Alfè, D., 1999. Ab Initio Molecular Dynamics, a Simple Algorithm for Charge Extrapolation. Computer Physics Communications, 118(1): 31–33 doi: 10.1016/S0010-4655(98)00195-7 |
Allen, M. P., Tildesley, D. J., 1997. Computer Simulation of Liquids. Oxford University Press, New York. 408 |
Bina, C. R., Helffrich, G. R., 1992. Calculation of Elastic Properties from Thermodynamic Equation of State Principles. Annu. Rev. Earth Planet. Sci. , 20: 527–552 doi: 10.1146/annurev.ea.20.050192.002523 |
Blöchl, P. E., 1994. Projector Augmented-Wave Method. Phys. Rev. B, 50(24): 17953–17979 doi: 10.1103/PhysRevB.50.17953 |
Brown, J. M., Shankland, T. J., 1981. Thermodynamic Parameters in the Earth as Determined from Seismic Profiles. Geophys. J. R. Astr. Soc. , 66(3): 579–596 doi: 10.1111/j.1365-246X.1981.tb04891.x |
Chen, G. L., Cooke, J. A., Gwanmesia, G. D., et al., 1999. Elastic Wave Velocities at Mg3Al2Si3O13—Pyrope Garnet to 10 GPa. American Mineralogist, 84(3): 384–388 doi: 10.2138/am-1999-0322 |
Conrad, P. G., Zha, C. S., Mao, H. K., et al., 1999. The High-Pressure, Single-Crystal Elasticity of Pyrope, Grossular, and Andradite. American Mineralogist, 84(3): 374–383 doi: 10.2138/am-1999-0321 |
Deuss, A., Woodhouse, J., 2001. Seismic Observations of Splitting of the Mid-transition Zone Discontinuity in Earth's Mantle. Science, 294(5541): 354–357 doi: 10.1126/science.1063524 |
Fisher, K. M., Wiens, D. A., 1996. The Depth Distribution of Mantle Anisotropy beneath the Tonga Subduction Zone. Earth and Planetary Science Letters, 142(1–2): 253–260 |
Gossler, J., Kind, R., 1996. Seismic Evidence for very Deep Roots of Continents. Earth and Planetary Science Letters, 138(1–4): 1–13 |
Gu, Y., Dziewonski, A. M., Agee, C. B., 1998. Global De-correlation of the Topography of Transition Zone Discontinuities. Earth and Planetary Science Letters, 157(1–2): 57–67 |
Gwanmesia, G. D., Zhang, J., Darling, K., et al., 2006. Elasticity of Polycrystalline Pyrope (Mg3Al2Si3O12) to 9 GPa and 1 000 ℃. Physics of the Earth and Planetary Interiors, 155(3–4): 179–190 |
Kresse, G., Furthmüller, J., 1996a. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mat. Sci. , 6(1): 15–50 doi: 10.1016/0927-0256(96)00008-0 |
Kresse, G., Furthmüller, J., 1996b. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B, 54(16): 11169–11186 doi: 10.1103/PhysRevB.54.11169 |
Leitner, B. J., Weidner, D. J., Liebermann, R. C., 1980. Elasticity of Single Crystal Pyrope and Implications for Garnet Solid Solution Series. Physics of the Earth and Planetary Interiors, 22(2): 111–121 doi: 10.1016/0031-9201(80)90052-7 |
Li, L., Weidner, D. J., 2008. Effect of Phase Transitions on Bulk Dispersion and Attenuation: Implications for the Earth. Nature, 454: 984–986 doi: 10.1038/nature07230 |
Li, L., Weidner, D. J., Brodholt, J., et al., 2005. Phase Stability of CaSiO3 Perovskite at High Pressure and Temperature: Insights from Ab Initio Molecular Dynamics. Physics of the Earth and Planetary Interiors, 155(3–4): 260–268 |
Li, L., Weidner, D. J., Brodholt, J., et al., 2006a. Elasticity of Mg2SiO4 Ringwoodite at Mantle Conditions. Physics of the Earth and Planetary Interiors, 157(3–4): 181–187 |
