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Structural, electronic, magnetic and mechanical properties of the full-Heusler compounds Ni2Mn(Ge,Sn) and Mn2NiGe

  • Naima Asli , Fethallah Dahmane ORCID logo EMAIL logo , Mohamed Mokhtari , Chahrazed Zouaneb , Mohammed Batouche , Houari Khachai , Vipul Srivastava , S. H. Naqib , Y. Al-Douri , Abdelmadjid Bouhemadou and Rabah Khenata
Published/Copyright: May 27, 2021

Abstract

Mn-Ni based full-Heusler alloys belong to novel half-metallic compounds with a promising set of physical properties for applications as functional materials. Based on first principles calculations, the electronic structures, the magnetic and mechanical properties of Ni2Mn(Ge,Sn) and Mn2NiGe full-Heusler alloys have been investigated in detail. The results revealed that the Mn2NiGe with Hg2CuTi type structure is more stable; on the other hand, for Ni2Mn(Ge,Sn), the Cu2MnAl type structure is more stable. The Mn2NiGe alloys are found to be half-metallic with an integer value of total magnetic moment of 4 μB which makes them interesting materials in the field of spintronics. The Ni2Mn(Ge,Sn) alloys exhibit metallic character in both Hg2CuTi and Cu2MnAl type structures. The calculated B/G ratios for all the considered compounds Ni2Mn(Ge,Sn) and Mn2NiGe are greater than 1.75; therefore, these alloys are ductile, and the calculated Cauchy’s pressure is positive, which also classified these compounds as ductile materials.


Corresponding author: Fethallah Dahmane, Département de sciences de la matière, Centre Universitaire de Tissemsilt, Tissemsilt38000, Algeria; and Laboratoire de Physique Quantique et de Modélisation Mathématique (LPQ3M), Département de Technologie, Université de Mascara, Mascara29000, Algeria, E-mail:

Funding source: The General Direction of Scientific Research and Technological Development (DGRSDT)

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: The Authors acknowledge the financial support of the General Direction of Scientific Research and Technological Development (DGRSDT).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] D. P. Rai, Sandeep, M. P. Ghimire, and R. K. Thapa, “Study of energy bands and magnetic properties of Co2CrSi Heusler alloy,” Bull. Mater. Sci., vol. 34, pp. 1219–1222, 2011. https://doi.org/10.1007/s12034-011-0233-y.Search in Google Scholar

[2] D. Amari, M. Mokhtari, F. Dahmane, et al.., “A comparative study between Hg2CuTi and Cu2MnAl type structures for Zr2CoZ (Z = Al, Ga, In) Heusler alloys,” Chin. J. Phys., vol. 60, pp. 450–461, 2019. https://doi.org/10.1016/j.cjph.2019.05.024.Search in Google Scholar

[3] K. M. Hossain, M. Zahid Hasan, and M. Lokman Ali, “Understanding the influences of Mg doping on the physical properties of SrMoO3 perovskite,” Results Phys., vol. 19, p. 103337, 2020. https://doi.org/10.1016/j.rinp.2020.103337.Search in Google Scholar

[4] K. M. Hossain and Z. Hasan, “Effects of negative chemical pressure on the structural, mechanical, and electronic properties of molybdenum-doped strontium ferrite,” Mater. Today Commun., vol. 26, p. 101908, 2021. https://doi.org/10.1016/j.mtcomm.2020.101908.Search in Google Scholar

[5] K. M. Hossain, S. K. Mitro, M. Anwar Hossain, J. Krishna Modak, M. Rasheduzzaman, and M. Zahid Hasan, “Influence of antimony on the structural, electronic, mechanical, and anisotropic properties of cubic barium stannate,” Mater. Today Commun., vol. 26, p. 101868, 2021. https://doi.org/10.1016/j.mtcomm.2020.101868.Search in Google Scholar

[6] M. Z. Hasan, M. Rasheduzzaman, and K. Monower Hossain, “Pressure-dependent physical properties of cubic SrBO3 (B = Cr, Fe) perovskites investigated by density functional theory,” Chin. Phys. B, vol. 29, no. 12, p. 123101, 2020. https://doi.org/10.1088/1674-1056/abab7f.Search in Google Scholar

