Band 108, Heft 1-2

A method based on the consideration of disagreement functions has been developed, for determination of the translation and orientation of a molecule in a structure, provided the molecular shape is known. This method has an advantage over the Fourier transform method, in that it is not limited to planar molecules. The translational problem is considerably easier to solve than the rotational one, as the latter leads to B essel functions, whereas the former can be expressed in a form of a P atterson -like map, called the “translation function”. An example of such a function is given for space group P [unk]. The translational solutions are represented by the highest peaks of the map.

A method is described whereby the optical orientation of plagioclases may be numerically described with the aid of three independent parameters (Euler-angles). An examination of their variation relative to the anorthite-content leads to an exact characterization of the high- and low-temperature optics, as well as of intermediate stages in which Si and Al are only partially ordered. It seems likely that such stages are considerably more frequent in nature than has hitherto been supposed.

A recording microphotometer is described which permits extending the natural linearity of X-ray films (blackening, S ≤ .38) up to a blackening of S = 1.05. Possibilities for additional improvements are discussed.

The influence of differences in the Al / Si -distribution of feldspars on the infrared absorption in the region of 7 to 16 μ is shown. Relations between the low- and high-temperature modifications of feldspars in view of their absorption spectrae are discussed. The value of infrared absorption measurements for the discussion of order/disorder problems is pointed out.

By means of two superpositions of P atterson diagrams, it is possible to obtain a model of the structure – at least, theoretically. Further superpositions, if possible m of them, where m is the number of atoms, lead to the electron density function ϱ ( xyz ). The relations of the electron density function to the individual product functions are derived, considering both vector differences and weights. The B uerger formula for these relations is corrected for those maxima which are used as displacement vectors. For Π m , the equation given in this paper is valid. The sum function is unfavorable compared to product function and minimum function. For centrosymmetrical structures one superposition of P atterson diagrams is sufficient, if a ± 2 r i vector is used. The relation of this function ( Π 2 ) to the electron density is easily understood. Generally one can say that the method of superposition of P atterson diagrams is able to yield the relative positions of the atoms of a structure – and, therefore, the electron density ϱ ( xyz ). The refinement can be carried out with the help of the customary procedures.

Minerals of the serpentine family are essentially divisible into two groups: chrysotile and antigorite types (the latter includes antigoritieal serpentines). Throughout, they are two-layer minerals. Their layers are formed by combining of a Si 2 O 5 layer and a brucite [ Mg ( OH ) 2 ]-like layer. The chemical formula of chrysotile, Mg 3 ( OH 4 ) Si 2 O 5 , is not valid for antigorite, the reason is a so-called “coincidence” deficiency of electroneutral atom groups. This deficiency is repeated along the crystallographical a axis with exactly defined (superperiod) distance. In the resulting superstructure of antigorite (which is a so-called “double half-wave” structure), we find two “half-waves” alternately connected by means of Mg -bridges. In contrast to the monoclinic chrysotile, here we find a larger interaction in the form of hydrogen bonds between two layers along the direction of the layer period c .

When heated, chalcopyrite ( α ) passes into a high temperature mixed-crystal phase ( γ ) at 550°, the sulphur content of which decreases with increasing temperature. At about 720° an end product is attained which is poorest in sulphur and which may sometimes be recorded by the X-ray diffraction method even at room temperature. It transforms, however, within a few days into the stable β -phase, which at 230° changes back again into γ . When chalcopyrite is heated to temperatures between 550° and 720°, the mixed crystal which has been formed breaks down into α + β on cooling. The β -phase has the formula Cu 17+ x Fe 17+ x S 32 ( x ≈ 0,6) and is cubic with the space group I [unk]3 m and a = 10.60 Å. The γ -phase is tetragonal with a = 10.58 and c = 5.37 Å.

Diglychie hydrobromide is orthorhombic, space group P 2 1 2 1 2 1 . The unit cell has edges a = 8.21 Å, b = 18.42, c = 5.40, and contains four molecules of composition 2( C 2 H 5 NO 2 ) · HBr . Intensity data were gathered by means of the D awton method, using precession and W eissenberg photographs. The bromine atom locations were determined from P atterson projections, and the structure was solved by the heavy atom method. It was refined by four sets of difference syntheses. The structure contains two non-equivalent, nearly planar molecular groups of [unk] which are held together by hydrogen and van der W aals ' bonds.

The dehydration curves of various chloritoids, in combination with X-ray investigations, showed clearly the existence of an anhydride with a crystal structure different from that of chloritoid. The structural features of this new form can be derived from the chloritoid structure (B rindley -H arrison structure). In addition to a description of the methods employed, the behavior of chloritoid during dehydration is discussed as derived from the proposed structure.

A simple arrangement is described to record the intensities with a Geiger-Müller counter with a fixed relative error. After the incidence of a fixed number of counts the counter is automatically shifted to an adjustable angle and the counting mechanism begins anew. A mechanical writer records the time.