Theoretical study of the elastic properties of the minerals Cu3TMSe4 (TM = V, Nb, Ta) by means of atomistic first-principles calculations
Main Article Content
Keywords
elastic properties, elastic constants, mechanical properties, density functional theory.
Abstract
The elastic properties of the family of isostructural minerals Cu3VSe4, Cu3NbSe4 and Cu3TaSe4 have been calculated for the first time using the state of the art in first-principles atomistic calculations, using Density Functional Theory and the Generalized Gradient Approximation for the exchangecorrelation energy functional. The elastic properties calculated are bulk modulus (B), the elastic constants (c11, c12 and c44), the Zener anisotropy factor (A), the isotropic shear modulus (G), the Young modulus (Y ), and the Poisson ratio (). By means of these quantities we also computed other thermodynamic properties such as the average transversal (st) and longitudinal (sl) sound velocities and the Debye temperature (D). The calculated values of B, c11, c12 and c44, G, Y and lead us to the conclusion that these compounds are compressible, fragile and brittle.
PACS: 91.60.Ba
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References
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[3] K. Klepp and D.Gurtner. Crystal structure of tricopper tetraselenidovanadate(V) Cu3VSe4. Zeitschrift fur Kristallographie - New Crystal Structures, ISSN 1433- 7266, 215(1), 4 (2000).
[4] M. Kars, A. Rebbah and H. Rebbah. Cu3NbS4. Acta Crystallographica Section E ISSN 1600-5368, 61(8), i180 (2005).
[5] G. Delgado, A. Mora, S. Duran, M. Muñoz and P. Grima-Gallardo. Structural characterization of the ternary compound Cu3Ta Se4. Journal of Alloys and Compounds, ISSN 0925-8388, 439(1-2), 346-349 (2007).
[6] G. Delgado, A. Mora, P. Grima-Gallardo, S. Duran, M. Muñoz and M. Quintero. Synthesis and characterization of the ternary chalcogenide compound Cu3NbTe4. Chalcogenide Letters, ISSN 1584-8663, 6(8), 335-338 (2009).
[7] D. Petritis, G. Mart´ınez, C. Levy-Clement and O. Gorochov. Investigation of the vibronic properties of Cu3VS4, Cu3NbS4 and Cu3TaS4 compounds. Physical Review B, ISSN 1098-0121, 23(12), 6773-6786 (1981).
[8] Hervé Arribard and Bernard Sapoval.Theory of mixed conduction due to cationic interstitials in the p-type semiconductor Cu3VS4. Electrochimica Acta, ISSN 00 1-4686, 24(7), 751-754 (1979).
[9] D.M. Schleich and M. Rosso. Li+ insertion studies in Cu3VS4. Solid State Ionics ISSN 0167-2738, 5(1), 383 (1981).
[10] A. Golub, N. Allali, D. Guyomard and M. Danot. Lithium intercalation -deintercalation reactions using matrixes with the sulvanite structure: Dimensionality lowering of the host-structure Materials Research Bulletin, ISSN 0025-5408, 30(8), 959-966 (1995).
[11] G. Cressy, C. Henderson and G. van der Laan.Use of L-edge X-ray absortion spectroscopy to characterize multiple valence states of 3d transition metals; a new probe for mineralogical and geochemical research, Physics and Chemistry of Minerals, ISSN 0342-1791, 20(2), 111-119 (1993).
[12] D.A. McKeown, I.S. Muller, K.S. Matlack and I.L. Pegg. X-ray absorption studies of vanadium valence and local environment in borosilicate waste glasses waste glasses using vanadium sulfide, silicate, and oxide standards, Journal of Non-Crystalline Solids, ISSN 0022-3093, 298(2-3), 160-175 (2002).
[13] G. van der Laan, R. Pattrick, C. Henderson and D. Vaughan. Oxidation state variations in copper minerals studied with Cu 2p X-ray absorption spectroscopyJournal of Physics and Chemistry of Solids, ISSN 0022-3697, 53(9), 1185-1190 (1992).
[14] G. van der Laan and I.W. Kirkman. The 2p absorption spectra of 3d transition metal compounds in tetrahedral and octahedral symmetry, Journal of Physics: Condensed Matter, ISSN 0953-8984, 4(16), 4189-4204 (1992).
[15] J.W. Tate, P.F. Newhouse, R. Kykyneshi, P.A. Hersh, J. Kinney, D.H. McIntyre and D.A. Keszler. Chalcogen-based transparent conductors, Thin Solid Films, ISSN 0040-6090, 516(17), 5795-5799 (2008).
[16] P.F. Newhouse, P.A. Hersh, A. Zakutayev, A. Richard, H.A.S. Platt, D.A. Keszler and J. Tate. Thin film preparation and characterization of wide band gap Cu3TaQ4 (Q = S or Se) p-type semiconductors, Thin Solid Films, ISSN 0040- 6090, 517(7), 2473-2476 (2009).
