Temperature variation of the effective Grüneisen parameter in caesium chloride structures

Abstract

A systematic investigation of the temperature variation of the effective Grüneisen parameter, γ eff. , has been carried out for the caesium chloride structure, on a model incorporating the Coulomb potential between the ions and a nearest neighbour interaction varying as r -n . As the value of n is increased from 8 to 30, the low temperature limit γ 0 of γ eff. is progressively reduced, while the high temperature limit γ ∞ increases. The value of γ 0 — γ ∞ is positive for n ≤ 15 and changes sign for n ≥ 20. Thus the trend and the extent of the temperature variation of γ eff. are sensitive to the value of n in the caesium chloride lattice. On the other hand in the NaCl lattice, the trend of the temperature variation of γ eff. is not affected by a variation of n . For n ≈ 16, the γ eff. value appears to be independent of temperature, though the individual Grüneisen parameters for the lattice frequencies vary widely. This case is an example of a type of perfect Grüneisen solid, the condition for the existence of which was given by Blackman. The Houston method with a constant normalization factor is shown to yield the correct trend of the temperature variation of γ eff. . A more elaborate normalization procedure alters the γ eff. values only slightly. Varying the ratio of the ionic masses has only a slight effect on γ( p ) and γ eff. . From the recently measured elastic data, it appears probable that the value of n pertinent to the caesium halides is about 15. n may increase slightly with increasing size of the anion. If this value of n is correct, the effective Gruneisen parameters for the caesium halides must vary only slightly with temperature. Probably one of the caesium halides will exhibit closely the behaviour of a perfect Grüneisen solid.