Raman spectra of crystalline double sulphates Part II. Ammonium double sulphates

Raman spectra of single crystals of (NH4)2M(SO4)2·6 H2O where M=Mg, Zn Ni or Co have been recorded using λ 2537 excitation. Interesting results concerning the substitution of the divalent atoms in the double sulphate lattice on the sulphate and ammonium frequencies are observed. The spectra of these double sulphates are discussed in the light of the known crystal structure details and in relation, to the spectra of the corresponding potassium double sulphates, reported recently by the author. The Raman spectrum of NaNH4SO4·2 H2O has also been recorded for the first time and the results obtained are also included.

Oscillations of a three-component assembly with or without magnetic field

The plasma is taken to be composed of singly ionized molecules, free electrons and neutral molecules, each of the component being described by the hydromagnetic equations, modified to take into account the displacement current, existence of free charge in the medium, and the modified current equation without involving the scalar conductivity. The basic equations are linearized and only small amplitude waves are considered. In the absence of any external magnetic field, the transverse and longitudinal modes of oscillation separate out. In the transverse part a coupled plasma oscillation occurs which could be propagated only above a certain critical frequency and in the longitudinal part one extraordinary mode of propagation occurs having a forbidden range of frequencies. When there is an external applied magnetic field, ordinary and extraordinary waves are propagated along the direction of the magnetic field, whereas only ordinary waves are propagated transverse to the magnetic field. The critical frequencies above which these waves are propagated are evaluated and, the possible explanation of this medium like behaviour could be the implicit assumption of conductivity being not a scalar.

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.

Non-linear couette flow with heat transfer using the B-G-K model

In recent years a large number of investigators have devoted their efforts to the study of flow and heat transfer in rarefied gases, using the BGK [1] model or the Boltzmann kinetic equation. The velocity moment method which is based on an expansion of the distribution function as a series of orthogonal polynomials in velocity space, has been applied to the linearized problem of shear flow and heat transfer by Mott-Smith [2] and Wang Chang and Uhlenbeck [3]. Gross, Jackson and Ziering [4] have improved greatly upon this technique by expressing the distribution function in terms of half-range functions and it is this feature which leads to the rapid convergence of the method. The full-range moments method [4] has been modified by Bhatnagar [5] and then applied to plane Couette flow using the B-G-K model. Bhatnagar and Srivastava [6] have also studied the heat transfer in plane Couette flow using the linearized B-G-K equation. On the other hand, the half-range moments method has been applied by Gross and Ziering [7] to heat transfer between parallel plates using Boltzmann equation for hard sphere molecules and by Ziering [83 to shear and heat flow using Maxwell molecular model. Along different lines, a moment method has been applied by Lees and Liu [9] to heat transfer in Couette flow using Maxwell's transfer equation rather than the Boltzmann equation for distribution function. An iteration method has been developed by Willis [10] to apply it to non-linear heat transfer problems using the B-G-K model, with the zeroth iteration being taken as the solution of the collisionless kinetic equation. Krook [11] has also used the moment method to formulate the equivalent continuum equations and has pointed out that if the effects of molecular collisions are described by the B-G-K model, exact numerical solutions of many rarefied gas-dynamic problems can be obtained. Recently, these numerical solutions have been obtained by Anderson [12] for the non-linear heat transfer in Couette flow,

Raman spectra of crystalline double sulphates

Raman spectra of single crystals of K2M(SO4)2 · 6 H2O where M=Mg, Zn, Ni or Co have been recorded for the first time using λ 2537 as the exciting radiation. The corresponding five single sulphates have also been studied. Interesting results concerning the substitution of magnesium, zinc, nickel or cobalt in the double sulphate lattice on the sulphate frequencies are observed. The lattice spectra of these double sulphates are analysed group theoretically and discussed in relation to the lattice spectra of the corresponding individual sulphates. Certain new results concerning the Raman spectra of the individual sulphates have also been obtained and in the case of CoSO4 · 7 H2O the spectrum has been recorded for the first time.