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Licensed Unlicensed Requires Authentication Published by De Gruyter August 11, 2020

Thermodynamic and thermoelastic properties of wurtzite-ZnS by density functional theory

  • Gianfranco Ulian ORCID logo , Daniele Moro and Giovanni Valdrè EMAIL logo
From the journal American Mineralogist

Abstract

In the present paper, we provide a detailed theoretical investigation on fundamental thermodynamic, thermomechanical, and electronic properties of wurtzite ZnS between 0–20 GPa and 0–2000 K, obtained by ab initio density functional theory and the B3LYP functional. Several properties, such as phonon dispersion relations, elastic and piezoelectric constants, and thermodynamic and thermoelastic behaviors were calculated and reported. The analysis of the data via volume-integrated third-order Birch-Murnaghan fitting resulted in K0 = 72.17(4) GPa, K′ = 3.87(1), and V0 = 85.781(1) Å3 at T = 0 K. The Born criteria for the mechanical stability of the mineral phase showed that wurtzite is unstable above about 19 GPa in static conditions. We calculated a direct bandgap for wz-ZnS of 4.86 eV at zero compression, which became an indirect one by increasing pressure above 17 GPa. The results are in good agreement with the experimental and theoretical ones reported in the literature, and further extend the knowledge of an important zinc sulfide phase, for both geological and industrial applications.

References cited

Adachi, S. (2005) Properties of Group IV, III-V, and II-VI Semiconductors. Wiley.10.1002/0470090340Search in Google Scholar

Bachmann, M., Czerner, M., Edalati-Boostan, S., and Heiliger, C. (2012) Ab initio calculations of phonon transport in ZnO and ZnS. European Physical Journal B, 85(5), 146.10.1140/epjb/e2012-20503-ySearch in Google Scholar

Baima, J., Erba, A., Maschio, L., Zicovich-Wilson, C.M., Dovesi, R., and Kirtman, B. (2016) Direct piezoelectric tensor of 3D periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method. Zeitschrift für Physikalische Chemie-International Journal of Research in Physical Chemistry & Chemical Physics, 230(5-7), 719–736.10.1515/zpch-2015-0701Search in Google Scholar

Barron, T.H.K., and Klein, M.L. (1965) Second-order elastic constants of a solid under stress. Proceedings of the Physical Society, 85, 523–532.10.1088/0370-1328/85/3/313Search in Google Scholar

Becke, A.D. (1993a) Density-functional thermochemistry. III. The role of exact exchange. Journal of Chemical Physics, 98(7), 5648–5652.10.1063/1.464913Search in Google Scholar

Becke, A.D. (1993b) A new mixing of Hartree-Fock and local Density-Functional Theories. Journal of Chemical Physics, 98(2), 1372–1377.10.1063/1.464304Search in Google Scholar

Bellefleur, G., Schetselaar, E., White, D., Miah, K., and Dueck, P. (2015) 3D seismic imaging of the Lalor volcanogenic massive sulphide deposit, Manitoba, Canada. Geophysical Prospecting, 63(4), 813–832.10.1111/1365-2478.12236Search in Google Scholar

Belmonte, D. (2017) First principles thermodynamics of minerals at HP-HT conditions: MgO as a prototypical material. Minerals 7, 183.10.3390/min7100183Search in Google Scholar

Belmonte, D., Gatti, C., Ottonello, G., Richet, P., and Zuccolini, M.V. (2016) Ab initio thermodynamic and thermophysical properties of sodium metasilicate, Na2SiO3 and their electron-density and electron-pair-density counterparts. Journal of Physical Chemistry A, 120(44), 8881–8895.10.1021/acs.jpca.6b08676Search in Google Scholar PubMed

Belmonte, D., Ottonello, G., Zuccolini, M.V., and Attene, M. (2017) The system MgO-Al2O3-SiO2 under pressure: A computational study of melting relations and phase diagrams. Chemical Geology, 461, 54–64.10.1016/j.chemgeo.2016.11.011Search in Google Scholar

