGA | 4.038 | 224.04 | 4.61 | 3.46 | ||
PBE sol-GGA | 4.029 | 223.07 | 4.71 | 3.46 | ||
Expt. | 4.029^{a} |
3.2 Electronic properties
3.3 Electronic charge density
3.4 Elastic properties
Calculated elastic constants of REPt_{3} (RE = Sc, Y and Lu) compounds at ambient pressure
Solids | Work | Approx. | C_{11} (GPa) | C_{12} (GPa) | C_{44} (GPa) |
---|---|---|---|---|---|
ScPt_{3} | Pre. | GGA | 248.69 | 185.43 | 92.26 |
Oth. | EMTO-LDA | 350.30^{f} | 194.10^{f} | 72.60^{f} | |
EMTO-GGA | 379.40^{f} | 206.90^{f} | 89.10^{f} | ||
EMTO-LAG | 355.80^{f} | 199.30^{f} | 74.30^{f} | ||
GGA | 286.58 ^{g} | 154.27^{g} | 113.91^{g} | ||
CASTEP | 290.74^{i} | 162.25^{i} | 111.77^{i} | ||
YPt_{3} | Pre. | GGA | 283.33 | 124.94 | 97.23 |
LuPt_{3} | Pre. | GGA | 265.44 | 159.01 | 71.75 |
3.5 Mechanical properties
Calculated Young’s modulus (E), shear modulus (G_{H}), anisotropic factor (A), Poisson’s ratio (σ), B/G_{H} ratio and Cauchy pressure (C_{12}–C_{44}) of REPt_{3} (RE = Sc, Y and Lu) compounds at ambient pressure
Solids | Work | Approx. | E (GPa) | G_{H} (GPa) | A | B/G_{H} | σ | C_{12}–C_{44} (GPa) | B/C_{44} |
---|---|---|---|---|---|---|---|---|---|
ScPt_{3} | Pre. | GGA | 164.39 | 60.11 | 2.91 | 3.43 | 0.36 | 93.16 | 2.23 |
Oth. | EMTO-LDA | 203.60^{f} | 74.70^{f} | 0.93^{f} | 3.33^{f} | 0.36^{f} | |||
GGA | 245.31^{g} | 94.79^{g} | 1.72^{g} | 2.09^{g} | 0.29^{g} | ||||
CASTEP | 234.41^{i} | 89.50^{i} | |||||||
YPt_{3} | Pre. | GGA | 230.05 | 89.56 | 1.22 | 1.98 | 0.28 | 27.71 | 1.82 |
LuPt_{3} | Pre. | GGA | 172.18 | 63.65 | 1.34 | 3.05 | 0.35 | 87.25 | 2.71 |
For A = 1 means a completely isotropic material, whereas a value smaller or larger than unity indicates the degree of elastic anisotropy. The calculated elastic anisotropic factor for all REPt_{3} (RE = Sc, Y and Lu) compounds is larger than unity, indicating that these materials can be regarded as elastically anisotropic materials. The bulk modulus is usually assumed to be a measure of resistance to volume change by applied pressure [39].
As suggested by Pugh’s [40], if B/G_{H}> 1.75; a material behaves in a ductile manner otherwise, the material behaves in a brittle manner. In the present work, the value of B/G_{H} ratio indicates that all the studied compounds are ductile in nature. This is in good agreement with the results found for ScPt_{3} [25]. Ganeshan et al. [41] have established a correlation between the bonding properties and ductility. Pettifor [42] has suggested that the angular character of atomic bonding in metals and compounds, which also relates to the brittle or ductile characteristics, can be described by the Cauchy pressure (C_{12}–C_{44}). Compounds having more positive Cauchy pressure tend to form bonds which are primarily metallic in nature where as for directional bonding with angular character, the Cauchy pressure is negative, with larger negative pressure representing a more directional character. Based on the calculated equilibrium Cauchy pressure (see Table 3), we may conclude that REPt_{3} (RE = Sc, Y and Lu) belongs to class of ductile materials. Young’s modulus is defined as the ratio of stress and strain, and is used to provide a measure of the stiffness of the solid, i.e., the larger value of E, the stiffer is the material. And the stiffer solids have covalent bonds [43].
It can be seen from Table 3 that the largest value E among the compounds is that of YPt_{3}, so we conclude that YPt_{3} is the stiffest one.
Bulk modulus is still used as a preliminary measure of the hardness of material but in order to confirm it, other properties must also be taken into account. A high bulk modulus does not mean that a material is hard. Elastic characteristics must be considered as well, and shear modulus might even provide a better correlation with hardness than bulk modulus. Covalent materials generally have a high shear modulus. The nature of bond can be predicted using Poisson’s ratio and reflect the stability of a crystal against shear [44].
The value of Poisson’s ratio is found to be ≈ 0.1 for covalent materials and ≈ 0.33 for metallic materials [45, 46]. It is observed from Table 3 that the value of Poisson’s ratio lies in between 0.28 and 0.36 for all these intermetallic compounds, signifying metallic bonding of REPt_{3} compounds. Frantsevich et al. [47] devised a rule on the base of Poisson’s ratio ‘σ’ to make a distinction between ductile and brittle materials. With respect to his criterion, the critical value of ‘σ’ is 0.26. For brittle materials the value of ‘σ’ should be less than 0.26. The value of Poisson’s ratio ‘σ’ in our calculation as reported in Table 3 is 0.36, 0.28 and 0.35 for ScPt_{3}, YPt_{3} and LuPt_{3} respectively, endorsing their ductile nature.
3.6 Thermal properties
Calculated density (ρ), longitudinal (v_{l}), transverse (v_{t}), average elastic wave velocities (v_{m}) and Debye temperature (θ_{D}) of REPt_{3} (RE = Sc, Y and Lu) compounds at ambient pressure
Solids | ρ*10^{3} (kg/m^{3}) | v_{l}(m/s) | v_{t} (m/s) | v_{m} (m/s) | θ_{D} (K) |
---|---|---|---|---|---|
ScPt_{3} | 16.238 | 4278 | 2046 | 2301 | 215 |
YPt_{3} | 15.958 | 4319 | 2375 | 2647 | 240 |
LuPt_{3} | 18.543 | 3887 | 1862 | 2094 | 192 |
4 Conclusion
In this paper, we have systematically studied the structural, electronic, elastic, mechanical and thermal properties of states of REPt_{3} (RE = Sc, Y and Lu) compounds by utilizing FP-LAPW method based on density functional theory as the exchange correlation energy. The lattice constants and bulk moduli are determined and are in excellent agreement with the available experimental data and theoretical values. We have additionally studied the mechanical properties of these compounds. The elastic constants have been calculated using the approach, the energy-strain method. The values obtained for ScPt_{3} are in reasonable agreement with those obtained previously. The calculated elastic constants satisfy the mechanical stability criterion and the ductility of REPt_{3} (RE = Sc, Y and Lu) is predicted by Pugh’s criterion. In addition to that the ductility properties of REPt_{3} (RE = Sc, Y and Lu) determined by Poisson’s ratio σ criterion are in good agreement with the results estimated by the B/G ratio. The band structure and densities of states DOS for these compounds are analyzed and compared. They showed that all materials exhibit metallic character. We have also calculated thermal properties for these compounds. We also report the variation of elastic constants and elastic moduli of these compounds with pressure over the range 0–16 GPa. For the lack of experimental as well as other theoretical results, we could not compare them. Hence our results can be considered as a prediction for these properties, which would be tested in the future both by experimentally and theoretically.
Notes
Acknowledgements
The authors are thankful to MPCST for the financial support.
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