J.S. Kasper

Clathrate Structure of Silicon Na8Si46 and NaxSi136 (x < 11).

The crystal structure of two new cubic phases in the silicon-sodium system have been solved from their x-ray diffraction patterns. Both structures are of the clathrate type found for gas hydrates, consisting of tetrahedral networks which are combinations of pentagonal dodecahedra with 14-face polyhedra in one case and with 16-face polyhedra in the other case. There is strict correspondence between the silicon positions and the oxygen positions of the hydrate structures. For one compound, Na8Si46, the centers of all polyhedra are occupied by sodium atoms. For the other compound, there occurs only partial occupancy of the polyhedral cages.

Phases of Fourier coefficients directly from crystal diffraction data

It is shown that the application of Schwarzs and Cauchys Inequalities to the formulas for calculating Fa** from, respectively, the density of scattering matter and the atomic positions in a crystal leads to relations between the magnitudes of some Fa~,s and the signs or phases of others. These relations are in the form of inequalities, which vary with the symmetry of the crystal under consideration. A table of the simplest inequalities applicable to crystals possessing each of the simple symmetry elements is included. Examples of the inequalities arising from the presence of combinations of symmetry elements are presented.

A New Dense Form of Solid Germanium.

A new form of solid germanium, of greater density than ordinary cubic germanium, can be formed by compressing cubic germanium at pressures exceeding 120 kilobars and reducing the pressure back to that of the atmosphere. The crystal structure is tetragonal, with a equal to 5.93 angstroms and c, to 6.98; 12 atoms per unit cell; and theoretical density, 5.91 grams per cubic centimeter. Electrically it behaves like a semiconductor. At temperatures above 200�C it reverts rather rapidly to the cubic form.

Crystal structure of tetragonal boron related to α-AlB12

Abstract Single crystals of the so-called β-tetragonal (or tetragonal II or III) boron modification have been obtained from boron deposits prepared by hydrogen reduction of BBr3 on tantalum filaments at 1200°C. Chemical analysis of the samples shows that this phase can be regarded as a true modification of pure elemental boron in contrast to α-tetragonal phases which require small amounts of foreign atoms to stabilize their boron framework. The lattice parameters (a = 10.14(1)A; c = 14.17(1)A) were obtained and refined from single crystal data. The unit cell contains four chemical units, B21 · 2B12 · B2.5 resulting in dc = 2.34 g cm−3 (dm = 2.36(2) g cm−3). The systematic extinctions are compatible with space group P41 or P43. The structure was determined from 1009 independent reflexions using a model derived from the recently solved structure of α - AlB12 (a = 10.161A; c = 14.283A; space group P41212 or P43212). The final R value (unweighted data) is 9.6%. Basically, the structure of this tetragonal form of boron consists of the same three-dimensional boron skeleton, built upon simple and twinned icosahedra, as that of α-AlB12. However, the defective twinned icosahedral B19 units in α-AlB12 are now completed (B21 units) in the related tetragonal boron. A number of interstitial sites, located at positions different from those occupied by aluminum in α-AlB12, are totally or partially filled by boron atoms and very probably increase the stability of the boron framework.

Single-crystal studies of β-Ag2HgI4

The structure and transformation behavior of β-Ag2HgI4 have been investigated by X-ray diffraction methods using single crystals. It has been verified that a single crystal of the β-form, stable at room temperature, transforms to a single crystal of the α-phase, stable above 50°C. The reverse transformation, α → β, on the other hand, is found to result in a multidomain arrangement of the β-phase and not to yield a new cubic modification. The β-structure is tetragonal: a = 6.322 (2) A, c = 12.605 (15) A, with space group I4 and Z = 2. The chalcopyrite type of cation ordering, proposed by Hahn et al. (7), is confirmed. The iodine arrangement is considerably distorted from ideal cubic close packing with preservation of normal cation-iodine distances. No significant amount of disorder or occupancy of vacant sites has been found.

Single crystal structure study of α-Ag2HgI4: Evidence for anharmonic vibration

Abstract X-ray diffraction intensities have been measured for two single crystals of α-Ag 2 HgI 4 at 66°C using Mo Kα radiation monochromated by reflection from a 002 graphite face. It is found that improvement on the simple zincblende description could be made either by considering all ions to be displaced by about 0.25 A along tetrahedral directions or by applying existing anharmonic theory for thermal motions. Although all ions are on appropriate sites to contribute to anharmonic effects, only a single anharmonic parameter, representing a weighted difference of two individual parameters, could be evaluated. The anharmonic treatment gives substantially better agreement for critical reflections of the class h + k + l = 4 n ± 1.

The crystal structure of SiB6

Abstract The accurate and detailed structure of the compound SiB 6 has been determined by single-crystal X-ray diffraction. The final R value was 6.1% for 4225 reflections. The cell is orthorhombic with space group Pnnm and a = 14.397(7) A, b = 18.318(9) A, c = 9.911(7)A, and from the electron density appears to contain 43 silicon atoms and 238 boron atoms. The structure contains many features found in other structures of boron-rich phases, and obeys the crystal chemistry rules established for them. It contains interconnected icosahedra, icosihexahedra, as well as several isolated boron and silicon atoms. An unusual feature of this structure is the presence of icosihexahedra containing silicon atoms similar to those found previously in BeB 3 .The accurate and detailed structure of the compound SiB/sub 6/ has been determined by single-crystal X-ray diffraction. The final R value was 6.1% for 4225 reflections. The cell is orthorhombic with space group Pnnm and a = 14.397(7) A, b = 18.318(9) A, c = 9.911(7) A, and from the electron density appears to contain 43 silicon atoms and 238 boron atoms. The structure contains many features found in other structures of boron-rich phases, and obeys the crystal chemistry rules established for them. It contains interconnected icosahedra, icosihexahedra, as well as several isolated boron and silicon atoms. An unusual feature of this structure is the presence of icosihexahedra containing silicon atoms similar to those found previously in BeB/sub 3/.

X-ray study of transition-metal dopants in β-boron☆

Abstract The atomic locations and concentrations of various transition element dopants in single crystals of β-boron have been studied by X-ray methods. The elements include Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zr, Nb, Hf, and Ta. These dopants do not enter normal boron positions in the framework at the concentrations studied; rather they occupy previously identified A1, A2, D, or E sites. The percentage occupancies of the several sites are correlated with the atomic sizes of the dopant atoms and their concentrations. Some differences between samples are related to their thermal histories. A number of competing interactions between six different, partially occupied boron sites and the dopant sites have been found. The doping mechanism is “displacive” rather than interstitial or substitutional.

The crystal structure of the ф phase in the boron-sodium system

Abstract The crystal structure of a complex boride, NaB 15 , has been determined by X-ray diffraction methods using single crystals. The structure consists principally of B 12 icosahedra arranged in a novel way but with additional boron atoms linking icosahedra together. The sodium atoms occur in large cages that result from the boron arrangement.

The electrical conductivity of single crystals of Ag2HgI4

Abstract Electrical conductivity measurements are reported for single crystal samples of Ag 2 HgI 4 in the temperature range between −17°C and 72°C. The results are interpreted in terms of two distinct regions of linear log conductivity versus reciprocal temperature behavior for β-Ag 2 HgI 4 , a phase transition region, and an α-Ag 2 HgI 4 region. The data reaffirm the anomalously high pre-exponential and activation energy terms in the conductivity equation for α-Ag 2 HgI 4 as compared with other AgI-type conductors. Thermo-emf measurements on polycrystalline Ag 2 HgI 4 samples are also reported.