Anharmonicity and the equation of state for gold

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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 (∂KT/∂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 (∂KT/∂P)T, we find that (∂KT/∂T)V is not zero but −11.5×10−3 GPa K−1 for high temperatures (T>θD, where θD is the Debye temperature). One consequence of this is that above θD the thermal pressure, PTH, along the room-pressure isobar can be expressed as PTH(T)−PTH(300)=[7.14×10−3 +(∂K T/∂T)v ln(Va/V)] ×(T−300) GPa for T at absolute temperature and Va 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, vp and vs, are also presented. One result is that the quantity ∂ ln vs/∂ ln vp at constant pressure is about 1.85 and is independent of temperature.

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