• D Krishnamurti

Articles written in Proceedings – Section A

• Evaluation of the elastic constants of diamond from its Raman frequencies

Expressions for the elastic constants of diamond have been derived in terms of the force constants calculated by Ramanathan which express the interaction of any atom with its 28 neighbours. The calculated values are: C11=9·6×1012; C12=3·9×1012; C44=4·2×1012 dynes/cm.2 while the values experimentally determined by Bhagavantam and Bhimasenachar are:$$C_{11} = 9 \cdot 5 \times 10^{12} ; C_{12} = 3 \cdot 9 \times 10^{12} ; C_{44} = 4 \cdot 3 \times 10^{12} dynes/cm.^2$$

• Evaluation of the specific heat of diamond from its Raman frequencies

The specific heat of diamond is evaluated from the knowledge of its vibration spectrum obtained principally from Raman effect studies. The vibration spectrum is known to consist of eight discrete monochromatic frequencies followed by a continuous spectrum of elastic vibrations. Accordingly, the specific heat is expressed as the sum of eight Einstein functions, supplemented by three Debye functions representing respectively the three types of elastic vibration possible in the crystal. A close agreement is found between the calculated and the experimental values over the entire range of temperatures between 70° K and 1100° K, which is all the more significant in view of the calculations being completely independent of the specific heat data themselves.

• On the iridescence of potassium chlorate crystals - Part I. Its spectral characters

Spectrograms obtained with five iridescent crystals of potassium chlorate at varying azimuths and obliquities of incidence have been obtained and are reproduced with the paper. Some of the results observed are explicable in terms of the general theory of the optical behaviour of a regularly stratified medium,viz., (a) the appearance of a whole series of subsidiary bands accompanying the principal maxima and distributed asymmetrically about them and (b) the variation of the spectral width of the principal maximum with change of azimuthal angle and obliquity of incidence. Other striking effects are however also observed which are not so explicable,viz., when the azimuthal angle is nearly zero, the principal band splits into a doublet the components of which drift apart progressively and also shift towards shorter wavelengths with increasing obliquity of incidence. When the azimuthal angle is 90° the crystals exhibit the principal maximum as a triplet, the central component of which has a width of the same order of magnitude as the separation of the doublet in the preceding case, while its outer components are much further apart.

• On the iridescence of potassium chlorate crystals - Part II. Polarisation effects

A simple explanation is given why the reflections vanish when the light is incident in the symmetry plane of the twinned crystals. Physical considerations enable the law of polarisation for twin-plane reflections to be derived for directions of incidence adjoining the plane of symmetry. It is further shown that the spectral character of the reflections stands in the closest relationship with the polarisation law thus derived. An explanation is given for the appearance of doublets and triplets respectively in the spectra observed when the incidence is oblique and the azimuth of such incidence is nearly zero and 90° respectively. It is a necessary consequence of the theory that the outer components in these two cases should be plane-polarised, in one case in the reciprocal fashion and in the other case normally. The theoretical results are strikingly confirmed by observations on the polarisation of the spectral components. Photographs are reproduced illustrating these effects.

• On the iridescence of potassium chlorate crystals - Part III. Some general observations

The paper describes the results of a study of an extensive collection of material. The spacing of the stratifications giving rise to monochromatic reflections has been found to range from 2·7µ to 0·14µ. The monochromatism becomes sensibly more perfect in the reflections of higher orders. Variations in intensity from order to order are also noticeable and these are ascribed to the alternate lamellæ in the twinning being of different thickness. Instead of a single series of monochromatic reflections, regularly spaced groups of reflection maxima are also observed in some cases. The components in each group of such reflections may be wide apart or else may be closely spaced. The nature of the stratifications in these cases is discussed.

• On the polarisation and spectral character of the iridescence of potassium chlorate crystals

It is shown from theoretical considerations and confirmed by the spectrograms reproduced in the paper that the sharply defined monochromatic reflection observed at nearly normal incidences splits up into a quartet in the general case of any arbitrary azimuth and obliquity of incidence. The outer components disappear thereby reducing the quartet into a doublet when the azimuthal angle is small. But if the azimuthal angle be 90° the two central components merge and the quartet reduces to a triplet. When the crystal is rotated in its own plane the two central components of the quartet come together, overlap and move out again in the same direction, thereby giving rise to a reversal of their polarisation characters. They owe their origin to the alternate layers of the polysynthetically twinned crystal being of unequal thickness.

• The structure and optical behaviour of iridescent crystals of potassium chlorate

Iridescent crystals of potassium chlorate exhibit geometric patterns of reflection and extinction respectively when a field of diffuse monochromatic light is viewed by reflection at or transmission through the crystal. The patterns consist in general of four closed curves, two of which are polarised with their vibration directions parallel to the plane of symmetry of the crystal and the two others perpendicular thereto. The configuration of the patterns exhibits a perfect concordance with the spectral character of the reflections or extinctions observed with incident white light at corresponding azimuths of incidence and thus furnishes a complete picture of such spectral behaviour. Photographs of the geometric patterns are reproduced with the paper as also of the conoscopic patterns exhibited by the iridescent crystals on the stage of a polarising microscope. The paper also reports the observation that the twinned crystals of potassium chlorate function as diffraction gratings and give polarised spectra when light traverses them along their composition planes of twinning.

