Szigeti Relation Research Articles

Compositional Dependence of Infrared Transmission in Ge‐Based Chalcogenide Glasses

As for an optically homogeneous glass with thickness tantamount to a few millimeters, the longer wavelength side of its optical transmission window normally takes shape as a result of multiphonon absorption. Mainly due to the complexity inherent in glass structures, a quantitative numerical assessment of the vibrational spectrum of a given glass composition is normally not a simple task. The conspicuously dissimilar infrared transmission edges between oxide and halide glasses, for example, can be understood qualitatively in terms of the Szigeti relation; however, the relatively insignificant but clearly distinguishable changes in infrared transmission edge resulting from compositional modification in a glass‐forming system are lacking a numerical assessment. Herein, it is experimentally verified that the infrared transmission edge of Ge‐based chalcogenide glasses can be correlated in a quantitative manner with their chemical composition through combining their average bond energy and molar mass. Ternary or quaternary chalcogenide glasses exceeding 100 different compositions are used to justify this numerical correlation.

On the interionic potentials and polarization models in alkali halide crystals

It is shown that the modified Szigeti relation can be used to make a critical assessment of various polarization models and interionic potentials in alkali halides. Various sets of interionic potentials derived recently are critically discussed. The importance of three body interactions in developing a potential model as well as a polarization model is demonstrated.

Pressure dependence of the effective charge of ionic crystals

For ionic crystals of NaCl and CsCl structures, the volume dependence of the effective ionic charge ( d ln s d ln V ) defined by the second Szigeti relation is calculated using low temperature experimental data. The need for experimental data of γ T at T→ 0°K is remarked upon. ( d ln s d ln V ) obtained independently with a deformation dipole model and a simple shell model. The results are compared. All models tend to give positive values of ( d ln s d ln V ), as expected.

Effective compressibilities of some ionic semi-conducting compounds of IV–VI group

An analysis of effective compressibilities of the ionic semiconductors PbS, PbSe, PbTe and SnTe has been performed within the framework of many body lattice theory (MLT). The extended three body force shell model (ETSM) which is ultimately based on MLT has been employed to evaluate the values of effective compressibilities of the solids under study. The mode/parameters have been calculated by using the expressions of elastic, optic and dielectric constants within the framework of the theory described in ETSM. The values of elastic constants and long wave optical vibration frequency have been used in the expressions as input data. It is found that the analysed values of fl*/fl are in close agreement with the results obtained froIrt Szigeti relation.

Perturbation‐theoretical model calculation of the lattice mechanics of low polarisability ionic crystals

AbstractStarting from the Hartree‐Fock wave functions of free ions different lattice mechanical properties of a low‐polarisability ionic solid, namely, the RbF crystal are calculated within the framework of the perturbation‐theoretical‐model approach of ionic solids developed by Basu and Sengupta. In a recent investigation it is shown that the dipolar polarisation in an ionic solid may be additively decomposed into three parts, two short range polarisation effects and a long range one apart from the displacement polarisation. From an analysis of the Szigeti relations it is found that both the short range polarisation effects in the low polarisability ionic crystals are small compared to those in high polarisability crystals. This fact leads to a major simplification in calculation for this group of solids. The overall agreement obtained broadly justifies the approximations. Since no crystal property is used to obtain the parameters the discrepancies clearly indicate the regions where the omitted interactions are important. Finally a critical analysis of the results is presented and the difficulties of the existing phenomenological models for these solids are also discussed.

Analysis of effective compressibilities in PbS, PbSe, PbTe and SnTe

An analysis of effective compressibilities in ionic semiconductors PbS, PbSe, PbTe and SnTe has been performed within the framework of many-body lattice theory (MLT). The extended three-body force shell model (ETSM) has been employed to obtain the values of effective compressibilities in the solids under study. The model parameters have been calculated using the expressions for elastic and dielectric constants within the framework of the ETSM. It is found that the predicted values of β ∗/β agree fairly well with the results obtained from the Szigeti relation.

Volume dependence of the effective ionic charge of alkaline-earth fluorides

Abstract The importance of the use of low temperature data with the second Szigeti relation is shown for the fluorite structure; a comparison with the NaCl and CsCl structures is given. The volume dependence of the generalized first Szigeti relation is used to calculate the Gruneisen parameter γ 1 with low temperature data; γ 1 is calculated with different models. Values of the volume dependence of the effective ionic charge are obtained independently using Hardy's model.

