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High resolution monochromatic synchrotron-radiation diffraction images of five, high quality epitaxial heterojunctions on silicon, gallium arsenide, and indium phosphide substrates display several forms of accommodation to lattice mismatch. From the images, we deduce a coherent set of factors for the loss of crystalline order in layered semiconducting crystals. Lattice mismatch is demonstrated in each of the systems by warping after layer deposition. Nevertheless, local lattice orientation is maintained across each layer interface. In two of the systems, one severely mismatched while the other is not, no arrays of dislocations appear. Sets of mixed linear lattice mismatch dislocations, consistent with identification as 60° dislocations, are found in two of the other systems with intermediate degrees of mismatch. A set of pure edge dislocations penetrating all layers is found in a system with a grid structure. These observations indicate that the formation of extensive arrays of dislocations during uniform one micrometer layer deposition depends not only on the extent of lattice mismatch and layer thickness but also on the degree of crystalline order of the substrate. Establishment of a nonpseudomorphic layer mismatched with the substrate by several tenths of a percent is an important factor, as previously determined. However, localized absence of crystalline order, e.g. in the form of scratches or dislocations in the substrate, appears also to be required for the formation of arrays of interface mismatch dislocations. Where these criteria are not fulfilled, the formation of dislocations in uniform layered systems is inhibited. Localized residual stress can initiate dislocation formation even where it would not appear in uniform layers. The images show also that crystalline disorder in state-of-the-art indium phosphide differs markedly from that in comparable gallium arsenide. Understanding of crystalline order in both monolithic materials is extended by this work.