Thermal Expansion of Caesium Halides with the CsCl Structure

Abstract

Thermal expansion of caesium halides has been approximated by a quasiharmonic approach (QHM)

Lattice constants and thermal expansion of H2O and D2O ice Ih between 10 and 265 K

“…The coefficients A 1 and A 2 were set to zero as the thermal expansivity and its temperature derivative are assumed to be 0 at T = 0 K. Under this assumption the validity of the polynomial expressions is from 0 to 265 K. Finally, we like to recall that a many-term polynomial expression was adopted to faithfully represent the measured data and not because there is a particular meaning in the various higher-order terms. We indicate that other approaches could be chosen based on various empirical quasi-harmonic approximations (Reeber & Wang, 1996;Wang & Reeber, 1995) with a different set of parameters; the validity of these approximations for the ice Ih case remains, however, to be proven and will not be attempted here. In concluding we note that the marked isotopic difference of lattice constants between deuterated and normal ice Ih so clearly established by our data is still far from being understood (Herrero & Ramírez, 2011).…”

A model for evaluating and predicting high-temperature thermal expansion

“…X i includes the effects of bulk modulus, volume, frequency distribution, and the Grüneisen parameter of the ith mode. For alkali halides and MgO, 11,12,15 the deviation of the lattice parameter at high temperature can be expressed empirically by a parabolic relationship. 5,[8][9][10] Because of the nature of the Einstein function, Eq.…”

“…Equation (5) has been applied to fit the experimental data of group IV elements, II-VI, and III -V compounds. 12,16 The small formation energies of these defects would indicate a vacancy ordering process. (5) will approach a constant at very high temperatures.…”

“…Reliable semiempirical, or theoretical models are useful for evaluating and predicting high temperature thermal expansion. 5,8-10 Wang and Reeber 11,12 have extended this n Einstein frequency model to include an empirically determined high-temperature parabolic relationship for predicting alkali halide thermal expansion. As indicated by Merchant et al, 1 "the parameters used for calculation have been obtained by curve fitting techniques, using not only the extensive phonon data measured by inelastic neutron scattering, but also the thermal expansion (and the temperature dependence of elastic constants) data which the models purport to predict."…”

Importance of dispersion in density functional calculations of cesium chloride and its related halides

“…4 which plots cell volumes for the B1 and B2 phases of the cesium halides at 0 K. Experimental values for the cell volumes at 0 K were corrected from the lowest measured temperature (293 K for CsF, 5 K for CsCl, and 20 K for CsBr and CsI) using experimental thermal expansion data. 42,43 In the case of the B1-CsCl phase the experimental value at 450 K was corrected to 0 K by assuming that this phase has the same thermal expansion coefficient as the B2 phase. Whereas the PBE functional consistently overestimates the volume (by an average of 9%), the LDA functional conversely underestimates the same quantity (by an average of 7%).…”