从X射线的衍射强度测定晶体的德拜特征温度

本文详尽地讨论了从X射线衍射强度测定均匀的且各向同性的晶体的德拜特征温度的方法。本方法指明:如将所有的计算强度对观察强度之比的自然对数In(I_calc/I_obs)对sin²θ/λ²标绘,则应该得到一条直线,这条直线的斜率为2B。在德拜的比热理论中,B可表示为(6h²T/MkΘ_D²){φ(x)+(x/4)},其中x=Θ_D/T。如使G=BMkT/6h²,则φ(x)+x/4=Gx²,既然已求得了B值,则这个方程式中的G是一个可量度的数。求解这个方程式可用图解法来进行。使y₁=Gx²,而y₂=φ(x)+x/4,则从这两个方程式的标绘可以得到两条曲线,这两条曲线的交点就是所要测定的x值,由x值可确定在测定温度时的特征温度。必须指出,由于Θ_D本身是温度的一个函数,本方法提供了一个在所需要的温度测定德拜特征温度的可能性。 关键词：

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

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 (I_calc/I_obs) 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/MkΘ_D²){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 Θ_D is the Debye characteristic temperature. X = Θ_D/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 Θ_D itself is a function of temperature, the method proposed affords a possibility of determining Debye temperatures at required temperatures.