William R. Busing

ANGLE CALCULATIONS FOR 3- AND 4-CIRCLE X-RAY AND NEUTRON DIFFRACTOMETERS.

Methods are derived for calculations useful in the operation of 3and 4-circle X-ray or neutron singlecrystal diffractometers. These include: (1) establishing the sample orientation from the cell parameters and the observed angles for two reflections, or from the observed angles for three reflections only, (2) calculating the angles for observing a given reflection either in a special setting or at a specified azimuthal angle, (3) obtaining the vectors needed for calculating absorption corrections, and (4) u sing observations of several reflections to refine cell and orientation parameters by the method of le ast squares.

NEUTRON DIFFRACTION STUDY OF CALCIUM HYDROXIDE

Single crystal neutron diffraction measurements on Ca(OH)2 at 20°C and —140°C confirm the x‐ray structure and the hydrogen positions previously postulated. Refinement of the neutron data by Fourier and least squares procedures yields a detailed description of the thermal motions. The amplitudes of the motion of the hydrogen atoms are compared with those deduced from infrared and Raman studies. The O–H distance, after allowance for asymmetric thermal motion, is 0.984 A.

Crystal and molecular structure of hydrogen peroxide

The coordinates and thermal parameters of the O and H atoms in solid H2O2 have been determined by a single‐crystal neutron‐diffraction study. Final values were obtained by least‐squares refinement based on 91 observed intensities of the hk0, hhl, and h0l reflections. The molecular parameters (uncorrected for the effect of thermal motion) are as follows: O–O distance, 1.453±0.007 A; O–H distance, 0.988±0.005 A; O–O–H angle, 102.7±0.3°; dihedral angle between the two O–O–H planes, 90.2±0.6°. Hydrogen bonding occurs with an O–H···O distance of 2.799±0.008 A. The O–H bond distance corrected for thermal motion is 1.008±0.005 A.Comparison of these results with those reported by others from studies of H2O2 vapor and of various crystals containing H2O2 indicates that the dihedral angle is quite sensitive to the environment of the molecule.

. A neutron- diffraction study

A computational model of a crystal consists of a description of the structure, a potential function for calculating its energy, and a way of adjusting the structure to minimize the calculated energy. External forces such as hydrostatic pressure or normal and shearing stresses can be simulated, and elastic constants can be calculated. A realistic model should reproduce both the experimental structure and the observed elastic properties.Such a model has been developed for α Mg2SiO4, the olivine orthosilicate known as forsterite. Coulomb energy is calculated for a structure consisting of Mg2+ ions and rigid SiO44−groups with partial charges on Si and O atoms. Both r−n and exponential expressions were tried for the repulsion energy, and the latter expression yields the best results. This model reproduces reasonably well the experimental structure, the observed elastic constants, and their pressure derivatives. The same model successfully describes γ Mg2SiO4, the cubic spinel polymorph related to ring-woodite. Comparison is made with similar calculations by other authors.

Computational modeling of the structure and elastic constants of the olivine and spinel forms of Mg2SiO4

The results of an infrared study of Ca(OH)/sub 2/ single crystals at room temperature and at liquid nitrogen temperature are reported. (J.E.D.)

Infrared Spectrum of Ca(OH)2

An intermolecular potential function model based on atom‐atom interactions was developed for crystalline hexachlorobenzene. The potential was constructed from terms including Coulomb interaction, van der Waals attraction, and exponential repulsion. Potential energy parameters were varied to obtain the best agreement between observed and calculated lattice energy, lattice parameters, molecular orientation, and optically active external mode frequencies. The results are compared with two other recently proposed potential function models for hexachlorobenzene.

Intermolecular potential function model for crystalline hexachlorobenzene

In the least squares method for simultaneous adjustment of several parameters, the coefficients of the normal equations are the elements of a symmetric positive-definite matrix. In order to solve the normal equations and evaluate the precision measures of the resulting parameters, inversion of this matrix of coefficients is required. Many available procedures for matrix inversion do not take advantage of the symmetry. Thus, when programmed for a high-speed computer, all <italic>n</italic><supscrpt>2</supscrpt> elements must be stored and manipulated, whereas only <italic>n</italic>(<italic>n</italic> + 1)/2 of them are independent. In order to allow a computer of given memory capacity to handle a large matrix, the following procedure for inverting a symmetric matrix has been devised.<supscrpt>1</supscrpt> <abstract>