Refractive index, dispersion, and birefringence of silicon carbide polytypes.
The refractive index of each of the four common silicon carbide polytypes has been measured over the visible range. The data were analyzed in an attempt to relate the birefringence to the relative hexagonal character of the polytype. A general relationship exists, namely, that the birefringence increases with increasing hexagonal character of the polytype. This relationship is not sufficiently precise to use for the identification of polytypes.
Optical Band Gap and Birefringence of ZnS Polytypes
Birefringence and optical band-gap measurements were performed at 20\ifmmode^\circ\else\textdegree\fi{}C on structurally uniform regions of ZnS crystals. The regions were of one of the following polytype structures: $4L$, $6L$, $10L$, $14L$, $24L$, $26L$, $28L$, $40L$, $120L$; cubic ($3L$) and hexagonal ($2L$) regions were also investigated for reference. No stacking disorder was discovered in the regions studied. It was found that the absorption-edge positions (for polarization parallel and perpendicular to the optic axis) as well as the degree of birefringence $\ensuremath{\Delta}n$ depend only on the value of a single structure parameter $\ensuremath{\alpha}$. This parameter is defined as the percentage of (00.1) planes stacked in hexagonal order; its values were determined directly by x-ray structure analysis. The absorption edge positions were found to be linear functions of $\ensuremath{\alpha}$. This linearity is explained on the basis of Birman's perturbation treatment for electron states with k vectors parallel to the $c$ axis. It implies that in a polytype the perturbation potential caused by partially hexagonal stacking is proportional to $\ensuremath{\alpha}$. The degree of birefringence was found to be proportional to $\ensuremath{\alpha}$; an outline of a simple dispersion treatment is given for the explanation of this proportionality. The established linear relationships between absorption edges, birefringence, and $\ensuremath{\alpha}$ allow calculation of absorption-edge positions and $\ensuremath{\alpha}$ values from birefringence measurements. This may facilitate investigations of structure-sensitive properties (e.g., the anomalous photovoltaic effect) of ZnS samples which are composed of regions differing from each other in structure.
Faulting in ZnS: analysis by a two‐parameter model
The two-parameter model of Jagodzinski has been employed to calculate the X-ray scattering from faulted ZnS. The agreement with the observed scattering from single crystals is sufficiently close to establish the need for the two independent parameters to define the one-dimensional disorder. Departure from perfect agreement is attributable to heterogeneity, or non-randomness, of the faulted structure, which is probably a result of the transformation mechanism. Direct evidence of independently diffracting domains has been obtained in a micro-diffraction study of the bands of uniform birefringence which accompany the disorder. Implications from the ZnS findings are made for other cases of one-dimensional disorder. An Appendix provides intermediate equations required for calculating Jagodzinski's function for any combination of a and ft.