A Comparative Study of Dynamical Behaviour of Ionic Lattices

Abstract

A critical study of all the three extensions of the shell model i.e. the breathing shell model (BSM), the deformable shell model (DSM), and the three-body force shell model (TSM) is further carried out for cesium chloride type ionic crystals on the similar pattern as reported earlier. These models are applied t o study comparatively the dynamical behaviour of cesium chloride (CsCI) and thallous bromide (TIBr). The results so obtained, again confirm the superiority of TSM over DSM and BSM, not only in explaining the phonon dispersion curves but also for interpreting the infrared (IR) and Raman spectral peaks and Debye temperature variations.Eine kritische Untersuchung aller drei Erweiterungen des Schalenmodells, das ,,breathing" Schalenmodell (BSM), das deformierbare Schalenmodell (DSM) und das Drei-Korper-Krafte-Schalenmodell (TSM), wird weiterhin fur Ionenkristalle vom Casiumchloridtyp nach dem schon friiher veroffentlichen Muster durchgefuhrt. Diese Modelle werden zum Vergleich des dynamischen Verhaltens von Casiumchlorid (CsCI) und Thalliumbromid (TlBr) benutzt. Die so erhaltenen Ergebnisse bestatigen erneut die ifberlegenheit des TSM uber DSM und BSM, nicht nur bei der Erklarung der Phononendispersionskurven sondern auch fur die Interpretation der Maxima der Infrarot (1R)-und Ramanspektren sowie der Anderungen der Debye-Temperatur.

Harmonic dynamical behaviour of thallous halides

“…As our PDS curves are derived from somewhat course mesh division of the Brillouin zone, we have used a critical point analysis [27] to present complex interpretation of the observed infra-red and Raman spectra. The assignments made by the present study along with those obtained from the TSM [12] listed in tables 3 and 4 for TlCl and TlBr respectively, show reasonably good agreement with the observed peaks corresponding to infra-red/Raman spectra of these halides. Our extensive study of two-phonon infra-red/Raman spectra is basically aimed to correlate the theoretical and optical experimental results.…”

“…X, M and R for both optical as well as acoustic branches. Quantitatively, the agreement achieved from our present model is comparatively better in the sense that some of the fitted parameters by other workers [11][12][13][14][15][16][17], have attained unrealistic values. Moreover, we have tested the adequacy of the present model by calculating the Debye temperature variations, two-phonon Raman and anharmonic elastic properties.…”

“…The VTSM assignments of infra-red/Raman peaks for these crystals using critical point analysis are listed in tables 3 and 4 and plotted with experimental peaks [6,7] in figure 3. Quantitative comparison of frequencies along the principal symmetry directions of the measured PDCs [1,2] and those reported from VTSM and TSM [12] as well as experimental values are presented in table 5. branches. The agreement achieved from the present model is also excellent for the LA, TA and LO branch along [q q 0] direction.…”

“…Input data along with the relevant references for TlCl and TlBr are presented in table 1 and the model parameters calculated using VTSM and TSM [12] are given in table 2. These model parameters have been used to calculate the complete phonon dispersion frequencies in the first Brillouin zone.…”

“…Availability of the measured data on phonon dispersion curves [1,2], Debye temperature variations [3,4] along with their theoretical values [5], two-phonon IR and Raman spectra [6,7], elastic constants [1,8] and dielectric constants [9,10] of thallous halides (TlCl and TlBr) and their interpretations by means of theoretical models [11][12][13][14][15][16][17] with moderate success, have motivated the authors to develop a lattice dynamical model for the satisfactory description of their interesting properties.…”