On the Inversion Temperature Function of the First Order (One Phonon) Scattering and the Determination of Debye Characteristic Temperatures

Starting from Laval's expression for the first-order thermal diffuse scattering (TDS 1 ), a new expression for the inversion temperature of TDS 1 , T max = m Θ D 2 d 2 hkl k /3 h 2 , has been obtained, valid for a crystal of any symmetry. T max is attained when ( u 2 )bar above 1/2 / d hkl = 16%. Every crystalline substance has a definite range where the above formula holds: the upper limit is T mp and the lower limit is Θ D . The melting temperature defines a d max for which the inversion phenomenon can be observable. The inversion curves of TDS 1 have been calculated for some metallic, ionic and molecular crystals. It is shown that KCl, Pb and Al, for which the inversion phenomenon has been reported, are not special cases. In molecular crystals this effect will be observable mainly at low temperatures. A method is given for determining Debye characteristic temperatures of crystals of any symmetry. This method is tested using Cartz's experimental T max for lead.