THE DETERMINATION OF DEBYE CHARACTERISTIC TEMPERATURES OF CRYSTALS FROM X-RAY DIFFRACTION INTENSITIES

Abstract

The methods of determining Debye characteristic temperatures from X-ray diffraction intensities for the case of homogeneous and isotropic crystals have been fully discussed.It is proposed that if the common logarithms of the ration of the calculated intensities to observed intensities log (Icalc/Iobs) of all diffraction lines are plotted against sin2θ, a straight line should be obtained, the slope of which gives 2Bloge/λ2, where B is a physical quantity to be determined contained in the Debye factor e(-2Bsin2θ/λ2) in the intensity expression, λ being the wave length of the radiation used. In the Debye theory of specific heats, B may be expressed as (6h2T/MkΘD2){Φ(x) + x/4}, where h and k represent Planck constant and Boltzmann constant respectively, M is the mass of the atom or of the group of atoms situated at the lattice points, T is the absolute temperature at the time of taking Debye-Scherrer photographs, and ΘD is the Debye characteristic temperature. X = ΘD/T, and φ(x) is a function of x, given in the original Debye theory. It is seen that if we let G=BMkT/6h2, then φ(x)+x/4=Gx2 Having obtained B, G in this equation is a measurable number, and solution of the equation may be performed graphically. By making Y1=Gx2 and Y2=φ(x)+x/4, the plotting of these two equations should give two curves, the intersection of which should give x which determines the characteristic temperature at that temperature.It is pointed out that owing to the fact that ΘD itself is a function of temperature, the method proposed affords a possibility of determining Debye temperatures at required temperatures.