Molecular model for U centres in caesium iodide

A molecular model has been developed to study the vibrations of U centres in caesium iodide. Employing the rigid ion model with nearest-neighbour short-range forces, the dynamical matrix of order 27 × 27 was solved to obtain the frequencies of the localized modes and the perturbed lattice modes. The results are compared with those obtained from the Green function method.

On cluster approximations of cellular automata

In this thesis I examine one commonly used class of methods for the analytic approximation of cellular automata, the so-called local cluster approximations. This class subsumes the well known mean-field and pair approximations, as well as higher order generalizations of these. While a straightforward method known as Bayesian extension exists for constructing cluster approximations of arbitrary order on one-dimensional lattices (and certain other cases), for higher-dimensional systems the construction of approximations beyond the pair level becomes more complicated due to the presence of loops. In this thesis I describe the one-dimensional construction as well as a number of approximations suggested for higher-dimensional lattices, comparing them against a number of consistency criteria that such approximations could be expected to satisfy. I also outline a general variational principle for constructing consistent cluster approximations of arbitrary order with minimal bias, and show that the one-dimensional construction indeed satisfies this principle. Finally, I apply this variational principle to derive a novel consistent expression for symmetric three cell cluster frequencies as estimated from pair frequencies, and use this expression to construct a quantitatively improved pair approximation of the well-known lattice contact process on a hexagonal lattice.

Molecular model for localised modes in zincblende structures

A molecular model for substitutional defects in a zincblende lattice has been worked out. The infrared absorption due to A1 in InSb and Li in GaAs are interpreted on the basis of this model.

Raman and infra-red spectra of crystalline ammonium sulphamate

Raman spectrum of a single crystal of ammonium sulphamate has been recorded for the two different orientations using λ 2537 resonance radiation of the mercury as the exciter. Thirty-four Raman lines have been observed of which eight belong to the lattice oscillations. Weak hydrogen bonding of NH2 group in the crystal was predicted. The infra-red absorption spectrum of the substance was taken in the powder form in potassium bromide disc, using Carl Zeiss UR10 IR spectrometer. Thirty-five absorption maxima could be identified.

Raman and infra-red spectra of crystalline potassium sulphamate

Raman spectrum of a single crystal of potassium sulphamate has been recorded for the first time using λ 2536 radiation of mercury as the exciter. Thirty-three Raman lines have been observed of which nine belong to the lattice oscillations. The infra-red absorption spectrum of the substance was taken in the powder form in potassium bromide disc using Carl Zeiss UR 10 IR spectrometer. Thirty-six absorption maxima could be identified of which twenty-five have been recorded for the first time. The analysis clearly shows that the N-H bond in the crystalline potassium sulphamate is not hydrogen-bonded to any appreciable extent.

Raman spectra of alkali halides

In this article, we present a comparative study of the Raman spectra of alkali halides in relation to the lattice dynamics ofBorn andRaman. It is shown that the experimentally observed limit of the second-order spectra in almost all the cases can be explained well by the Lyddane-Sachs-Teller relation. It is also seen, while, an explanation of the second-order Raman spectrum of a crystal of diamond or zinc blende structure requires the frequencies from the critical points,W, Gamma, X andL inBorn's analysis, the frequencies fromGamma, X andL alone are sufficient and necessary for an interpretation of the same onRaman's model. Some similarities in the determination of the long wave properties of crystals like elastic constants and limiting frequencies of the lattice vibrations in the symmetry directions in both the models are pointed out.

Raman spectrum of crystalline aminosulphonic acid

The Raman spectrum of a single crystal of sulphamic acid has been recorded withλ 2537 excitation. Thirty-eight lines have been observed, of which twenty-nine have been recorded for the first time. Seven Raman lines with shifts in the region 50–155 cm.−1 have been assigned to the lattice oscillations, two at 177 and 240 cm.−1 have been attributed to the low-frequency hydrogen bond vibrations.. The splitting of the degenerate modes and the appearance of N-H....O bonded stretching vibrations are consistent with the structural data which expect the presence of the free molecule as a Zwitter ion with only slight distortion from C3v symmetry.

Raman spectrum of crystalline cadmium acetate dihydrate

The Raman spectrum of a single crystal of cadmium acetate dihydrate has been recorded for the first time using λ 2537 excitation. Twenty-three lines have been observed out of which ten have been attributed to the internal oscillations of the acetate ion, nine to the lattice modes, two to low-frequency hydrogen bond vibrations. A line at 308 cm.−1 and the continuum 3250–3560 cm.−1 have been assigned to the Cd-O6 and internal vibrations of the water molecules.

Raman spectra of ferro-electric crystals Part IV. Lithium hydrazinium sulphate (LiN2H5SO4)

The Raman spectrum of lithium hydrazinium sulphate has been recorded both in the single crystal form and in aqueous solutions. The crystal exhibits thirty-eight Raman lines having the frequency shifts 52, 70, 104, 146, 174, 220, 260, 302, 350, 454, 470, 610, 630, 715, 977, 1094, 1115, 1132, 1177, 1191, 1260, 1444, 1493, 1577, 1630, 1670, 2205, 2484, 2553, 2655, 2734, 2848, 2894, 2939, 3028, 3132, 3290 and 3330 cm.−1 The aqueous solution gave rise to six Raman lines at 452, 980, 1050–1200, 1260, 1425 and 1570 cm.−1 apart from a maximum at 180 cm.−1 in the ‘wing’ accompanying the Rayleigh line. The observed Raman lines have been assigned as arising from the vibrations of the SO4 ion, N2H5+ ion, Li-O4 group, hydrogen bond and the lattice. The influence of the hydrogen bond on the N-H stretching vibrations has been pointed out. The various features of the observed spectrum strongly support the hypothesis that the NH3 group in the crystal is rotating around the N-N axis at room temperature.

