Becke, A. D.: Density-functional thermochemistry. III. The role of exact
exchange, J. Chem. Phys., 98, 5648–5652, https://doi.org/10.1063/1.464913, 1993.
Belmonte, D.: First principles thermodynamics of minerals at HP-HT
conditions: MgO as a prototypical material, Minerals, 7, 183, https://doi.org/10.3390/min7100183, 2017.
Belmonte, D., Ottonello, G., and Vetuschi Zuccolini, M.: Melting of
α-Al
2O
3 and vitrification of the undercooled alumina liquid: ab
initio vibrational calculations and their thermodynamic implications, J.
Chem. Phys., 138, 064507, https://doi.org/10.1063/1.4790612, 2013.
Belmonte, D., Ottonello, G., and Vetuschi Zuccolini, M.: Ab initio
thermodynamic and thermophysical properties of sapphirine end-members in the
join Mg
4Al
8Si
2O
20-Mg
3Al
10SiO
20, Am.
Mineral., 99, 1449–1461, https://doi.org/10.2138/am.2014.4833, 2014.
Belmonte, D., Gatti, C., Ottonello, G., Richet, P., and Vetuschi Zuccolini, M.: Ab initio thermodynamic and thermophysical properties of sodium
metasilicate, Na
2SiO
3, and their electron-density and
electron-pair-density counterparts, J. Phys. Chem. A, 120, 8881–8895,
https://doi.org/10.1021/acs.jpca.6b08676, 2016.
Belmonte, D., Ottonello, G., and Vetuschi Zuccolini, M.: The system
MgO-Al
2O
3-SiO
2 under pressure: a computational study of
melting relations and phase diagrams, Chem. Geol., 461, 54–64, https://doi.org/10.1016/j.chemgeo.2016.11.011, 2017a.
Belmonte, D., Ottonello, G., and Vetuschi Zuccolini, M.: Ab initio-assisted
assessment of the CaO-SiO
2 system under pressure, CALPHAD, 59, 12–30,
https://doi.org/10.1016/j.calphad.2017.07.009, 2017b.
Bina, C. R. and Helffrich, G.: Phase transition Clapeyron slopes and
transition zone seismic discontinuity topography, J. Geophys. Res.-Sol.
Ea., 99, 15853–15860, https://doi.org/10.1029/94JB00462, 1994.
Bindi, L., Griffin, W. L., Panero, W. R., Sirotkina, E., Bobrov, A., and
Irifune, T.: Synthesis of inverse ringwoodite sheds light on the subduction
history of Tibetan ophiolites, Sci. Rep., 8, 5457, https://doi.org/10.1038/s41598-018-23790-9, 2018.
Born, M. and Huang, K.: Dynamical Theory of Crystal Lattices, Oxford
University Press, Oxford, UK, ISBN 9780198503699, 1954.
Brown, J. M. and Shankland, T. J.: Thermodynamic parameters in the Earth as
determined from seismic profiles, Geophys. J. Int., 66, 579–596, https://doi.org/10.1111/j.1365-246X.1981.tb04891.x, 1981.
Chen, M., El Goresy, A., and Gillet, P.: Ringwoodite lamellae in olivine:
clues to olivine-ringwoodite phase transition mechanisms in shocked
meteorites and subducting slabs, P. Natl. Acad. Sci. USA, 101,
15033–15037, https://doi.org/10.1073/pnas.0405048101, 2004.
Chopelas, A.: Thermal expansivity of mantle relevant magnesium silicates
derived from vibrational spectroscopy at high pressure, Am. Mineral., 85,
270–278, https://doi.org/10.2138/am-2000-2-301, 2000.
Chopelas, A., Boehler, R., and Ko, T.: Thermodynamics and behavior of
γ-Mg
2SiO
4 at high pressure: implications for
Mg
2SiO
4 phase equilibrium, Phys. Chem. Miner., 21, 351–359,
https://doi.org/10.1007/BF00203293, 1994.
Christensen, U. and Yuen, D. A.: Layered convection induced by phase
transitions, J. Geophys. Res.-Sol. Ea., 90, 10291–10300, https://doi.org/10.1029/jb090ib12p10291, 1985.
De La Pierre, M. and Belmonte, D.: Ab initio investigation of majorite and
pyrope garnets: lattice dynamics and vibrational spectra, Am. Mineral., 101,
162–174, https://doi.org/10.2138/am-2016-5382, 2016.
