Abstract
BY suitable averaging, the following relations may be derived for polycrystalline aggregates consisting of randomly oriented and ideally closely packed particles of any substance crystallizing in the cubic system: C′11 and C′44 are the thickness and shear elastic constants of a plate of the aggregate and C11, C12 and C44 are the elastic constants of the corresponding single crystal. If the crystal is such that the Cauchy relation C12 = C44 holds good, the above equations become dependent on one another and reduce to C′11 = 3C′44 = (C11 + 2C12). If C12≠C44, they remain independent but may be combined to give 3(C′11 − 4 (C′44 = (C11 + 2 (C12. Thus, the measurement of (C′11 and (C′44 will enable us not only to state whether the Cauchy relation holds good for the crystal under investigation, but also to evaluate the bulk modulus K, which is (C11 + 2C12).
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References
Bhagavantam, S., and Bhimasenachar, J., Proc. Ind. Acad. Sci., 20, 298 (1944); Nature, 156, 23 (1945).
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BHAGAVANTAM, S., RAO, T. Compressibilities of Cubic Crystalline Powders: a New Method of Measurement. Nature 168, 744 (1951). https://doi.org/10.1038/168744a0
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DOI: https://doi.org/10.1038/168744a0
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