• The structure and optical behaviour of iridescent shells

Some remarkable optical effects exhibited by nacreous shells have been observed and reported, the following amongst others: The monochromatic reflections and extinctions split into two polarised components at oblique incidences as a result of the birefringence of the material. Light traversing the stratifications obliquely suffers extinction by reason of diffusion by the crystallites of aragonite, this being most rapid for the component of vibration in the plane of incidence. Striking changes are also observed in the character of the diffusion haloes with increasing obliquity of observation, a particularly noteworthy feature being that the different parts of the diffusion field are differently polarised.

• The structure and optical behaviour of pearls

The paper embodies a study of the structure of the material composing pearls and of the optical effects which they display. The following topics are dealt with: (1) Birefringence, (2) X-ray-diffraction patterns, (3) The reflection-diffraction spectra, (4) The diffusion haloes of reflection and transmission, (5) The whispering-gallery effect, (6) The spectral character of iridescence and the influence of birefringence thereon, (7) The transmission spectra. The most noteworthy result of the investigation is to show that the diffusive properties of nacre play a major role no less important than that of the reflection by its stratifications in the optics of pearls.

• On the chromatic diffusion halo and other optical effects exhibited by pearls

The paper discusses the origin and character of the coloured diffusion halo exhibited by pearls surrounding the reflected image of a light source seen at their surface. Twelve photographs illustrative of various types of halo are reproduced. Other aspects of the optical behaviour of pearls are also described and discussed with illustrative photographs.

• The Raman spectrum of diamond

The Raman spectra of fourteen different diamonds exhibiting diverse characters in their optical behaviour (viz., transparency in the infra-red and ultra-violet regions of the spectrum, birefringence and the intensity and colour of the luminescence) were recorded. The principal Raman line is found to have a frequency shift of 1331·7 ± 0·2 cm.−1 which agrees closely with the value of 1331·8 cm.−1 reported earlier. There were no observable variations in the frequency shift, width or intensity of the line in the several cases studied.

• Raman spectra of borax, kernite and colemanite

The Raman spectra of borax, (Na2B4O7·10H2O), kernite (Na2B4O7·4H2O) and colemanite (Ca2B6O11·5H2O) have been investigated using λ 2536·5 as exciting radiation. The spectrum of colemanite is reported for the first time. Many additional lines hitherto unreported have been found in the case of kernite and borax. The spectrum of borax exhibits seven lines, besides four bands due to water of crystallisation while the spectrum of kernite is found to consist of twenty-eight lines and six water bands. Colemanite exhibits nineteen Raman lines, and three bands due to water of crystallization. The observed spectra are discussed in relation to the known structures of the substances.

• Raman spectra of nickel sulphate crystals

• Evaluation of the four elastic constants of some cubic crystals

• Raman spectrum of magnesite

The Raman spectrum of magnesite (MgCO3) has been investigated and found to be analogous in its features to that of calcite, as is to be expected in view of the similarity of structure. The frequency shifts observed are: 212 (w), 332 (st), 735 (w), 1096 (st) and 1460 (?) cm.−1 All the frequencies and especially the two lowest are notably higher than for calcite and this is explicable as due to the smaller interionic distances and correspondingly larger force constants.

• The raman spectrum of calcite and its interpretation

The paper reports the results of a study of the Raman spectrum of calcite recorded with prolonged exposures.

The principal Raman shift of 1086 cm.-1 is accompanied by much weaker satellites whose frequency shifts are 1067, 1072 and 1075 cm.-1 The o ctave of the principal mode is recorded as a sharp line with a frequency shift of 2173 cm.-1 with a diffuse companion of comparable intensity which is a superposition of the octaves of the three satellites. The 1436 cm.-1 Raman shift likewise has satellites at 1399, 1412 and 1418 cm.-1 and its octave is feebly recorded as a sharp line, while the octaves of the satellites are also observed in its vicinity. The origin of the satellite radiations is discussed and it is shown that they represent the superlattice vibration frequencies of the calcite structure which are feebly excited.

The appearance of a sharp Raman line with a frequency shift of ± 221 cm.-1 is confirmed and it is shown to arise from a normal mode usually considered as inactive.

The two intense Raman shifts of 155 and 282 cm.-1 exhibit a highly unsymmetrical broadening, as also wings of low intensity spread out over the whole range of frequency shifts between - 300 cm.-1 to + 600 cm.-1 This spectrum is explicable as arising from a very feeble excitation of the whole group of forty lattice and superlattice frequencies of the calcite structure and their overtones and combinations.

