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Chemical vapor deposition of germanium onto the silicon (001) surface at atmospheric pressure and 600 degrees Celsius has previously been shown to produce distinct families of smaller (up to 6 nanometers high) and larger (all approximately 15 nanometers high) nanocrystals. Under ultrahigh-vacuum conditions, physical vapor deposition at approximately the same substrate temperature and growth rate produced a similar bimodal size distribution. In situ scanning tunneling microscopy revealed that the smaller square-based pyramids transform abruptly during growth to significantly larger multifaceted domes, and that few structures with intermediate size and shape remain. Both nanocrystal shapes have size-dependent energy minima that result from the interplay between strain relaxation at the facets and stress concentration at the edges. A thermodynamic model similar to a phase transition accounts for this …