Diamond polytypes and their vibrational spectra

Abstract

A series of diamond polytype structures are described and their IR and Raman vibrational modes predicted. The diamond polytypes are analogous to the well-known silicon carbide polytypes. The intermediate 6H diamond polytype was recently identified by single crystal electron diffraction of vapor precipitated diamond powder. In addition, end member polytypes of 3C (cubic diamond) and 2H diamond (hexagonal lonsdaleite) have been previously established, and polytypes such as 4H, 8H, 15R, and 21R diamond are predicted, but may be difficult to isolate and identify. The various diamond polytype structures differ only in the stacking sequences of identical puckered hexagonal carbon layers. These identical carbon layers lie parallel to the cubic 3C {111} and the hexagonal 2H {001} planes. A new method for uniquely labeling the structural layers in the polytype stacking sequences is presented. Factor group analysis was used to determine the IR and Raman selection rules for five diamond polytypes with structures intermediate between those of end members diamond and lonsdaleite. Brillouin zone folding techniques were used to determine band positions, in analogy with analyses of SiC polytypes discussed in the literature. The results predict that (i) all diamond polytypes are Raman active, (ii) limiting polytypes 3C and 2H are not IR active, and (iii) polytypes 4H, 6H, 8H, 15R, and 21R have IR active modes.