Effect of Pressure on Electronic, Mechanical and Dynamic Properties for Orthorhombic WP
Year 2023,
Volume: 36 Issue: 4, 1759 - 1773, 01.12.2023
Ceren Tayran
,
Mehmet Çakmak
Abstract
The structural, mechanical, electronic and dynamic features of MnP-type WP have been presented under 0-50 GPa hydrostatic pressure utilizing density functional theory. The lattice constants, values of volumes and bond lengths have been decreased with increasing pressure. It has been found that results of electronic band structures show that WP preserves its metallic feature under pressure. It has been observed that electronic band structures shifted up in Y–Γ and Γ–X symmetry points under pressure. The partial density of states indicates that hybridization occurs between W-d and P-p orbitals and also W–d orbital is dominated at all pressures. It is obtained that the mechanical properties of WP are increased with increasing pressure. Additionally, WP becomes more ductile under pressure. According to phonon dispersions, it has been investigated that WP is dynamically stable under pressure applied.
Supporting Institution
T.C. Strategy and Budget Directorate
Project Number
2019K1292587
References
- [1] Rundqvist S., “Phosphides of the B31 (MnP) Structure Type”, Acta Chemica Scandinavica, 16: 287-292, (1962).
- [2] Rundqvist S., Lundström, T. “X-Ray Studies of Molybdenum and Tungsten Phosphides”. Acta Chemica Scandinavica, 17: 37-46, (1963).
- [3] Joshi, R., Sahariya, J., Mund, H.S., Bhamu, K.C., Tiwari, S., Ahuja B.L., “Compton profiles of MoP and WP: Validation of second-order generalized gradient approximation,” Computational Materials Science, 53(1): 89-93, (2012).
- [4] Wu, W, Cheng, J.-G., Matsubayashi, K., Kong, P., Lin, F., Jin C., Wang, N., Uwatoko, Y., Luo, J., “Superconductivity in the vicinity of antiferromagnetic order in CrAs,” Nature Communications, 5: 5508, (2014).
- [5] Kotegawa, H., Nakahara, S., Tou, H., Sugawara, H. “Superconductivity of 2.2 K under Pressure in Helimagnet CrAs”, Journal of the Physical Society of Japan, 83: 093702, (2014).
- [6] Kotegawa, H., Nakahara, Akamatsu, R., Tou, H., Sugawara, H., Harima, H., “Detection of an Unconventional Superconducting Phase in the Vicinity of the Strong First-Order Magnetic Transition in CrAs Using 75As-Nuclear Quadrupole Resonance”, Physical Review Letters, 114: 117002, (2015).
- [7] Cheng, J.-G., Matsubayashi, K., Wu, W., Sun, J. P., Lin, F. K., Luo, J. L., Uwatoko, Y., “Pressure-Induced Superconductivity on the border of Magnetic Order in MnP,” Physical Review Letters, 114: 117001, (2015).
- [8] Liu, Z., Wu, W., Zhao, Z., Zhao, H., Cui, J., Shan, P., Zhang, J., Yang, C., Sun, P., Wei, Y., Li, S., Zhao, J., Sui, Y., Cheng, J., Lu, L., Liu, G., Superconductivity in WP single crystals”, Physical Review B, 99: 184509, (2019).
- [9] Cuono G., Forte, F., Cuoco, M., Islam, R., Luo, J., Noce C., Autieri, C., “Multiple band crossings and Fermi surface topology: Role of double nonsymmorphic symmetries in MnP-type crystal structures,” Physical Review Materials, 3(9): 095004, (2019).
- [10] Wu, W., Cheng, L., Matsubayashi, K., Kong, P., Lin, F., Jin, C., Wang, N., Uwatoko, Y., Luo, J., “Superconductivity in the vicinity of antiferromagnetic order in CrAs,” Nature Communications, 5: 5508, (2014).
- [11] Chen R. Y., Wang, N. L., “Progress in Cr- and Mn-based superconductors: a key issues review,” Reports on Progress in Physics, 82: 012503, (2019).