De La Pierre, M., Orlando, R., Maschio, L., Doll, K., Ugliengo, P., and
Dovesi, R.: Performance of six functionals (LDA, PBE, PBESOL, B3LYP, PBE0,
and WC1LYP) in the simulation of vibrational and dielectric properties of
crystalline compounds. The case of forsterite Mg
2SiO
4, J. Comput.
Chem., 32, 1775–1784, https://doi.org/10.1002/jcc.21750, 2011.
Demichelis, R., Civalleri, B., Ferrabone, M., and Dovesi, R.: On the
performance of eleven DFT functionals in the description of the vibrational
properties of aluminosilicates, Int. J. Quantum Chem., 110, 406–415,
https://doi.org/10.1002/qua.22301, 2010.
Deuss, A. and Woodhouse, J.: Seismic observations of splitting of the
mid-transition zone discontinuity in Earth's mantle, Science, 294, 354–357,
https://doi.org/10.1126/science.1063524, 2001.
Deuss, A., Redfern, S. A. T., Chambers, K., and Woodhouse, J. H.: The nature
of the 660-kilometer discontinuity in Earth's mantle from global seismic
observations of PP precursors, Science, 311, 198–201, https://doi.org/10.1126/science.1120020, 2006.
Dorogokupets, P. I., Dymshits, A. M., Sokolova, T. S., Danilov, B. S., and
Litasov, K. D.: The equations of state of forsterite, wadsleyite,
ringwoodite, akimotoite, MgSiO
3-perovskite, and post-perovskite and
phase diagram for the Mg
2SiO
4 system at pressures of up to 130 GPa, Russ. Geol. Geophys., 56, 172–189, https://doi.org/10.1016/j.rgg.2015.01.011, 2015.
Dovesi, R., Saunders, V. R., Roetti, C., Orlando, R., Zicovich-Wilson, C.
M., Pascale, F., Civalleri, B., Doll, K., Harrison, N. M., and Bush, I. J.:
CRYSTAL14 User's Manual, Università di Torino, Torino, Italy, 382 pp.,
https://www.crystal.unito.it/Manuals/crystal14.pdf (last access: 23 March 2022), 2014.
Erba, A., Mahmoud, A., Belmonte, D., and Dovesi, R.: High pressure elastic
properties of minerals from ab initio simulations: the case of pyrope,
grossular and andradite silicate garnets, J. Chem. Phys., 140, 124703,
https://doi.org/10.1063/1.4869144, 2014.
Evarestov, R. A. and Losev, M. V.: All-electron LCAO calculations of the LiF
crystal phonon spectrum: influence of the basis set, the
exchange-correlation functional, and the supercell size, J. Comput. Chem.,
30, 2645–2655, https://doi.org/10.1002/jcc.21259, 2009.
Fabrichnaya O. B., Saxena, S. K., Richet, P., and Westrum, E. F.:
Thermodynamic Data, Models, and Phase Diagrams in Multicomponent Oxide
Systems, Springer, Berlin Heidelberg, Germany, 198 pp., https://doi.org/10.1007/978-3-662-10504-7, 2004.
Feng, L., Lin, Y., Hu, S., Xu, L., and Miao, B.: Estimating compositions of
natural ringwoodite in the heavily shocked Grove Mountains 052049 meteorite
from Raman spectra, Am. Mineral., 96, 1480–1489, https://doi.org/10.2138/am.2011.3679, 2011.
Fiquet, G., Richet, P., and Montagnac, G.: High-temperature thermal
expansion of lime, periclase, corundum and spinel, Phys. Chem. Minerals, 27,
103–111, https://doi.org/10.1007/s002690050246, 1999.
Frost, D. J.: The structure and sharpness of (Mg,Fe)
2SiO
4 phase
transformations in the transition zone, Earth Planet. Sci. Lett., 216,
313–328, https://doi.org/10.1016/S0012-821X(03)00533-8, 2003.
Guyot, F., Boyer, H., Madon, M., Velde, B, and Poirier, J. P.: Comparison of
the Raman microprobe spectra of (Mg,Fe)
2SiO
4 and Mg
2GeO
4
with olivine and spinel structures, Phys. Chem. Miner., 13, 91–95,
https://doi.org/10.1007/BF00311898, 1986.
Hazen, R. M.: Comparative compressibilities of silicate spinels: anomalous
behaviour of (Mg,Fe)
2SiO
4, Science, 259, 206–209, https://doi.org/10.1126/science.259.5092.206, 1993.
Helffrich, G.: Practical use of Suzuki's thermal expansivity formulation,
Phys. Earth Planet. Int., 116, 133–136, https://doi.org/10.1016/S0031-9201(99)00130-2, 1999.
