Volume 123, Issue 2

The structure of grossularite has been refined from neutron and x-ray diffraction data. During the least-squares refinement different weighting schemes were employed. The most reliable parameters were calculated with experimental weights. The accuracy of the oxygen parameters was not sufficient to detect a difference between the position of the nucleus and the center of mass of the electron cloud. Temperature parameters calculated from low-temperature (77°K) neutron data were nearly the same as those found from room-temperature data.

X-ray scattering factors for Na + , F − and Ne are calculated from analytic Hartree-Fock solutions. In addition to form factors computed from free-space solutions for this triad, scattering factors for Na + and F − are presented which are calculated from several approximations to the solid-state wave functions for those ions. The influence on the form factors of the simulated crystalline environments which are incorporated in these functions is examined and discussed. The analytic form factors obtained from the free-space solutions are compared with previous results of numerical calculations.

The expressions relating the integrated optical density (as obtained from an integrating Weissenberg goniometer) with the average or maximum density of a reflection have been deduced. These expressions have been used to estimate the increase in exposure time of an integrated Weissenberg photograph over normal exposure time.

The crystal structure of Hf 2 S has been determined from two-dimensional single-crystal data. Each S atom is surrounded by six Hf atoms in trigonal prismatic coordination, while each Hf is surrounded by a distorted octahedron of three S and three Hf. The structure is related to the anti-NbS 2 type. Hf 2 S has two formula units in a unit cell of space group P 6 3 / mmc or P 6 3 mc with unit-cell dimensions a = 3.37 Å and c = 11.79 Å.

It is possible to use superposition methods on high-speed computers to calculate image-seeking functions from three-dimensional data. The shortcomings of one method which will be called “Integrale Superposition” is discussed. In this method the values of a Patterson map are stored in the computer memory at integral coordinates of a chosen grid of the cell. If a searching vector does not lie on a grid point, interpolation between values of the neighbouring grid points will be necessary. Operating on high-order image-seeking functions, the accumulation of errors by interpolation and the increasing loss of valuable information will cause difficulties. Another limitation of this method is caused by the size of the computer memory. A superposition of weighted and shifted Patterson maps, generated by any simple Fourier-program from modified Fourier coefficients, yields an image-seeking function of any type, provided this function has the characteristics of a superposition function. This method will be called “Funktionelle Superposition”. It can be extended to any order of the function, without having the limitations of the first method. It will be shown that a third method, to obtain image-seeking functions directly by Fourier summation of properly modified coefficients, does not save any computational effort in the case of the product and the minimum function. The relation of the addition function to a number of similar functions is discussed and the formulas to obtain their Fourier coefficients are given.

Cleavage faces of calcite of scalenohedral habit have been etched in citric acid. Stratigraphic etch pattern produced on the cleavage faces have been carefully studied. It is observed that the stratigraphic pattern is displaced while crossing cleavage steps. Exact correpondence in the magnitude of the displacement on matched faces and also the correspondence of such pattern on the two opposite sides of a crystal plate have been observed. From the angles made by the different sides of the stratigraphic pattern with each other, and the displacement of the pattern while crossing cleavage steps it is conjectured that the pattern reveals the edges of the weak planes deposited during the growth of the crystal. The implications are discussed.