Biernacki, S., and Scheffler, M. (1989) Negative Thermal-Expansion of Diamond and Zincblende Semiconductors. Physical Review Letters, 63(3), 290–293.10.1103/PhysRevLett.63.290Search in Google Scholar

Birch, F. (1947) Finite elastic strain of cubic crystal. Physical Review, 71, 809–824.10.1103/PhysRev.71.809Search in Google Scholar

Born, M., and Huang, K. (1954) Dynamical Theory of Crystal Lattices. Clarendon Press, Oxford.Search in Google Scholar

Brafman, O., and Mitra, S. S. (1968) Raman effect in wurtzite- and zinc-blende-type ZnS single crystals. Physical Review, 171, 931.10.1103/PhysRev.171.931Search in Google Scholar

Brainerd, J.G. (1949) Standards on piezoelectric crystals. Proceedings of the IRE, 37, 1378–1395.10.1109/JRPROC.1949.229975Search in Google Scholar

Cardona, M., Kremer, R.K., Lauck, R., Siegle, G., Munoz, A., Romero, A.H., and Schindler, A. (2010) Electronic, vibrational, and thermodynamic properties of ZnS with zinc-blende and rocksalt structure. Physical Review B, 81(7).10.1103/PhysRevB.81.075207Search in Google Scholar

Catti, M., Noel, Y., and Dovesi, R. (2003) Full piezoelectric tensors of wurtzite and zinc blende ZnO and ZnS by first-principles calculations. Journal of Physics and Chemistry of Solids, 64(11), 2183–2190.10.1016/S0022-3697(03)00219-1Search in Google Scholar

Chang, E., and Barsch, G.R. (1973) Pressure dependence of single crystal elastic constants and anharmonic properties of wurtzite. Journal of Physics and Chemistry of Solids, 34(9), 1543–1563.10.1016/S0022-3697(73)80226-4Search in Google Scholar

Chen, X.Q., Niu, H., Li, D., and Li, Y. (2011) Modeling hardness of polycrystalline materials and bulk metallic glasses. Intermetallics, 19(9), 1275–1281.10.1016/j.intermet.2011.03.026Search in Google Scholar

Cline, C.F., Dunegan, H.L., and Henderson, G.W. (1967) Elastic constants of hexagonal BeO, ZnS, and CdSe. Journal of Applied Physics, 38, 1944–1948.10.1063/1.1709787Search in Google Scholar

Desgreniers, S., Beaulieu, L., and Lepage, I. (2000) Pressure-induced structural changes in ZnS. Physical Review B, 61(13), 8726–8733.10.1103/PhysRevB.61.8726Search in Google Scholar

Doll, K. (2001) Implementation of analytical Hartree-Fock gradients for periodic systems. Computer Physics Communications, 137, 74–78.10.1016/S0010-4655(01)00172-2Search in Google Scholar

Doll, K., Harrison, N.M., and Saunders, V.R. (2001) Analytical Hartree-Fock gradients for periodic systems. Journal of Quantum Chemistry, 82(1), 1–13.10.1002/1097-461X(2001)82:1<1::AID-QUA1017>3.0.CO;2-WSearch in Google Scholar

Dovesi, R., Erba, A., Orlando, R., Zicovich-Wilson, C.M., Civalleri, B., Maschio, L., Rerat, M., Casassa, S., Baima, J., Salustro, S., and Kirtman, B. (2018) Quantum-mechanical condensed matter simulations with CRYSTAL. Wiley Interdisciplinary Reviews-Computational Molecular Science, 8(4), E1360.10.1002/wcms.1360Search in Google Scholar

Erba, A. (2014) On combining temperature and pressure effects on structural properties of crystals with standard ab initio techniques. Journal of Chemical Physics, 141(12), 124115.10.1063/1.4896228Search in Google Scholar

