The change of complete symmetry of the crystals during the phase transitions in ferroelectrics and ferromagnetics

The extension of the superposition principle of the symmetries (P. Curie principle of symmetry) for the case of complete symmetry is given. The enumeration of all crystallographical groups of complete symmetry is presented, the number of elements having complete symmetry for each class of the crystals being indicated. The change of complete symmetry of the crystals under the phase transitions is obtained by superimposing the elements of complete symmetry of polar or axial vectors on the one hand, and the elements of complete symmetry of the crystals on the other. The tables of complete symmetry changes for the cubic, rhombic, monoclinic and triclinic crystals during the ferroelectric and ferromagnetic phase transitions are given.

Raman spectra of single crystals of adipic and sebacic acids and a study of the hydrogen bond vibrations in carboxylic acid dimers

Raman spectra of single crystals of adipic and sebacic acids have been photographed for the first time using λ 2537 excitation. The spectra have been divided into four regions: (a) internal frequencies; (b) summations and overtones; (c) external vibrations; and (d) low-frequency hydrogen bond oscillations. Tentative correlations have been given for all the internal frequencies and summations and overtones. A series of diffuse weak bands observed in the spectra of both these acids in the not, vert, similar2400–2800 cm−1 have been explained as a superposition of O---H frequencies lowered due to hydrogen bond formation over the summations and overtones of fundamentals mainly in the not, vert, similar1000–1500 cm−1 region. Rotatory type of external oscillations of the two formula units of these molecules in their unit cells have been identified at 76, 99, 118 and 165 cm−1 in adipic acid and 66, 95, 117 and 177 cm−1 in the spectrum of sebacic acid. A brief discussion of the low frequency hydrogen bond vibrations in these acids has been made. Making use of the Lippincott—Schroeder potential and assuming a highly anharmonic potential curve for the hydrogen bond, the vibrational frequencies of the bond have been theoretically evaluated. There is very good agreement between these and the experimental values. The results for adipic acid in cm−1 are: 304 (0 → 1), 270 (1 → 2), 241 (2 → 3), 222 (3 → 4) 201 (4 → 5), 183 (5 → 6). In the case of sebacic acid some of the intermediate and higher transitions are absent in the spectrum recorded by the author. From the above data for adipic acid the dissociation energy of the hydrogen bond was evaluated as 5·9 kcal/mole in fair agreement with the values derived from conventional methods.

Structure of the hydrogen-bonded water molecule in crystals

A correlation of the structural data on IS hydrates obtained by x-ray diffraction, neutron diffraction, and proton magnetic resonance reveals that when a water molecule is hydrogen bonded into a crystal structure and the angle subtended at the donor water oxygen by the acceptor atoms deviates from the vapor H-O-H angle, bent hydrogen bonds are formed in preference to distortion of the H-O-H angle. Theoretical justification for this result is obtained from energy considerations by calculating the energy of formation of bent hydrogen bonds on the basis of the Lippincott-Schroeder potential function model for the hydrogen bond and the energy of deformation of the H-O-H angle from spectroscopic force constants.

Flow of a maxwell liquid fluid between two rotating coaxial cones having the same vertex

We consider the secondary flows arising in the motion of a Maxwell fluid between two rotating coaxial cones having the same vertex. We find that in any meridian plane passing through the common axis of the cones, the flow field is divided into two regions. Such a division of flow field was first reported by Bhatnagar and Rathna.

Critical phenomena in the coexistence curve of the binary liquid system

The coexistence curve of the carbondisulphide-acetic anhydride system has been measured. The shape of the curve in the critical region (Xc ≈ 70.89 mole % mole % CS2 and Tc ≈ 30.56° C) is determined by the equation |X′ - X″| = Bx (1 - T/Tc)β with the critical indices β = 0.34 ± 0.01 and Bx = 1.7 ± 0.1 over a range 10-6 < (Tc - T)/Tc < 10-2. The values of β and Bx agree with those of other systems and the theoretical predictions of the Ising model.

Atomically resolved scanning tunneling microscopy on perovskite manganite single crystals

Atomically resolved scanning tunneling microscopy was conducted on cleaved single crystals of the cubic perovskite Pr0.68Pb0.32MnO3.Several different surface configurations could be resolved including a frequent square arrangement with atomic distances in excellent agreement to the bulk lattice constant of the cubic structure. We also observed stripe formation and a surface reconstruction. The latter is likely related to a polar rare earth-oxygen terminated surface. (C) 2010 American Institute of Physics.

