Elastic properties of six silicate garnet end members from accurate ab initio simulations
Tóm tắt
The elastic properties of six silicate garnet end members, among the most important rock-forming minerals, are investigated here for the first time via accurate ab initio theoretical simulations. The Crystal program is used, which works within periodic boundary conditions and allows for all-electron basis sets to be adopted. From the computed elastic tensor, Christoffel’s equation is solved along a set of crystallographic directions in order to fully characterize the seismic wave velocity anisotropy in such materials. Polycrystalline isotropic aggregate elastic properties are derived from the computed single-crystal data via the Voigt-Reuss-Hill averaging procedure. Transferability of the elastic properties from end members to their solid solutions with different chemical compositions is also addressed.
Tài liệu tham khảo
Anderson DL (1989) Theory of the earth. Blackwell Scientific Publications, Boston
Anderson DL, Bass JD (1986) Transition region of the earth’s upper mantle. Nature 320:321–328
Auld BA (1973) Acoustic Fields and Waves in Solids. Krieger Publishing Company, Malabar, Florida
Authier A, Zarembowitch A (2006) Elastic properties. In: Authier A (eds) International Tables for Crystallography, Vol D. Wiley, pp. 72
Babuška V, Fiala J, Kumazawa M, Ohno I, Sumino Y (1978) Elastic properties of garnet solid-solution series. Phys Earth Planet Int 16:157–176
Baima J, Erba A, Orlando R, Rérat M, Dovesi R (2013) Beryllium oxide nanotubes and their connection to the flat monolayer. J Phys Chem C 117:12864–12872
Bass JD (1986) Elasticity of uvarovite and andradite garnets. J Geophys Res 91:7505–7516
Bass JD (1989) Elasticity of grossular and spessartite garnets by brillouin spectroscopy. J Geophys Res 94:7621–7628
Bass JD, Anderson DL (1984) Composition of the upper mantle: Geophysical tests of two petrological models. Geophys Res Lett 11:229–232
Becke AD (1993) Density-functional thermochemistry III. The role of exact exchange. J Chem Phys 98:5648
Belmonte D, Ottonello G, Zuccolini MV (2013) Melting of α-Al2O3 and vitrification of the undercooled alumina liquid: Ab initio vibrational calculations and their thermodynamic implications. J Chem Phys 138(6):064507
Bonczar LJ, Graham EK, Wang H (1977) The pressure and temperature dependence of the elastic constants of pyrope garnet. J Geophys Res 82:2529–2534
Broyden CG (1970) The convergence of a class of double-rank minimization algorithms 1. General considerations. J Inst Math Appl 6:76–90
Chai M, Brown JM, Slutsky LJ (1997) The elastic constants of a pyrope-grossular-almandine garnet to 20 GPa. Geophys Res Lett 24:523–526
Chen G, Miletich R, Mueller C, Spetzler HA (1997) Shear and compressional mode measurements with GHz ultrasonic interferometry and velocity-composition systematics for the pyrope-almandine solid solution series. Phys Earth Planet Int 99:273–287
Chen G, Cooke JA, Gwanmesia GD, Liebermann RC (1999) Elastic wave velocities of Mg3Al2Si3O13-pyrope garnet to 10 GPa. Am Miner 84:384–388
Chopelas A, Reichmann HJ, Zhang L (1996) Sound velocities of five minerals to mantle pressures determined by the sideband fluorescence method. In: Dyar MD, McCammon C, Schaefer MW (eds) Mineral Spectroscopy, Geochem. Soc., Washington, D.C., pp. 229
Civalleri B, D’Arco P, Orlando R, VR Saunders RD (2001) Hartree-Fock geometry optimisation of periodic systems with the crystal code. Chem Phys Lett 348:131–138
Dal Corso A, Posternak M, Resta R, Baldereschi A (1994) Ab initio study of piezoelectricity and spontaneous polarization in ZnO. Phys Rev B 50:10715–10721
D’Arco P, Freyria Fava F, R Dovesi VRS (1996) Structural and electronic properties of pyrope garnet: An ab initio study. J Phys: Condens Matter 8:8815
Doll K (2001) Implementation of analytical Hartree-Fock gradients for periodic systems. Comput Phys Commun 137:74–88
Doll K, Saunders V, Harrison N (2001) Analytical Hartree-Fock gradients for periodic systems. Int J Quantum Chem 82:1–13
