Study of Cohesion, Harmonic and Anharmonic Elastic Properties of CaF₂—SrF₂ Mixed Crystals

Abstract

Cohesive and harmonic and anharmonic elastic properties are investigated of CaF,-SrF, mixed crystals using a three-body interaction potential which consists of the long-range Coulomb and three-body interactions and short-range van der Waals attraction and overlap repulsion, effective upto the second neighbour ions. This two parameter model potential successfully predicts the cohesive energy, the higher order elastic constants, and the pressure derivatives of the second order elastic constants of CaF,-SrF, mixed crystals.Mit einem Dreikorperwechselwirkungspotential, das aus der weitreichenden Coulomb-und Dreikorperwechselwirkung und der kurzreichweitigen van der Waals-Anziehung und Uberlappungsabstohng bis zu den zweiten Nachbarionen besteht, werden die KohLsions-sowie die harmonischen und anharmonischen Elastizitatseigenschaften von CaF,-SrF,-Mischkristallen untersucht. Dieses Zweiparametermodellpotential sagt erfolgreich die Kohiisionsenergie, die elastischen Konstanten hoherer Ordnung und die Druckableitungen der elastischen Konstanten zweiter Ordnung fur CaF,-SrF,-Mischkristalle voraus.

Interionic Forces and Elastic Properties of Na2S

“…It is seen froin this Table that the qualitative features of the TOEC are identical in Na,S and CaF, though they differ in magnitude. The larger values of Cln, C123, and C,,, in CaF, might be because the first-neighbour force constants are quite larger in CaF, in comparison to those of Na,S [12]. The similarity in the magnitudes of CIBB, GI,,, and C,,, in both the solids indicates that the short-range interactions are not so effective in these constants.…”

Analysis of Combination Rules for Elastic Constants of Mixed Ionic Crystals

“…A numerical analysis based on different sets reveals that the results are so close to each other that either the difference is insignificant or it is of the order of experimental uncertainty (around 1%). I n Tables 1 and 2 we T a b l e 1 Elastic constants (in 1010 Pa) of mixed KCll-,Er, crystals calculated using different sets of combination rules based on (a) Shanker and Jain model [5]; (b) Singh et al model [6]; (c) Giri (Al-,B,) is the bulk modulus of the mixed system, K(A) and K(B) are the bulk moduli of the two end members A and B, respectively, and V(A) and B(B) denote the molar volumes of A and B, respectively. Equation (11) has been found to produce good agreement with experimental elastic data for mixed ionic crystals [8,9,20,211.…”

“…KCl1-,Br, and Cal-,Sr,F2 for the entire range of composition.It has recently been pointed out byVarotsos and Lazaridou [8] that the values of the bulk modulus K for mixed CaF,-SrF, crystals estimated from the Varotsos model[9] differ significantly from the corresponding values obtained by Singh et al[6] by assuming K to be linearly dependent on the concentration of the Sr2+ ion. The Varotsos model is based on the expression where K…”

“…Bulk modulus (in 10'" Pa) of mixed Cal-,Sr,F, crystals caIculated using (a) Shanker and Jain model[5]; (b) Singh et al model[6]; (c) Giri and Mitra model [7]; (d) Varotsos model[8] …”