Elastic, optical, and dielectric properties and their pressure derivatives of rutile‐structure oxides in a modified rigid ion approximation

Abstract

The elastic and static dielectric constants and their first pressure derivatives, and the optical mode frequencies and mode gammas a t zero wave vector have been calculated for GeO,, TiO,, and SnO, from a modified rigid ion model, in which first and second nearest neighbor central force repulsive interaction of Born-Mayer type and oxygen-cation-oxygen angle bending forces are included. The nine free parameters of the model are determined from a least squares f i t to the zero pressure values of the optical frequencies and elastic constants. The agreement with the experimental optical and elastic data a t zero pressure is very good, and fair to moderate for the pressure derivatives.Die elastischen Konstanten, die statischen Dielektrizitatskonstanten, deren Druckkoeffizienten und die Frequenzen und mikroskopischen Gruneisen-Parameter der optischen Schwingungen in der Zonenmitte wurden fur GeO,, TiO, und SnO, mittels eines modifizierten Modells starrer Ionen berechnet, in dem Zentralkrafte vom Born-Mayer-Typ zwischen nachsten und ubernachsten Nachbarn und Federbindungen fur die Verzerrung der Sauerstoff-Kation-Sauerstoff-Winkel beriicksichtigt sind. Die neun freien Parameter des Modells wurden mittels der Methode der kleinsten Quadrate aus den optischen Frequenzcn und elastischen Konstanten bei verschwindendem Druck bestimmt. Die ubereinstimmung mit den gemessenen optischen und elastischen Daten bei verschwindendem Druck ist gut und die mit den Druckkoeffizienten und mikroskopischen Griineisen-Parametern ma0ig.

High-pressure Raman study of the ferroelastic rutile-to-CaCl2phase transition inZnF2Perakis1, Lampakis2, Boulmetis3 et al. 2005Phys. Rev. B264220View full textAdd to dashboardCite

“…27, long-range interactions are also included. The ␥ values of this work and the calculated ones 26,27 are summarized in Table I, showing better agreement of our data with those of Ref. 27.…”

“…12͒. This is reasonable bearing in mind the negative theoretical Grüneisen parameters 26,27 for this mode and the softening of the shear elastic constant ͑C 11 -C 12 ͒ /2 of ZnF 2 with pressure. 29 It is pointed out that this elastic constant describes 12,30 the transverse acoustic mode propagating along the ͕110͖ direction ͑in the a-b plane͒ and is coupled 3 with the rotational atomic displacements which correspond to the B 1g optical mode of rutile-type crystals.…”

“…From the, almost, linear dependence of ͑A 1g ͒ and ͑E g ͒ with pressure ͑Fig. 3͒, Grüneisen parameters ␥ T = ͑B / 0 ͒ / ‫ץ͑‬ / ‫ץ‬P͒ have been evaluated for these modes, where B͑=1 / ͒ is the bulk modulus ͑, the volume compressibility͒ and 0 the mode frequency at ambient conditions; in these calculations we have used the measured bulk modulus data for ZnF 2 of Gerlich et al 25 In the absence of previous relevant experimental data, we compare our gamma values with theoretical ones based on a rigid ion model with a Born-type potential for nearest-neighbor interactions; 26,27 in the model of Ref. 27, long-range interactions are also included.…”

“…This agreement indicates that Coulomb interactions may play a significant part in the nature of the atomic bonding in ZnF 2 and is compatible with the conclusion drawn in a very recent near-edge x-ray-absorption fine structure study 28 that ZnF 2 is the most ionic among a number of rutilestructured difluorides, such as MnF 2 , FeF 2 , CoF 2 , and NiF 2 . In Table I, the calculated 26,27 Grüneisen parameters for the other two B 1g and B 2g modes are also included, showing a negative value for the former phonon.…”

Surface-enhanced Raman scattering of SnO2bulk material and colloidal solutions

“…Two modes are infrared active (the single A 2u and the triply degenerate E u ), four are Raman active (the three nondegenerate A 1g , B 1g , B 2g modes and the doubly degenerate E g one) and two others are silent (the A 2g and B 1u modes). The A 1g mode is a vibration along the c axis while the E u mode involves movements in the xy plane [27][28][29][30][31][32][33] . Figure 1 shows the Raman spectrum collected on the surface of a pellet obtained by hot pressing SnO 2 powder.…”