- [12] Wang, Y., Feng, Y., Cheng, J.-G., Wu, W., Luo, J. L., Rosenbaum, T. F., “Spiral magnetic order and pressure-induced superconductivity in transition metal compounds,” Nature Communications, 7: 13037, (2016).
- [13] Autieri C., Noce, C., “First-principles study of structural, magnetic and electronic properties of CrAs,” Philosophical Magazine, 97: 3276, (2017).
- [14] Autieri, C., Cuono, G., Forte, F., Noce, C., “Low energy bands and transport properties of chromium arsenide,” Journal of Physics: Condensed Matter, 29: 224004, (2017).
- [15] Motizuki, K., Ido, H., Itoh, T., Morifuji, M., “Electronic Structure and Magnetism of 3d-Transition Metal Pnictides”, Springer Series in Materials Science (Springer-Verlag, Berlin) (2010).
- [16] Roberts, B. W., “Superconductive Materials and Some of Their Properties (National Bureau of Standards),” Washington, DC, (1969).
- [17] Guerin, R., Jacques, M., Prigent, J., “Etude des chaines metal-metal dans la structure type MnP: Les arseniure et phosphure “MoAs” et WP et leurs solutions solides avec) les composes MX (M = élément de transition 3d; X = As, P)”, Materials Research Bulletin, 10(9): 957-965, (1975).
- [18] Kandler, H., Reiss, B., Naturforschg, Z., “Zur Kristallstruktur der intermetallischen Phasen MoAs und Mo5As”, Zeitschrift für Naturforschung, 21a: 549-554, (1966).
- [19] Fjellvåg, H., Selte, K., Danihelka, P., “Structural and Magnetic Properties of Mn(1-t) Mo(t)As”, Acta Chemica Scandinavica, A38: 789–794, (1984).
- [20] Faller, F.E., Biltz W., Meisel, K., Zumbusch, M.Z., “Beiträge zur systematischen Verwandtschaftslehre. 99. Über Phosphide von Wolfram, Molybdän und Chrom”, Zeitschrift für anorganische und allgemeine Chemie, 248: 209, (1941).
- [21] Schönberg, N., “An X-Ray Investigation of Transition Metal Phosphides”, Acta Chemica Scandinavica, 8: 226-239, (1954).
- [22] Bachmayer, K., Nowotny, H., Kohl, A., “Die Struktur von TiAs”, Physikalische, Anorganische und Analytische Chemie, 86: 39-43, (1955).
- [23] Gopalakrishnan, J., Pandey, S., Rangan, K. K., “Convenient Route for the Synthesis of Transition-Metal Pnictides by Direct Reduction of Phosphate, Arsenate, and Antimonate Precursors,” Chemistry of Materials, 9(10): 2113-2116, (1997).
- [24] Lesnyak V.V., Stratiichuk D.A., Sudavtsova V.S., Slobodyanik S., “Preparation of Al, Cr, Nb, Mo, and W Monophosphides from a Lithium Metaphosphate Melt,” Russian Journal of Applied Chemistry, 74(8): 1274–1277, (2001).
- [25] Jaiganesh R., Eithiraj D., Kalpana, G., “Theoretical study of electronic, magnetic and structural properties of Mo and W based group V (N, P, As, Sb and Bi) compounds,” Computational Materials Science, 49(1): 112-120, (2010).
- [26] Tayran, C., Çakmak, M., “Electronic structure, phonon and superconductivity for WP 5d-transition metal”, Journal of Applied Physics, 126: 175103, (2019).
- [27] Kresse, G., Hafner, J., “Ab initio molecular dynamics for liquid metals”, Physical Review B, 47: 558(R), (1993).
- [28] Kresse, G., Furthmüller J., “Efficiency of ab-initio total-energy calculations for metals and semiconductors using a plane-wave basis set”, Computational Materials Science, 6: 15, (1996).
- [29] Kresse, G., Joubert, D., “From ultrasoft pseudopotentials to the projector augmented-wave method”, Physical Review B, 59: 1758, (1999).
