Path integral Monte Carlo and density functional molecular dynamics simulations of warm dense MgSiO3

In order to provide a comprehensive theoretical description of ${\mathrm{MgSiO}}_{3}$ at extreme conditions, we combine results from path integral Monte Carlo and density functional molecular dynamics simulations and generate a consistent equation of state for this material. We consider a wide range of temperature and density conditions from ${10}^{4}$ to ${10}^{8}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and from 0.321 to 64.2 $\mathrm{g}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ (0.1- to 20-fold the ambient density). We study how the L and K shell electrons are ionized with increasing temperature and pressure. We derive the shock Hugoniot curve and compare with experimental results. Our Hugoniot curve is in good agreement with the experiments, and we predict a broad compression maximum that is dominated by the K shell ionization of all three nuclei while the peak compression ratio of 4.70 is obtained when the Si and Mg nuclei are ionized. Finally we analyze the heat capacity and structural properties of the liquid.

[1]  R. Rompe,et al.  Ergebnisse der Plasmaphysik und der Gaselektronik , 1967 .

[2]  Molecular dissociation in hot, dense hydrogen. , 1996, Physical review letters.

[3]  Ceperley,et al.  Path integral monte carlo calculation of the deuterium hugoniot , 2000, Physical review letters.

[4]  B. Militzer.  Hydrogen–Helium Mixtures at High Pressure , 2004, cond-mat/0411458.

[5]  G. Schubert,et al.  Treatise on geophysics , 2007 .

[6]  J. Tsuchiya,et al.  Phase transition in MgSiO 3 perovskite in the earth's lower mantle , 2004 .

[7]  B. Militzer,et al.  Path integral Monte Carlo simulation of the low-density hydrogen plasma. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[9]  T. Ahrens,et al.  The MgSiO3 system at high pressure: Thermodynamic properties of perovskite, postperovskite, and melt from global inversion of shock and static compression data , 2009 .

[10]  Path integral Monte Carlo simulations of silicates , 2000, cond-mat/0010315.

[11]  G. Kresse,et al.  From ultrasoft pseudopotentials to the projector augmented-wave method , 1999 .

[12]  Gilbert W. Collins,et al.  Dissociation of liquid silica at high pressures and temperatures. , 2006, Physical review letters.

[13]  B. Militzer,et al.  Characterization of the State of Hydrogen at High Temperature and Density , 1999, physics/9910010.

[14]  Blöchl,et al.  Projector augmented-wave method. , 1994, Physical review. B, Condensed matter.

[15]  D. Ceperley,et al.  Simulation of quantum many-body systems by path-integral methods , 1984 .

[16]  T. Guillot,et al.  Composition and fate of short-period super-Earths: The case of CoRoT-7b , 2009, 0907.3067.

[17]  Beaver Court,et al.  High Energy Density , 1992 .

[18]  William J. Nellis,et al.  Shock Compression of Liquid Helium to 56 GPa (560 kbar) , 1984 .

[19]  Ceperley,et al.  Equation of state of the hydrogen plasma by path integral Monte Carlo simulation. , 1994, Physical review letters.

[20]  Gilbert W. Collins,et al.  Diamond at 800 GPa. , 2009, Physical review letters.

[21]  Path integral Monte Carlo simulations of hot dense hydrogen , 2000 .

[22]  L. Stixrude,et al.  Self-consistent thermodynamic description of silicate liquids, with application to shock melting of MgO periclase and MgSiO3 perovskite , 2009 .

[23]  Robert E. Street,et al.  Elements of Gasdynamics And the Classical Theory of Shock Waves , 1970 .

[24]  Dense plasma effects on nuclear reaction rates. , 2004, Physical review letters.

[25]  D. Ceperley.  Path integrals in the theory of condensed helium , 1995 .

[26]  N. Mermin.  Thermal Properties of the Inhomogeneous Electron Gas , 1965 .

[27]  D. Sasselov,et al.  The role of high-pressure experiments on determining super-Earth properties , 2009 .

[28]  P. Velarde,et al.  Equation of State for laboratory astrophysics applications , 2011 .

[29]  B. Militzer,et al.  Path integral Monte Carlo calculation of the momentum distribution of the homogeneous electron gas at finite temperature , 2003, High Energy Density Physics.

[30]  First principles calculations of shock compressed fluid helium. , 2006, Physical review letters.

[31]  Equilibrium contact probabilities in dense plasmas , 2004, cond-mat/0408551.

[32]  D. Ceperley,et al.  Path-integral calculations of normal liquid 3He. , 1992, Physical review letters.

[33]  G. Zou,et al.  Structural stability of polymeric nitrogen: A first-principles investigation. , 2010, The Journal of chemical physics.

[34]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[35]  J.-P. Davis,et al.  Measurement of the principal isentropes of lead and lead–antimony alloy to ∼400 kbar by quasi-isentropic compression , 2005 .

[36]  William H. Press,et al.  Numerical recipes in C , 2002 .

[37]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[38]  S. Seager,et al.  Mass-Radius Relationships for Solid Exoplanets , 2007, 0707.2895.

[39]  D. Hicks,et al.  Shock formation and the ideal shape of ramp compression waves. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Jones,et al.  Crystallization of the one-component plasma at finite temperature. , 1996, Physical review letters.

[41]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[42]  David M. Ceperley,et al.  An optimized method for treating long-range potentials , 1995 .

[43]  B. Militzer.  Correlations in hot dense helium , 2009, 0902.4281.

[44]  L. Stixrude,et al.  Structure and Freezing of MgSiO3 Liquid in Earth's Lower Mantle , 2005, Science.

[45]  Peter A. Seidl,et al.  Progress in beam focusing and compression for warm-dense matter experiments , 2008 .

[46]  T. Ahrens,et al.  Shock‐compressed MgSiO3 glass, enstatite, olivine, and quartz: Optical emission, temperatures, and melting , 2004 .

[47]  R. Feynman,et al.  Quantum Mechanics and Path Integrals , 1965 .

[48]  T. Mattsson,et al.  Shock compression of a fifth period element: liquid xenon to 840 GPa. , 2010, Physical review letters.

[49]  F. Douchin,et al.  Dense astrophysical plasmas , 2002, physics/0211089.

[50]  P. Cox,et al.  The complete ISO spectrum of NGC 6302 , 2001, astro-ph/0103504.

[51]  J. Kress,et al.  Calculation of a deuterium double shock Hugoniot from ab initio simulations. , 2001, Physical review letters.

[52]  R. Ahuja,et al.  High-pressure melting of MgSiO3. , 2005, Physical review letters.

[53]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.