• K R Rao

      Articles written in Pramana – Journal of Physics

    • Lattice dynamics of beryllium

      B A Dasannacharya P K Iyengar R V Nandedkar K R Rao A P Roy C L Thaper

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      Phonon frequencies in beryllium along the principal symmetry directions have been determined by means of the slow neutron inelastic scattering technique. The data are analysed in terms of a six-neighbour force constant model and the force constants are evaluated. It is concluded that strong tensor forces are present in beryllium and the importance of this finding to basic theories of lattice dynamics is pointed out.

    • Normalisation and assessment of neutron diffraction data from liquids

      K R Rao B A Dasannacharya

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      A couple of normalisation criteria have been proposed to assess liquid structure data over the past decade. In this paper, a critical examination of these and other plausible criteria is made. Neutron diffraction data from liquid krypton measured by Clayton and Heaton is used to study these criteria. It is shown that if the structure factorS (Q)=1+γ (Q) satisfies the Krogh-Moe relation, namely$$\rho _{0 = \frac{1}{{2\pi ^2 }}} {\text{ }}\mathop \smallint \limits_{\text{0}}^\infty {\text{ }}Q^{\text{2}} {\text{ }}\gamma {\text{ (}}Q{\text{) }}dQ$$ whereQ is the wavevector transfer andρ0 the mean atomic number density,S (Q) is properly normalised. Subjecting such data to the other criteria would reveal, however, the quality of data in so far as systematic errors and/or termination errors are concerned. If the data is measured with reasonable accuracy to sufficiently large values of the wavevector transfer all these criteria would assess the quality of the data to almost the same extent. This is established in this paper by improving and extending the liquid krypton data by procedures similar to that of Kaplow, Strong and Averbach and subjecting this revised data to the various criteria. It is concluded, thereby, that (i) one can study the neutron diffraction data from liquids using any of the criteria mentioned in the paper to improve the quality of the data and (ii) for normalisation purposes the simple relation {ie328-2} would suffice.

    • A simple white beam neutron diffraction technique

      A H Venkatesh K R Rao

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      White beam neutron diffraction by time-of-flight (TOF) technique has been studied over a number of years as it is believed to be the most convenient method to investigate solids in a fixed geometry. This technique needs a pulsed neutron source and a suitable multichannel, analysing system. The entire system is in general, mechanically quite intricate and expensive.

      We have investigated an alternative technique to achieve the end result of a constant geometry around the diffracting sample. This involves the use of a single crystal as an analyser to study diffraction pattern from the sample bathed in a white beam and diffracting at any fixed scattering angle. In this paper we report the results of our investigations and have compared this technique with other diffraction techniques. Taking Si, KCl and KNO3 as typical specimens we have illus. trated the results of our technique and we find that the results are comparable to those obtained by conventional neutron diffraction and TOF diffraction. The technique is simple in mechanical design and data acquisition. It can be easily adapted for high pressure diffraction which is being attempted.

    • Inelastic neutron scattering from and lattice dynamics of α-KNO3

      K R Rao S L Chaplot P K Iyengar A H Venkatesh P R Vijayaraghavan

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      Coherent inelastic neutron scattering techniques are employed to measure several branches of the phoon dispersion relation in KNO3 in its orthorhombic (α-phase or phase II) form at room temperature. Group theoretical selection rules for external modes of the crystal have been used in the measurements along the three symmetry directions Σ(ξ00), Δ(0ξ0) and Λ(00ξ).

      Theoretical investigation of the lattice dynamics of the crystal is carried out on the basis of a rigid molecular-ion model using the external mode formalism. A two-body potential consisting of the Coulombic interaction and the Born-Mayer type short range interaction is assumed. The effective charges and radii of different atoms are determined by applying the stability criterion for the crystal. Dispersion curves are calculated, representation by representation, making use of group theoretical information. Comparison of theoretical results with experimental information on elastic constants, optical data and neutron results are made. Agreement between theoretical and the various experimental results may be considered very satisfactory.