Polarisation studies on the Raman spectra of cubic crystals - Part II: Calcium fluoride and potassium aluminium sulphate

Polarisation characters of the Raman lines of calcium fluoride (fluorspar) and potassium aluminium sulphate (alum) were investigated under the following conditions. Unpolarised light was incident normally on a face of the crystal making an angle 22.5° with a cubic face and the light scattered transversely along a cubic axis was analysed by a double image prism kept with its principal axes inclined at 45° to the vertical. Under these conditions the depolarisation factors of the Raman lines belonging to the totally symmetric (A), the doubly degenerate (E) and the triply degenerate (F) modes should be respectively =1, >1 and <1. The characteristic Raman line of CaF2 at 322 cm-1 exhibited a depolarisation value less than 1, showing thereby that the corresponding mode is a triply degenerate one (F). The Raman lines observed in the spectrum of K-alum were also classified and the results were compared with those given by previous investigators using standard crystal orientations.

Optical properties of magnetic crystals

From symmetry considerations and using generalized Onsager relations, it is shown that 66 of the 90 magnetic classes, consisting of 29 single colour and 37 double colour ones, can exhibit what may be called the strain gyrotropic rotation. Similarly, 69 of the 90 magnetic classes, consisting of 21 single colour and 48 double colour ones, can exhibit what may be called the strain gyrotropic birefringence. A crystal in the class m3 or m3 m is interesting as it can exhibit strain gyrotropic rotation despite its being cubic and incapable of exhibiting gyrotropic rotation in the unstressed state. Similarly, a crystal in the class m3 m, is interesting as it can exhibit strain gyrotropic birefringence despite its being cubic and incapable of exhibiting gyrotropic birefringence in the unstressed state.

Ultrasonic studies in chemically active liquid media (1) aqueous solution of N2O4

Using a pulse method the ultrasonic absorption has been studied in the frequency range of 2 to 10 Mc/s in dilute aqueous solutions of nitrogen tetroxide gas at room temperature. The absorption peaks (αλ vs frequency) observed in this study are attributed to the ionic dissociation reaction of the nitrous acid into its constituent ions. The rate constants of the forward and backward reactions are calculated using the theory of Tabuchi. The variation of the logarithm of the rate constant of the bimolecular ionic reaction, namely, log10 kb, with the square root of ionic strength qualitatively follows Brönsted's theory for ionic reactions in solutions.

Raman spectra of single crystals of dicarboxylic acids - Part I. β-malonic acid and β-succinic acid

Raman spectra of single crystals of β-malonic acid and β-succinic acid have been photographed using λ 2536·5 radiation. 32 Raman lines have been recorded in the case of β-malonic acid. Of these 21 lines have been recorded for the first time. The three intense lattice lines at 52, 90 and 144 cm.-1 have been attributed to rotational lattice oscillations. 29 Raman lines in the case of β-succinic acid have been recorded. The entire lattice spectrum and many internal frequencies have been recorded for the first time. The three intense lattice lines at 80, 135 and 160 cm.-1 have been assigned to the rotational oscillations of the two molecules of the succinic acid in the unit cell.

Polarisation studies on the Raman spectra of cubic crystals - Part I. Sodium chlorate

neral expressions have been derived for the intensities of the three classes of Raman lines namely totally symmetric A, doubly degenerate E and triply degenerate F, in the case of cubic crystals under the following conditions. The direction of the incident beam which is polarised with its electric vector inclined at an angle α to the normal to the scattering plane makes an angle Θ with one of the cubic axes of the crystal. The transversely scattered light is analysed by a double image prism with its principal axes inclined at angle β to the normal to the scattering plane, which is horizontal. For incident unpolarised light and Θ=22 1/2°, and the scattered light being analysed by a double image prism rotated through 45° from the position when its principal axes are vertical and horizontal ρ{variant} for A lines is equal to one, for E lines >1 and for F lines <1. This gives a method of classifying the Raman lines of a cubic crystal in a single setting. The results have been experimentally verified in sodium chlorate.