An asymptotic expansion for the entropy of hardhyphen;sphere alkali halide crystals withNsmall and large particle pairs is obtained:SN/NkBsime;tgr;rarr;13thinsp;ln(sgr;ls2e)/(lgr;llgr;s) +3thinsp;ln(tgr;1/3minus;1)+3thinsp;lnthinsp;egr;minus;Cminus;Degr;minus;Eegr;2+sdot;sdot;sdot;,wherekBis the Boltzman constant,eis the natural number, tgr; is the ratio of the system volume to its high compression limiting volume,lgr;landlgr;sare the mean thermal de Broglie wavelengthslsqb;lgr;=(h2/2pgr;mkBT)1/2,mbeing the massrsqb; of the large and small particles, respectively,sgr;lsis the hardhyphen;sphere collision diameter of nearest neighbor large and small particles;C,D,E, etc. are wellhyphen;defined parameters dependent on the small to large particle radius ratio and the lattice structure, andegr;=lsqb;(tgr;1/3minus;1) +(1minus;sgr;ls/sgr;lsprime;)rsqb;,wheresgr;lsprime;is the average distance between nearest neighbor large and small particles in the high compression limit. If the small to large particle radius ratio is less thansqrt;2minus;1for the rsquo;rsquo;NaClrsquo;rsquo; lattice and less thansqrt;3minus;1for the rsquo;rsquo;CsClrsquo;rsquo; latticesgr;lssgr;lsprime;.For greater small to large particle radius ratiossgr;ls=sgr;lsprime;.The result differs from the asymptotic expansion for a crystal ofNuniform spheres obtained by Salsburg, Stillinger, and cohyphen;workers lsqb;J. Chem. Phys.49, 4857 (1968)rsqb; in that it contains the additional logarithmic term 3thinsp;lnthinsp;egr; and a smallness parameter egr; that differs fromtgr;1/3minus;1,used by the earlier workers. Estimates of the leading parameterCwere made using the modified cell cluster expansion. The predicted entropies of the alkali metal fluoride salts approach the experimental values at temperatures approaching the melting point which is consistent with the contention that the hard sphere contribution to the entropy dominates other contributions at high temperatures. The predicted difference between the entropies of the two alkali halide lattices is also consistent with the experimental data at higher temperatures.
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