The Crystal Structure of Cahnite

partial fulfillment of the requirements for the degree of Master of Science. Cahnite is one of the few crystals which had been assigned to crystal class 4. A precession study showed that its diffraction sphol is 4/m I-/-, which contains space groups I4, I4E, and14/. Because of the known 4 morphology, it must be assigned to space group I4. The unit cell, whose dimensions are a = 7.11A, o = 6.201, contains two formula weights of Ca BAsO (OH)L. The structure was studied with the aid of in ensity medsurements made with a single-crystal diffractometer. Patterson s ntheses were first made for projections along the c, a, and 110 directions. The atomic numbers of the atoms are in the ratio As:Ca.0:B = 33:20:8:5, so that the Patterson peaks are dominated by the atom pairs containing arsenic as one member of the pair. Since there are only two arsenic atoms in a body-centered cell, one As can be arbitrarily assigned to the origin. Then the major peaks of the Patterson syntheses are at locations of atoms in the structure. The structure, determined approximately in this manner, was refined by two-dimensional difference maps, and later by least squares using all hkl reflections recordable with CuKecradiation. The structure consist I of As tetrahedrally surrounded by oxygen at a distance of 1.67 and B tetrahedrally surrounded by oxygen at a distance of 1.47. Although the tetrahedra do not share oxygens, they are linked together by hydrogen bonds. The Ca atoms are each swrrounded by 8 oxygen atoms at an average distance of 2.46A. Because of interest in the use of the equi-inclination single-crystal diffractometer for the systematic collection of three-dimensional diffraction intensities, general analytical expressions for T and #which can be evaluated by a digital computer have been derived in an appendix. Another appendix gives an analysis of some experimental techniques in crystal structure analysis. Abstract Introduction 1