Erba, A., Mahmoud, A., Belmonte, D., and Dovesi, R. (2014) High pressure elastic properties of minerals from ab initio simulations: The case of pyrope, grossular and andradite silicate garnets. Journal of Chemical Physics, 140(12).10.1063/1.4869144Search in Google Scholar

Erba, A., Maul, J., Demichelis, R., and Dovesi, R. (2015) Assessing thermochemical properties of materials through ab initio quantum-mechanical methods: the case of alpha-Al2O3 Physical Chemistry Chemical Physics, 17(17), 11670–11677.10.1039/C5CP01537ESearch in Google Scholar

Ferahtia, S., Saib, S., Bouarissa, N., and Benyettou, S. (2014) Structural parameters, elastic properties and piezoelectric constants of wurtzite ZnS and ZnSe under pressure. Superlattices and Microstructures, 67, 88–96.10.1016/j.spmi.2013.12.021Search in Google Scholar

Ferrero, M., Rerat, M., Orlando, R., and Dovesi, R. (2008) Coupled perturbed Hartree-Fock for periodic systems: The role of symmetry and related computational aspects. Journal of Chemical Physics, 128(1).10.1063/1.2817596Search in Google Scholar

Frey, F., Jagodzinski, H., and Steger, G. (1986) On the phase-transformation zinc blends to wurtzite. Bulletin De Mineralogie, 109(1-2), 117–129.10.3406/bulmi.1986.7921Search in Google Scholar

Hebbache, M., and Zemzemi, M. (2004) Ab initio study of high-pressure behavior of a low compressibility metal and a hard material: Osmium and diamond. Physical Review B, 70(22).10.1103/PhysRevB.70.224107Search in Google Scholar

Hill, R. (1952) The elastic behaviour of a crystalline aggregate. Proceedings of the Physical Society, London, Section A, 65, 349–354.10.1088/0370-1298/65/5/307Search in Google Scholar

Hu, C.E., Zeng, Z.Y., Cheng, Y., Chen, X.R., and Cai, L.C. (2008) First-principles calculations for electronic, optical and thermodynamic properties of ZnS. Chinese Physics B, 17(10), 3867–3874.10.1088/1674-1056/17/10/053Search in Google Scholar

Kandpal, K., and Gupta, N. (2018) Perspective of zinc oxide based thin film transistors: A comprehensive review. Microelectronics International, 35(1), 52–63.10.1108/MI-10-2016-0066Search in Google Scholar

Kang, Y.S., Zhao, G.J., and Liang, X.X. (2017) First-principle study of the lattice dynamic and thermodynamic properties of Zn-based semiconductors with wurtzite structure. Physica B-Condensed Matter, 515, 51–55.10.1016/j.physb.2017.04.005Search in Google Scholar

Karazhanov, S.Z., Ravindran, P., Kjekhus, A., Fjellvag, H., Grossner, U., and Svensson, B.G. (2006) Electronic structure and band parameters for ZnX (X = O, S, Se, Te). Journal of Crystal Growth, 287(1), 162–168.10.1016/j.jcrysgro.2005.10.061Search in Google Scholar

Kowalczuk, P.B., Snook, B., Kleiv, R.A., and Aasly, K. (2018) Efficient extraction of copper and zinc from seafloor massive sulphide rock samples from the Loki’s Castle area at the Arctic Mid-Ocean Ridge. Minerals Engineering, 115, 106–116.10.1016/j.mineng.2017.10.015Search in Google Scholar

Landolt-Börnstein (1986) Landolt-Börnstein Tables. Springer.Search in Google Scholar

Lee, C.T., Yang, W.T., and Parr, R.G. (1988) Development of the Colle-Salvetti Correlation-Energy formula into a functional of the electron-density. Physical Review B, 37(2), 785–789.10.1103/PhysRevB.37.785Search in Google Scholar

Madelung, O., and Schulz, M. (1982) Numerical Data and Functional Relationships in Science and Technology. New Series. Group III: Crystal and Solid State Physics. Springer, Berlin.Search in Google Scholar