Li, L., Weidner, D. J., Brodholt, J., et al., 2006b. Elasticity of CaSiO3 Perovskite at High Pressure and High Temperature. Physics of the Earth and Planetary Interiors, 155(3–4): 249–259 |
Li, L., Weidner, D. J., Brodholt, J., et al., 2009. Ab Initio Molecular Dynamics Study of Elasticity of Akimotoite MgSiO3 at Mantle Conditions. Physics of the Earth and Planetary Interiors, 173(1–2): 115–120 |
Mittal, R., Chaplot, S. L., 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(9): 094302 doi: 10.1103/PhysRevB.64.094302 |
Montagner, J. P., Kennett, B. L. N., 1996. How to Reconcile Body-Wave and Normal Mode—Reference Earth Models. Geophys. J. Int. , 125(1): 229–248 doi: 10.1111/j.1365-246X.1996.tb06548.x |
Nye, J. F., 1957. Physical Properties of Crystals. Oxford University Press, Ely House, London |
Oganov, A. R., Brodholt, J. P., Price, G. D., 2001a. Ab Initio Elasticity and Thermal Equation of State of MgSiO3 Perovskite. Earth and Planetary Science Letters, 184(3–4): 555–560 |
Oganov, A. R., Brodholt, J. P., Price, G. D., 2001b. The Elastic Constants of MgSiO3 Perovskite at Pressures and Temperatures of the Earth's Mantle. Nature, 411(6840): 934–937 doi: 10.1038/35082048 |
Pavese, A., 1999. Quasi-harmonic Computer Simulations of the Structural Behaviour and EOS of Pyrope at High Pressure and High Temperature. Phys. Chem. Minerals, 26(8): 649–657 doi: 10.1007/s002690050230 |
Perdew, J. P., Chevary, J. A., Vosko, S. H., et al., 1992. Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation. Phys. Rev. B, 46(11): 6671–6687 doi: 10.1103/PhysRevB.46.6671 |
Revenaugh, J., Jordan, T. H., 1991. The ScS Phase in the Reflection of S-Waves from the Core-Mantle Boundary. Journal of Geophysical Research-Solid Earth, 96(B12): 19763–19780 doi: 10.1029/91JB01486 |
Shearer, P. M., 1990. Seismic Imaging of Upper-Mantle Structure with New Evidence for a 520-km Discontinuity. Nature, 344(6262): 121–126 doi: 10.1038/344121a0 |
Sinogeikin, S. V., Bass, J. D., 2000. Single-Crystal Elasticity of Pyrope and MgO to 20 GPa by Brillouin Scattering in the Diamond Cell. Physics of the Earth and Planetary Interiors, 120(1–2): 43–62 |
Sinogeikin, S. V., Bass, J. D., 2002. Elasticity of Pyrope and Majorite-Pyrope Solid Solutions to High Temperatures. Earth and Planetary Science Letters, 203(1): 549–555 doi: 10.1016/S0012-821X(02)00851-8 |
Stackhouse, S., Brodholt, J. P., Wookey, J., et al., 2004. The Effect of Temperature on the Seismic Anisotropy of the Perovskite and Post-Perovskite Polymorphs of MgSiO3. Earth and Planetary Science Letters, 230(1–2): 1–10 |
Wang, Y., Perdew, J. P., 1991. Correlation Hole of the Spin-Polarized Electron-Gas, with Exact Small-Wave-Vector and High Density Scaling. Phy. Rev. B, 44(24): 13298–13307 doi: 10.1103/PhysRevB.44.13298 |
Wang, Y., Weidner, D. J., Zhang, J. Z., et al., 1998. Thermal Equation of State of Garnets along the Pyrope-Majorite Join. Physics of the Earth and Planetary Interiors, 105(1–2): 59–71 |
Zhang, J., Herzberg, C., 1994. Melting of Pyrope, Mg3Al2Si3O12, at 7–16 GPa. American Mineralogist, 79(5–6): 497–503 |