Dovesi R, Orlando R, Civalleri B, Roetti C, Saunders VR, Zicovich-Wilson CM (2005) Crystal: a computational tool for the ab initio study of the electronic properties of crystals. Z Kristallogr 220:571–573
Dovesi R, Saunders VR, Roetti C, Orlando R, Zicovich-Wilson CM, Pascale F, Doll K, Harrison NM, Civalleri B, Bush IJ, D’Arco P, Llunell M (2010) CRYSTAL09 User’s manual. Università di Torino, Torino, http://www.crystal.unito.it
Dovesi R, De La Pierre M, Ferrari AM, Pascale F, Maschio L, Zicovich-Wilson CM (2011) The IR vibrational properties of six members of the garnet family: A quantum mechanical ab initio study. Am Mineral 96:1787–1798
Duffy TS, Anderson DL (1989) Seismic velocities in mantle minerals and the mineralogy of the upper mantle. J Geophys Res 94:1895–1912
Erba A, Dovesi R (2013) Photoelasticity of crystals from theoretical simulations. Phys Rev B 88:045121
Erba A, El-Kelany KE, Ferrero M, Baraille I, Rérat M (2013a) Piezoelectricity of SrTiO3: An ab initio description. Phys Rev B 88:035102
Erba A, Ferrabone M, Baima J, Orlando R, Rérat M, Dovesi R (2013b) The vibration properties of the (n,0) boron nitride nanotubes from ab initio quantum chemical simulations. J Chem Phys 138:054906
Fletcher R (1970) A new approach to variable metric algorithms. Comput J 13:317–322
Goldfarb D (1970) A family of variable-metric methods derived by variational means. Math Comput 24:23–26
Goto T, Ohno I, Sumino Y (1976) The determination of elastic constants of natural pyrope-almandine garnet by means of rectangular parallelepiped resonance method. Phys Earth 24:149–158
Halleck PM (1973) The compression and compressibility of grossular garnet: a comparison of x-ray and ultrasonic methods. Ph.D. dissertation p 82
Hensen BJ (1976) The stability of pyrope-grossular garnet with excess silica. Contrib Mineral Petrol 55:279–292
Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11:357–372
Isaak DG, Graham EK (1976) The elastic properties of an almandine-spessartine garnet and elasticity in the garnet solid solution series. J Geophys Res 81:2483–2489
Jiang F, Speziale S, Shieh SR, Duffy TS (2004) Single-crystal elasticity of andradite garnet to 11 GPa. J Phys:Condens Matter 16:S1041
Karki BB, Stixrude L, Clark SJ, Warren MC, Ackland GJ, Crain J (1997) Structure and elasticity of MgO at high pressure. Am Mineral 82:51–60
Karki BB, Stixrude L, Wentzcovitch RM (2001) High-pressure elastic properties of major materials of earth’s mantle from first principles. Rev Geophys 39:507–534
Kawai K, Tsuchiya T (2012) First principles investigations on the elasticity and phase stability of grossular garnet. J Geophys Res Solid Earth 117:B02202
Koch W, Holthausen MC (2000) A Chemist’s Guide to Density Functional Theory. Wiley-VCH Verlag, Weinheim (Federal Republic of Germany)
Lacivita V, D’Arco P, Orlando R, Dovesi R, Meyer A (2013a) Anomalous birefringence in andradite-grossular solid solutions. A quantum-mechanical approach. Phys Chem Miner. doi:10.1007/s00269-013-0612-6
Lacivita V, Erba A, Noël Y, Orlando R, D’Arco P, Dovesi R (2013b) Zinc oxide nanotubes: An ab initio investigation of their structural, vibrational, elastic, and dielectric properties. J Chem Phys 138:214706
Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785–789
Leitner BJ, Weidner DJ, Liebermann RC (1980) Elasticity of single crystal pyrope and implications for garnet solid solution series. Phys Earth Planet Int 22:111–121
Li L, Weidner DJ (2011) Ab initio molecular dynamic simulation of the elasticity of Mg3Al2Si3O12 pyrope. J Earth Science 22:169–175
Lu C, Mao Z, Lin JF, Zhuravlev KK, Tkachev SN, Prakapenka VB (2013) Elasticity of single-crystal iron-bearing pyrope up to 20 GPa and 750 K. Earth and Planetary Science Letters 361(0):134 – 142
Meyer A, Pascale F, Zicovich-Wilson CM, Dovesi R (2010) Magnetic interactions and electronic structure of uvarovite and andradite garnets. an ab initio all-electron simulation with the CRYSTAL06 program. Int J Quantum Chem 110(2):338–351
