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VLab development team UNIVERSITY OF MINNESOTA Indiana University Florida State

Thermoelastic Properties within VLab. Thermoelastic Properties within VLab. VLab development team UNIVERSITY OF MINNESOTA Indiana University Florida State Louisiana State University. Method. --- Density Functional Theory (Hohenberg and Kohn, 1964) --- LDA and GGA

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VLab development team UNIVERSITY OF MINNESOTA Indiana University Florida State

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  1. Thermoelastic Properties within VLab Thermoelastic Properties within VLab VLab development team UNIVERSITY OF MINNESOTA Indiana University Florida State Louisiana State University

  2. Method • --- Density Functional Theory • (Hohenberg and Kohn, 1964) • --- LDA and GGA • (Ceperley and Alder, 1985) • (Perdue at al.,1996) • --- Plane wave basis – pseudopotential • (Troullier and Martins, 1991 • von Bar and Car) • --- Variable Cell Shape Molecular Dynamics • (Wentzcovitch, 1991) • --- Density Functional Perturbation Theory for phonons +QHA • (Baroni et al., 1987) • --- Quantum ESPRESSO package (DEMOCRITOS)

  3. Thermodynamic Method • VDoS and F(T,V) within the QHA N-th (N=3,4,5…) order isothermal (eulerian or logarithm) finite strain EoS IMPORTANT: crystal structure and phonon frequencies depend on volume alone!!….

  4. Typical Computational Experiment (Wentzcovitch, Martins, and Price, PRL 1993) Damped dynamics (Wentzcovitch, 1991) P = 150 GPa

  5. Summation (integration) over the Brillouin Zone Ex: square BZ is the “multiplicity” of a point determined by symmetry • In general: • Compute and diagonalize the dynamical matrix at few ’s (CPU intensive procedure) • Extract “force constants” • Recompute dynamical matrices at several points using those force constants • Summation over tetrahedral volume elements is very accurate for DoSs

  6. Phonon dispersions in MgO (Karki, Wentzcovitch, de Gironcoli and Baroni, PRB 61, 8793, 2000) - cubic 2 atoms/cell Exp: Sangster et al. 1970

  7. Zero Point Motion Effect MgO ZP F (Ry) Volume (Å3) Karki, Wentzcovitch,de Gironcoli, Baroni, Science 1999 Static300KExp (Fei 1999) V (Å3) 18.5 18.8 18.7 K (GPa) 169 159 160 K´ 4.18 4.30 4.15 K´´(GPa-1) -0.025 -0.030

  8. Adiabatic thermoelastic constant tensor CijS(T,P) kl equilibrium structure re-optimize 11x8x6=528 runs for MgO 11x6x16=1056 runs for MgSiO3-pv

  9. 300 K 1000K 2000K 3000 K 4000 K Cij(P,T) cij (Oganov et al,2001) MgSiO3-pv (Wentzcovitch, Karki, Cococciono, de Gironcoli, Phys. Rev. Lett. 2004)

  10. Today • Demo (real run) to fit the allocated time • Regatta, Altix, and Macs at MSI • Thermodynamic properties of MgO • Parameter sampling 11 pressures, 4x4x4 q-grid (8 q in the IBZ) • Plots of thermodynamic properties

  11. MgSiO3-perovskite and MgO 4.8 (256) Exp.: [Ross & Hazen, 1989;Mao et al., 1991; Wang et al., 1994; Funamori et al., 1996; Chopelas, 1996; Gillet et al., 2000; Fiquet et al., 2000]

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