A geometric model of growth for cubic crystals: Diamond

• A geometric model of the morphology of growth of a single crystal with cubic symmetry is presented.
• An implementation of the model is readily available software is made available
• The morphology of a penetration twinned crystal on the growing {100} surface is implemented in a separate model.
• New stability conditions for penetration twins on growing {100} and {111} surfaces are presented based on the growth parameters.

A mathematical and software implementation of a geometrical model of the morphology of growth in a cubic crystal system, such as diamond, is presented based on the relative growth velocities of four low index crystal planes: {100}, {110}, {111}, and {113}. The model starts from a seed crystal of arbitrary shape bounded by {100}, {110}, {111} and/or {113} planes, or a vicinal (off axis) surface of any of these planes. The model allows for adjustable growth rates, times, and seed crystal sizes. A second implementation of the model nucleates a twinned crystal on a {100} surface and follows the evolution of its morphology. New conditions for the stability of penetration twins on {100} and {111} surfaces in terms of the alpha, beta, and gamma growth parameters are presented.

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