HR: 10:35h
AN: MR12A-02 INVITED    [Abstracts]
TI: Quantum Monte Carlo Computations for Equations of State, Phase Transitions, and Elasticity of Silica
AU: * Cohen, R E
EM: cohen@gl.ciw.edu
AF: Geophysical Laboratory, Carnegie Institution, 5251 Broad Branch Rd., N.W, Washington, DC 20015, United States
AU: Militzer, B
EM: militzer@gl.ciw.edu
AF: Geophysical Laboratory, Carnegie Institution, 5251 Broad Branch Rd., N.W, Washington, DC 20015, United States
AU: Wu, Z
EM: zhigang@berkeley.edu
AF: Berkeley Nanosciences and Nanoengineering Institute (BNNI), University of California at Berkeley 210 McLaughlin Hall # 1726 University of California, Berkeley, CA 94720-1726, United States
AU: Driver, K
EM: driver@mps.ohio-state.edu
AF: Physics Dept., Ohio State University, 1040 Physics Research Building 191 West Woodruff Avenue, Columbus, OH 43210-1117, United States
AU: Rios, P L
EM: pl275@cam.ac.uk
AF: TCM, Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, United Kingdom
AU: Towler, M
EM: mdt26@cam.ac.uk
AF: TCM, Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, United Kingdom
AU: Needs, R
EM: rn11@cam.ac.uk
AF: TCM, Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, United Kingdom
AB: We have performed Quantum Monte Carlo (QMC) computations for silica in the quartz, stishovite, and α- PbO₂ structures as functions of compression as benchmark computations. QMC uses no approximate density functional, and the many-body, correlated, Schrödinger equation is effectively solved stochastically. In spite of the great success of DFT there are still some fundamental problems that need improvement. First is the need for increased accuracy for some rather ordinary materials such as silica. Although the local density approximation (LDA) gives excellent results for individual silica phases, such as the CaCl₂ transition [1,2], it is not so good for comparing energetics of very different structures, such as quartz versus stishovite. LDA predicts stishovite to be the stable ground state structure rather than quartz. One of the first great successes of the Generalized Gradient Approximation (GGA) was to give the correct energy difference between quartz and stishovite [3]. Less well appreciated is the fact that almost all other properties, such as structure, equations of state, elastic constants, etc., are worse with the GGA than the LDA. Our QMC results will be used to improve density functionals, and show the way towards more accurate computations for Earth materials. Thermal contributions are included using density functional perturbation theory with the code ABINIT. We have also computed the shear elastic constant c₁₁-c₁₂ in stishovite, which is associated with the phase transition to the CaCl₂ structure [1], with QMC. We find excellent agreement with experiments. We find that the main differences between QMC and DFT are crystalline phase dependent energy and pressure shifts. This work is supported by NSF grants EAR-0530282, EAR-0310139, and by DOE contract DE-FG02-99ER45795 to John Wilkins. Computations were performed on Blueice at NCAR under a BTS grant, Tungsten and Abe at NCSA, Franklin at NERSC within the friendly user program, and at the Carnegie Institution of Washington. [1] Cohen, R.E., First-principles predictions of elasticity and phase transitions in high pressure SiO2 and geophysical implications, in High Pressure Research in Mineral Physics: Application to Earth and Planetary Science, M.H. Manghnani and Y. Syono, Editors. 1992, AGU: Washington, D.C. p. 425-432. [2] Kingma, K.J., R.E. Cohen, R.J. Hemley, and H.-K. Mao, Transformation of silica to a denser phase at lower- mantle pressures. Nature, 1995. 374: p. 243-245. [3] Hamann, D.R., Generalized gradient theory for silica phase transitions. Phys. Rev. Lett., 1996. 76(4): p. 660- 663.
DE: 3909 Elasticity and anelasticity
DE: 3919 Equations of state
DE: 3924 High-pressure behavior
SC: Mineral and Rock Physics [MR]
MN: 2007 Fall Meeting