- [30] Perdew, J.P., Burke, K., Ernzerhof, M., “Generalized Gradient Approximation Made Simple”, Physical Review Letters, 77: 3865-3868, (1994). [Erratum Phys. Rev. Lett. 78, 1396 (1997)].
- [31] Blöchl, P.E., “Projector augmented-wave method”, Physical Review B, 50: 17953, (1994).
- [32] Kresse, G., Furthmüller J., “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set”, Physical Review B, 54: 11169, (1996).
- [33] Monkhorst, H.J., Pack, J.D., “Special points for Brillouin-zone integrations”, Physical Review B, 13: 5188, (1976).
- [34] Momma, K., Izumi, F., “VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data”, Journal of Applied Crystallography, 44: 1272-1276, (2011).
- [35] Togo, A., Tanaka I., “First principles phonon calculations in materials science”, Scripta Materialia, 108: 1-5, (2015).
- [36] Kanaya, K., Abe, S., Yoshida, H., Kamigaki, K., Kaneko, T., “Magnetic and structural properties of pseudo-binary compounds CrAs1−xPx”, Journal of Alloys and Compounds, 383: 189, (2004).
- [37] Niu, Q., Yu, W. C., Yip, K. Y., Lim, Z. L., Kotegawa, H., Matsuoka, E., Sugawara, H., Tou, H., Yanase, Y., Goh, S.K., “Quasilinear quantum magnetoresistance in pressure-induced nonsymmorphic superconductor chromium arsenide”, Nature Communications, 8: 15358, (2017).
- [38] Ashcroft, N.W., Mermin, N.D., “Solid State Physics”, Saunders, Philadelphia, (1976).
- [39] Sailuam W., Phacheerak, K., Bootchanont, A., Fongkaew, I., Limpijumnong S., “Elastic and mechanical properties of hydroxyapatite under pressure: A first-principles investigation”, Computational Condensed Matter, 24: e00481, (2020).
- [40] Ravindran, P., Fast, L., Korzhavyi, P.A., Johnnsson, B., Wills, J., Eriksson, O., “Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2”, Journal of Applied Physics, 84(9): 4891, (1998).
- [41] Mattesini M., Matar, S.F., “Density-functional theory investigation of hardness, stability, and electron-energy-loss spectra of carbon nitrides with C11N4 stoichiometry”, Physical Review B, 65: 075110, (2002).
- [42] Wu, Z.J., Zhao, E.J., Xiang, H.P., Hao, X.F., Liu X.J., Meng, J., “Crystal structures and elastic properties of superhard IrN2 and IrN3 from first principles”, Physical Review B, 76: 054115, (2007).
- [43] Birch F., “Finite Elastic Strain of Cubic Crystals”, Physical Review, 71: 809, (1947).
- [44] M. Born, K. Huang, “Dynamical Theory of Crystal Lattices”, Clarendon, Oxford,1956.
- [45] Beckstein, O., Klepeis, J.E., Hart, G.L.W., Pankratov O., “First-principles elastic constants and electronic structure of α−Pt2Si and PtSi”, Physical Review B, 63: 134112, (2001).
- [46] Wallace D.C., “Thermodynamics of Crystals”, Wiley, New York (Chap. 1), (1972).
- [47] Jong, M. de, Chen, W., Angsten, T., Jain, A., Notestine, R., Gamst, A., Sluiter, M., Krishna Ande, C., Zwaag, S. van der, Plata, J. J., Toher, C., Curtarolo, S., Ceder, G., Persson, K. A., Asta, M., “Charting the complete elastic properties of inorganic crystalline compounds”, Scientific Data, 2: 150009, (2015).
- [48] [Gaillac, R., Pullumbi, P., Coudert, F.-X., “ELATE: an open-source online application for analysis and visualization of elastic tensors”, Journal of Physics-Condensed Matter, 28: 275201, (2016).
- [49] Voigt, W., “Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik)”, Teubner, Leipzig, (1928).