Majumdar, A.J., and Roy, R. (1965) Thermal expansion of ZnS from 2 to 317 K. Journal of Applied Physics, 38, 1531–1534.Search in Google Scholar

Malehmir, A., Durrheim, R., Bellefleur, G., Urosevic, M., Juhlin, C., White, D.J., Milkereit, B., and Campbell, G. (2012) Seismic methods in mineral exploration and mine planning: A general overview of past and present case histories and a look into the future. Geophysics, 77(5), Wc173–Wc190.10.1190/geo2012-0028.1Search in Google Scholar

Marmier, A., Lethbridge, Z.A.D., Walton, R.I., Smith, C.W., Parker, S.C., and Evans, K.E. (2010) ElAM: A computer program for the analysis and representation of anisotropic elastic properties. Computer Physics Communications, 181(12), 2102–2115.10.1016/j.cpc.2010.08.033Search in Google Scholar

Monkhorst, H.J., and Pack, J.D. (1976) Special points for Brillouin-zone integrations. Physical Review B, 8, 5188–5192.10.1103/PhysRevB.13.5188Search in Google Scholar

Nye, J.F. (1957) Physical Properties of Crystals. Oxford University Press.Search in Google Scholar

Ono, S., and Kikegawa, T. (2018) Phase transition of ZnS at high pressures and temperatures. Phase Transitions, 91(1), 9–14.10.1080/01411594.2017.1350958Search in Google Scholar

Ossai, C.I., and Raghavan, N. (2018) Nanostructure and nanomaterial characterization, growth mechanisms, and applications. Nanotechnology Reviews, 7(2), 209–231.10.1515/ntrev-2017-0156Search in Google Scholar

Ottonello, G., Civalleri, B., Ganguly, J., Perger, W.F., Belmonte, D., and Zuccolini, M.V. (2010) Thermo-chemical and thermo-physical properties of the high-pressure phase anhydrous B (Mg14Si5O24 An ab-initio all-electron investigation. American Mineralogist, 95(4), 563–573.10.2138/am.2010.3368Search in Google Scholar

Özgür, Ü., Alivov, Y.I., Liu, C., Teke, A., Reshchikov, M.A., Doǧan, S., Avrutin, V., Cho, S.J., and Morko, H. (2005) A comprehensive review of ZnO materials and devices. Journal of Applied Physics, 98(4), 1–103.10.1063/1.1992666Search in Google Scholar

Pankratz, L.B., and King, E.G. (1965) High-temperature heat contents and entropies of two zinc sulfides and four solid solutions of zinc and iron sulfides. U.S. Bureau of Mines, 6708.Search in Google Scholar

Parlinski, K., Li, Z.Q., and Kawazoe, Y. (1997) First-principles determination of the soft mode in cubic ZrO2 Physical Review Letters, 78(21), 4063–4066.10.1103/PhysRevLett.78.4063Search in Google Scholar

Pascale, F., Zicovich-Wilson, C.M., Gejo, F.L., Civalleri, B., Orlando, R., and Dovesi, R. (2004) The calculation of the vibrational frequencies of crystalline compounds and its implementation in the CRYSTAL code. Journal of Computational Chemistry, 25(6), 888–897.10.1002/jcc.20019Search in Google Scholar PubMed

Peintinger, M.F., Oliveira, D.V., and Bredow, T. (2013) Consistent gaussian basis sets of Triple-Zeta valence with polarization quality for solid-State Calculations. Journal of Computational Chemistry, 34(6), 451–459.10.1002/jcc.23153Search in Google Scholar PubMed

Perdew, J.P., Burke, K., and Ernzerhof, M. (1996) Generalized gradient approximation made simple. Physical Review Letters, 77(18), 3865–3868.10.1103/PhysRevLett.77.3865Search in Google Scholar PubMed

Perger, W.F. (2010) First-principles calculation of second-order elastic constants and equations of state for lithium azide, LiN3 and lead azide, Pb(N32 International Journal of Quantum Chemistry, 110(10), 1916–1922.10.1002/qua.22351Search in Google Scholar

