Lattice dynamics and the high-pressure equation of state of Au

Abstract

Elastic constants and zone-boundary phonon frequencies of gold are calculated by total energy electronic structure methods to twofold compression. A generalized force constant model is used to interpolate throughout the Brillouin zone and evaluate moments of the phonon distribution. The moments are used to calculate the volume dependence of the Grüneisen parameter in the fcc solid. Using these results with ultrasonic and shock data, we formulate the complete free energy for solid Au. This free energy is given as a set of closed form expressions, which are valid to compressions of at least V /V 0 = 0.65 and temperatures up to melting. Beyond this density, the Hugoniot enters the solid-liquid mixed phase region. Effects of shock melting on the Hugoniot are discussed within an approximate model. We compare with proposed standards for the equation of state to pressures of ∼ 200 GPa. Our result for the room temperature isotherm is in very good agreement with an earlier standard of Heinz and Jeanloz.

Reaction boundary between akimotoite and ringwoodite + stishovite in MgSiO3

“…We used the EOS of gold by Dorogokupet and Dewaele (2007). This EOS has been repeatedly investigated in the previous experimental and theoretical studies (e.g., Jamieson et al 1982;Anderson et al 1989;Holzapfel et al 2001;Takemura 2001Takemura , 2007Okube et al 2002;Shim et al 2002;Boettger 2003;Dewaele et al 2004;Greeff et al 2004;Souvatzis et al 2006;Dorogokupet and;Dewaele 2007;Fei et al 2007;Holzapfel and Nicol 2007). However, the validity of the EOS of gold is still questionable.…”

A self-consistent thermodynamic model of metallic systems. Application for the description of gold

“…What is more, the electronic subsystem with its kinetic and exchange energy has been taken into account. The electronic energy has been considered in better approximation than in previous works 27,31 .…”

“…For instance, the thermal volume expansion coefficient α p is given by Eq. (27), whereas the isothermal compressibility κ T is given by Eq. (28).…”

“…Only in few papers an attempt has been made to construct the full thermodynamic description based on the expression for the free energy. The thermodynamic potential considered there contains the elastic (static) energy, vibrational energy, as well as the electronic contribution 27,31 . In this context it is worth mentioning that recently the computational method for the Gibbs energy has been presented, which is suitable for solids under the quasi-harmonic approximation 44 .…”

Exploring Thermal and Mechanical Properties of Selected Transition Elements under Extreme Conditions: Experiments at High Pressures and High Temperatures

“…High-pressure crystal stability of Cu and Au make them good candidates for a high-pressure calibration standard. Several mathematical EoS have been formulated (Heinz D, 1984;Batani et al, 2000;Shim et al, 2002;Greeff and Graf, 2004;Greeff et al, 2006) to predict their P-V-T behavior. .…”