- [50] Reuss A., “Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle”, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 9: 49-58, (1929).
- [51] Hill, R., “The Elastic Behaviour of a Crystalline Aggregate”, Proceedings of the Physical Society, 65(5): 349–354, (1952).
- [52] Pugh, S. F., “XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals”, Philosophical Magazine, 45: 823-843, (1954).
- [53] Young, A. F., Sanloup, C., Gregoryanz, E., Scandolo, S., Hemley, R. J., Mao, H. K., “Synthesis of Novel Transition Metal Nitrides IrN2 and OsN2”, Physical Review Letters. 96(15): 155501, (2006).
- [54] Yang, X., Hao, A., Wang, X., Liu, X., Zhu, Y., “First-principles study of structural stabilities, electronic and elastic properties of BaF2 under high pressure”, Computational Materials Science, 49: 530-534, (2010).
- [55] Pettifor, D.G., “Theoretical predictions of structure and related properties of intermetallics”, Materials Science and Technology, 8(4): 345-349, (1992).
- [56] Chen, H., Lei, X., Long, J., Huang, W., “The elastic and thermodynamic properties of new antiperovskite-type superconductor CuNNi3 under pressure”, Materials Science in Semiconductor Processing, 27: 207-211, (2014).
- [57] Wu, Z. J., Zhao, E. J., Xiang, H. P., Hao, X. F., Liu, X. J., Meng, J., “Crystal structures and elastic properties of superhard IrN2 and IrN3 from first principles”, Physical Review B, 76: 054115, (2007).
- [58] Yang, R., Zhu, C., Wei, Q., Du, Z., “Investigations on structural, elastic, thermodynamic and electronic properties of TiN, Ti2N and Ti3N2 under high pressure by first-principles”, Journal of Physics Chemistry of Solids, 98: 10-19, (2016).
- [59] Haines, J., Léger, J., Bocquillon, G., “Synthesis and Design of Superhard Materials”, Annual Review of Materials Research, 31: 1–23, (2001).
- [60] Qi, C., Jiang, Y., Liu, Y., Zhou, R., “Elastic and electronic properties of XB2 (X=V, Nb, Ta, Cr, Mo, and W) with AlB2 structure from first-principles calculations”, Ceramics International, 40(4): 5843-5851, (2014).
- [61] Kanoun, M.B., Goumri-Said, S., Reshak, A.H., Merad, A.E., “Electro-structural correlations, elastic and optical properties among the nanolaminated ternary carbides Zr2AC”, Solid State Science, 12(5): 887–898, (2010).
- [62] Wen, Y., Wang, L., Liu, H., Song, L., “Ab Initio Study of the Elastic and Mechanical Properties of B19 TiAl”, Crystals, 7: 39, (2017).
- [63] Papadimitriou, I., Utton, C., Scott, A., Tsakiropoulos, P., “Ab Initio Study of Binary and Ternary Nb3(X, Y) A15 Intermetallic Phases (X, Y = Al, Ge, Si, Sn)”, Metallurgical and Materials Transactions A, 46(2): 566-576, (2015).
- [64] Abadias, G., Kanoun, M.B., Goumri-Said, S., Koutsokeras, L., Dub, S.N., Djemia, Ph., “Electronic structure and mechanical properties of ternary ZrTaN alloys studied by ab initio calculations and thin-film growth experiments”, Physical Review B, 90: 144107, (2014).
- [65] Chen, H., Lei, X., Long, J., Huang, W., “The elastic and thermodynamic properties of new antiperovskite-type superconductor CuNNi3 under pressure”, Materials Science in Semiconductor Processing, 27: 207-211, (2014).
- [66] Tian, Y.J. Xu, B., Zhao, Z.S., “Microscopic theory of hardness and design of novel superhard crystals.”, International Journal of Refractory Metals and Hard Materials, 33: 93-106 (2012).
- [67] Chen, X.Q., Fu, C.L., Krčmar, M., “Electronic and Structural Origin of Ultraincompressibility of 5d Transition-Metal Diborides MB2 (M=W, Re, Os)”, 100: 196403 (2008).
