Diamond polytypes and their vibrational spectra
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A.W. Phelps Diamond Materials Inc., State College, Pennsylvania 16801
W. B. White Materials Research Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802 (Received 12 April 1990; accepted 17 July 1990)
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.
I. INTRODUCTION
Carbon exhibits a number of polymorphs: graphite, diamond, lonsdaleite which is sometimes referred to as hexagonal diamond, and at least six forms of carbynes (cross-linked linear carbon chains).1"3 Cubic diamond and lonsdaleite have well-characterized crystal structures which differ in only one dimension, and are the limiting structures of what we postulate to be a series of diamond polytype structures. Our recent identification of an intermediate diamond polytype structure, 6Hhexagonal diamond, in diamond particles precipitated homogeneously from an activated vapor phase helps to substantiate this postulate.4'5 The identification of this 6H polytype was based on comparisons of single crystal electron diffraction d-spacings with x-ray diffraction patterns calculated for diamond polytypes. Holcombe6 calculated patterns for 4H, 6H, 8H, and 10H diamond phases from structures developed by replacing all silicon atoms by carbon in analogous SiC polytype structures. Phelps et al.1 calculated patterns for 15R and 21R diamond structures which were based on two common silicon carbide rhombohedral polytypes. The focus of this paper is on the structural nature and the vibrational spectra of diamond polytypes which J. Mater. Res., Vol. 5, No. 11, Nov 1990
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are analogous to seven common silicon carbide polytypes.8"11 The diamond polytyp
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