Volume 108, Issue 3-4

During the course of the structure analyses the space group D 2 h 13 - Pnmm assumed by O ftedahl (1932) and F rondel (1941) had to be forsaken in favour of the hemihedral space group C 2 v 7 – Pn 2 m . The structures were deduced from the P atterson diagrams by means of the superposition method. The x -and z -parameters were refined step by step by F ourier syntheses. The y -parameter derived from the superpositions had to be corrected by trial and error. Other methods used during the investigation are shortly discussed. Apart from slight differences in parameters both minerals have identical structures and show very close relationship to the analogous Bi -compound aikinite and also to stibnite Sb 2 S 3 .

A theory for the crystal growth in supercooled melts is developed. This theory states that the growth of a crystal is caused by continuous presence of kinks on its surfaces. Added to this is a frequent formation of two-dimensional nuclei on the face. The assumption of lattice faults leads to an explanation for the finite increase in the speed of crystallization at the melting point. From 3° supercooling on, a frequent formation of two-dimensional nuclei starts, which finally plays the dominating role. The calculated values not only match the experiment curves of the speed of crystallization qualitatively, but they also permit a satisfactory quantitative interpretation. In order to determine the free enthalpy of activation of the self diffusion, the viscosity of supercooled salol was determined.

There are two possibilities α [or β ] for a substituent ( Br ) at C 7 in the sterol molecule (Fig. 1), oriented trans [or cis ] to the H at C 8 (or the methyl group C 18 at C 10 ). The two C 7 –epimers are strongly laevo–(= I) resp. less dextro-rotarory (= II). The problem arised as to the configuration ( α or β ) of the laevo-rotarory compounds (I). This question was solved by an X-ray analysis of 7-bromocholesteryl-bromide ( S 1 ), -chloride ( S 2 ) and -methylether ( S 3 ) (Fig. 2), which turned out to be isotypical in space group C 2 2 – P 2 1 with Z = 2 molecules per unit cell (dimensions see Table 3, p. 210). – P atterson projections // a , b and c (Fig. 3) yielded the positions of the four Br -atoms. Applying the heavy atom method, the isomorphous method (comparison of S 1 and S 2 ), the combination of both methods and the P atterson superposition method (Fig. 8–10) for the sign's determination, F ourier projections // b (Fig. 4–7) were obtained for S 1 and S 2 which partly gave a very good resolution of most of the atoms of the sterol molecule. These electron maps showed univocally that in the investigated compounds S 1 and S 2 (of type I) the Br -atom at C 7 is in α -position (i. e. trans to H at C 8 ) (Fig. 11–12). – The long axis of the molecule lies approximately in (010); the mean ring-plane is tilted by about 20° around the direction [20[unk]] out of (010). Therefore the molecules are forming layers // (010) which are superimposed by the 2 1 -screw axis (Fig. 13). The crystal and the molecular structure of these compounds ( S 1 , S 2 ) are very similar to those of cholesteryl iodide (form B) (C arlisle -C rowfoot , 1945) (Fig. 14). – All calculations have been performed quite from the beginning by means of IBM-machines.

Pectolite is triclinic, space group P [unk], with 15 nonhydrogen atoms in the asymmetric unit. Its crystal structure has been determined by solving the three P atterson projections by the use of image-seeking functions. The P atterson projection P ( xz ) was solved after finding two conjugate peaks on the map. These located two sets of inversion peaks upon each of which a scaled minimum function was based. These two functions of rank 2 were combined to give the more powerful minimum function of rank 4. This was such a good approximation to the electron density that the general nature of the structure could be deduced from it. The P atterson projections P ( xy ) and P ( yz ), and their solution by minimum functions (as well as other evidence) suggested that pectolite has a substructure, so that it became possible to apply substructure theory 2,3 . Accordingly, the partial P atterson projections ∂P ( xy ) and ∂P ( yz ) were computed and solved for the locations of the atoms of the complement structure. The three projections of pectolite were refined by successive Fourier syntheses and by difference maps. The structure of pectolite has already been described 1 . It is based upon single silica chains differing from the pyroxene-type chains. The Na atoms have an unorthodox environment, and show considerable anisotropic thermal motion. The hydrogen atoms bond together oxygen atoms of two different tetrahedra.

In continuation of a systematic study of compositions which may yield phases with structures analogous to those of SiO 2 the following compounds have been prepared, treated under a variety of ‘p’–‘t’ conditions and studied: FePO 4 , FeAsO 4 , MnPO 4 , BPO 4 , AlVO 4 . Quartz forms are obtained from FePO 4 , MnPO 4 and BPO 4 and cristobalite forms for BPO 4 and MnPO 4 . Phase diagrams for the systems FePO 4 and MnPO 4 are given. Powder and unit cell X-ray data are given on the phases studied. The ionic size limitation on the formation of silica structures is demonstrated empirically.

An attempt is made to obtain indications of the structure of the electron gas from a discussion of the crystal structures, and on the other hand, to understand better structural data from considerations of the correlations in the electron gas. The assumption of a lattice-like positional correlation of the electrons leads to energetically acceptable results, if participation of the outer kernal electrons of the T atom on the positional correlation is assumed. By means of a discussion of the 3-dimensional electron distribution, it is possible to explain why TB 2 compounds, with B -elements of the fifth and sixth columns prefer the types C2, C18, and C6, while on the other hand the TB 2 compounds with B elements of the third and fourth columns prefer the C1 und C16 type. The positional correlations mentioned are in agreement with the tables of the substances of each type. They lead to a better understanding of the energetic favorability of the structures. Since the possible positional correlations of the electrons are less numerous than the observed positional correlations of the atoms, the discussion given here is of interest and represents an addition to the structural considerations which are in use.

This paper is concerned with a description of the numerous structural types of cadmium iodide that have recently been discovered. Structural data are given for the ten polytypes designated as 2 H , 4 H , 6 H ( a ) , 6 H ( b ) , 8 H , 10 H , 12 H ( a ) , 12 H ( b ) , 12 H ( c ) and 14 H . Twenty-two other polytypes ranging from 16 H to 64 H are also reported, but their structures are still unknown. Nearly 50% of the 157 crystals studied have the 4 H structure, while the remaining ones have rare or disordered structures. A definite series of related cadmium iodide structures has been discovered. This structural series that has a R amsdell zigzag sequence represented by ‘22 … 11’ is discussed in some detail. The second part of this paper, which will appear in the future, will be concerned with an explanation of polytypism based upon the theory that the different structures result from the spiral growth of crystals as a result of screw dislocations.

The method of curves of equal blackness or intensity (“equidensometry”) is applied to D ebye -S cherrer diagrams. This leads to an important refinement of the interference picture, and accordingly to a considerable increase in the accuracy of the measurements.