- [68] Jain, A., Ong, S. P., Hautier, G., Chen, W., Richards, W. D., Dacek, S., Cholia, S., Gunter, D., Skinner, D., Ceder, G., Persson, K. A., “Commentary: The Materials Project: A materials genome approach to accelerating materials innovation”, APL Materials, 1: 011002, (2013).
Year 2023,
Volume: 36 Issue: 4, 1759 - 1773, 01.12.2023
Ceren Tayran
,
Mehmet Çakmak
Project Number
2019K1292587
References
- [1] Rundqvist S., “Phosphides of the B31 (MnP) Structure Type”, Acta Chemica Scandinavica, 16: 287-292, (1962).
- [2] Rundqvist S., Lundström, T. “X-Ray Studies of Molybdenum and Tungsten Phosphides”. Acta Chemica Scandinavica, 17: 37-46, (1963).
- [3] Joshi, R., Sahariya, J., Mund, H.S., Bhamu, K.C., Tiwari, S., Ahuja B.L., “Compton profiles of MoP and WP: Validation of second-order generalized gradient approximation,” Computational Materials Science, 53(1): 89-93, (2012).
- [4] Wu, W, Cheng, J.-G., Matsubayashi, K., Kong, P., Lin, F., Jin C., Wang, N., Uwatoko, Y., Luo, J., “Superconductivity in the vicinity of antiferromagnetic order in CrAs,” Nature Communications, 5: 5508, (2014).
- [5] Kotegawa, H., Nakahara, S., Tou, H., Sugawara, H. “Superconductivity of 2.2 K under Pressure in Helimagnet CrAs”, Journal of the Physical Society of Japan, 83: 093702, (2014).
- [6] Kotegawa, H., Nakahara, Akamatsu, R., Tou, H., Sugawara, H., Harima, H., “Detection of an Unconventional Superconducting Phase in the Vicinity of the Strong First-Order Magnetic Transition in CrAs Using 75As-Nuclear Quadrupole Resonance”, Physical Review Letters, 114: 117002, (2015).
- [7] Cheng, J.-G., Matsubayashi, K., Wu, W., Sun, J. P., Lin, F. K., Luo, J. L., Uwatoko, Y., “Pressure-Induced Superconductivity on the border of Magnetic Order in MnP,” Physical Review Letters, 114: 117001, (2015).
- [8] Liu, Z., Wu, W., Zhao, Z., Zhao, H., Cui, J., Shan, P., Zhang, J., Yang, C., Sun, P., Wei, Y., Li, S., Zhao, J., Sui, Y., Cheng, J., Lu, L., Liu, G., Superconductivity in WP single crystals”, Physical Review B, 99: 184509, (2019).
- [9] Cuono G., Forte, F., Cuoco, M., Islam, R., Luo, J., Noce C., Autieri, C., “Multiple band crossings and Fermi surface topology: Role of double nonsymmorphic symmetries in MnP-type crystal structures,” Physical Review Materials, 3(9): 095004, (2019).
- [10] Wu, W., Cheng, L., Matsubayashi, K., Kong, P., Lin, F., Jin, C., Wang, N., Uwatoko, Y., Luo, J., “Superconductivity in the vicinity of antiferromagnetic order in CrAs,” Nature Communications, 5: 5508, (2014).
- [11] Chen R. Y., Wang, N. L., “Progress in Cr- and Mn-based superconductors: a key issues review,” Reports on Progress in Physics, 82: 012503, (2019).
- [12] Wang, Y., Feng, Y., Cheng, J.-G., Wu, W., Luo, J. L., Rosenbaum, T. F., “Spiral magnetic order and pressure-induced superconductivity in transition metal compounds,” Nature Communications, 7: 13037, (2016).
- [13] Autieri C., Noce, C., “First-principles study of structural, magnetic and electronic properties of CrAs,” Philosophical Magazine, 97: 3276, (2017).
