Burton-Cabrera-Frank (BCF) theory has proven to be a versatile analysis to relate surface morphology and dynamics during crystal growth to the underlying mechanisms of adatom diffusion and attachment at steps. For an important class of crystal surfaces, including the basal planes of hexagonal close-packed and related systems, the steps in a sequence on a vicinal surface can exhibit properties that alternate from step to step. Here we develop BCF theory for such surfaces, to relate observables such as the alternating terrace widths as a function of growth conditions to the kinetic coefficients for adatom attachment at steps. We include the effects of step transparency and step-step repulsion. A general solution is obtained for the dynamics of the terrace widths assuming quasi-steady-state adatom distributions on the terraces, and an explicit simplified analytical solution is obtained under widely applicable approximations. We obtain expressions for the steady-state terrace fractions as a function of growth rate. Limiting cases of diffusion-limited, attachment-limited, and mixed kinetics are considered.
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