Sixteen combinational frequency shifts have been recorded. Seven of them are explained as combinations with the 1086 cm.-1 Raman line and the the nine others as combinations with 875 cm.-1 Some of the observed combinations violate the selection rules.

• The raman spectrum of quartz and its interpretation

• The Raman spectra of crystalline sulphates of Ni and Mn

The paper reports the results of investigations on the Raman spectra of NiSO4·6H2O (tetragonal and monoclinic forms), NiSO4·7H2O (orthorhombic) and MnSO4·4H2O (monoclinic). Using λ 2536·5 resonance radiation of mercury for excitation of the Raman effect, it has been possible to observe a large number of frequency shifts. The spectra exhibit striking differences between themselves and also a few characters of general similarity. These are largely explicable in terms of the crystal symmetry and structure of these substances. In all the cases studied, the internal frequencies of the sulphate ion exhibit multiplicities owing to the lowering of the symmetry of the SO4 ion in the crystalline state and due to the number of ions present in the unit cell.

• The Raman and infra-red spectra of some solid hydroxides - Part I. Raman effect data

The paper reports the results of an investigation on the Raman spectra of eleven solid hydroxides using the λ 2536·5 resonance radiation of mercury arc for the excitation of the Raman effect. The cases studied (most of them for the first time) consist of the hydroxides of Li, Na and K and their monohydrates, the hydroxides of Ca, Mg and Al, and the octahydrated hydroxides of Sr and Ba. The facts of observation are discussed in relation to the crystal structure and the infra-red absorption data of these crystals in two separate parts following this paper.

• The Raman and infra-red spectra of some solid hydroxides - Part II. Correlation with crystal structure

The paper discusses the results reported in Part I in relation to the crystal structures of the substances. From a comparison of the facts with the theoretically expected picture of the spectrum, the salient features exhibited by the spectra have been explained, in addition to identification and assignment of the frequencies wherever feasible. The progressive variations in the hydroxyl shifts exhibited by the different hydroxides and their hydrates are explicable as due to the interactions of the hydroxyls with each other and also with their neighbouring water molecules in the case of the hydrates.

• The Raman and infra-red spectra of some solid hydroxides - Part III. Discussion of the infra-red data

In each of the cases of LiOH, LiOH·H2O, NaOH, Ca(OH)2 and Mg (OH)2 the stretching vibrations of the hydroxyls antisymmetrically with respect to the centre of inversion give rise in infra-red absorption to a single sharp intense maximum at about 3650 cm.−1 as is to be theoretically expected. In all cases, the infra-red active hydroxyl frequency is found to be higher than the corresponding Raman active mode and the origin of this feature is explained.

The spectrum of Ca (OH)2 recorded with single crystals exhibits on either side of the principal maximum due to the hydroxyl vibration, numerous other maxima which have hitherto remained unexplained. Some of them arise due to combinations between the observed Raman active lattice frequencies and the infra-red active hydroxyl frequency. The rest are explicable as combinations between the Raman active hydroxyl frequency and infra-red active lattice frequencies. Features similar to those observed in the spectrum of Ca (OH)2 are exhibited by Mg (OH)2 also, and have been explained in an analogous fashion. No experimental data regarding the infra-red active lattice frequencies of Ca (OH)2 and the Raman active and infra-red active lattice frequencies of Mg (OH)2 are available. The values of these are also revealed by the above analysis.

• The Raman spectra of aragonite, strontianite and witherite

The Raman spectra of the three crystals are recorded using the λ 2536·5 radiation of mercury and eleven new lines of low intensity are reported. These include the appearance in the cases of SrCO3 and BaCO3 of the line corresponding to the Raman-inactive mode of the free-ion, this line being of progressively diminishing intensity in the three cases owing to the structures progressively approaching that of hexagonal symmetry. The similarities and the differences observed in the three spectra are also correlated with the details of the crystal structures.

• The Raman spectra of polycrystalline solids

The paper discusses the experimental techniques with regard to the recording of the Raman spectra of polycrystalline solids. The present studies on the typical cases of polycrystalline gypsum, and calcite in the form of a finely divided powder show that the Rasetti technique can be successfully employed to obtain clear spectra of such substances and also indicate the scope for further improvements in the techniques. It emerges that the polycrystalline nature of the gypsum and the finely divided form of the powder studied have no observable influence on their spectra.

• The Raman spectrum of rutile

The Raman spectrum of rutile has been investigated both at room temperature and at the temperature of liquid air. The Raman lines which, at room temperature are quite wide, are observed to sharpen greatly at the low temperature. The different Raman-active fundamentals are identified and the paper also elucidates the several subsidiary features which are observed in spectrograms recorded with prolonged exposures.

• Infrared absorption spectra of ethyl,n-propyl andn-butyl stearates

The paper reports the IR absorption spectra (700–1500 cm−1) of ethyl,n-propyl andn-butyl stearates in their liquid and crystalline phases and discusses in detail the band assignments.

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