X-ray diffraction patterns from faulted face-centered cubic and diamond cubic crystals
Davis, Hugh Miller, Jr.
Clark, John R.
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Calculations have been made in an attempt to predict the effects of microscopically fine twinning and of stacking faults on the x-ray diffraction patterns which can be expected from single crystals of materials having the face-centered-cubic or diamond cubic structures. The existence and the effects on x-ray scattering of a coincidence lattice and multiple unit cell in twinned structure are discussed. Additional diffraction peaks are found to appear in diffraction patterns from twinned structures at reciprocal space positions which have non-integer coordinates when referred to the reciprocal lattice of an untwined crystal. These extra peaks lead to layer line spacings in rotating crystal patterns which are found to be proportional to 3(-n) here n is the order of the twinning involved. The extension of methods for determining the effects of random stacking and twinning faults on X-ray diffraction patterns, developed by Paterson and Guentert, is shown to predict non-zero intensities from those planes in faulted diamond crystals which have Miller indices such that h+k+l = 4n+2. It is suggested that this provides a partial explanation of the well known "forbidden" reflections from planes of the form (222) in crystals having the diamond cubic structure. The positions and intensities of the (222) reflections from a small diamond have been confirmed using a Weissenberg goniometer.
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