Hernández, E. M., Brodholt, J., and Alfè, D.: Structural,
vibrational and thermodynamic properties of Mg
2SiO
4 and
MgSiO
3 minerals from first-principles simulations, Phys. Earth Planet.
Int., 240, 1–24, https://doi.org/10.1016/j.pepi.2014.10.007,
2015.
Holland, T. J. B. and Powell, R.: An improved and extended internally
consistent thermodynamic dataset for phases of petrological interest,
involving a new equation of state for solids, J. Metam. Geol., 29, 333–383,
https://doi.org/10.1111/j.1525-1314.2010.00923.x, 2011.
Inoue, T., Tanimoto, Y., Irifune, T., Suzuki, T., Fukui, H., and Ohtaka, O.:
Thermal expansion of wadsleyite, ringwoodite, hydrous wadsleyite and hydrous
ringwoodite, Phys. Earth Planet. Int., 143–144, 279–290, https://doi.org/10.1016/j.pepi.2003.07.021, 2004.
Ishii, T., Huang, R, Myhill, R., Fei, H., Koemets, I., Liu, Z., Maeda, F.,
Yuan, L., Wang, L., Druzhbin, D., Yamamoto, T., Bhat, S., Farla, R.,
Kawazoe, T., Tsujino, N., Kulik, E., Higo, Y., Tange, Y., and Katsura, T.:
Sharp 660 km discontinuity controlled by extremely narrow binary post-spinel
transition, Nat. Geosci., 12, 869–872, https://doi.org/10.1038/s41561-019-0452-1, 2019.
Jacobs, M. H. G., Schmid-Fetzer, R., and van den Berg, A. P.: Phase
diagrams, thermodynamic properties and sound velocities derived from a
multiple Einstein method using vibrational densities of states: an
application to MgO-SiO
2, Phys. Chem. Miner., 44, 43–62, https://doi.org/10.1007/s00269-016-0835-4, 2017.
Jeanloz, R.: Infrared spectra of olivine polymorphs:
α,
β
phase and spinel, Phys. Chem. Minerals, 5, 327–341, https://doi.org/10.1007/BF00307542, 1980.
Katsura, T., Yokoshi, S., Song, M., Kawabe, K., Tsujimura, T., Kubo, A.,
Ito, E., Tange, Y., Tomioka, N., Saito, K., Nozawa, A., and Funakoshi,
K.-I.: Thermal expansion of Mg
2SiO
4 ringwoodite at high pressures,
J. Geophys. Res.-Sol. Ea., 109, B12209, https://doi.org/10.1029/2004JB003094, 2004.
Katsura, T., Yoneda, A., Yamazaki, D., Yoshino, T., and Ito, E.: Adiabatic
temperature profile in the mantle, Phys. Earth Planet. Int., 183, 212–218,
https://doi.org/10.1016/j.pepi.2010.07.001, 2010.
Kiefer, B., Stixrude, L., and Wentzcovitch, R. M.: Calculated elastic
constants and anisotropy of Mg
2SiO
4 spinel at high pressure,
Geophys. Res. Lett., 24, 2841–2844, https://doi.org/10.1029/97GL02975, 1997.
Kiefer, B., Stixrude, L., and Wentzcovitch, R.: Normal and inverse
ringwoodite at high pressures, Am. Mineral., 84, 288–293, https://doi.org/10.2138/am-1999-0311, 1999.
Kohanoff, J.: Electronic Structure Calculations for Solids and Molecules:
Theory and Computational Methods, Cambridge University Press, Cambridge,
UK, ISBN 9780521815918, 2006.
Kojitani, H., Inoue, T., and Akaogi, M.: Precise measurements of enthalpy of
postspinel transition in Mg
2SiO
4 and application to the phase
boundary calculation, J. Geophys. Res.-Sol. Ea., 121, 729–742,
https://doi.org/10.1002/2015JB012211, 2016.
Lee, C., Yang, E., and Parr, R. G. : Development of the Colle-Salvetti
correlation-energy formula into a functional of the electron density, Phys.
Rev. B, 37, 785–789, https://doi.org/10.1103/PhysRevB.37.785, 1988.
Li, L., Weidner, D. J., Brodholt, J., Alfè, D., and Price, G. D. :
Elasticity of Mg
2SiO
4 ringwoodite at mantle conditions, Phys.
Earth Planet. Int., 157, 181–187, https://doi.org/10.1016/j.pepi.2006.04.002, 2006.