- [14] Autieri, C., Cuono, G., Forte, F., Noce, C., “Low energy bands and transport properties of chromium arsenide,” Journal of Physics: Condensed Matter, 29: 224004, (2017).
- [15] Motizuki, K., Ido, H., Itoh, T., Morifuji, M., “Electronic Structure and Magnetism of 3d-Transition Metal Pnictides”, Springer Series in Materials Science (Springer-Verlag, Berlin) (2010).
- [16] Roberts, B. W., “Superconductive Materials and Some of Their Properties (National Bureau of Standards),” Washington, DC, (1969).
- [17] Guerin, R., Jacques, M., Prigent, J., “Etude des chaines metal-metal dans la structure type MnP: Les arseniure et phosphure “MoAs” et WP et leurs solutions solides avec) les composes MX (M = élément de transition 3d; X = As, P)”, Materials Research Bulletin, 10(9): 957-965, (1975).
- [18] Kandler, H., Reiss, B., Naturforschg, Z., “Zur Kristallstruktur der intermetallischen Phasen MoAs und Mo5As”, Zeitschrift für Naturforschung, 21a: 549-554, (1966).
- [19] Fjellvåg, H., Selte, K., Danihelka, P., “Structural and Magnetic Properties of Mn(1-t) Mo(t)As”, Acta Chemica Scandinavica, A38: 789–794, (1984).
- [20] Faller, F.E., Biltz W., Meisel, K., Zumbusch, M.Z., “Beiträge zur systematischen Verwandtschaftslehre. 99. Über Phosphide von Wolfram, Molybdän und Chrom”, Zeitschrift für anorganische und allgemeine Chemie, 248: 209, (1941).
- [21] Schönberg, N., “An X-Ray Investigation of Transition Metal Phosphides”, Acta Chemica Scandinavica, 8: 226-239, (1954).
- [22] Bachmayer, K., Nowotny, H., Kohl, A., “Die Struktur von TiAs”, Physikalische, Anorganische und Analytische Chemie, 86: 39-43, (1955).
- [23] Gopalakrishnan, J., Pandey, S., Rangan, K. K., “Convenient Route for the Synthesis of Transition-Metal Pnictides by Direct Reduction of Phosphate, Arsenate, and Antimonate Precursors,” Chemistry of Materials, 9(10): 2113-2116, (1997).
- [24] Lesnyak V.V., Stratiichuk D.A., Sudavtsova V.S., Slobodyanik S., “Preparation of Al, Cr, Nb, Mo, and W Monophosphides from a Lithium Metaphosphate Melt,” Russian Journal of Applied Chemistry, 74(8): 1274–1277, (2001).
- [25] Jaiganesh R., Eithiraj D., Kalpana, G., “Theoretical study of electronic, magnetic and structural properties of Mo and W based group V (N, P, As, Sb and Bi) compounds,” Computational Materials Science, 49(1): 112-120, (2010).
- [26] Tayran, C., Çakmak, M., “Electronic structure, phonon and superconductivity for WP 5d-transition metal”, Journal of Applied Physics, 126: 175103, (2019).
- [27] Kresse, G., Hafner, J., “Ab initio molecular dynamics for liquid metals”, Physical Review B, 47: 558(R), (1993).
- [28] Kresse, G., Furthmüller J., “Efficiency of ab-initio total-energy calculations for metals and semiconductors using a plane-wave basis set”, Computational Materials Science, 6: 15, (1996).
- [29] Kresse, G., Joubert, D., “From ultrasoft pseudopotentials to the projector augmented-wave method”, Physical Review B, 59: 1758, (1999).
- [30] Perdew, J.P., Burke, K., Ernzerhof, M., “Generalized Gradient Approximation Made Simple”, Physical Review Letters, 77: 3865-3868, (1994). [Erratum Phys. Rev. Lett. 78, 1396 (1997)].
- [31] Blöchl, P.E., “Projector augmented-wave method”, Physical Review B, 50: 17953, (1994).
