Transmission Laue photographs of single crystal gamma and preferentially oriented polycrystalline beta and alpha oxygen samples are described and analyzed. Parent beta and daughter alpha oxygen patterns are observed to be remarkably similar, but also exhibit characteristic differences. Spot positions are essentially unchanged from beta to alpha oxygen patterns; however, beta oxygen spots either transform into larger alpha oxygen spots or split into two or three alpha oxygen spots. The reverse is observed on transforming from alpha to beta oxygen. These observations are interpreted as a consequence of the threefold symmetry of beta oxygen, i.e., beta oxygen may be deformed in each of three ways to form alpha oxygen. Using the measured spot positions and relative intensities, including an estimation of spot wavelengths in favorable cases, an analysis of the patterns leads to the determination of the alpha oxygen orientations, and their relative amounts, present in three different preferentially oriented samples. The second component of the full orientation relation, (010)agr;parallel to one of (1macr;2.0)bgr;, (21macr;.0)bgr;or (1macr;1macr;.0)bgr;, is determined, in addition to that found in earlier work, (001)agr;parallel to (00.1)bgr;. A theory of the beta to alpha transformation which accounts for these and other features is proposed; it involves essentially a shear, with small dilatations, parallel to the (00.1)bgr;layer and in one of the three directions lsqb;1macr;2macr;0rsqb;bgr;, lsqb;210rsqb;bgr;or lsqb;1macr;10rsqb;bgr;. The strain matrix for the transformation is derived. No unique orientation relationship was found in the gamma to beta transformation. In particular, a previously proposed mechanism requiring lcub;111rcub;ggr;to be parallel to (00.1)bgr;was found not to hold for three samples examined.
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