The vibrational spectrum has been calculated for an isotopically disordered cubic Bravais crystal in which a fraction q of the atoms have mass M′ and the remainder have mass M. The calculation is valid for all q and is correct to third order in the parameter λ=M/M′ − 1. Numerical results are presented for a face-centred cubic crystal with central forces between nearest and next-nearest neighbour atoms and with M′=1·15M.
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Humphrey J. Maris (1966) studied this question.
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