Estimation of Force Constants and Phonon Frequencies of Ternary Semiconducting Compounds with Chalcopyrite Structure from Specific Heat Data

Abstract

The force constants of a Keating model are calculated for CuInS, and AgInTe, from spectral moments by means of the traces of powers of the dynamical matrix. The spectral moments are derived from measurements of specific heat given in the literature. By diagonalizing the dynamical matrix composed with the calculated force constants the phonon frequencies in the centre of Brillouin zone are obtained. The comparison with published data from measurements on CoInS, shows reasonable agreement.Die Kraftkonstimten eiiies Keating-Modells werden fur CuInS, und AgInTe, aus den spektralen Momenten mit Hilfe der Spuren von Potenzen der dynamischen Matrix berechnet. Die spelitralen Noniente werden aus in der Literatur gegebenen Messungen der spezifischen Wirmeknpazitiit abgeleitet. Durrh Diagonalisierung der aus den berechneten Kraftkonstanten aufgestellten dynamischen Matrix werden die Phononenfrequenzen im Zentrum der Brillouinzone bestimmt. Der Vergleicli mit publizierten MeBwerten an CuInS, ergibt eine ziemlich gute ubereinstimmung.

A Frequency Sum Rule and Spectral Moments in Lattice Dynamics

“…Moreover, we now know that B2(ra)ch < 2 4 3 , Bn(ra)ch > 2 4 G for n = 4, 6 (A21 (cf. the figures) which enables us to make a more specific study of the error limits than done in the Appendix of [7]. As a result, the force constant ,8 has a lower value than that estimated in [7] ; this is in accordance with results of other authors quoted in [7].…”

“…I n [7] the Rosenstock sum rule has in fact been generalized in some sense, but neither [ 6 ] nor 171 give a proof of this generalized s u m rule. I n the present communication an even more general frequency sum rule than that used in [7] is shown to be valid and its possible applications are outlined. We shall now define the non-negative scalar quantities…”

“…The failure of the same method applied to similar diamond-or sphalerite-type crystals (s = 2 ) was tentatively explained in [7] by assuming that (Al) is not well fulfilled for lattices having smaller primitive cells. This assumption has in fact been confirmed by the results of the present communication.…”

“…Recently, following a suggestion by Leibfried [ 6 ] , the connection between slims of the type (1) and the spectral moments of the frequency spectrum has heen employed [ 7 ] to estimate the force constants of some ternary semiconducting compounds ; the spectral moments were taken from thermal measurements. I n [7] the Rosenstock sum rule has in fact been generalized in some sense, but neither [ 6 ] nor 171 give a proof of this generalized s u m rule.…”

Trends in the high-temperature heat capacities of ternary chalcopyrite semiconductors

“…For CulnSe2 and CulnTe2, the variation of 0D with T was estimated according to the relations given in [8,19], by using the interatomic force constants from [20]. The resulting /XCp curves are shown in Fig.…”