Mittal R, Chaplot SL, Choudhury N (2001) Lattice dynamics calculations of the phonon spectra and thermodynamic properties of the aluminosilicate garnets pyrope, grossular, and spessartine M3Al2Si3O12 (M=Mg, Ca, and Mn). Phys Rev B 64:094302
Musgrave MJP (1970) Crystal Acoustics. Holden-Day, San Francisco, California
Novak GA, Gibbs GV (1971) The crystal chemistry of the silicate garnets. Am Mineral 56:791–825
Nye JF (1957) Physical properties of crystals. Oxford University Press, Oxford
O’Neill B, Bass JD, Smyth JR, Vaughan MT (1989) Elasticity of a grossular-pyrope-almandine garnet. J Geophys Res 94:17819–17824
O’Neill B, Bass JD, Rossman GR, Geiger CA, Langer K (1991) Elastic properties of pyrope. Phys Chem Miner 17:617–621
Ottonello G, Civalleri B, Ganguly J, Perger WF, Belmonte D, Vetuschi Zuccolini M (2010) Thermo-chemical and thermo-physical properties of the high-pressure phase anhydrous b (Mg14Si5O24): An ab-initio all-electron investigation. Am Mineral 95:563–573
Pascale F, Zicovich-Wilson C, Orlando R, Roetti C, Ugliengo P, Dovesi R (2005) Vibration frequencies of Mg3Al2Si3O12 pyrope. an ab initio study with the crystal code. J Phys Chem B 109:6146–6152
Pavese A (1999) Quasi-harmonic computer simulations of the structural behaviour and EOS of pyrope at high pressure and high temperature. Phys Chem Miner 26:649–657
Perger WF, Criswell J, Civalleri B, Dovesi R (2009) Ab-initio calculation of elastic constants of crystalline systems with the crystal code. Comput Phys Commun 180:1753–1759
Rickwood PC, Mathias M, Siebert JC (1968) A study of garnets from eclogite and peridotite xenoliths found in kimberlite. Contrib Mineral Petrol 19:271–301
Ringwood AE (1975) Composition and Petrology of the Earth’s Mantle. McGraw-Hill, New York
Saghi-Szabo G, Cohen RE, Krakauer H (1998) First-principles study of piezoelectricity in PbTiO3. Phys Rev Lett 80:4321–4324
Shanno DF (1970) Conditioning of quasi-newton methods for function minimization. Math Comput 24:647–656
Sinogeikin SV, Bass JD (2000) Single-crystal elasticity of pyrope and MgO to 20 GPa by Brillouin scattering in the diamond cell. Phys Earth Planet Int 120:43–62
Soga N (1967) Elastic constants of garnet under pressure and temperature. J Geophys Res 72:4227–4234
Sumino Y, Anderson LO (1982) Elastic constants of minerals. In: Carmichael RS (ed) Handbook of Physical Properties of Rocks. CRC Press, Boca Raton, Florida, pp. 39
Suzuki I, Anderson OL (1983) Elasticity and thermal expansion of a natural garnet up to 1000 K. J Phys Earth 31:125–138
Tosoni S, Pascale F, Ugliengo P, Orlando R, Saunders VR, Dovesi R (2005) Quantum mechanical calculation of the oh vibrational frequency in crystalline solids. Mol Phys 103:2549–2558
Tsuchiya T, Kawamura K (2001) Systematics of elasticity: Ab initio study in b1-type alkaline earth oxides. J Chem Phys 114:10086
Valenzano L, Meyer A, Demichelis R, Civalleri B, Dovesi R (2009) Quantum-mechanical ab initio simulation of the Raman and IR spectra of Mn3Al2Si3O12 spessartine. Phys Chem Minerals 36(7):415–420
Valenzano L, Pascale F, Ferrero M, Dovesi R (2010) Ab initio quantum-mechanical prediction of the IR and Raman spectra of Ca3Cr2Si3O12 uvarovite garnet. Int J Quantum Chem 110(2):416–421
Verma RK (1960) Elasticity of some high-density crystals. J Geophys Res 65:757–766
Wang H, Simmons G (1974) Elasticity of some mantle crystal structures 3. spessartite-almandine garnet. J Geophys Res 79:2607–2613
Wang Z, Ji S (2001) Elasticity of six polycrystalline silicate garnets at pressure up to 3.0 GPa. Am Miner 86:1209–1218
Webb SL (1989) The elasticity of the upper mantle orthosilicates olivine and garnet to 3 GPa. Phys Chem Minerals 16:684–692
Winkler B, Dove MT, Leslie M (1991) Static lattice energy minimization and lattice dynamics calculations on aluminosilicate minerals. Am Mineral 76:313–331
Yeganeh-Haeri A, Weidner DJ, Ito E (1990) Elastic properties of the pyrope-majorite solid solution series. Geophys Res Lett 17:2453–2456
Zicovich-Wilson CM, Torres FJ, Pascale F, Valenzano L, Orlando R, Dovesi R (2008) Ab initio simulation of the IR spectra of pyrope, grossular, and andradite. J Comput Chem 29:2268–2278