[17] F. Zwick, H. Berger, M. Grioni, G. Margaritondo, L. Forró, J. LaVeigne, D. B. Tanner and M. Onellion. Coexisting one-dimensional and three-dimensional spectral signatures in TaTe4, Physical Review B, ISSN 1098-0121, 59(11), 7762- 7766 (1999).
[18] N. Shannon and R. Joynt. The spectral, structural and transport properties of the pseudogap system (TaSe4)2I , Solid State Commun, ISSN 0038-1098 115(8), 411-415 (2000).
[19] S. Debus and B. Harbrecht. NbxTa7−xS2 (x=2.73), a structurally distinct (Nb, Ta)-rich sulfide obtaining its stability from the dissimilar cohesive energy of the two metals, Journal of Alloys and Compounds, ISSN 0925-8388, 338(1-2), 253-260 (2002).
[20] Y. Aiura, H. Bando, R. Kitagawa, S. Maruyama, Y. Nishihara, K. Horiba, M. Oshima, O. Shiino and M. Nakatake. Electronic structure of layered 1T-TaSe2 in commensurate charge-density-wave phase studied by angle-resolved photoemission spectroscopy, Physical Review B, ISSN 1098-0121, 68(7), 073408 - 073408-4 (2003).
[21] F. Dimroth and S. Kurtz. High-efficiency multijunction solar cells, Materials Research Society Bulletin, ISSN 0883-7694, 32(3), 230-235 (2007).
[22] Federico Capasso. Band-Gap Engineering: From Physics and Materials to New Semiconductor Devices, Science, ISSN 0036-8075, 235(4785), 172-176 (1987).
[23] W.F. Espinosa García, A.L. Morales Aramburo and J.M. Osorio Guillén. Electronic properties of the sulvanite compounds: Cu3TMS4 (TM = V, Nb, Ta), Revista Colombiana de Física, ISSN 0120-2650, 40(1), 36-39 (2008).
[24] S. Adachi, Properties of Group-IV, III-V and II-VI Semiconductors. ISBN 0- 470-09032-4. John Wiley & Sons, West Sussex (2005)
[25] L. D. Landau and E. M. Lifshitz. Theory of elasticity. ISBN 075062633X. Butterworth-Heinemann, 3rd ed. New York (1986).
[26] L. Thomsen. Weak elastic anisotropy, Geophysics, ISSN 0016-8033, 51(10), 1954-1966 (1986).
[27] P. Hohenberg and W. Kohn. Inhomogeneous Electron Gas, Physical Review, ISSN 0031-899X, 136(3B), B864-B871 (1964).
[28] W. Kohn and L. J. Sham. Self-consistent equations including exchange and correlation effects, Physical Review, ISSN 0031-899X, 140(4A), A1133-A1138 (1965).
[29] J. Perdew, K. Burke and M. Ernzerhof. Generalized gradient approximation made simple, Physical Review Letters, ISSN 0031-9007, 77(18), 3865 - 3868 (1996).
[30] P. E. Blochl. Projector augmented-wave method, Physical Review B, ISSN 0163- 1829, 50(24), 17953-17979 (1994).
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[32] G. Kresse and J. Furthmuller. Efficient iterative schemes for ab initio totalenergy calculations using a plane-wave basis set , Physical Review B, ISSN 1098- 0121, 54(16), 11169-11186 (1996).
[33] H.J. Monkhorst and J.D. Pack. Special points for Brillouin-zone integrations, Physical Review B, ISSN 0163-1829, 13(12), 5188-5192 (1976).
[34] P. Soderlind, O. Eriksson, J. M. Wills and A. M. Boring. Theory of elastic constants of cubic transition metals and alloys, Physical Review B, ISSN 0163- 1829, 48(9), 5844-5851 (1993).
[35] P. Vinet, J.R. Smith, J.H. Rose and J. Ferrante. Temperature effects on the universal equation of state of solids , Physical Review B.ISSN 0163-1829, 35(4), 1945-1953 (1987).
[36] Cz. Jasiukiewicz and V. Karpus. Debye temperature of cubic crystals, Solid State Communications, ISSN 0038-1098, 128(5), 167-169 (2003).
[37] Marvin L. Cohen. Calculation of bulk moduli of diamond and zinc-blende solids Physical Review B. ISSN 0163-1829, 32(12), 7988-7991 (1985).
[38] James F. Shackelford, William Alexander and J. S. Park. CRC practical handbook of materials selection, ISBN 0849337097. CRC-Press, USA (1995).
[39] W. Voigt. Lehrbuch der Kristallphysik , ISBN 0384648401. Teubner, Leipzig, (1928).
[40] A. Reuss. Berechnung der Fliebgrenze von Mischkristallen auf Grund der Plastizitatsbedingung fur Einkristalle, Zeitschrift f¨ur Angewandte Mathematik und Mechanik, ISSN 0044-2267, 9 (1), 49-58 (1929).
[41] R. Hill. The Elastic Behaviour of a Crystalline Aggregate, Proceedings of the Physical Society A, ISSN 0370-1298, 65(5), 349-354 (1952).