S. Ramaseshan

Isomorphous replacement and anomalous scattering

When two or more crystals have the same structure except for the replacement or addition of one or a few (usually heavy) atoms, phase determination using isomorphous replacement can be resorted to. In most practical instances, the atomic form factor is a real number. When the absorption edge of an atom is close to the wavelength of the incident radiation, the form factor becomes complex and the atom becomes an anomalous scatterer. Anomalous scattering can be used for phase determination and also for determining the absolute configuration. The effects of isomorphous replacement and anomalous scattering are often complementary. Although they have been in use from the 1930s, the most useful applications of the two approaches have been in macromolecular crystallography from the 1950s. Robust methods have been developed for their use in the determination and refinement of heavy-atom positions in protein heavy-atom derivatives and in the calculation of phase angles. With the advent of tunable synchrotron radiation, methods based only on anomalous scattering have become prominent. This chapter describes the development in the area up to the mid-1980s. The subsequent developments in isomorphous replacement and anomalous scattering have been almost exclusively concerned with macromolecular crystallography. They are discussed in International Tables for Crystallography Volume F .

Magneto-Optic Rotation in Birefringent Media—Application of the Poincaré Sphere

It is pointed out that the concept of the Poincare sphere appreciably simplifies the mathematical treatment of phenomena accompanying the passage of polarized light through a medium which exhibits birefringence, optical activity or both simultaneously. This is exemplified by using the Poincare sphere to evolve techniques which could be used for determining the true Faraday rotation in the presence of birefringence. When birefringence is present, measurements made with the half-shade at the polarizer and analyzer ends are not equivalent. In either arrangement, the errors introduced as a result of birefringence are largely reduced by taking the mean of two measurements for opposite directions of the field. Formulae are also derived by which the magnitudes of the error can be calculated for the particular experimental set up, knowing the value of the birefringence. In certain cases, even this need not be known, and the true rotation can be determined purely from measurements of the apparent rotations for two different azimuths of the incident plane of polarization.

A new approach to repulsion in ionic crystals

Abstract An empirical approach is attempted to make the repulsion potential of ions in an ionic crystal structure independent and crystal independent so that once the repulsion parameters for an ion are evaluated in one compound, in one structure, they could be used for that ion in any crystal. The repulsion between ions is postulated to be due to the increase in the internal energy of the ions arising from the distortion and the compression at the points of contact with their neighbours. Using an exponential form for the compression energy involving two parameters per ion, a repulsion potential for ionic crystals is proposed which includes the repulsion between nearest and next nearest neighbours. The repulsion parameters for the alkali and halogen ions have been determined to fit the behaviour of 20 alkali halides over the pressure range 0–45 kbars. The r.m.s. percentage deviations from experiment, of the calculated values of lattice spacing and compressibility are respectively 0.997% and 6.76%. The calculated radii of the ions in the various compounds compare well with the experimental values deduced from electron density maps. The advantages of the present form of the repulsion potential over earlier forms are discussed.

Repulsion parameters of ions and radicals-application to perovskite structures

Abstract The compressible ion approach to repulsion which has been shown to work well for the alkali halides ( J. Phys. Chem. Solids 37 , 395 (1976) ; Curr. Sci. 46 , 359 (1977)) has been extended to other cubic ionic crystals. Repulsion parameters have been refined for a number of ions and radicals viz., Cu + , Ag + , Tl + , Mg 2+ , Ca 2+ , Sr 2+ , Ba 2+ , Zn 2+ , Cd 2+ , Hg 2+ , Mn 2+ , Fe 2+ , Co 2+ , Ni 2+ , Sm 2+ , Eu 2+ , Yb 2+ , Pb 2+ , H − , O 2− , S 2− , Se 2− , Te 2− , NH 4 + , SH − , SeH − , BrO 3 − , ClO 3 − , ClO 4 − , CN − , NH 2 − , NO 3 − , BH 4 − , BF 4 − , SO 4 2− , NH 2− . Using these parameters, calculations have been made on the lattice spacings and compressibilities of a number of perovskite-like crystals of the form A + B 2+ C 3 − . The predicted values agree well with experiment. In the case of four crystals viz., LiBaF 3 , LiBaH 3 , LiEuH 3 and LiSrH 3 , there were large discrepancies between the calculated and observed lattice spacings. When these crystals were assumed to be of the inverse perovskite structure, calculations showed good agreement with the experimental data.

Partial structure factors in a liquid or amorphous binary system using anomalous scattering

A method based on the anomalous scattering of either x rays or neutrons has been suggested to separate the partial structure factors in a liquid or amorphous binary system.

Optical properties of mixtures of right- and left-handed cholesteric liquid crystals

A rigorous theory is developed of the optical properties of a mixture of right-handed and left-handed cholesteric liquid crystals, taking into account the effect of absorption. The dependence of the rotatory power and circular dichroism on pitch and on sample thickness is discussed.

Anomalous temperature dependence of the thermo-power in the high pressure phase of cerium

Abstract The thermo-electric behaviour of Cerium in the region lying below and above the critical point for the ψ-α transition is reported. The anomalous temperature dependence and the continous decrease of the thermo-electric power with pressure in the α phase are correlated with the models developed by Blandin et al. and Hirst.

Phase transitions in ytterbium under pressure (semimetal-semiconductor transition)

The semimetal-semiconductor transition in ytterbium has been studied in the pressure range 0.50 kbar and up to 600 degrees C using the Seebeck coefficient as a tool. In the FCC phase the thermoelectric power exhibits a marked increase with pressure and the semimetal-semiconductor transition is observed as a change in the slope. In the semiconducting phase the thermopower initially increases very rapidly with pressure followed by a steep decrease at higher pressures. The temperature coefficient of thermopower in the semiconducting phase increase is large and positive in contrast to the semimetallic phase. The FCC-HCP transformation at high temperatures is reported. A semimetal-semiconductor transition in the HCP phase has also been observed. The experimental results are discussed qualitatively on the basis of a simplified two-band model.

Thermoelectric power of cerium at high pressures

The electronic phase transition in cerium occurring near 7 kbar pressure at room temperature which is attributed to the 4f–5d electron promotion has been studied using thermoelectric power as a tool. The important results that have emerged out of this work are: (a) the relatively large variation in the absolute thermoelectric power ofγ-cerium (normal fcc phase) with pressure prior to the phase transition (in contrast to the rather small resistivity change with pressure in this region); (b) a sharp decrease in the thermoelectric power accompanying the iso-structuralγ-α phase transition; and (c) the continuous decrease in the thermoelectric power ofα-cerium (collapsed fcc phase) with pressure, ultimately changing sign at higher pressures. An explanation based on the “virtual bound state” model is proposed to account for these results.

Piezo-Rotatory Coefficients and Crystal Symmetry

A first-order phenomenological theory of the effect of stress on the optical rotatory power of crystals has been worked out. This paper reports the forms of the matrices of the piezo-rotation tensor in different crystal classes. Two very interesting results have emerged. The first is that the piezo-rotation tensor is an axial tensor of fourth rank. The second is that stress should induce optical activity in certain non-optically active crystals.