Experimentally, the values reported for in microwave plasma CVD of single crystal diamond growth are in the range[11-13, 20] We present in figure 5 the morphology of an isolated penetration twin on the {100} surface for a few values of in the range listed above. We have also analytically determined the stability conditions for a penetration twin growing on a {111} surface in the same manner used above. The conditions for a stable penetration twin on a {111} surface are: , or And for a contact twin on a {111}, the conditions are the same as for the existence of {111} surfaces: We have not yet implemented a specific cdf program to show the morphology of the penetration twin on {111}, but hopefully this will be available by the time of publication. CONCLUSION: A geometric model of growth of a cubic crystal has be implemented in readily available software. New conditions for the stability of penetration twins on {100} and {111} surfaces have been determined. Such modeling has value in designing growth conditions optimized to particular properties. For example, the incorporation of impurities, dopants, and the formation of structural defects depends on the local surface structure. Each of the low index planes in the model has a different stereochemical structure and thus the bulk material grown under a particular low index surface (often referred to as the will have different physical properties reflecting the ‘growth sector’) local defects and impurities in the growth sector. For example, the <111> growth sectors in
Experimentally, the values reported for in microwave plasma CVD of single crystal diamond growth are in the range[11-13, 20] We present in figure 5 the morphology of an isolated penetration twin on the {100} surface for a few values of in the range listed above. We have also analytically determined the stability conditions for a penetration twin growing on a {111} surface in the same manner used above. The conditions for a stable penetration twin on a {111} surface are: , or And for a contact twin on a {111}, the conditions are the same as for the existence of {111} surfaces: We have not yet implemented a specific cdf program to show the morphology of the penetration twin on {111}, but hopefully this will be available by the time of publication. CONCLUSION: A geometric model of growth of a cubic crystal has be implemented in readily available software. New conditions for the stability of penetration twins on {100} and {111} surfaces have been determined. Such modeling has value in designing growth conditions optimized to particular properties. For example, the incorporation of impurities, dopants, and the formation of structural defects depends on the local surface structure. Each of the low index planes in the model has a different stereochemical structure and thus the bulk material grown under a particular low index surface (often referred to as the ‘growth sector’) will have different physical properties reflecting the local defects and impurities in the growth sector. For example, the <111> growth sectors in
GeometricModel-revised2.docx