Intensity of X-ray Diffraction by a One-dimensionally Disordered Crystal (III) The Close-packed Structure.

概要

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The general intensity equation for X-rays diffracted by a one-dimensionally disordered crystal with any value of the correlation range s i.e. [numerical formula]. was applied to the case of the close-packed structure. The obtained result is [numerical formula] in which V_0 is the layer from factor of the number of layers, l=23^<5-1>, x_y=x_<y0>s^<i0y>, which are the Z roots of the Characteristic equation of [numerical formula] which are the roots of the l simultaneous equations of [numerical formula] and two H's the higher terms which, when lx_yl=1, give the Laue function whose maximum is at φ=0_v. The characteristic equation is derived from the general difference equation [numerical formula] from which we can easily obtain the difference equations that Wilson and Jagodzinski derived in the cases of s=2 and 3 by the use of rather complicated genealogical tables. We showed the correspondence of our results in the cases of s=2 and 3 with those obtained by Wilson, Jagodzinski, Hendricks and Teller. The above matrices are those of l/2-th order. The elements in x_n are the probabilities of finding the. same kind of layer at the(j+n)-th position as that at the j-th position and h=x_0. Those in αβ and (1-α)βμ are the probabilities of finding the layer after the other layers in the cubic and hexagonal manners respectively. When 2h+k=3m, I=V_0V_0*(sin^2Nφ/2)/(sin^2φ/2) without giving any diffuse line.
社団法人日本物理学会の論文
1954-04-25