On the pressure dependence of the effective ionic charge of cesium halides

The importance of temperature effects in the use of the second Szigeti relation to calculate the volume dependence of the effective ionic charge of cesium halide crystals is studied. The effect obtained is larger than the one for alkali halide crystals of the NaCl structure. Positive values of (∂ ln s/∂ In v) are obtained using low temperature experimental data with the Grüineisen parameter γ t ( T → 0K) calculated using the generalized first Szigeti relation. Values of γ t are also obtained with a rigid ion model and they differ little from the previous ones.

An estimate of the pressure dependence of the dielectric constant in alkali halides

AbstractThe determination of the pressure dependence of the static dielectric constant, ϵS, from the Szigeti relations, demands the knowledge of the volume dependence of the Szigeti charge e*, which unfortunately is unknown. By using the classical Lorentz‐Lorenz relation and connecting the ionic polarizability to the bulk modulus a simple relation for dϵS/dP is derived; although it gives the correct order of magnitude, the calculated values exceed the experimental ones by a factor 1.2 to 2. This difference is possibly due to the increase of e* with pressure. A simple relation for the Gruneisen constant of the transverse optical mode is also given.

Temperature dependence of Szigeti effective charge of alkali halides

Abstract The second Szigeti relation was used to obtain the temperature dependence of the Szigeti effective charge, es. The results are discussed in the framework of the deformation dipole model. Recent experimental data are used to show that the volume derivatives of es of most ionic solids are positive, thus providing evidence that the deformation dipole model is qualitatively valid.

Transverse optic mode Gruneisen parameter and dielectric properties of alkali halides

The well known Szigeti relations for the dielectric theory of ionic crystals have been critically examined by investigating the volume dependence of dielectric behaviour of alkali halides. It has been predicted that the strain derivative of effective ionic charge parameter should be nearly equal to zero. Values of transverse optic mode Gruneisen parameter for NaCl structure alkali halides have been estimated.

Effect of anharmonicity on the K ≈ 0 modes of MgO and ZnS

AbstractExperimental investigations are made of the infrared transmission spectra of MgO and ZnS in the region of the fundamental lattice absorption at room temperature. The magnitude of the effect of anharmonicity has been calculated and discussed in the light of symmetry of spectra at the resonance frequencies. The effective ionic charge and compressibility of Szigeti's relations are calculated and the significance of these results is discussed from the point of view of various models of dielectric behaviour.

The dielectric constant of ionic solids and its change with hydrostatic pressure

Abstract We have measured the low frequency dielectric constant and its change with hydrostatic pressure of a variety of ionic solids of varying purity. Dielectric constants have been measured using a geometrical technique in association with a three-terminal transformer bridge system, a similar system also being used for the measurement of changes with pressure. It is shown that trace impurities do not give rise to greatly disproportionate effects. Some comparisons are made with and some conclusions are drawn from the Clausius-Mossotti equation, the Szigeti relations, and the model of Dick and Overhauser.

Infrared Lattice Vibrational Spectra of AgCl, AgBr, and AgI

The infrared transmission spectra of AgCl, AgBr, and AgI have been measured between 400–30 cm−1 at room temperature and at 143°K. Strong absorptions characteristic of the transverse optic modes were found, together with weak subsidiary absorptions arising from multiphonon combinations. The longitudinal optic modes of silver chloride and silver bromide were obtained from the reflection spectra of thin, silver halide films deposited on a silvered substrate. Capacitance measurements were used to determine the static dielectric constant of AgI; ε0=7.0±0.3. For a series of isomorphous I—VII compounds having large reduced masses, approximately linear relations are found between νt2 and the reciprocal reduced masses. The Szigeti relations for effective charge and compressibility were calculated and their significance is discussed.

Long-Wave Lattice Dynamics of the Fluorite Structure

A simple shell model is used to calculate expressions for the long-wavelength vibrational eigenfrequencies and elastic constants of the fluorite (Ca${\mathrm{F}}_{2}$ type) lattice. The concept of effective charge is introduced and expressions analogous to the Szigeti relations for lattices with diatomic unit cells are given. These and other relations between the acoustic and optical properties derived for the dipole shell model are in better agreement with the measured properties of the alkaline-earth fluorides than are those derived for a rigid-ion model. The large deviation from the Cauchy relation ${C}_{12}={C}_{44}$ seems to be largely explainable in terms of the shell-model correction to the internal strain.

