The thermal properties of alkali halide crystals IV. Analysis of thermal expansion measurements

In part II the momentsvn¯and the low-frequency expansions of lattice frequency distributions were obtained by analyzing experimental heat capacities. We now derive from thermal expansion data the volume dependence of the moments and of the low-frequency coefficients, analyzing the Grüneisen functionγ(T,V)=βV/χsCp. The volume dependence of the moments and ofΘ0Cis conveniently expressed by the functionγ(n)=−dlnvD(n)/dln⁡V, wherevD(n)=12(n+3)vn¯1/n. Individual values of γ(n) obtained by the analysis are useful in estimating the volume dependence of various crystal properties, notablyC_Vand the Debye-Waller effect. The analysis is carried out for NaCl and KCl. The volume dependence of the low-frequency expansion can in principle be obtained from low-temperature data, but experimental accuracy in fact allows an estimate only of γ₀≡ γ( — 3); the results are thus wholly expressed by γ(n) curves for each salt. These curves are determined to within a few parts per cent for — 2 ≤n≤ 0, but the uncertainty increases to about 10% for γ( — 3). Forn> 0 the uncertainty increases so rapidly that the curves in this range must be considered as only provisional ; this is partly because present thermodynamic data fix the volume dependence of γ(T, V) only between very wide limits. The values obtained for y( —3) agree moderately well with values estimated from the pressure dependence of elastic constants; the comparison neither confirms nor rules out the possibility of at least a shallow minimum in the γ(T) curves at low temperatures. The general shape of the γ(n) carves is in rough agreement with the predictions of the Kellerman rigid ion model, with a maximum in γ(n) forn> 2. For the Kellerman model the fall in γ(n) asn→ ∞ is shown to be due to the longitudinal optical modes, which at the long-wave limit have individual γ values lower than γ(2) or γ(4). The primaryC_Pdata for sodium chloride of Morrison & Patterson (1956) are tabulated in an appendix, because they were not given in the original paper.