Technical Notes - Locations and Sizes of Interstitial Holes in the Alpha-Uranium Lattice

THE purpose of this note is to indicate the locations and sizes of various interstitial holes in the orthorhombic uranium lattice based on a hard-sphere model. First, plane configurations of three and four atoms will be examined, and then the true interstices surrounded by four atoms in space and by five atoms in space will be obtained. The data and notation contained in a report by Tucker' will be used. Plane Configurations Fig. 1 presents the orthorhombic uranium lattice made of spheres touching at the closest interatomic distance. The three light-colored spheres in the ab plane are illustrative of the first type of configuration to be examined. If one edge of the unit cell is taken as the origin, the three atoms can be represented by the vectors [Oi + Oj + Ok], [ai + Oj + Ok] and [(a/2)i + (b/2)j + Ok] where i, j, and k are respectively parallel to a, b, and c. In the future, this notation will be shortened to [000], [a00] and [a/2 b/2 0], respectively. A vector R = [r s t] de-scribes the position of the hole surrounded by the atoms. Since the center of the hole must be equidistant from the three atoms R2 = r2 + s2 + t2 = (r-a)2 + s2 + t2 = (r-a/2)2 + (s-b/2)2 + t2. R = [a/2 (b/4) - (a2/4b) 0] is the solution of these