Tweed microstructures III. Origin of the tweed contrast in p andyNi-Al alloys

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Abstract
In the previous two papers in this series we have described our observations of tweed microstructures in several phases of the nickel-aluminium system. In this paper we attempt to provide the theoretical basis for understanding those observations, and similar observations in other systems. By making the assumption that the atoms are displaced by static waves with 〈110〉 polarization vectors and with propagation vectors in the 〈110〉 directions with a range of wavelengths, we derive the diffuse diffraction effects and simulate tweed contrast using kinematic diffraction theory. Making use of our observations on Cu-Zn and Ni-Al alloys, wo show that the tweed microstructure is in fact a manifestation of 〈110〉〈lT0〉displacement waves. We then consider possible causes of such waves, and apply the methods of Krivoglaz and Khachaturyan to this problem. The data available from electron microscopy are insufficient to pinpoint a definite cause, but other information suggests statistical fluctuation of composition or an order parameter. Such fluctuations are present in all alloys; it is the softening of the C elastic constant in /? alloys that results in large displacements of the atoms.