[7] M. Rasheduzzaman, K. M. Hossain, S. K. Mitro, M. A. J. Hadi, J. K. Modak, and M. Z. Hasan, “Structural, mechanical, thermal, and optical properties of inverse-Heusler alloys Cr2CoZ (Z = Al, In): a first-principles investigation,” Phys. Lett., vol. 385, p. 126967, 2021. https://doi.org/10.1016/j.physleta.2020.126967.Search in Google Scholar

[8] I. Zutic, J. Fabian, and S. D. Sharm, “Spintronics: fundamentals and applications,” Rev. Mod. Phys., vol. 76, p. 323, 2004.10.1103/RevModPhys.76.323Search in Google Scholar

[9] A. Candan, G. Uğur, Z. Charifi, H. Baaziz, and M. R. Ellialtıoğlu, “Electronic structure and vibrational properties in cobalt-based full-Heusler compounds: a first principle study of Co2MnX (X=Si, Ge, Al, Ga),” J. Alloys Compd., vol. 560, pp. 215–222, 2013. https://doi.org/10.1016/j.jallcom.2013.01.102.Search in Google Scholar

[10] N. Arıkan, A. İyigör, A. Candan, et al.., “Electronic and phonon properties of the full-Heusler alloys X2YAl (X = Co, Fe and Y = Cr, Sc): a density functional theory study,” J. Mater. Sci., vol. 49, pp. 4180–4190, 2014.10.1007/s10853-014-8113-7Search in Google Scholar

[11] R. Masrour, A. Jabar, S. Labidi, et al.., “Study of structural, elastic, thermal, electronic and magnetic properties of heusler Mn2NiGe: an Ab initio calculations and Monte Carlo simulations,” Mater. Today Commun., vol. 26, p. 101772, 2021. https://doi.org/10.1016/j.mtcomm.2020.101772.Search in Google Scholar

[12] M. E. Jamer, L. G. Marshall, G. E. Sterbinsky, L. H. Lewis, and D. Heiman, “Low-moment ferrimagnetic phase of the Heusler compound Cr2CoAl,” J. Magn. Magn Mater., vol. 394, pp. 32–36, 2015. https://doi.org/10.1016/j.jmmm.2015.06.020.Search in Google Scholar

[13] Z. Addadi, B. Doumi, A. Mokaddem, et al.., “Electronic and ferromagnetic properties of 3d(V)-Doped (BaS) barium sulfide,” J. Supercond. Nov. Magn., vol. 30, pp. 917–923, 2017. https://doi.org/10.1007/s10948-016-3894-3.Search in Google Scholar

[14] F. Dahmane, A. Tadjer, B. Doumi, D. Mesri, H. Aourag, and A. Sayede, “First principles study of the electronic structures and magnetic properties of transition metal-doped cubic indium nitride,” Mater. Sci. Semicond. Process., vol. 21, pp. 66–73, 2014. https://doi.org/10.1016/j.mssp.2014.01.037.Search in Google Scholar

[15] F. Dahmane, D. Mesri, A. Tadjer, et al.., “Electronic structure, magnetism and stability of Co2CrX (X =Al, Ga, In) ab initio study,” Mod. Phys. Lett. B, vol. 30, p. 1550265, 2016. https://doi.org/10.1142/s0217984915502656.Search in Google Scholar

[16] K. A. Kilian and R. H. Victora, “Electronic structure of Ni2MnIn for use in spin injection,” J. Appl. Phys., vol. 87, p. 7064, 2000. https://doi.org/10.1063/1.372932.Search in Google Scholar

[17] B. Hamri, B. Abbar, A. Hamri, O. Baraka, A. Hallouche, and A. Zaoui, “Electronic structure and mechanical properties of X2MnSn (X = Cu, Ni, Pd) under hydrostatic pressure: GGA + U calculations,” Comput. Condens. Matter, vol. 3, pp. 14–20, 2015. https://doi.org/10.1016/j.cocom.2014.12.003.Search in Google Scholar

[18] F. Dahmane, D. Mesri, B. Doumi, et al.., “Ab initio investigation of half-metallic behaviour in the full-heusler X2MnGe (X = Sc, Fe, Ni),” J. Supercond. Nov. Magnetism, vol. 28, no. 7, pp. 2063–2069, 2015. https://doi.org/10.1007/s10948-015-2994-9.Search in Google Scholar

