X-ray diffraction approach to grain boundary and volume diffusion

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Abstract
A generalized two‐dimensional diffusion model has been developed which consists of an array of boundaries coupled to the free surface and to the substrate lattice. The model makes use of three nonlinear partial differential equations which describe lattice, grain boundary, and surface diffusion. This two‐dimensional model has been programmed for the IBM 360 computer using a finite‐difference solution to give concentrations as a function of time. An x‐ray intensity simulation program is developed to give integrated diffracted intensity for a given concentration distribution. This simulated intensity is compared with experimental intensity. Data are presented from a sample containing 8 μ of Ni on a (111)‐oriented Cu crystal diffused for various times at 900°C and a similar sample with 6.5 μ of Ni diffused at 600°C. The simulations are in good agreement with experimental intensity bands. Activation energies and frequency factors are given for volume and grain boundary diffusion which are in good agreement with those literature values that are available. After a diffusion treatment at 600°C, it was found that pipe diffusion makes an important contribution to the volume diffusion coefficient. At 900°C this does not appear to be true. The contribution from pipe diffusion correlates with rocking curve data except for compositions close to that of the free surface.