A simple model for calculating the bulk modulus of the mixed ionic crystal: NH4Cl1−x Br x

Abstract

The ammonium halides are an interesting systems because of their polymorphism and the possible internal rotation of the ammonium ion. The static properties of the mixed ionic crystal NH 4 Cl 1−x Br x have been recently investigated, using the three-body potential model (TDPM) by applying Vegard's law. Here, by using a simple theoretical model, we estimate the bulk modulus of the alloys NH 4 Cl 1−x Br x , in terms of the bulk modulus of the end members alone. The calculated values are comparable to those deduced from the three-body potential model (TDPM) by applying Vegard's law.

A tentative model for estimating the compressibility of rock-salt AgCl x Br 1 − x alloys

“…(6). In other words in our former publications [16,18] dealt either with mixed alkali halides or with ammonium halides, we calculated the first and second pressure derivatives of the bulk modulus on the basis of Eq. (6) under pressure using a least squares fit to a second order Murnaghan equation as it will be described in the next section.…”

“…We employ here a simple model, that has been also recently [16] used for the calculation of the compressibility of multiphased mixed alkali halides crystals grown by the melt method [17] using the miscible alkali halides, i.e., NaBr and KCl, which have a simple cubic space lattice of the NaCl-type and measured in a detailed experimental study by Padma and Mahadevan [17]. This model has been also successfully applied [18] to the mixed crystal NH 4 Cl 1-x Br x considering that NH 4 Cl and NH 4 Br have a simple cubic space lattice structure of the CsCl-type. In this paper we report the remarkable finding that this simple model produces in the case of AgCl x Br 1-x alloys equally successful results as in the mixed alkali halides and mixed ammonium halides despite the aforementioned significant differences in their physical properties and especially the lack [6] of a unified explanation with simple theories of the elastic properties of silver halides and alkali halides, as mentioned above.…”

Thermodynamic estimation the compressibility of ferropericlase under high pressure

“…Previous studies have demonstrated that considering υ d 2,1 to be independent of composition can achieve good approximation in different mixed systems; [14][15][16][17][18] thus, υ d 2,1 can be determined from the end members using the following equation…”

“…Recently, a series of publications, [14][15][16][17] based on a thermodynamic model, 18 has attempted to predict the compressibility of a multiphased mixed system in terms of the elastic data of the end members. This approach has been highly successful in mixed ionic crystals, such as alkali halides, 14,15,18 transition metal alloys 16,17 and Earth materials.…”

“…This approach has been highly successful in mixed ionic crystals, such as alkali halides, 14,15,18 transition metal alloys 16,17 and Earth materials. 19,20 On the basis of this concept, the present study mainly aims to examine whether the compressibility of the (Mg 1−x Fe x )O solid solution can be estimated using only the elastic data of end members.…”