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In this paper we apply a mosaic crystal model for dynamical x-ray diffraction to step-graded metamorphic semiconductor device structures containing dislocations. This model represents an extension of the previously-reported phase-invariant model, which is broadly applicable and serves as the basis for the x-ray characterization of metamorphic structures, allowing determination of the depth profiles of strain, composition, and dislocation density. The new model has more general applicability and is more appropriate for step-graded metamorphic device structures, which are of particular interest for high electron mobility transistors and light emitting diodes. Here we present the computational details of the mosaic crystal model and demonstrate its application to step-graded InxGa1-xAs/GaAs (001) and InxAl1-xAs/GaAs (001) metamorphic buffers and device structures. [ABSTRACT FROM AUTHOR]