The P6a/m space group and the structure given by both N&ray-Szab5 (1930) and Mehmel (1930) for the hexagonal crystal fluorapatite, Cal0(POd)~F ~, have long been accepted as essentially correct. In view of the importance of the apatite structure in many fields, it was felt that a refinement of this structure would be of value.The study reported here was made with crystals of synthetic hydroxyapatite, Cal0(POd)e(OH)2, prepared by hydrolyzing CaHPO4 in a platinum-lined, hydrothermal bomb. The details of the synthesis are published elsewhere (Perloff & Posner, 1956). The atomic parameters given below are for hydroxyapatite. As this compound and fluorapatite are isomorphous, with nearly the same unit-cell size, the refined parameters should apply to both. Powder diffraction results gave the unit cell dimensions of hydroxyapatite as a = 9-432 , c ----6.881/~. Three-dimensional, single-crystal, X-ray diffraction data were obtained, using the multiple-film technique with a Nordus integrating Weissenberg camera. Nickelfiltered, Cu Kc~ radiation and Kodak NO-SCREEN film were employed. The intensities of the integrated spots were measured with a Baird Associates Inc. I)ensitometer-Comparator, corrected with the appropriate Lorentz and polarization factors, and converted to a set of observed structure factors. These were scaled to the calculated structure factors, based on the N~ray-Szab6 parameters, by matching the sums of the observed and calculated structure factors. No corrections for absorption or extinction were made. The former correction was trivial because of the small size of the crystals used. The crystals were 0.14 ram. long and 0.06 ram. wide for the c-axis rotation photographs, and 0.07 mm. long and 0-05 ram. wide for the a-axis rotation photographs.There are about 470 possible, independent reflections for hydroxyapatite using Cu Ka radiation. About 450 of these were within the range of the data recorded, and only 330 reflections were detectable while the remainder were considered as having an observed intensity of zero. The independent, non-zero reflections, after conversion to structure factors, were used in a least-squares refinement of the 19 variable parameters (12 atomic position parameters and seven isotropic temperature factors for the seven atoms). The parameters of the early apatite studies were used as a starting point for the least.squares refinement. The process was performed on the IBM 704 electronic computer using the program written by Dr

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The structures of the ditellurides of niobium and tantalum which have been worked out as part of this project, have similar metal-metal chains parallel to the b axis except that the chains are made of three rows of metal atoms rather than two. Details of this work are presented in a companion paper (Brown, 1966 The structure was solved by conventional Patterson and electron-density syntheses utilizing the heavy atom to establish the initial phases. Least-squares refinement on three-dimensional data yielded a residual R = 7.1 Yo.The results reveal an unusual type of borate framework. All boron atoms are tetrahedrally coordinated. The unusual feature is the occurrence of an oxygen atom common to three tetrahedra.Although the tetrahedra form a three-dimensional network by corner sharing, the borate network gives the appearance of a layer-like structure because there are comparatively few links in the e direction. The layers can be described in terms of chains (parallel to a) of six-membered rings having B-O edges in common. These chains are joined by non-ring oxygens to form layers parallel to the a b plane.The Sr coordination is not clearly defined. There are nine nearest-neighbor oxygen atoms at distances ranging from 2.52 to 2.84 A. There are six more oxygen atoms at 3.04 to 3.20/~ which could conceivably be considered as part of the Sr coordination sphere.

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The crystal structure of the high temperature form of BaO.B203 (m.p. 1095 + 5°C) was determined by conventional three-dimensional Patterson and electron-density syntheses. The heavy atom technique was used to establish the initial phases. BaO.B203 crystallizes in the trigonal system, space group R Sc, with 18 formula units per hexagonal cell. Unit-cell dimensions, referred to hexagonal axes, are a=b=7-235, c=39.192/~. Least-squares refinement with 498 independent reflections yielded a reliability index of 5.7 %, based on the observed data only. The anion in the structure is a nearly planar []3306] 3-group constructed of three BO3 triangles each of which shares two of the three corners. The structure contains two crystallographically distinct barium atoms located in positions having point symmetries 32 and 3. About the barium in the 32 point symmetry position the oxygens are arranged in a trigonal prism. About the barium which lies in the 3 point symmetry position the oxygen coordination is ninefold.