Volume 119, Issue 1-2

The space group of imidazol has been redetermined as C 2 h 5 – P 2/ 1 / c . The convolution-molecule method in conjunction with the method of diffuse scattering was used for the determination of the orientation and the translation parameters of the molecules und a trial structure was derived. Symmetry relations among the convolution molecules and between convolution molecules and the space group were brought out and used in the course of parameter determination.

The semihydrates of pentamethylethylalcohol and of four other alcohols of similar, approximately spherical molecular structure have been investigated. The needle-shaped crystals have the orthorhombic space group C 2 v 21 – Iba 2 with eight alcohol and four water molecules per unit cell. The structure of the pentamethyl-ethylalcohol hydrate has been determined. Parallel to the needle direction infinite chains are formed by hydrogen bonds …O w = (O A ) 2 = O w = (O A ) 2 = O w …, the oxygen atoms O w of the water molecules being surrounded by four oxygen atoms O A of the alcohol molecules in a nearly tetrahedral position.

Fourier-transform theory applied to Patterson syntheses in which the coefficients are modulated by a known or assumed partial structure lead to criteria, based upon peak heights and upon geometrical positions, which allow electron-density extraction procedures in which incorrectly placed atoms can be identified. Modified Fourier syntheses are presented also for relative enhancement of the correct structure over the background, and for location of the third coordinates of atoms for which two coordinates are already known.

Single crystal droplets of Au, Cu, Ag, Pb, In, Cu 3 Au, and Ge have been grown in vacuum by two simple methods. In each case graphite crucibles were employed and served as a surface for point contact so that the droplets could solidify in the absence of a containment shell, free of mechanical and thermal stresses. The crystals approximate spheres ranging from 50 to 600 microns in diameter and are thus ideally suited for x-ray diffraction studies in transmission. Although the surface tension properties of the materials were important to the successful growth characteristics, it was also observed that exclusion of foreign nuclei and elimination of mechanical and thermal stresses were equally significant.

Structural work on mordenite suggested a possible structure for dachiardite a rare zeolite occurring on Elba, Italy. This trial structure has been confirmed and partially refined by two-dimensional Fourier syntheses.

The structural properties necessary for a crystal face to grow layer after layer are considered. The growth layer (slice) must have a minimum thickness d hkl and therefore the same composition as the crystal. The slice must contain periodic bond chains in at least two different directions. For ionic crystals the slice should not have a dipole moment perpendicular to its plane. It is found that sometimes a particular intermittent way of growth can occur when there are two or more equivalent periodic bond chains per primitive cell. The character of these faces is between flat and stepped. The structural properties of periodic bond chains are considered. These chains are determined by the intersection of two slices. This explains the unequal development of parts of one zone since, for different parts, the chains are not necessarily the same. The effect of pseudosymmetry on the character of a face is pointed out. Finally a practical method is given that allows one to derive from the structure all the faces that can grow layer after layer.

This paper describes a simple back-reflection x-ray camera for thermal studies from –180°C to 200°C. This is a modification of the Unicam singlecrystal goniometer S 25. The camera effectively eliminates any temperature gradient along the length of the specimen and the temperature can be maintained constant to ± 0.5°C. The deposition of ice on the specimen at low temperatures is also successfully prevented. Using this camera the lattice thermal expansion of melt-grown single crystals of NaCl was measured over the range –180° to 200°C. These results are in very good agreement with the macroscopic thermal expansion of the same batch of crystals made by Dr. R. Srinivasan , as also those obtained by other authors for this substance. This agreement suggests that if lattice defects are present in NaCl at room temperature they must be uniformly distributed throughout the volume of the crystal.

A series of rare-earth phosphates, arsenates, vanadates, tantalates and niobates have been reacted at pressures up to 80,000 atm. and temperatures up to 600°C. The structures of the high-pressure phases “quenched” to ambient conditions have been evaluated by x-ray powder diffractometry. The majority of the arsenates (Sm–Lu) and vanadates (Pr–Lu) undergo a reconstructive transformation from the xenotime- to the scheelite-type structure. The transformation from the monazite- to the scheelite-type structure was observed in PrAsO 4 and NdAsO 4 . The xenotime ⇌ monazite transition was not observed in any phase. Equilibrium p - t curves have been determined for several of these transitions and densities of the high- and low-pressure forms compared.