[19] H. Rached, D. Rached, R. Khenata, A. H. Reshak, and M. Rabah, “First-principles calculations of structural, elastic and electronic properties of Ni2MnZ (Z = Al, Ga and In) Heusler alloys,” Phys. Status Solidi B, vol. 246, p. 1580, 2009. https://doi.org/10.1002/pssb.200844400.Search in Google Scholar

[20] K. A. Kilian and R. H. Victora, “Electronic structure of the Ni/sub 2/MnIn/InAs [100] interface relevant to spin injection,” IEEE Trans. Magn., vol. 37, p. 1976, 2001. https://doi.org/10.1109/20.951026.Search in Google Scholar

[21] O. Benguerine, Z. Nabi, B. Benichou, et al.., “Structural, elastic, electronic and magnetic properties of Ni2MnSb, Ni2MnSn and Ni2MnSb0.5Sn0.5 magnetic shape memory alloys,” Rev. Mexic. Fisica, vol. 66, pp. 121–126, 2020. https://doi.org/10.31349/revmexfis.66.121.Search in Google Scholar

[22] J. Li, Z. Zhang, Y. Sun, et al.., “The thermodynamic, electronic and magnetic properties of Ni2MnX (X=Ge, Sn, Sb) Heusler alloys: a quasi-hormonic Debye model and first principles study,” Phys. B Condens. Matter, vol. 409, pp. 35–41, 2013. https://doi.org/10.1016/j.physb.2012.10.006.Search in Google Scholar

[23] H.-L. Yan, H.-X. Liu, M.-J. Zhang, et al.., “Electronic origin of the main-group element dependences of elastic moduli in the Ni2Mn-based magnetic shape memory alloys,” J. Phys. Chem. Solid., vol. 148, p. 109671, 2021. https://doi.org/10.1016/j.jpcs.2020.109671.Search in Google Scholar

[24] S. E. Kulkova, S. S. Kulkov, and A. V. Subashiev, “Ab-initio investigation of electronic and magnetic properties of Heusler alloys,” Comput. Mater. Sci., vol. 36, p. 249, 2006. https://doi.org/10.1016/j.commatsci.2004.11.019.Search in Google Scholar

[25] H. Luo, F. Meng, G. Liu, et al.., “Electronic structure and possible martensitic transformation in Mn2NiGe and Ni2MnGe,” Intermetallics, vol. 38, pp. 139–143, 2013. https://doi.org/10.1016/j.intermet.2013.03.004.Search in Google Scholar

[26] H. Luo, G. Liu, Z. Feng, et al.., “Effect of the main-group elements on the electronic structures and magnetic properties of Heusler alloys Mn2NiZ (Z=In, Sn, Sb),” J. Magn. Magn Mater., vol. 321, pp. 4063–4066, 2009. https://doi.org/10.1016/j.jmmm.2009.08.002.Search in Google Scholar

[27] P. Blaha, K. Schwarz, G. K. H. Madsen, D. Hvasnicka, and J. Luitz, WIEN2k, an Augmented Plane Wave Local Orbitals Program for Calculating Crystal Properties, Austria, Karlheinz Schwarz, Techn. Universit Wien, 2001.Search in Google Scholar

[28] J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett., vol. 77, p. 3865, 1996. https://doi.org/10.1103/physrevlett.77.3865.Search in Google Scholar

[29] F. D. Murnaghan, “The compressibility of media under extreme pressures,” Proc. Natl. Acad. Sci. U.S.A., vol. 30, p. 5390, 1944.10.1073/pnas.30.9.244Search in Google Scholar PubMed PubMed Central

[30] H. Luo, Z. Zhu, G. Liu, et al.., “Prediction of half-metallic properties for the Heusler alloys Mn2CrZ (Z=Al, Ga, Si, Ge, Sb): a first-principles study,” J. Magn. Magn Mater., vol. 320, pp. 421–428, 2008. https://doi.org/10.1016/j.jmmm.2007.06.021.Search in Google Scholar

[31] N. Xing, Y. Gong, W. Zhang, J. Dong, and H. Li, “First-principle prediction of half-metallic properties for the Heusler alloys V2YSb (Y=Cr, Mn, Fe, Co),” Comput. Mater. Sci., vol. 45, p. 489, 2009. https://doi.org/10.1016/j.commatsci.2008.11.008.Search in Google Scholar

