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A self-consistent calculation of an accurate Gruneisen equation of state for solids that exhibit a linear relation of Us to up (i.e., shock velocity to particle velocity) is described. The calculation is based on a determination of the volume dependence of the temperature-independent Gruneisen parameter γ by an approach considerably simpler than those commonly used in the past. The equation of state is obtained from the shock Hugoniot and the solution to a simple first-order differential equation in the compression. Detailed results are presented for copper. γ is calculated within well specified limits, and the computed isotherms give pressures accurate to within 1% at a given volume for pressures up to 550 kb.
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David J. O’Keeffe (1970) studied this question.
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