Measurements of the stress-density states achieved during shock compression of X-, Y-, and Z-cut crystalline quartz are presented. For the elastic shocks comparison is made with predictions based on acoustic measurements of the second- and third-order elastic coefficients, and observed differences, which are substantial, are used to calculate two of the fourth-order coefficients. The values of c1111 and c3333 are found to be 159.3 ± 20% × 1012 and 184.9 ± 20% × 1012 dynes/cm², respectively. This procedure, employing the difference between acoustic measurements and shock wave measurements to evaluate higher-order elastic coefficients, should be generally applicable to solids that sustain large-amplitude elastic waves.
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Richard Fowles (1967) studied this question.
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