Volume 121, Issue 1

The vectors h and h ′ are specified. The magnitudes r and r ′ of the vectors r and r ′ respectively, as well as the angle φ r between r and r ′, are also given. All orientations in space of the triangle determined by r , r ′, and φ r are assumed to be equally probable. Under these conditions the average value of exp {2 φi ( h · r + h ′ · r ′)} is found. This result is of basic importance in utilizing partial or complete a priori knowledge of molecular structure as an aid in solving the phase problem.

Various compounds of the Na x TiO 2 -type with the general formula A x (B y Ti 8− y )O 16 (A = Na, B = Mg,Co,Ni,Zn,Al,Ti 2+,3+ ,Cr,Fe,Ga) have been prepared by solid-state reactions. A compound of this type also appears during primary crystallization in some glasses of the system Na 2 O–TiO 2 –SiO 2 . The crystallographic data of “freudenbergite” given by McK ie were confirmed by single-crystal x-ray studies of these compounds. All compounds prepared so far can show non-stoichiometric compositions within a wide range.

A method of investigation is described which makes possible the determination solely from neutronographic and x-ray measurements of all the structure parameters of ferrites containing three sorts of cations. The results obtained by this method on Mg-Mn ferrites are reported.

The usual statistical tests for detecting a centre of symmetry cannot be directly applied to certain feldspar structures because of the occurrence of “translational pseudosymmetry” in them. An examination of the problem of intensity distribution in pseudosymmetric structures shows that a certain class of reflections (the “ a ” type in feldspars) exhibits, as a first approximation, the nature of the distribution corresponding to the “average structure”. This is illustrated with six of the plagioclases, all of which are found to have centrosymmetric distributions. A simple method is suggested for estimating the extent of pseudosymmetry in such structures, and this is illustrated with an example. The recently proposed statistical tests for relatedness or isomorphism have also been applied to the plagioclase feldspars. These tests confirm the general earlier ideas concerning the structural relatedness of the different members of the series. They show good agreement with other approximate measures of structural relatedness available for these structures. The advantage of these methods is that they are based only on the observed intensities, and one is therefore able to obtain quantitative statistical measures of the relatedness amongst structures without having to wait for the ultimate structure analysis.

M itchell has deduced the polytypic structures that would arise from theoretical screw dislocations in the 6 H , 4 H and 15 R phases of silicon carbide, by the spiral-growth mechanism of F rank , and compared these with the structures actually observed. In doing so, he assumed that at the instant of the creation of a screw dislocation, the initial platelet consists of a completed number of unit cells and that the exposed ledge, irrespective of its own structure, can wind over itself in a close-packed manner, thereby repeating its own zig-zag sequence indefinitely during the subsequent spiral growth. It is shown that both these assumptions are not justified and that the use of Zhdanov symbols alone leads to incorrect results. The possible polytypic structures that can be derived from theoretical screw dislocations of different Burgers vectors are rededuced with corrected assumptions, by considering the different possible structures of the exposed ledge in terms of ABC layers and investigating the stacking of these layers during the subsequent spiral growth of the ledge. The results so obtained differ markedly from those of M itchell . In particular a much larger number of structure series are shown to be actually possible. The results are compared with the polytypic structures reported so far.

The cleavage faces of transparent calcium fluoride crystals collected from Amba Dungar of Chhota-Udepur, Gujarat State, have been etched and the etch pattern has been optically studied. It is observed that the point-bottomed pits are eccentric. By etching matched pairs of cleavage faces for successively different periods, it has been shown that point bottoms of the point-bottomed pits follow linear path. It is also observed that the eccentricity in the case of matched pits on matched faces is in the same sense. The eccentricities of the pits have been explained by postulating the existence of inclined linear dislocation lines in the body of the crystal. The inclinations of the dislocation lines have been computed from the measurements made on the pits, and it is observed that they are the same in case of matched pits on matched pairs. Thus it is conjectured that the pits nucleate at the site of inclined dislocation lines. This is also confirmed by etching the matched faces, one by one etchant and the other with a different etchant. It is shown that dislocation lines have different inclinations, but large majority of them are inclined at angles between 16° to 20° with the normal to the cleavage face.

Pure SiC crystals of lamellar and columnar habit were investigated by microscopic and x-ray techniques. All columnar crystals proved to be of one definite polytype without one-dimensional disorder, whereas in most lamellar specimens different polytypes were found in coalescence. Many lamellar crystals showed one-dimensional disorder; in each case it appeared locally and not throughout the specimen. The experimental data suggest that polytypism and one-dimensional disorder are determined by the kinetics of crystal growth.

Melt-grown CsJ crystals were found to show a distinct cleavage on {110} when the applied stress coincides well with this lattice plane. Plastic deformation of CsJ crystals produces gliding following the slip system {110} [001].

The paper describes some recent experiences in the application of a combination of the Monte-Carlo and Optimal-Shift methods to direct structure determination, the Optimal-Shift method to a rough refinement of trial structures, and the Monte-Carlo method to scaling of intensities.

A non-uniform distribution of faces in a zone parallel to a periodic bond chain is to be expected when a kinked face is situated between two flat faces. This occurs when the repeat distance d hkl is affected by glide planes, screw axes or pseudosymmetry in such a way that the number of periodic bond chains per period within a layer d hkl becomes smaller than one. Examples are given for the diamond and sphalerite structure types and for quartz.