    • Neutron, x-ray and lattice dynamical studies of paraelectric Sb2S3

      K R Rao S L Chaplot V M Padmanabhan P R Vijayaraghavan

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      Neutron and x-ray diffraction studies of Sb2S3 indicate extensive diffuse scattering in the plane perpendicular to the chain axis of polymer-like (Sb4S6)n molecules. The crystal structure of the paraelectric phase is said to be orthorhombic with space group D2h16 with four molecules per unit cell. The observed diffuse scattering may be due to static disorder or some dynamical effects. In this paper the authors have examined the possible dynamical origin by recourse to lattice dynamical studies. Dispersion relation of phonons along the three symmetry directionsa*,b* andc* is evaluated based on a lattice dynamical model incorporating Coulomb, covalent and a Born-Mayer-like short range interactions. Group theoretical analysis based on the group of neutral elements of crystal sites (GNES) was essential in order to examine and aid in the numerical computations. The group theoretical technique involving GNES extended to ‘pseudo-molecular’ systems is also discussed in this context.

      The phonon dispersion relation shows that there are rather flat TA-TO branches of very low frequency in thea andc directions which may give rise to diffuse scattering. The branches along theb-axis are quite dissimilar to those alonga andc axes because of anisotropy. Variation of the potential parameters leads to instability of the lowest TA-TO branch. This is suggestive of a temperatures or pressure-dependent phase transition. However since these modes are optically ‘silent’ one needs to carry out either high resolution neutron scattering or ultrasonic studies to confirm various aspects of the theoretical studies.

    • Lattice dynamics of MgSiO3 perovskite

      Narayani Choudhury S L Chaplot K R Rao Subrata Ghose

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      A lattice dynamical study of the geophysically important mineral MgSiO3 in its orthorhombic perovskite phase, with space group Pnma (D2h16) has been carried out using a rigid ion model, with the potential consisting of Coulombic and short-ranged interactions. With the help of program DISPR, the ionic charges and radii were optimized using the equilibrium conditions. The resulting potential model is employed to predict the elastic constants and the phonon dispersion relations. The computed long wavelength optic modes are in good agreement with the corresponding experimental Raman and infrared active bands. The phonon density of states has been obtained and is used to evaluate the specific heat, the mean square displacements and thermal parameters of atoms.

    • Phonon density of states of tetracyanoethylene from coherent inelastic neutron scattering at Dhruva reactor

      S L Chaplot R Mukhopadhyay P R Vijayaraghavan A S Deshpande K R Rao

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      Inelastic neutron scattering experiments to determine phonon density of states of coherent scattering samples of polycrystalline complex solids are generally intensity-limited and therefore are feasible only at high flux facilities. Phonon density of states of the monoclinic phase of tetracyanoethylene at 300 K, obtained using the medium resolution triple axis spectrometer at the new Indian medium flux reactor Dhruva are reported here. The raw data is converted to the “neutron weighted” phonon density of states by applying suitable corrections. Comparison made with results from a theoretical calculation based on a semirigid molecule model of lattice dynamics is fair. Results from Dhruva are also consistent with that obtained (to be published) at the high flux pulsed neutron source (ISIS) of the Rutherford Appleton Laboratory in United Kingdom.

    • Phase transformation and electrical resistivity of tetracyanoethylene under pressure

      P Ch Sahu K Govinda Rajan Mohammad Yousuf R Mukhopadhyay S L Chaplot K R Rao

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      This paper reports the phase transformation behaviour of tetracyanoethylene (TCNE) under pressure as revealed by AC electrical resistivity, its time evolution and X-ray diffraction studies. An irreversible transformation from monoclinic to cubic phase occurs at 2.1±0.1 GPa and is indicated by a sharp resistivity drop at this pressure. The time evolution of resistivity studies indicate that this transformation occurs via an intermediate phase having resistivity higher than either of the two crystalline phases. Finally, the kinetics of phase transformations obtained by time evolution of resistivity is compared with the X-ray studies on the pressure quenched TCNE.

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