Crystalline C, Si and Ge in a lonsdaleite (hexagonal diamond) structure are studied by plane-wave pseudopotential calculations in the scheme of density-functional theory and the local density approximation. The same calculations with generalized gradient corrections and also for the cubic diamond phases of these elements are also performed for comparison. Our results show that the bulk moduli are quite similar between the diamond and lonsdaleite polytypes of these elements. The theoretical bulk modulus of lonsdaleite C is 0.2-0.3% higher than diamond. It is expected to replace diamond as the hardest material in the world. The LDA result shows lonsdaleite Ge as a semimetal for its zero band gap at its Gamma point. Considering the exchange-correlation energy correction, it is estimated that lonsdaleite Ge is a semiconductor with a small direct band gap.
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