- [32] Kresse, G., Furthmüller J., “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set”, Physical Review B, 54: 11169, (1996).
- [33] Monkhorst, H.J., Pack, J.D., “Special points for Brillouin-zone integrations”, Physical Review B, 13: 5188, (1976).
- [34] Momma, K., Izumi, F., “VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data”, Journal of Applied Crystallography, 44: 1272-1276, (2011).
- [35] Togo, A., Tanaka I., “First principles phonon calculations in materials science”, Scripta Materialia, 108: 1-5, (2015).
- [36] Kanaya, K., Abe, S., Yoshida, H., Kamigaki, K., Kaneko, T., “Magnetic and structural properties of pseudo-binary compounds CrAs1−xPx”, Journal of Alloys and Compounds, 383: 189, (2004).
- [37] Niu, Q., Yu, W. C., Yip, K. Y., Lim, Z. L., Kotegawa, H., Matsuoka, E., Sugawara, H., Tou, H., Yanase, Y., Goh, S.K., “Quasilinear quantum magnetoresistance in pressure-induced nonsymmorphic superconductor chromium arsenide”, Nature Communications, 8: 15358, (2017).
- [38] Ashcroft, N.W., Mermin, N.D., “Solid State Physics”, Saunders, Philadelphia, (1976).
- [39] Sailuam W., Phacheerak, K., Bootchanont, A., Fongkaew, I., Limpijumnong S., “Elastic and mechanical properties of hydroxyapatite under pressure: A first-principles investigation”, Computational Condensed Matter, 24: e00481, (2020).
- [40] Ravindran, P., Fast, L., Korzhavyi, P.A., Johnnsson, B., Wills, J., Eriksson, O., “Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2”, Journal of Applied Physics, 84(9): 4891, (1998).
- [41] Mattesini M., Matar, S.F., “Density-functional theory investigation of hardness, stability, and electron-energy-loss spectra of carbon nitrides with C11N4 stoichiometry”, Physical Review B, 65: 075110, (2002).
- [42] Wu, Z.J., Zhao, E.J., Xiang, H.P., Hao, X.F., Liu X.J., Meng, J., “Crystal structures and elastic properties of superhard IrN2 and IrN3 from first principles”, Physical Review B, 76: 054115, (2007).
- [43] Birch F., “Finite Elastic Strain of Cubic Crystals”, Physical Review, 71: 809, (1947).
- [44] M. Born, K. Huang, “Dynamical Theory of Crystal Lattices”, Clarendon, Oxford,1956.
- [45] Beckstein, O., Klepeis, J.E., Hart, G.L.W., Pankratov O., “First-principles elastic constants and electronic structure of α−Pt2Si and PtSi”, Physical Review B, 63: 134112, (2001).
- [46] Wallace D.C., “Thermodynamics of Crystals”, Wiley, New York (Chap. 1), (1972).
- [47] Jong, M. de, Chen, W., Angsten, T., Jain, A., Notestine, R., Gamst, A., Sluiter, M., Krishna Ande, C., Zwaag, S. van der, Plata, J. J., Toher, C., Curtarolo, S., Ceder, G., Persson, K. A., Asta, M., “Charting the complete elastic properties of inorganic crystalline compounds”, Scientific Data, 2: 150009, (2015).
- [48] [Gaillac, R., Pullumbi, P., Coudert, F.-X., “ELATE: an open-source online application for analysis and visualization of elastic tensors”, Journal of Physics-Condensed Matter, 28: 275201, (2016).
- [49] Voigt, W., “Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik)”, Teubner, Leipzig, (1928).
- [50] Reuss A., “Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle”, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 9: 49-58, (1929).
- [51] Hill, R., “The Elastic Behaviour of a Crystalline Aggregate”, Proceedings of the Physical Society, 65(5): 349–354, (1952).
- [52] Pugh, S. F., “XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals”, Philosophical Magazine, 45: 823-843, (1954).
