Anharmonicity and the equation of state for gold

Abstract

The temperature dependence of the thermodynamic and the elastic properties of elemental gold are found from published data. It is shown that measurements for (∂K_T/∂P)_T near 5.5 are more thermodynamically consistent than are higher values of this parameter which have been reported earlier. Using 5.5 for (∂K_T/∂P)_T, we find that (∂K_T/∂T)_V is not zero but −11.5×10⁻³ GPa K⁻¹ for high temperatures (T>θ_D, where θ_D is the Debye temperature). One consequence of this is that above θ_D the thermal pressure, P_TH, along the room‐pressure isobar can be expressed as P_TH(T)−P_TH(300)=[7.14×10⁻³ +(∂K _T/∂T)_v ln(V_a/V)] ×(T−300) GPa for T at absolute temperature and V_a being the volume at ambient conditions. These results give thermal pressure values near those previously reported at small compressions, but give lower thermal pressures at large compressions. This study suggests that in order to ensure thermodynamic consistency, the value of d ln γ/d ln V is near 2.5–3.0 which is higher than values of 1.0 and 1.7 reported previously (γ is the Grüneisen ratio). Calculations giving the compressional and shear wave velocities, v_p and v_s, are also presented. One result is that the quantity ∂ ln v_s/∂ ln v_p at constant pressure is about 1.85 and is independent of temperature.