LXXXII. On the thermal expansion of solids at low temperatures

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Abstract
Following recent experiments in which Grüneisen's γ was observed to decrease at temperatures below 0·3 Θ, an investigation is made of the variation of γ with temperature according to the lattice dynamics of Born and von Kármán. γ is defined as a function of T, and a general analysis applicable to all lattices is used to derive the low and high temperature limits γ 0 and γ ∞. By expressing γ as a quotient of power series in T-1 it is shown that the main variation between these limits occurs at temperatures of the order of 0·2 Θ. Calculations are carried out for a cubic close packed lattice with central forces between nearest neighbours; it is found that γ ∞-γ 0=0·3, and that the behaviour of γ is qualitatively similar to that found experimentally in monatomic metals. The amount of variation in γ is decreased when interaction between more distant neighbours is taken into account, and a model representing the heavier inert gas solids gives γ ≈ 3 and γ ∞-γ 0 ≈ 0·15.

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