Li, L., Brodholt, J., and Alfè, D.: Structure and elasticity of hydrous
ringwoodite: a first principle investigation, Phys. Earth Planet. Int., 177,
103–115, https://doi.org/10.1016/j.pepi.2009.07.007, 2009.
Meng, Y., Weidner, D. J., Gwanmesia, G. D., Liebermann, R. C., Vaughan, M.
T., Wang, Y., Leinenweber, K., Pacalo, R. E., Yeganeh-Haeri, A., and Zhao,
Y.: In situ high
P-
T X ray diffraction studies on three polymorphs (
α,
β,
γ) of Mg
2SiO
4, J. Geophys. Res.-Sol. Ea., 98, 22199–22207, https://doi.org/10.1029/93JB02383, 1993.
Meng, Y., Fei, Y., Weidner, D. J., Gwanmesia, G. D., and Hu, J.: Hydrostatic
compression of
γ-Mg
2SiO
4 to mantle pressures and 700 K:
thermal equation of state and related thermoelastic properties, Phys. Chem.
Minerals, 21, 407–412, https://doi.org/10.1007/BF00203299, 1994.
Ming, L. C., Manghnani, M. H., Kim, Y. H., Usha-Devi, S., Xu, J.-A., and
Ito, E.: Thermal expansion studies of (Mg,Fe)
2SiO
4-spinels using
synchrotron radiation, in: Thermodynamic Data: Systematics and Estimation,
Advances in Physical Geochemistry, Vol. 10, edited by: Saxena, S. K.,
Springer-Verlag, New York, NY, 315–334, https://doi.org/10.1007/978-1-4612-2842-4_12, 1992.
Nestola, F.: Ringwoodite: its importance in Earth Sciences, in: Highlights
in Mineralogical Crystallography, edited by: Armbruster, T. and Danisi, R.
M., De Gruyter, Berlin, Germany, 127–147, https://doi.org/10.1515/9783110417104-007, 2016.
Núñez-Valdez, M., da Silveira, P., and Wentzcovitch, R. M.:
Influence of iron on the elastic properties of wadsleyite and ringwoodite,
J. Geophys. Res.-Sol. Ea., 116, B12207, https://doi.org/10.1029/2011JB008378, 2011.
Oganov, A. R., Brodholt, J. P., and Price, G. D.: Ab initio elasticity and
thermal equation of state of MgSiO
3 perovskite, Earth Planet. Sci.
Lett., 184, 555–560, https://doi.org/10.1016/S0012-821X(00)00363-0, 2001.
Ottonello, G., Civalleri, B., Ganguly, J., Vetuschi Zuccolini, M., and Noel,
Y.: Thermophysical properties of the
α-
β-
γ polymorphs
of Mg
2SiO
4: a computational study, Phys. Chem. Minerals, 36,
87–106, https://doi.org/10.1007/s00269-008-0260-4, 2009.
Ottonello, G., Civalleri, B., Ganguly, J., Perger, W. F., Belmonte, D., and
Vetuschi Zuccolini, M.: Thermo-chemical and thermo-physical properties of
the high-pressure phase anhydrous B (Mg
14Si
5O
24): an
ab-initio all-electron investigation, Am. Mineral., 95, 563–573, https://doi.org/10.2138/am.2010.3368, 2010.
Panero, W. R.: Cation disorder in ringwoodite and its effects on wave speeds
in the Earth's transition zone, J. Geophys. Res.-Sol. Ea., 113, B10204,
https://doi.org/10.1029/2008JB005676, 2008.
Parlinski, K., Li, Z. Q., and Kawazoe, Y.: First-principles determination of the soft mode in cubic ZrO
2, Phys. Rev. Lett., 78, 4063–4066, https://doi.org/10.1103/PhysRevLett.78.4063, 1997.
Pearson, D. G., Brenker, F. E., Nestola, F., McNeill, J., Nasdala, L.,
Hutchison, M. T., Matveev, S., Mather, K., Silversmit, G., Schmitz, S.,
Vekemans, B., and Vincze, L.: Hydrous mantle transition zone indicated by
ringwoodite included within diamond, Nature, 507, 221–224, https://doi.org/10.1038/nature13080, 2014.
Piekarz, P., Jochym, P. T., Parlinski, K., and Łażewski, J.:
High-pressure and thermal properties of
γ-Mg
2SiO
4 from
first-principles calculations, J. Chem. Phys., 117, 3340–3344, https://doi.org/10.1063/1.1494802, 2002.
