Shell Model Calculation of Microscopic Grüneisen Parameters for Rocksalt‐Type Materials

Abstract

The microscopic Gruneisen parameters have been calculated for the two optical modes in the Brillouin zone center and for the four modes a t the Brillouin zone edge in [loo] for nine alkali halides and MgO. A six parameter shell model which takes into account anion polarizability, non-central first nearest neighbor interaction and central forces between second neighbors has been used, and the pressure dependence of the frequencies is obtained from the assumption of a pressure independent core-shell force constant. The parameters of the model are determined from experimental data of the elastic constants, from the high and low frequency dielectric constants, from the pressure derivatives of these quantities, and from the zero pressure value of the transverse optical frequency in the zone center. Good to fair agreement with the available experimental data is found. It i s suggested that the discrepancies are mainly due to the limited experimental accuracy. The results confirm that the B1 + B2 phase transformation in alkali halides is not due to an instability of the TA mode a t the [IOO] zone boundary.Die mikroskopischen Gruneisen-Parameter wurden fur die beiden optischen Schwingungen in der Mitte der Brillouin-Zone und fur die vier Schwingungen an der Oberflache der Brillouin-Zone in der [100]-Richtung fur neun Alkalihalogenide und MgO berechnet. Es wurde ein Schalenmodell mit sechs Parametern benutzt, in dem die Polarisierbarkeit der Anionen berucksichtigt wird und allgemeine Kopplungsparameter fur die Wechselwirkung zwischen nachsten Nachbarn und Zentralkrafte zwischen uberniichsten Nachbarn angenommen wurden. Fur die Berechnung der Druckabhangigkeit der Frequenzen wurde die Kraftkonstante fur die Wechselwirkung zwischen Kern und Schale als konstant angenommen. Die Parameter des Modells wurden aus den gemessenen elastischen Konstanten, aus der statischen und optischen Dielektrizitatskonstante, aus der Druckabhkngigkeit dieser GroBen sowie aus der transversalen optischen Grenzfrequenz bei Atmospharendruck bestimmt. Die nbereinstimmung mit den verfugbaren experimentellen Werten ist gut bis miilig. Die auftretenden Unterschiede sind wahrscheinlich durch die begrenzte experimentelle Genauigkeit bedingt. Die Ergebnisse bestatigen, daB die Phasenumwandlung von der B1-in die B2-Struktur nicht durch eine Instabilitat der transversalen akustischen Frequenz an der Oberflarhe der Brillouin-Zone in der [100]-Richtung ausgelost wird.

Dispersion Relations of Mode Grüneisen Parameters in Rubidium Halides

“…It seems that the measured value at the X-point is too negat,ive; when one t,ries to move the TA branch towards more negative ualnes, then the averaged behaviour gives too large negat,ive mean Griineisen constants or thermal expansion coeffi-cients when compared with White's [5] experiments. The y(TA) values a t the X-point are listed in Table 3 ; there is satisfactory agreement with Barsch and Achar's [12] calculation also in the general shape of the mode Griineisen dispersion curves. Since the transition pressures listed in Table 3 are rather low one might think of non-linear pressure effects being important in the neutron experiments.…”

“…It,s importance for the mode Griineisenparameters is an open question. Some aspects of t.he cation-anion influences on the mode Griineisen parameters and Griineisen constants are elucidated in the article of Barsch and Achar (1971) [12]. The long-ranged Coulomb contributions seem to be rather important for the TA and LA branches.…”

“…Opt,ical values at. the r-point are reported for RbI in [13] and by Lowndes (cit,ed in [12]). No data are available for RbF.…”

“…A transverse optical data cited in Namjoshi et a]. [13], A longitndinal optical data hy Lowndes cited in[12], and neutron experiment by Saunderson[ll] …”

Shell Model Calculation of Thermal Expansion of Alkali Halides and Magnesium Oxide

“…For RbCl only theoretical results will be presented, since no experimental thermal expansion data are available. For nine of the ten materials considered in t,he present paper and for NaCI, the microscopic Gruneisen parameters (mode gammas) have been calculated before on the basis of the shell model for the two optical modes in the zone center, and for the four modes a t the [loo] zone edge [ 8 ] . Good agreement with experimental values of mode gammas, as far as available, was found.…”