The structure of the dihydrate of the nonreducing disaccharide a,a-trehalose (a-D-glucopyranosyl a-D-glucopyranoside) has been determined independently by direct methods in three different laboratories. There are four units C~2H22Ol~.2H20 in an orthorhombic cell (P212a2a) with a= 12"230 (2), Comparison of coordinates suggests that their standard errors may have been underestimated by a factor of ~2. The a,a-trehalose molecule has approximate C2 symmetry, but there are some significant structural differences between the two chemically equivalent halves. The angles at the ring oxygen atoms are 114-0 and 114-2°; the angle at the glycosidic oxygen is 115.8 °. The two rings have Cl conformations; the conformations about the linking C-O bonds are stabilized by the conformational 6anomeric effect' and also by a complex system of hydrogen bonds involving all of the hydroxyl groups, both water molecules, and one ring oxygen. By hydrogen bonding each glucopyranosy] moiety is linked to the other in the same molecule indirectly through two different water molecules. The helical arrangement of hydrogen bonds about the screw axes parallel to e suggests the possibility of observing ferroelectric behavior.

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It is well established by X-ray crystal analysis that the mineral constituent of bone and of the enamel and dentine of teeth is essentially hydroxy-apatite Ca5OH(PO4)3, and that hydroxy-apatite has a structure differing only in small details from that of the well-crystallized mineral fluor-apatite Ca5F(PO4)3. The main difference, and in fact the only fully established one, between the two structures is that the hydroxy-apatite has a slightly larger unit cell than that of the fluor-apatite. The structure of the latter has been determined by Náray-Szabó, and by Mehmel who finally agrees with Náray-Szabó. We have made what is probably a more accurate determination of the structure, using more extensive X-ray data.

The structure of CaHPO 4. 2 tt20 has been determined, and refined to a moderate accuracy (standard deviation of oxygen positions about 0.03 A, R approximately 26%). The structure is similar to that of gypsum, but there is a definite change of cell dimensions and a small shift in atomic parameters. The hydrogen atoms are probably situated between pairs of water molecules. The structure contains corrugated sheets of composition CaPO4, with the waters in layers between them. IntroductionDiealcium phosphate is of interest as a mineral (brushite) which is isomorphous with the corresponding arsenate (pharmacolite). The crystals are very similar to those of gypsum, with which, indeed, it forms a mixed series (Hill & Hendricks, 1936; 0'Daniell, 1939; Smith, Lehr & Brown, 1955). It can be grown into very fine large crystals, and we are obliged to the Research Department of the Tennessee Valley Authority for specimens which were used for the cutting of crystal plates for Geiger-counter spectrometry. Smaller crystals were grown for this work by the Research Department of Scottish Agricultural Industries Limited. THE CRYSTAL STRUCTURE OF DICALCIUM PHOSPHATE DIHYDRATE Optical goniometry, unit cell and space groupThe crystals were tabular on the b face, with edges made up from {110}, {112} and {121} faces. The smaller crystals used showed variations in their interracial angles of up to 4'. The larger crystals, although of brilliant appearance, showed variations of up to 10' in different parts of the same face. The small crystals showed the full symmetry 2/m of the monoclinic system, but the large crystals showed no mirror plane, and were evidently grown in a very unsymmetrical manner. Cell dimensions were deduced from the positions of the high-order spots, and the following cell was adopted: a=5.812+0.002, b=15.180±0.003, c=6.239±0.002 ,&.,This cell differs from those adopted by Miers and by Groth, but it is the smallest possible cell and corresponds to that suggested by Bragg (1937). The cell has a volume of 492.9 j~3, and the calculated density is 2.318 g.cm. -s, whilst the value of the measured ,L Fig. 1. Projection of the structure on to a plane perpendicular to [101]. Determination of atomic parametersThe general positions of space group I2/a are eightfold in number, whilst Ca and P atoms occur only four times in the cell. Thus Ca and P are in special positions, either on the twofold axes or the centres of symmetry (although the latter is impossible for a PO4 group).Examination of the (hkO) intensities showed that the h even values are considerably stronger than the h odd ones, and this fact is readily explicable by supposing that the Ca and P atoms are both on the twofold axes with a y difference of almost ½. A Patterson synthesis carried out on the (hkO) planes showed that values Ca at (30/120, 49/120) and P at (30/120, 39/120) for x and y were satisfactory. The z coordinates of these atoms are zero (if we are to put them on the twofold axes) so that the heavy-atom positions are thus known. The oxygen atoms were found ...

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