Prencipe, M., Noel, Y., Bruno, M., and Dovesi, R.: The vibrational spectrum
of lizardite-1
T [Mg
3Si
2O
5(OH)
4] at the
Γ point: a contribution from an ab initio periodic B3LYP calculation, Am. Mineral., 94, 986–994, https://doi.org/10.2138/am.2009.3127, 2009.
Prencipe, M., Bruno, M., Nestola, F., De La Pierre, M., and Nimis, P.:
Toward an accurate ab initio estimation of compressibility and thermal
expansion of diamond in the [0, 3000 K] temperature and [0, 30 GPa]
pressures ranges, at the hybrid HF/DFT theoretical level, Am. Mineral., 99,
1147–1154, https://doi.org/10.2138/am.2014.4772, 2014.
Preudhomme, J. and Tarte, P.: Infrared studies of spinels – II. The
experimental bases for solving the assignment problem, Spectrochim. Acta,
27A, 845–851, https://doi.org/10.1016/0584-8539(71)80163-0, 1971.
Ringwood, A. E.: Composition and Petrology of the Earth's Mantle,
McGraw-Hill, New York, NY, https://doi.org/10.1180/minmag.1977.041.317.30, 1975.
Saikia, A., Frost, D. J., and Rubie, D. C.: Splitting of the 520-kilometer
seismic discontinuity and chemical heterogeneity in the mantle, Science,
319, 1515–1518, https://doi.org/10.1126/science.1152818, 2008.
Sasaki, S., Prewitt, C. T., Sato, Y., and Ito, E.: Single-crystal X ray study
of
γ Mg
2SiO
4, J. Geophys. Res.-Sol. Ea., 87,
7829–7832, https://doi.org/10.1029/JB087iB09p07829, 1982.
Schmeling, H., Marquart, G., and Ruedas, T.: Pressure- and
temperature-dependent thermal expansivity and the effect on mantle
convection and surface observables, Geophys. J. Int., 154, 224–229,
https://doi.org/10.1046/j.1365-246X.2003.01949.x, 2003.
Schmerr, N. and Garnero, E. J.: Upper mantle discontinuity topography from
thermal and chemical heterogeneity, Science, 318, 623–626, https://doi.org/10.1126/science.1145962, 2007.
Shearer, P. M.: Transition zone velocity gradients and the 520 km
discontinuity, J. Geophys. Res.-Sol. Ea., 101, 3053–3066, https://doi.org/10.1029/95JB02812, 1996.
Sinogeikin, S. V., Bass, J. D., and Katsura, T.: Single-crystal elasticity
of ringwoodite to high pressures and high temperatures: implications for 520 km seismic discontinuity, Phys. Earth Planet. Int., 136, 41–66, https://doi.org/10.1016/S0031-9201(03)00022-0, 2003.
Suzuki, I., Ohtani, E., and Kumazawa, M.: Thermal expansion of
γ-Mg
2SiO
4, J. Phys. Earth, 27, 53–61, https://doi.org/10.4294/jpe1952.27.53, 1979.
Thiéblot, L., Roux, J., and Richet, P.: High-temperature thermal
expansion and decomposition of garnets, Eur. J. Mineral., 10, 7–15,
https://doi.org/10.1127/ejm/10/1/0007, 1998.
Tosi, N., Yuen, D. A., de Koker, N., and Wentzcovitch, R. M.: Mantle
dynamics with pressure- and temperature-dependent thermal expansivity and
conductivity, Phys. Earth Planet. Int., 217, 48–58, https://doi.org/10.1016/j.pepi.2013.02.004, 2013.
Ulian, G. and Valdrè, G.: Equation of state of hexagonal hydroxylapatite
(P6
3) as obtained from density functional theory simulations, Int. J.
Quantum Chem., 118, e25553, https://doi.org/10.1002/qua.25553, 2018.
Wallace, D. C.: Thermodynamics of Crystals, John Wiley & Sons, Inc., New
York, NY, ISBN 9780471918554, 1972.
White, W. B. and DeAngelis, B. A.: Interpretation of the vibrational spectra
of spinels, Spectrochim. Acta, 23A, 985–993, https://doi.org/10.1016/0584-8539(67)80023-0, 1967.
Yu, Y. G. and Wentzcovitch, R. M.: Density functional study of vibrational
and thermodynamic properties of ringwoodite, J. Geophys. Res.-Sol. Ea.,
111, B12202, https://doi.org/10.1029/2006JB004282, 2006.