β-PtO₂: Phononic, thermodynamic, and elastic properties derived from first-principles calculations

Abstract

β-PtO₂ is a useful transition metal dioxide, but its fundamental thermodynamic and elastic properties remain unexplored. Using first-principles calculations, we systematically studied the structure, phonon, thermodynamic and elastic properties of β-PtO₂. The lattice dynamics and structural stability of β-PtO₂ under pressure were studied using the phonon spectra and vibrational density of states. The vibrational frequencies of the optical modes of β-PtO₂ increase with elevating pressure; this result is comparable with the available experimental data. Then, the heat capacities and their pressure responses were determined based on the phonon calculations. The pressure dependence of the Debye temperature was studied, and the results were compared in two distinct aspects. The elastic moduli of β-PtO₂ were estimated through the Voigt–Reuss–Hill approximation. The bulk modulus of β-PtO₂ increases linearly with pressure, but the shear modulus is nearly independent of pressure. Our study revealed that the elastic stiffness coefficients C₄₄, C₅₅ and C₆₆ play a primary role in the slow variation of the shear modulus.

Keywords

phonons / thermodynamic and elastic properties / β-PtO ₂ / first-principles calculations

References

[1] C. Z. Yuan, H. B. Wu, Y. Xie, and X. W. Lou, Mixed transition-metal oxides: Design, synthesis, and energyrelated applications, Angew. Chem. Int. Ed. 53(6), 1488 (2014)

[2] Z. Chen, R. J. Xiao, C. Ma, Y. B. Qin, H. L. Shi, Z. W. Wang, Y. J. Song, Z. Wang, H. F. Tian, H. X. Yang, and J. Q. Li, Electronic structure of YMn₂O₅ studied by EELS and first-principles calculations, Front. Phys. 7(4), 429 (2012)

[3] Y. Y. Qi, Z. W. Niu, C. Cheng, and Y. Cheng, Structural and elastic properties of Ce₂O₃ under pressure from LDA+Umethod, Front. Phys. 8(4), 405 (2013)

[4] N. Sabourault, G. Mignani, A. Wagner, and C. Mioskowski, Platinum oxide (PtO₂): A potent hydrosilylation catalyst, Org. Lett. 4(13), 2117 (2002)

[5] L. Maya, L. Riester, T. Thundat, and C. S. Yust, Characterization of sputtered amorphous platinum dioxide films, J. Appl. Phys. 84(11), 6382 (1998)

[6] L. B. Hunt, The Story of Adams’ Catalyst, Platin. Met. Rev. 6, 150 (1962)

[7] M. M. Najafpour and S. M. Hosseini, Highly dispersed PtO₂ on layered Mn oxide as water-oxidizing catalysts, Int. J. Hydrogen Energy 41(16), 6798 (2016)

[8] S. Putzien, E. Louis, O. Nuyken, and F. E. Kühn, PtO₂ as a “self-dosing” hydrosilylation catalyst,Catal. Sci. Technol. 2(4), 725 (2012)

[9] R. Wu, and W. H. Weber, The mechanism of the rutileto- CaCl₂ phase transition: RuO₂ and β-PtO₂, J. Phys.: Condens. Matter 12(30), 6725 (2000)

[10] Y. Yang, O. Sugino, and T. Ohno, Band gap of β-PtO₂ from first-principles, AIP Adv. 2(2), 022172 (2012)

[11] R. K. Nomiyama, M. J. Piotrowski, and J. L. F. Da Silva, Bulk structures of PtO and PtO₂ from density functional calculations, Phys. Rev. B 84(10), 100101 (2011)

[12] H. R. Hoekstra, S. Siegel, and F. X. Gallagher, Reaction of platinum dioxide with some metal oxides, Adv. Chem. Ser. 98, 39 (1971)

[13] S. Siegel, H. R. Hoekstra, and B. S. Tani, The crystal structure of beta-platinum dioxide, J. Inorg. Nucl. Chem. 31(12), 3803 (1969)

[14] M. P. H. Fernandez and B. L. Chamberland, A new high pressure form of PtO₂, J. Less Common Met. 99(1), 99 (1984)

[15] K. J. Range, F. Rau, U. Klement, and A. M. Heyns, β-PtO₂: High pressure synthesis of single crystals and structure refinement, Mater. Res. Bull. 22(11), 1541 (1987)

[16] G. Kresse and J. Hafner, Ab initiomolecular dynamics for liquid metals, Phys. Rev. B 47(1), 558 (1993)

[17] G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initiototal-energy calculations using a plane-wave basis set, Phys. Rev. B 54(16), 11169 (1996)

[18] D. M. Ceperley and B. J. Alder, Ground state of the electron gas by a stochastic method, Phys. Rev. Lett. 45(7), 566 (1980)

[19] J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23(10), 5048 (1981)

[20] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77(18), 3865 (1996)

[21] G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59(3), 1758 (1999)

[22] H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13(12), 5188 (1976)

[23] A. Togo, F. Oba, and I. Tanaka, First-principles calculations of the ferroelastic transition between rutile-type and CaCl₂-type SiO₂ at high pressures, Phys. Rev. B 78(13), 134106 (2008)

[24] S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+Ustudy, Phys. Rev. B 57(3), 1505 (1998)

[25] Y. Yang, O. Sugino, and T. Ohno, Possible magnetic behavior in oxygen-deficient β-PtO₂, Phys. Rev. B 85(3), 035204 (2012)

[26] F. D. Murnaghan, The compressibility of media under extreme pressures, Proc. Natl. Acad. Sci. USA 30(9), 244 (1944)

[27] S. Zhuo and K. Sohlberg, Platinum dioxide phases: Relative thermodynamic stability and kinetics of interconversion from first-principles,Physica B 381(1–2), 12 (2006)

[28] W. H. Weber, G. W. Graham, and J. R. McBride, Raman spectrum of β-PtO₂: Evidence for the D₂h₁₂-to-D₄h₁₄ phase transition, Phys. Rev. B 42(17), 10969 (1990)

[29] G. Grimvall, Thermophysical Properties of Materials, Elsevier, 1999

[30] P. Debye, Zur Theorie der spezifischen Wärmen, Ann. Phys. 344(14), 789 (1912)

[31] P. L. Dulong and A.T. Petit, Recherches sur quelques points importans de la theorie de la Chaleur, 1819

[32] J. P. Watt, Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with orthorhombic symmetry, J. Appl. Phys. 50(10), 6290 (1979)

[33] A. Reuss, Account of the liquid limit of mixed crystals on the basis of the plasticity condition for single crystal, Z. Angew, Math. Mech. 9, 49 (1929)

[34] R. Hill, The elastic behaviour of a crystalline aggregate, Proc. Phys. Soc. Lond. 65, 349 (1952)

[35] W. Voigt, Lehrbuch der Kristallphysik, Teubner, Leipzig, 1928

[36] E. Schreiber, O. L. Anderson, and M. Saga, Elastic Constants and Their Measurement, McGraw-Hill, New York, 1973

[37] O. L. Anderson, A simplified method for calculating the Debye temperature from elastic constants, J. Phys. Chem. Solids 24(7), 909 (1963)

[38] H. J. Reichmann and S. D. Jacobsen, Sound velocities and elastic constants of ZnAl₂O₄ spinel and implications for spinel-elasticity systematics, Am. Mineral. 91(7), 1049 (2006)

[39] H. J. Reichmann and S. D. Jacobsen, High-pressure elasticity of a natural magnetite crystal, Am. Mineral. 89(7), 1061 (2004)

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