The Structure Analysis of AuCu₃ by Means of a Fourier Transformation of X-ray Diffuse Scatterings

Abstract

The method of analysing the two-dimensional disordered structure using the function;
\varphi_H(x₁,x₂)=∫∫A(s₁,s₂)\fracsinπa₁(s₁−s₁^H)π(s₁−s₁^H)
·\fracsinπa₂(s₂−s₂^H)π(s₂−s₂^H)exp2πi{(s₁−s₁^H·x₁)+s₂−s₂^H·x₂)}ds₁ds₂
is described, where s₁^H and s₂^H mean the coordinates of a relpoint H(=hk0), and A(s₁, s₂) the amplitude of the diffuse scattering at the point (s₁, s₂) in reciprocal space.
The method is applied to the disordered structure of Cu₃Au projected upon (001), giving the statistical parameters describing the atomic composition of each atomic site. The unit cell compositions, which are readily derived from the atomic site compositions, are found appreciably deviated from those corresponding to the bulk composition of Cu₃Au, the Au-rich cell being surrounded by the Cu-rich ones. This suggests that the ordering of this alloy progresses rather by the inter- changes of neighbouring atoms than by the growth of domains in which Au atoms are supposed not to come in contact with each other.
In Appendices remarks are given in relation to the short-range order parameters, and the significances of phase assignments for diffuse scatterings are discussed.