[32] L. Jia, Z. Zhang, Y. Sun, et al.., “The thermodynamic, electronic and magnetic properties of Ni2MnX (X=Ge, Sn, Sb) Heusler alloys: a quasihormonic Debye model and first principles study,” Physica B, vol. 409, pp. 35–41, 2013.10.1016/j.physb.2012.10.006Search in Google Scholar

[33] Y. Y. Cherkashin, Y. I. Gladyshevskiy, P. I. Kripyakevich, and Y. B. Kuz’ma, J. Inorg. Chem. USSR, vol. 3, p. 650, 1958.Search in Google Scholar

[34] V. A. Oksenenko, L. N. Trofimova, Y. N. Petrov, Y. V. Kudryavtsev, J. Dubowik, and Y. P. Lee, “Structural dependence of some physical properties of the Ni2MnGe Heusler alloy films,” J. Appl. Phys., vol. 99, p. 063902, 2006. https://doi.org/10.1063/1.2180434.Search in Google Scholar

[35] S. Aǧduc and G. Gokoǧlu, “Ab initio lattice dynamics of Ni2MnX (X = Sn, Sb) magnetic shape memory alloys,” J. Alloys Compd., vol. 9, p. 511, 2012.10.1016/j.jallcom.2011.08.092Search in Google Scholar

[36] Z.-J. Wu, E.-J. Zhao, H.-P. Xiang, H. Xian-feng, X.-J. Liu, and J. Meng, “Crystal structures and elastic properties of superhard IrN2 and IrN3 from first principles,” Phys. Rev. B, vol. 76, p. 054115, 2007.10.1103/PhysRevB.76.054115Search in Google Scholar

[37] S. Takeshi, “Nuclear magnetic resonance in Heusler Alloys: Ni2MnSn, Co2MnSn and Ni2MnSb,” J. Phys. Soc. Japan, vol. 28, p. 313, 1970.10.1143/JPSJ.28.313Search in Google Scholar

[38] S. Jha, H. M. Seyoum, M. Demarco, et al.., “Site and probe dependence of hyperfine magnetic field in L21 Heusler alloys X2MnZ (X=Ni, Cu, Rh, Pd and Z=Ga, Ge, In, Sn, Pb),” Hyperfine Interact., vol. 16, p. 685, 1983. https://doi.org/10.1007/bf02147342.Search in Google Scholar

[39] A. Ayuela, J. Enkovaara, K. Ullakko, and R. M. Nieminen, “Structural properties of magnetic Heusler alloys,” J. Phys. Condens. Matter, vol. 11, p. 2017, 1999. https://doi.org/10.1088/0953-8984/11/8/014.Search in Google Scholar

[40] L. Spina, Y.-Z. Jia, B. Ducourant, M. Tillard, and C. Z. Belin, “Compositional and structural variations in the ternary system Li – Al – Si,” Kristallografiâ, vol. 218, p. 740, 2003. https://doi.org/10.1524/zkri.218.11.740.20305.Search in Google Scholar

[41] H. Nowotny and F. Holub, “Untersuchungen an metallischen Systemen mit Flu spatphasen,” Monatsh. Chem., vol. 91, p. 877, 1960. https://doi.org/10.1007/bf00929560.Search in Google Scholar

[42] K. Refson, P. R. Tulip, and S. J. Clark, “Variational density-functional perturbation theory for dielectrics and lattice dynamics,” Phys. Rev. B, vol. 73, p. 155114, 2006. https://doi.org/10.1103/physrevb.73.155114.Search in Google Scholar

[43] M. D. Segall, P. J. Lindan, M. A. Probert, et al.., “First-principles simulation: ideas, illustrations and the CASTEP code,” J. Phys. Condens. Matter, vol. 14, p. 2717, 2002. https://doi.org/10.1088/0953-8984/14/11/301.Search in Google Scholar

[44] R. Vali, “Phonons and heat capacity of LaAlO3,” Comput. Mater. Sci., vol. 44, pp. 779–782, 2008. https://doi.org/10.1016/j.commatsci.2008.05.029.Search in Google Scholar

[45] R. Vali, “Structural phases of SrHfO3,” Solid State Commun., vol. 148, pp. 29–31, 2008. https://doi.org/10.1016/j.ssc.2008.07.018.Search in Google Scholar

[46] R. Vali, “Lattice dynamics of cubic SrZrO3,” J. Phys. Chem. Solid., vol. 69, pp. 876–879, 2008. https://doi.org/10.1016/j.jpcs.2007.09.022.Search in Google Scholar