Studies on oxovanadium (IV) oxalate hydrates

The oxalato complexes, VOC2O4·2H2O and VOC2O4·4H2O, are described. Their magnetic moments correspond to one unpaired electron showing the tetravalency of vanadium. They are monomeric in aqueous solution. Thermal studies suggest VO2 formation when the compounds are decomposed. Infrared spectra reveal covalent bonding between the vanadium and the oxalate group and the coordinated water. The tetrahydrate has also some lattice held water. The weak band at 780 mμ and a shoulder at 600 mμ are due to d ↔ d transitions and the absorption in the ultra violet is due to charge transfer within the VO2+ group. The dihydrate is assigned a stable five co-ordinated pyramidal structure; while the tetrahydrate, a distorted octahedron with one water molecule loosely bound along the V---O axis and the other outside the co-ordination sphere.

Dimethyl sulphoxide complexes of titanyl, zirconyl and thorium perchlorates

TiO·5DMSO(ClO4)2, ZrO·8DMSO(ClO4)2 and Th·12DMSO(ClO4)4 are prepared by reaction of the respective metal perchlorates with an excess of dimethyl sulphoxide. The last two complexes yield ZrO·6DMSO(ClO4)2 and Th·6DMSO(ClO4)4 on heating around 185°C, while the titanyl complex explodes at 190°C. The extra DMSO molecules in the zirconyl and thorium complexes seem to be held in the lattice. In the parent complexes, the co-ordinated DMSO molecules are bonded by oxygen to the metal atoms while in the DMSO complexes of zirconyl and thorium perchlorates, obtained by heating at 185°C, the bonding involves the sulphur, indicating a change in the bonding during the process of heating.

Raman spectrum of diglycine barium chloride monohydrate

The Raman spectrum of diglycine barium chloride monohydrate in the single crystal form has been recorded using λ 2536·5 excitation. 43 Raman lines (9 lattice and 34 internal) have been recorded. Satisfactory assignments have been given for most of the observed Raman lines. It is concluded from a comparison of the Raman spectrum of this compound with those of glycine and of other addition compounds of glycine, that the glycine unit exists in the zwitterion form in the structure of diglycine barium chloride monohydrate.

Raman spectrum of triglycine selenate (G3Se), [(NH2CH2COOH)3 H2SeO4]

The Raman spectrum of a single crystal of triglycine selenate G3Se which is ferroelectric below 22° C. has been photographed using λ 2537 excitation. 42 Raman lines have been recorded of which 6 belong to the lattice spectrum, 3 are due to NH...O oscillations and the remaining 33 are due to internal oscillations of the ions of glycine and SeO4--. There is a close similarity between the spectrum of triglycine selenate and the spectrum of its isomorph, triglycine sulphate, the frequency shifts due to the SO4-- ion being replaced by the frequency shifts due to the SeO4-- ion. The existence of glycine in the zwitterion form in the structure of G3Se is substantiated by the appearance in the Raman spectrum of lines which are attributable to NH3+ groups and COO- groups. The appearance of the additional C-H line at 2982 cm.-1 in the spectrum of triglycine selenate which is absent in the spectrum of α-glycine indicates the existence of planar monoprotonated glycine also in the structure, as indicated by X-ray studies.

Raman spectrum of lanthanum ethyl sulphate nonahydrate

Raman spectrum of a single crystal of lanthanum ethyl sulphate has been recorded for the first time using the λ 2537 radiation Forty-one lines have been identified out of which eight belong to the lattice oscillations, seven to the internal vibrations of the water molecule and the remaining twenty-six to the internal vibrations of the ethyl sulphate group. The Raman spectrum of ethyl sulphate (liquid) has also been recorded using the λ 4358 excitation and is compared with the spectrum of lanthanum ethyl sulphate. Thirty Raman lines could be identified in the spectrum of ethyl sulphate, of which fourteen are recorded for the first time. Probable assignments of the observed frequencies are also given. The sulphate group is found to have O-SO3 structure in lanthanum ethyl sulphate, while it has a co-ordination {Mathematical expression} in ethyl sulphate.

The Raman spectrum of boric acid

The Raman spectrum of crystalline boric acid is recorded using mercuryλ2537 excitation. Fifteen Raman lines, three of them belonging to the lattice spectrum, are reported. Satisfactory assignments of all the observed Raman frequencies are made using the available X-ray crystal structure data. From the presence of a new high frequency Raman band at about 3420 cm.−1 it is suggested that there might be a small number of long, weak O-H....O hydrogen bonds in the crystal, in addition to the hydrogen bonds of moderate strength reported from X-ray diffraction data.