Perger, W.F., Criswell, J., Civalleri, B., and Dovesi, R. (2009) Ab-initio calculation of elastic constants of crystalline systems with the CRYSTAL code. Computer Physics Communications, 180(10), 1753–1759.10.1016/j.cpc.2009.04.022Search in Google Scholar

Prencipe, M., Scanavino, I., Nestola, F., Merlini, M., Civalleri, B., Bruno, M., and Dovesi, R. (2011) High-pressure thermo-elastic properties of beryl (Al4Be6Si12O36 from ab initio calculations, and observations about the source of thermal expansion. Physics and Chemistry of Minerals, 38(3), 223–239.10.1007/s00269-010-0398-8Search in Google Scholar

Robie, R.A., and Hemingway, B.S. (1995) Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 Pascals) pressures and at higher temperatures. U.S. Geological Survey Bulletin 2131. U.S. Geological Survey, Denver, Colorado.Search in Google Scholar

Sang, L., Liao, M., and Sumiya, M. (2013) A comprehensive review of semiconductor ultraviolet photodetectors: From thin film to one-dimensional nanostructures. Sensors (Switzerland), 13(8), 10482–10518.10.3390/s130810482Search in Google Scholar PubMed PubMed Central

Sharma, M., Mishra, D., and Kumar, J. (2019) First-principles study of the structural and electronic properties of bulk ZnS and small ZnnSn nanoclusters in the framework of the DFT plus U method. Physical Review B, 100(4), 12.10.1103/PhysRevB.100.045151Search in Google Scholar

Sinha, T., Lilhare, D., and Khare, A. (2018) Effects of various parameters on structural and optical properties of CBD-grown ZnS thin films: A review. Journal of Electronic Materials, 47(2), 1730–1751.10.1007/s11664-017-5876-zSearch in Google Scholar

Stuve, J.M. (1974) Low-temperature heat capacities of sphalerite and wurtzite, 7940. U.S. Bureau of Mines.Search in Google Scholar

Togo, A., and Tanaka, I. (2015) First principles phonon calculations in materials science. Scripta Materialia, 108, 1–5.10.1016/j.scriptamat.2015.07.021Search in Google Scholar

Uchida, N., and Saito, S. (1972) Elastic and photoelastic constants of α-ZnS. Journal of Applied Physics, 43(3), 971–976.10.1063/1.1661316Search in Google Scholar

Ulian, G., and Valdrè, G. (2015a) Density functional investigation of the thermophysical and thermo-chemical properties of 2M1 muscovite. American Mineralogist, 100(4), 935–944.10.2138/am-2015-5086Search in Google Scholar

Ulian, G., and Valdrè, G. (2015b) Density functional investigation of the thermophysical and thermochemical properties of talc [Mg3Si4O10(OH)2 Physics and Chemistry of Minerals, 42(2), 151–162.10.1007/s00269-014-0708-7Search in Google Scholar

Ulian, G., and Valdrè, G. (2015c) Structural, vibrational and thermophysical properties of pyrophyllite by semi-empirical density functional modelling. Physics and Chemistry of Minerals, 42(7), 609–627.10.1007/s00269-015-0748-7Search in Google Scholar

Ulian, G., and Valdrè, G. (2017) Effects of fluorine content on the elastic behavior of topaz Al2SiO4(F,OH)2 American Mineralogist, 102(1-2), 347–356.10.2138/am-2017-5668Search in Google Scholar

Ulian, G., and Valdrè, G. (2018a) Anisotropy and directional elastic behavior data obtained from the second-order elastic constants of portlandite Ca(OH)2 and brucite Mg(OH)2 Data in Brief, 21, 1375–1380.10.1016/j.dib.2018.10.139Search in Google Scholar PubMed PubMed Central

Ulian, G., and Valdrè, G. (2018b) Effect of mechanical stress on the Raman and Infrared bands of hydroxylapatite: a quantum mechanical first principle investigation. Journal of the Mechanical Behavior of Biomedical Materials, 77, 683–692.10.1016/j.jmbbm.2017.10.029Search in Google Scholar PubMed

