Atomic mean-square displacements and the critical-voltage effect in cubic solid solutions

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Abstract
The critical-voltage phenomena observed in high-voltage electron microscope images of bend contours as well as in corresponding Kikuchi or convergent-beam diffraction patterns provide sensitive methods of determining submicroscopic alloy parameters such as Debye temperatures, short-range order, and atomic scattering factors. Only a very limited number of critical voltages can be observed in metal crystals in the voltage range usually available, 100 to 1200 kV, so that quantitative interpretation of the data must be based on a few-parameter model which incorporates all the pertinent factors. A satisfactory two-parameter model has been developed which can be used to interpret or compute the critical voltages of substitutional solid solutions as functions of composition, temperature and short-range order. In the alloy systems Fe-Cr, Ni-Au, Cu-Au and Cu-Al, sufficient critical voltage data are available to derive the model parameters which pertain to atomic bonding in the lattice. In addition to atomic scattering amplitudes, the critical voltage depends strongly on the atomic mean-square displacements. The static contribution to the mean-square displacements is large in alloys with large atomic-radius disparity, and is especially sensitive to short-range order in f.c.c. solid solutions. Well-defined best estimates for the model parameters are used to predict the critical voltage and its sensitivity to composition, temperature and short-range order for a large number of solid solutions. Systems for which critical-voltage studies may be of considerable interest are indicated.