[47] D. V. Suetin and I. R. Shein, “Electronic structure, mechanical and dynamical stability of hexagonal subcarbides M2C (M = Tc, Ru, Rh, Pd, Re, Os, Ir, and Pt): ab initio calculations,” Phys. Solid State, vol. 60, pp. 213–224, 2018. https://doi.org/10.1134/s1063783418020282.Search in Google Scholar

[48] R. A. de Groot, F. M. Mueller, P. G. V. Engen, and K. H. Buschow, “New class of materials: half-metallic ferromagnets,” Phys. Rev. Lett., vol. 50, p. 2024, 1983. https://doi.org/10.1103/physrevlett.50.2024.Search in Google Scholar

[49] Q.-L. Fang, X.-M. Zhao, J.-M. Zhang, and K.-W. Xu, “Magnetic properties and half-metallic in bulk and (001) surface of Ti2MnAl Heusler alloy with Hg2CuTi-type structure,” Thin Solid Films, vol. 558, pp. 241–246, 2014. https://doi.org/10.1016/j.tsf.2014.03.007.Search in Google Scholar

[50] C. M. Fang, G. A. de Wijs, and R. A. de Groot, “Spin-polarization in half-metals (invited),” J. Appl. Phys., vol. 91, p. 8340, 2002. https://doi.org/10.1063/1.1452238.Search in Google Scholar

[51] G. D. Liu, X. F. Dai, H. Y. Liu, et al.., “Mn2CoZ (Z = Al, Ga, In, Si, Ge, Sn, Sb) compounds: Structural, electronic, and magnetic properties,” Phys. Rev. B, vol. 77, p. 014424, 2008. https://doi.org/10.1103/physrevb.77.014424.Search in Google Scholar

[52] S. Skaftouros, K. özdoğan, E. Şasıoğlu, and I. Galanakis, “Generalized Slater-Pauling rule for the inverse Heusler compounds,” Phys. Rev. B: Condens. Matter Mater. Phys., vol. 87, p. 024420, 2013. https://doi.org/10.1103/physrevb.87.024420.Search in Google Scholar

[53] H. Luo, Y. Xin, B. Liu, et al.., “Competition of L21 and XA structural ordering in Heusler alloys X2CuAl (X = Sc, Ti, V, Cr, Mn, Fe, Co, Ni),” J. Alloys Compd., vol. 665, pp. 180–185, 2016. https://doi.org/10.1016/j.jallcom.2015.11.207.Search in Google Scholar

[54] M. Pugaczowa-Michalska, “Electronic structure, equilibrium and magnetic properties of Ni2MnGe: ab initio study,” J. Alloys Compd., vol. 427, pp. 54–60, 2007. https://doi.org/10.1016/j.jallcom.2006.03.036.Search in Google Scholar

[55] E. Şaşıoğlu, L. M. Sandratskii, and P. Bruno, “First-principles calculation of the intersublattice exchange interactions and Curie temperatures of the full Heusler alloys Ni2MnX (X = Ga, In, Sn, Sb,” Phys. Rev. B, vol. 70, p. 024427, 2004.10.1103/PhysRevB.70.024427Search in Google Scholar

[56] T. Charpin, A Package for Calculating Elastic Tensors of Cubic Phases Using WIEN, Paris, France, Laboratory of Geometrix F-75252, 2001.Search in Google Scholar

[57] R. Ullah, M. A. Ali, G. Murtaza, A. Mahmood, and S. M. Ramay, “An investigation of structural, elastic, mechanical, electronic, magnetic and thermoelectric properties of ferromagnetic half metallic EuCrO3,” Mater. Sci. Semicond. Process., vol. 122, p. 105487, 2021. https://doi.org/10.1016/j.mssp.2020.105487.Search in Google Scholar

[58] R. B. Behram, M. A. Iqbal, S. M. Alay-e-Abbas, et al.., “Theoretical investigation of mechanical, optoelectronic and thermoelectric properties of BiGaO3 and BiInO3 compounds,” Mater. Sci. Semicond. Process., vol. 41, p. 297, 2016. https://doi.org/10.1016/j.mssp.2015.09.010.Search in Google Scholar

