Technical Notes - Crystallographic Angles for Titanium and Zirconium

THE angles between the crystallographic planes in cubic crystals have been given by Bozorth,¹ in magnesium, zinc, and cadmium by Salkovitz,² and in tin by Nicholas. The determination of the orientation of single crystals and the study of plastic deformation require the knowledge of these angles and are often facilitated by use of a standard projection. Tables of these angles and standard projections have not been published for titanium or zirconium which have c/a ratios considerably less than those hexagonal metals for which this data is available. Accordingly, Table I has been prepared giving these angles. Fig. 1 presents a standard (0001) projection of titanium. The angle between (h1k1i1l1) and (h2k2i2l2) was calculated by means of the formula: h1h2 + K1K2 + 1/2 (h1k2 + h2k1 + cos 4 = [(hi2 + K + h1k1 + 3/4 l12 (h2² + C" a² 3/4 — l1 l2 C² k2²+ h2k2 + 3/4 —l2²) ] 1/2 c² The c/a ratio for titanium is taken from the data