- [53] Young, A. F., Sanloup, C., Gregoryanz, E., Scandolo, S., Hemley, R. J., Mao, H. K., “Synthesis of Novel Transition Metal Nitrides IrN2 and OsN2”, Physical Review Letters. 96(15): 155501, (2006).
- [54] Yang, X., Hao, A., Wang, X., Liu, X., Zhu, Y., “First-principles study of structural stabilities, electronic and elastic properties of BaF2 under high pressure”, Computational Materials Science, 49: 530-534, (2010).
- [55] Pettifor, D.G., “Theoretical predictions of structure and related properties of intermetallics”, Materials Science and Technology, 8(4): 345-349, (1992).
- [56] Chen, H., Lei, X., Long, J., Huang, W., “The elastic and thermodynamic properties of new antiperovskite-type superconductor CuNNi3 under pressure”, Materials Science in Semiconductor Processing, 27: 207-211, (2014).
- [57] Wu, Z. J., Zhao, E. J., Xiang, H. P., Hao, X. F., Liu, X. J., Meng, J., “Crystal structures and elastic properties of superhard IrN2 and IrN3 from first principles”, Physical Review B, 76: 054115, (2007).
- [58] Yang, R., Zhu, C., Wei, Q., Du, Z., “Investigations on structural, elastic, thermodynamic and electronic properties of TiN, Ti2N and Ti3N2 under high pressure by first-principles”, Journal of Physics Chemistry of Solids, 98: 10-19, (2016).
- [59] Haines, J., Léger, J., Bocquillon, G., “Synthesis and Design of Superhard Materials”, Annual Review of Materials Research, 31: 1–23, (2001).
- [60] Qi, C., Jiang, Y., Liu, Y., Zhou, R., “Elastic and electronic properties of XB2 (X=V, Nb, Ta, Cr, Mo, and W) with AlB2 structure from first-principles calculations”, Ceramics International, 40(4): 5843-5851, (2014).
- [61] Kanoun, M.B., Goumri-Said, S., Reshak, A.H., Merad, A.E., “Electro-structural correlations, elastic and optical properties among the nanolaminated ternary carbides Zr2AC”, Solid State Science, 12(5): 887–898, (2010).
- [62] Wen, Y., Wang, L., Liu, H., Song, L., “Ab Initio Study of the Elastic and Mechanical Properties of B19 TiAl”, Crystals, 7: 39, (2017).
- [63] Papadimitriou, I., Utton, C., Scott, A., Tsakiropoulos, P., “Ab Initio Study of Binary and Ternary Nb3(X, Y) A15 Intermetallic Phases (X, Y = Al, Ge, Si, Sn)”, Metallurgical and Materials Transactions A, 46(2): 566-576, (2015).
- [64] Abadias, G., Kanoun, M.B., Goumri-Said, S., Koutsokeras, L., Dub, S.N., Djemia, Ph., “Electronic structure and mechanical properties of ternary ZrTaN alloys studied by ab initio calculations and thin-film growth experiments”, Physical Review B, 90: 144107, (2014).
- [65] Chen, H., Lei, X., Long, J., Huang, W., “The elastic and thermodynamic properties of new antiperovskite-type superconductor CuNNi3 under pressure”, Materials Science in Semiconductor Processing, 27: 207-211, (2014).
- [66] Tian, Y.J. Xu, B., Zhao, Z.S., “Microscopic theory of hardness and design of novel superhard crystals.”, International Journal of Refractory Metals and Hard Materials, 33: 93-106 (2012).
- [67] Chen, X.Q., Fu, C.L., Krčmar, M., “Electronic and Structural Origin of Ultraincompressibility of 5d Transition-Metal Diborides MB2 (M=W, Re, Os)”, 100: 196403 (2008).
- [68] Jain, A., Ong, S. P., Hautier, G., Chen, W., Richards, W. D., Dacek, S., Cholia, S., Gunter, D., Skinner, D., Ceder, G., Persson, K. A., “Commentary: The Materials Project: A materials genome approach to accelerating materials innovation”, APL Materials, 1: 011002, (2013).