Rhodonite has space group P [unk] and unit-cell parameters a = 7.682 Å, b = 11.818 Å, c = 6.707 Å, α = 92.355°, β = 93.948°, and γ = 105.665°. A trial structure determined through application of the minimum function to the Patterson function, P ( xyz ), was improved and refined with Fourier syntheses and least squares. Planes containing octahedrally coordinated cations alternate with planes of tetrahedrally coordinated Si ions between planes of approximately close-packed oxygen ions. Tetrahedra are linked to form chains with a repeat unit of five tetrahedra. Octahedrally coordinated cations occupy five general equipoints, with Ca preferentially distributed in one position, and Mg and Fe in another. Octahedra share edges to form bands extending parallel to the silica chains and separated by a rift of unoccupied octahedrally coordinated sites.

Hodgkinsonite, Zn 2 Mn[(OH) 2 |SiO 4 ], is a pneumatolytie mineral of Franklin, New Jersey, with lattice constants: a = 8.171, b = 5.316, c = 11.761 Å, β = 95° 15′; Z = 4, space group P 2 1 / a . Intensities hkl were collected with a single-crystal equi-inclination diffractometer. The structure was obtained from the three-dimensional Patterson synthesis by applying the minimum function. Atomic parameters and isotropic temperature factors were refined by least squares to R = 0.067. Correction for anomalous scattering of the Mn atoms was applied. The SiO 4 tetrahedron is almost regular with an average Si–O distance of 1.626 Å and average O–O distance of 2.655 Å. The two Zn atoms are surrounded by four O atoms forming a distorted tetrahedron. Average Zn–O distances are 1.969 Å and 1.974 Å and O–O distances 3.211 Å and 3.216 Å respectively. The Mn atom is octahedrally coordinated by five OH groups and one O atom. The average Mn–O distance is 2.222 Å and the corresponding O–O distance is 3.133 Å. The ZnO 4 tetrahedra share a corner with the SiO 4 tetrahedra and form two-dimensional networks Zn 2 SiO 4 , ( A ), parallel to (001). Similarly the MnO 6 octahedra form two-dimensional networks, ( B ), extending parallel to (001), and link two Zr 2 SiO 4 networks together. The structural principle is ‥ ABAABA ‥ in the direction of the c axis. Hodgkinsonite is not isotypic with norbergite, Mg 3 [(OH) 2 |SiO 4 ], and does not belong to the humite group.

This paper demonstrates the use of the potential-energy function of G rüneisen to explain why the distances between nearest neighbors in face-centered cubic crystals are greater than those in body-centered crystals, and also why there are two distances for nearest neighbors in hexagonal close-packed structures. The results of sample calculations are in moderate agreement with available x-ray data.

Comparison of the results of Shubnikov and of Pabst showed that 10 duplications must be eliminated from the enumeration by the former. After this change and adjustment to a common point of view agreement of the results is found. The total count of Pabst 's point groups is corrected to 67.

The lattice constants and probable space groups of CaSeO 4 · 2H 2 O, CaSeO 4 · ½ H 2 O and CaSeO 4 were determined. CaSeO 4 · 2H 2 O and CaSeO 4 · ½ H 2 O are isomorphous with the corresponding sulphates, but CaSeO 4 , although orthorhombic, has not the space group of CaSO 4 . The linear coefficients of thermal expansion in the three axial directions were determined for CaSeO 4 .

Freudenbergite is shown to be monoclinic with unit-cell dimensions a = 12.305 Å, b = 3.822 Å, c = 6.500 Å, β = 107.30°, diffraction symbol 12/ m 1 C …, and unit-cell contents approximating to (Na,K) 2 (Ti,Nb) 6 (Fe III ,Si) 2 (O,OH) 18 . It exhibits slight structural resemblance to pseudobrookite. A 15 R -högbomite polytype is associated with freudenbergite at Katzenbuckel.