The low-temperature thermal expansion and vibrational properties of alkaline earth fluorides

Abstract

Interferometric measurements of the linear thermal expansion coefficients α of CaF2, SrF2 and BaF2 between 20 and 273 °K are reported. The results are believed to be accurate to within 2% down to 50 °K, falling to 15% at 25 °K. The Gruneisen parameters γ = βV/CVχT, calculated from the volume expansion coefficients β and earlier heat capacity and elasticity measurements, fall with diminishing temperature. The quasi-harmonic approximation has been applied to calculate the maximum frequencies νD(n) of the Debye distributions having the same nth moments as the actual crystals, which display minima at n [similar, equals] -1 5, -2.0 and -2.5 for CaF2, SrF2 and BaF2, respectively, and νD(n) has been found to fall with increasing mass of the alkaline earth ion. The volume dependence of the moments γ(n) = -d ln γD(n)/d ln V for -3 <or= n <or= 4 falls quite rapidly as n becomes increasingly negative, and γ(n) diminishes with increasing mass of the alkaline earth ion.