[59] S. A. Khandy and D. C. Gupta, “Structural, elastic and magneto-electronic properties of half-metallic BaNpO3 perovskite,” Mater. Chem. Phys., vol. 198, p. 380, 2017. https://doi.org/10.1016/j.matchemphys.2017.06.033.Search in Google Scholar

[60] A. Bouhemadou and R. Khenata, “Ab initio study of structural phase stability and elastic properties of ScSb and YSb under pressure effect,” Phys. Lett. A, vol. 362, p. 476, 2007. https://doi.org/10.1016/j.physleta.2006.10.054.Search in Google Scholar

[61] V. Kanchana, G. Vaitheeswaran, and A. Svane, “Calculated structural, elastic and electronic properties of SrCl2,” J. Alloys Compd., vol. 455, p. 480, 2008. https://doi.org/10.1016/j.jallcom.2007.01.163.Search in Google Scholar

[62] R. Khenata, A. Bouhemadou, M. Hichour, H. Baltache, D. Rached, and M. Rérat, “Elastic and optical properties of BeS, BeSe and BeTe under pressure,” Solid State Electron., vol. 50, p. 1382, 2006. https://doi.org/10.1016/j.sse.2006.06.019.Search in Google Scholar

[63] A. Bouhemadou, R. Khenata, and M. Maamache, “Structural phase stability and elastic properties of lanthanum monochalcogenides at high pressure,” J. Mol. Struct.: THEOCHEM, vol. 777, p. 5, 2006. https://doi.org/10.1016/j.theochem.2006.08.031.Search in Google Scholar

[64] S. Q. Wang and H. Q. Ye, “First-principles study on elastic properties and phase stability of III–V compounds,” Phys. Status Solidi B, vol. 240, p. 48, 2003. https://doi.org/10.1002/pssb.200301861.Search in Google Scholar

[65] W. Voigt, “Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper,” Ann. Phys. Chem., vol. 274, p. 573, 1889. https://doi.org/10.1002/andp.18892741206.Search in Google Scholar

[66] A. Reuss, “Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle,” Z. Angew. Math. Mech., vol. 9, p. 49, 1929. https://doi.org/10.1002/zamm.19290090104.Search in Google Scholar

[67] R. Hill, “The elastic behaviour of a crystalline aggregate,” Proc. Phys. Soc. A, vol. 65, p. 349, 1952. https://doi.org/10.1088/0370-1298/65/5/307.Search in Google Scholar

[68] J. Wang, S. Yip, S. R. Phillpot, and D. Wolf, “Crystal instabilities at finite strain,” Phys. Rev. Lett., vol. 71, p. 4182, 1993. https://doi.org/10.1103/physrevlett.71.4182.Search in Google Scholar

[69] S. F. Pugh, “XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals,” Philos. Mag., vol. 45, p. 823, 1954. https://doi.org/10.1080/14786440808520496.Search in Google Scholar

[70] V. Kanchana, G. Vaitheeswaran, Y. Ma, Y. Xie, A. Svane, and O. Eriksson, “Density functional study of elastic and vibrational properties of the Heusler-type alloys Fe2VAl and Fe2VGa,” Phys. Rev. B, vol. 80, p. 125108, 2009. https://doi.org/10.1103/physrevb.80.125108.Search in Google Scholar

[71] D. G. Pettifor, “Theoretical predictions of structure and related properties of intermetallics,” Mater. Sci. Technol., vol. 8, p. 345, 1992.10.1179/mst.1992.8.4.345Search in Google Scholar

[72] I. N. Frantsevich, F. F. Voronov, and S. A. Bokuta, Elastic Constants and Elastic Moduli of Metals and Insulators Handbook, I. N. Frantsevich, Ed., Kiev, Naukuva Dumka, 1983, pp. 60–180.Search in Google Scholar

[73] J. Haines, J. M. Leger, and G. Bocquillon, “Synthesis and design of superhard materials,” Annu. Rev. Mater. Res., vol. 31, p. 10, 2001. https://doi.org/10.1146/annurev.matsci.31.1.1.Search in Google Scholar

[74] R. E. Newnham, Properties of Materials and Anisotropy, Symmetry, Structure, New York, NY, USA, Oxford University Press, 2005.10.1093/oso/9780198520757.003.0005Search in Google Scholar

Received: 2020-11-30
Revised: 2021-05-01
Accepted: 2021-05-09
Published Online: 2021-05-27
Published in Print: 2021-08-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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