Trends in the Characteristic Phonon Frequencies of the NaCl-, Diamond-, Zinc-Blende-, and Wurtzite-Type Crystals

Several correlations are noted among the characteristic phonon frequencies of the I—VII, II—VI, III—V, and IV—IV compounds. In particular, the following linear relations are established: (1) between the Szigeti effective ionic charge q* and the zone center optical phonon separation (ν1—νt)/νt for the II—VI and III—V compounds; (2) between νt2 and ν12, and the reciprocal reduced mass 1/μ for the II—VI and III—V compounds, between νt2 and a/χμ, in the case of the alkali halides where a and χ are the lattice constant and compressibility, respectively; (3) between χ and an where n=4 for the zinc blende and n=3 for the alkali halides; and (4) between q* and α——α+, the difference between the atomic polarizability of the II—VI and III—V compounds. Comparison of observed and calculated compressibilities reveals that the Brout and Szigeti relations are more applicable to the IV—IV and III—V compounds, and to a lesser degree to the II—VI compounds, than to the alkali halides for which they were originally proposed.

Infrared lattice reflection spectra of LiCl, LiBr, KF, RbF, and CsF

The infrared lattice reflection spectra of LiCl, LiBr, KF, RbF and CsF have been measured in the spectral region from 95 to 1500 cm −1 and have been analysed by the Kramers-Krönig method. The following fundamental dispersion frequencies have been obtained: LiCl, 191 ± 2 cm −1; LiBr, 159 ± 4 cm −1; KF, 190 ± 2 cm −1; RbF, 156 ± 2 cm −1; CsF, 115(?) cm −1. The effective charges and compressibilities have been computed with the aid of the Szigeti relations.

Sum Rule for Lattice Vibrations in Ionic Crystals

It is shown that in lattices of tetrahedral symmetry with two ions to a unit cell, in the approximation of nearest neighbor repulsive interactions, for a given wave vector q, $\ensuremath{\Sigma}\stackrel{6}{i=1}{{\ensuremath{\omega}}_{i}}^{2}(\mathrm{q})=\frac{1}{\ensuremath{\beta}}\frac{18}{\overline{M}}{r}_{0},$ where ${\ensuremath{\omega}}_{i}(\mathrm{q})=\mathrm{angular}\mathrm{frequency}$ of the $i\mathrm{th}$ mode for a given wave vector q, $\overline{M}=\frac{{m}_{+}{m}_{\ensuremath{-}}}{({m}_{+}+{m}_{\ensuremath{-}})}$, ${m}_{+}=\mathrm{mass}\mathrm{of}\mathrm{positive}\mathrm{ion}$, ${m}_{\ensuremath{-}}=\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{negative}\mathrm{ion}$, ${r}_{0}=\mathrm{interionic}\mathrm{distance}$, and $\ensuremath{\beta}$ is the coefficient of compressibility. This theorem serves as a useful check on numerical work as well as a relation for the downward curvature of the optical modes at small $q$ in terms of the speed of sound. In the limit of small $q$, this relation becomes the first Szigeti relation. A similar theorem is true for low-density electron gases where the electrons localize on a lattice. Here one can show that $\ensuremath{\Sigma}\stackrel{3}{i=1}{{\ensuremath{\omega}}_{i}}^{2}(\mathrm{q})={{\ensuremath{\omega}}_{\mathrm{pl}}}^{2},$ where ${{\ensuremath{\omega}}_{\mathrm{pl}}}^{2}=\frac{4\ensuremath{\pi}n{e}^{2}}{m}$, which is the classical plasma frequency. (This last relation was first derived by Kohn.)

Theory of the Dielectric Constants of Alkali Halide Crystals

The simple classical theories of the dielectric constants and compressibility of ionic crystals lead to two relations among the experimental quantities from which arbitrary parameters have been eliminated, the Szigeti relations. Neither is satisfied by the data, indicating the inadequacy of these simple theories. The short-range repulsive interaction between ions with closed shell electron configurations is investigated, and an approximate interpretation of the Born-Mayer potential in terms of overlap integrals is developed. These results are applied to the interaction of model ions consisting of rigid charged shells bound to cores by harmonic restoring forces. Using this model, polarization mechanisms neglected in the simple dielectric constant theory, the "short range interaction polarization," and the "exchange charge polarization" are described. Both arise from charge redistributions occurring when the ions move with resulting changes in electron overlaps. Applied to a crystal, these ion models permit the derivation of generalizations of the Szigeti, Clausius-Mossotti, and Lorenz-Lorentz relations. The $\frac{{e}^{*}}{e}$ of the second Szigeti relation can then be calculated and comparison with the $\frac{{e}^{*}}{e}$ values derived from experimental data imply that the above polarization mechanisms must be at least in part responsible for the deviation of this parameter from unity. The failure of the first Szigeti relation is discussed and attributed to the inadequacy of the treatment of compressibility. The additivity feature of the simple theory and its absence in the refined theory are discussed in relation to the so-called vacuum and crystal ion polarizabilities.