Elastic constants of some NaCl type alkali halides

Abstract

Second and third order elastic constants of NaCI, NaBr, KF, KCI, KBr, and RbBr have been calculated using the Born model of ionic solids. Short range repulsive interactions have been included up to second nearest neighbors using an expression of the form A exp ( -r / b ) where b is the repulsive parameter. A distinction is made between the like and unlike ion interactions. Van der Wads terms are also included. When the room temperature lattice parameter is used, the elastic constants satisfy the Cauchy relations. Experimental data show that many of the alkali halides fail to satisfy the Cauchy relations. This aspect is examined by using the quasi-harmonic approximation as developed by Leibfried and his associates. Linear temperature coefficients of the elastic constants are also calculated in the high temperature limit. I n order to assess the contributions of the van der Waals terms, elastic constants are also calculated by dropping the van der Waals terms in the expressions for the elastic constants. Calculated values of the elastic constants are compared with the available experimental data.Die elastischen Konstanten zweiter und dritter Ordnung werden mit dem Bornschen Modell fur Ionenfestkorper fur NaCI, NaBr, KF, KCI, KBr und RbBr herechnet. Kurzreichende Abstohngswechselwirkung wird bis zu den zweiten nachsten Nachbarn durch einen Ausdruck der Form A exp (-r/b), mit b als Abstohngsparameter, berucksichtigt. Es wird zwischen der Wechselwirkung gleicher und ungleicher Ionen unterschieden. Van der Waals-Terme werden ebenfalls berucksichtigt. Wenn die Gitterkonstante bei Zimmertemperatur benutzt wird, erfullen die elastischen Konstanten die Cauchy-Relationen. Experimentelle Ergebnisse zeigen, daB viele Alkalihalogenide die Cauchy-Relationen nicht erfullen. Diese Erscheinung wird mit der von Leibfried und Mitarbeitern entwickelten quasi-harmonischen Naherung untersucht. I m Grenzfall hoher Temperaturen werden auch die linearen Temperaturkoeffizienten der elastischen Konstanten berechnet. Urn den Beitrag der Van der Waals-Terme abzuschatzen, werden die elastischen Konstanten berechnet, indem die Van der Waals-Terme in die Ausdrucke fur die elastischen Konstanten einbezogen werden. Die berechneten Werte fur die elastischen Konstanten werden mit den zur Verfugung stehenden experimentellen Werten verglichen.

Pressure Derivatives of the Elastic Constants of NaBr and KF

“…The latter set of equations relate the pressure derivatives of the effective elastic constants to the second and third order elastic constants of the stress free crystals. It should be noted that the theoretical expressions for dcip/dp used by Lincoln et al [6] and used in our analysis can be shown to be identical to those given by Miller and Smith [9].…”

“…We note that the Cauchy relation (cx2 = c4J is nearly satisfied for NaBr whereas Table 1 Adiabatic elastic constants and their pressure derivatives for NaBr and KF*) at 25 "C (cop in units of 10" dyn/cm2; ac& are dimensionless) [ 6 ] . The derivatives dc:,/dp can be evaluated for a given pairwise interaction using equations (8) and (9) of [6] and equations (74), (75), and (76) of [ B ] .…”

“…The short range inter- Table 1 of [ 6 ] . Comparison of our experimental results with the calculations is made in Tables 2 and 3.…”

“…The derivatives dc:,/dp can be evaluated for a given pairwise interaction using equations (8) and (9) of [6] and equations (74), (75), and (76) of [ B ] . The latter set of equations relate the pressure derivatives of the effective elastic constants to the second and third order elastic constants of the stress free crystals.…”

“…Anumber of such measurements on several alkali halides are now available [7 to 131. I n part, the present work on NaBr and K F was undertaken t o assess the theoretical conclusions reached by Lincoln et al [6] regarding the sign of dc;,/dp.…”