Band 122, Heft 1-2

The crystal structure of bis -cyclo-octadien-nickel, Ni(C 8 H 12 ) 2 , has been determined from x-ray diffraction data. The space group is P [unk]– C i 1 and the unit cell, with a = 10.84, b = 9.12, c = 7.38 Å, α = 109.95°, β = 84.72°, γ = 108.13°, contains two molecules, each of which has the symmetry 222. The four C–C double bonds of each molecule are elongated by 0.05 Å compared to normal double bonds and form a quasi-tetrahedral arrangement around the nickel atom with the distances Ni–C all equal to 2.12 Å.

A direct procedure, designed for application in high-speed computation, is described for the determination of x-ray absorption corrections in the equi-inclination Weissenberg, Eulerian orienter, and precession geometries. Crystal shapes with re-entrant angles may be treated. The main restriction on the specimen shape is that it be representable by a combination of functions which may be expressed analytically. The crystal volume is subdivided into volume elements which are represented by a collection of grid points. The grid points are established as submultiples of the maximum dimensions of the crystal and are tested to reject those which lie outside the crystal volume. Only half of the grid points which are contained within the crystal need be considered explicitly when the crystal has a centrosymmetric shape. Unit vectors are established, relative to the crystal, in the directions of both the incident and diffracted beams for each reflection. These vectors are expressed in terms of reciprocal-cell dimensions in a form which may be evaluated by a computer. Distances from each grid point to the surface of the crystal are determined as multiples of these vectors and are summed to evaluate the transmission factor. If the crystal has re-entrant angles, the path lengths are tested to take account of portions of the beam paths which lie outside the crystal. Application of the procedure in a program written in FORTRAN and the speed and accuracy of the program will be evaluated in a later paper.

The crystal structure of bis -methallylnickel has been determined from three-dimensional x-ray diffraction data. The space group is P 2 1 / c − C 2 h 5 , with a = 6.05; b = 13,48; c = 5.83 Å; β = 117.1°. The unit cell contains 2 molecules with Ni in centres of symmetry. The methallyl groups are symmetrically bonded to the nickel in an anti-sandwich arrangement. This causes the intramolecular symmetry to be 2/ m . The methallyl groups are found to be nonplanar and the Ni–C bonds are quite short (average 2.02 Å).

A technique is described using unscreened Weissenberg photographs to determine the absolute orientation of a crystal relative to the axis of the goniometer head on which it is mounted. The photographs are interpreted by means of specially constructed charts; both the derivation of the charts and their application are discussed. The deduced orientation of the crystal is represented in stereographic projection, thus permitting immediate determination of the angular corrections which must be made on the goniometer arcs to bring any desired crystallographic direction into coincidence with the goniometer axis. The orienting technique is applicable only when indexed Weissenberg diffraction photographs of the particular material are available; it is therefore especially useful where several specimens of the same or similar material are being investigated.

The structure of an intermediate orthopyroxene, Mg 0.93 Fe 1.07 Si 2 O 6 with cell dimensions a = 18.310, b = 8.927, c = 5.226 Å; space group: Pbca , derived from a high-grade metamorphic rock, has been refined by the method of least squares using three-dimensional intensity data. The R factor for 1028 reflections is 0.118. The average standard deviation of M–O, as well as Si–O bond lengths is 0.014 Å. Mg 2+ and Fe 2+ are virtually completely ordered, the ordering scheme being the same as that proposed by G hose (1962). The M 1 site, corresponding to the Mg site in diopside, CaMgSi 2 O 6 , contains 85% Mg 2+ and 15% Fe 2+ and the M 2 site, corresponding to the Ca site in diopside, contains 90% Fe 2+ and 10% Mg 2+ . M 2 –O 2 (2.07 Å) and M 2 –O 5 (2.04 Å) bonds are significantly shorter than the sum of P auling 's crystal radii (2.16 Å) and have considerable covalent character. The two crystallographically distinct silicate chains have slightly different configurations, caused by slight rotations of Si 1 and Si 2 tetrahedra, with Si 1 –O 1 and Si 2 –O 4 as axes. The average Si–O bond length is 1.63 Å. The non-bridging Si–O bonds (1.60 Å) are significantly shorter than the bridging Si–O bonds (1.66 Å).

On the basis of the newly acquired knowledge of the crystal structure of the trioctahedral micas a new theoretical curve is proposed which permits the x-ray determination of octahedral Mg and Fe content in biotites from the relative intensities of the 004, 005, 006 reflections. It is believed that the error in this x-ray determination is not greater than ± 0.5 atoms of Mg or Fe for six octahedral sites.