Ulian, G., and Valdrè, G. (2018c) Second-order elastic constants of hexagonal hydroxylapatite (P63) from ab initio quantum mechanics: comparison between DFT functionals and basis sets. International Journal of Quantum Chemistry, 118(5), e25500.10.1002/qua.25500Search in Google Scholar

Ulian, G., and Valdrè, G. (2018d) Equation of state of hexagonal hydroxylapatite P63) as obtained from density functional theory simulations. International Journal of Quantum Chemistry, 118(12), e25553.10.1002/qua.25553Search in Google Scholar

Ulian, G., and Valdrè, G. (2019a) Equation of state and second-order elastic constants of portlandite Ca(OH)2 and brucite Mg(OH)2 Physics and Chemistry of Minerals, 46(2), 101–117.10.1007/s00269-018-0989-3Search in Google Scholar

Ulian, G., and Valdrè, G. (2019b) Thermomechanical, electronic and thermodynamic properties of ZnS cubic polymorphs: an ab initio investigation on the zinc-blende–rock-salt phase transition. Acta Crystallographica, B75, 1042–1059.10.1107/S2052520619012630Search in Google Scholar PubMed

Ulian, G., Tosoni, S., and Valdrè, G. (2014) The compressional behaviour and the mechanical properties of talc [Mg3Si4O10(OH)2 a density functional theory investigation. Physics and Chemistry of Minerals, 41(8), 639–650.10.1007/s00269-014-0677-xSearch in Google Scholar

Ulian, G., Moro, D., and Valdrè, G. (2018) First principle investigation of the mechanical properties of natural layered nanocomposite: Clinochlore as a model system for heterodesmic structures. Composite Structures, 202, 551–558.10.1016/j.compstruct.2018.02.089Search in Google Scholar

Valdez, L.A., Caravaca, M.A., and Casali, R.A. (2019) Ab-initio study of elastic anisotropy, hardness and volumetric thermal expansion coefficient of ZnO, ZnS, ZnSe in wurtzite and zinc blende phases. Journal of Physics and Chemistry of Solids, 134, 245–254.10.1016/j.jpcs.2019.05.019Search in Google Scholar

Wallace, D.W. (1998) Thermodynamics of Crystals. Dover Publications.Search in Google Scholar

Wang, S.Q. (2006) First-principles study of the anisotropic thermal expansion of wurtzite ZnS. Applied Physics Letters, 88(6), 061902.10.1063/1.2172145Search in Google Scholar

Wang, Y., Wang, J.J., Wang, W.Y., Mei, Z.G., Shang, S.L., Chen, L.Q., and Liu, Z.K. (2010) A mixed-space approach to first-principles calculations of phonon frequencies for polar materials. Journal of Physics: Condensed Matter, 22(20).10.1088/0953-8984/22/20/202201Search in Google Scholar PubMed

Wang, K., Xub, X., Ma, L., Wang, A., Wang, R., Luo, J., and Wen, S. (2017) Studies on triboluminescence emission characteristics of various kinds of bulk ZnS crystals. Journal of Luminescence, 186, 307–311.10.1016/j.jlumin.2017.02.006Search in Google Scholar

Xu, Y.N., and Ching, W.Y. (1993) Electronic, optical, and structural properties of some wurtzite crystals. Physical Review B, 48(7), 4335–4351.10.1103/PhysRevB.48.4335Search in Google Scholar PubMed

Xu, X., Li, S., Chen, J., Cai, S., Long, Z., and Fang, X. (2018) Design principles and material engineering of ZnS for optoelectronic devices and catalysis. Advanced Functional Materials, 28(36), 1802029.10.1002/adfm.201802029Search in Google Scholar

Received: 2019-10-18
Accepted: 2020-02-02
Published Online: 2020-08-11
Published in Print: 2020-08-26

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