The aluminum-boron phase described recently as beta AlB 12 is shown to consist of two crystallographically related, intergrown phases with the bulk stoichiometry of C 2 Al 3 B 48 . One phase ( A ) is orthorhombic with a = 12.34 Å, b = 12.63 Å and c = 5.08 Å and space group Cmma or C 2 ma . The other phase ( B ) is also orthorhombic with a = 6.17 Å, b = 12.63 Å and c = 10.16 Å and space group Ammm , A 222 or A 2 mm . Twinning is always present and occurs across the (110) and (1[unk]0) faces. Occasionally an unusual type of twinning appears in which the a and b axes of both phases are parallel. This is interpreted as evidence of a disproportionation from a single high-temperature phase. This has been verified experimentally. The high-temperature phase ( C ) is tetragonal with a = 8.82 Å, c = 5.09 Å and space group P 4/ nmm , P 4/ n or P 4 2 / n . The transformation, which is reversible, is gradual and complete at about 850°C.

This study is concerned with the establishment of structural properties common to all borides and modifications of boron which contain B 12 polyhedral units. It has been found that all unit-cell dimensions in these structures can be derived from simple arrangements of B 12 units which can be regarded as large metallic atoms that form interstitial compounds. The B 12 units can also group together to form larger units such as the recently reported B 84 . These are also treated as individual entities. On this basis all the structures have been classified into three simple packing models: 1. cubic closest packing, 2. hexagonal closest packing, and 3. tetragonal close packing. Occurrence of tetragonal close packing with 10 closest neighbors is unusual and is discussed in detail. The proposed simple models and their subclassifications lead to a successful interpretation of observed data and should provide a basis for prediction of possible structures of the B 12 borides.

The approximate crystal structures of ammonium and rubidium imidodisulphates or iminodisulphonates, NH(SO 3 NH 4 ) 2 and NH(SO 3 Rb) 2 , have been investigated by x-rays. Both crystals are monoclinic and have structures related to the previously determined structure of potassium imidodisulphate but they are not isomorphous. Refinement by the method of least squares in terms of the simplified structure, with partial three-dimensional data collected from the ammonium salt at room temperature, gave a discrepancy index of 0.29 over 292 reflections. Although deviations from the full symmetry prevented the accurate determination of bond lengths, the approximate values derived of 1.74 ± 0.04 Å for S–N and 1.48 ± 0.03 Å for mean S–O are comparable with the lengths found in the potassium salt. For rubidium imidodisulphate, least-squares refinement was unsatisfactory, and it is concluded that the deviations of the true structure from that assumed in the pseudocell are greater. Room-temperature infrared spectra of ammonium, potassium, and rubidium imidodi-sulphates are closely similar, and the nuclear magnetic-resonance line widths of the ammonium and rubidium salts do not broaden significantly when the temperature is lowered from 280 to 80°K.

A new boron-silicon phase that is isotypic with β boron has been prepared. The data indicate a composition of B 14 Si. This new phase and a previously reported aluminum-boron phase are interpreted as interstitial derivatives of β boron.

Reflection properties of the mica-cleavage plane (001) for x-rays were investigated up to the 20th order with the aid of an x-ray spectrometer and by the rotating-crystal method. They were compared with calculated structure amplitudes. The results of the different procedures were in good agreement. Intense spectra can be obtained especially in the 3rd and 5th, and still in the 4th, 8th, and 11th orders of reflection.

Morphology and x-ray study of hexaantipyrine perchlorate complexes of Mg ++ , Ca ++ and Zn ++ show that they are isomorphous, crystallizing in the space group P [unk] with one molecule in the unit cell. A similar study shows that copper pentaantipyrine perchlorate crystallizes with a tetramolecular unit cell, space group P 2 1 / a . The cell dimensions are: Mg(C 11 H 12 ON 2 ) 6 (ClO 4 ) 2 : a = 14.06, c = 9.76 Å Ca(C 11 H 12 ON 2 ) 6 (ClO 4 ) 2 : a = 14.33, c = 9.78 Å Zn(C 11 H 12 ON 2 ) 6 (ClO 4 ) 2 : a = 14.14, c = 9.61 Å Cu(C 11 H 12 ON 2 ) 5 (ClO 4 ) 2 : a = 19.52, b = 16.27, c = 18.99 Å, β = 102°36′

From single crystals of Hg 2 (CH 3 COO) 2 a monoclinic unit-cell with a = 5.18 4 , b = 5.96 2 , c = 12.16 7 Å, β = 100.05° was established which contains two formula units. The probable space groups are C 2 h 3 − C 2/ m , C s 3 − Cm or C 2 3 − C 2.