B1-B2 Transition Research Articles

Phase transitions in ionic crystals under ultrahigh pressures

Structural phase transitions induced in alkali-halide crystals by an ultrahigh pressure are investigated. The pressure of the B1–B2 transition in an infinite crystal is calculated with the use of ion pair interaction potentials obtained by the self-consistent method in the context of nonuniform electron gas theory. In the approximation of seven coordination spheres, relative changes in volumes of B1 and B2 modifications of a number of alkali-halide crystals are calculated.

Structural Properties of KBr: Elastic Behaviour and Pressure Effects

We have studied the pressure induced B1-B2 transition and the elastic behaviour of KBr using three-body potential model. It is found that the inclusion of the three-body forces in the potential model yields more reasonable values of phase transition pressure, second-order elastic constants and bulk modulus than those obtained by others (wherever available). Results of high-pressure experiments carried out on KBr for volume transitions are also reported in this paper in order to verify theoretical studies.

Structural phase stability of ThSb and ThAs under pressure

The high-pressure behaviour of thorium monopnictides is of considerable interest as these systems exhibit structural phase transitions under pressure. At ambient conditions these compounds crystallize in the NaCl-type (B1) structure. Experiments show that with the application of pressure these compounds transform to the CsCl-type (B2) structure. ThSb and ThAs are found to exhibit B1–B2 transition in the pressure range between 9–12 GPa and 1826 GPa respectively. In this work, we present the electronic and high-pressure behaviour of ThAs and ThSb performed using the tight-binding linear muffin-tin orbital method. The total energies within the atomic sphere approximation were calculated as a function of volume for both the B1 and B2 structures. The total energy calculations reveal that both ThSb and ThAs are stable in the B1 structure at ambient conditions and undergo structural transition to the B2 structure at pressures 78 and 240 kbar respectively, which are in good agreement with the experimental values. The calculated values of equilibrium lattice parameter and the transition pressure are found to be in good agreement with the experimental results.

Pressure-induced structure change of molten KCl

Abstract Energy-dispersive X-ray diffraction experiments of molten KCl under high pressure have been carried out by using synchrotron radiation. The diffraction profiles of molten KCl were acquired just above the melting temperature of KCl up to 4 GPa. The reduced structure factor S(Q)'s for molten KCl do not show any change in their primary features, except for a gradual increase in the first peak intensity with increasing pressure. This implies that molten KCl does not show a first-order phase transition, such as the B1-B2 transition, found in solid KCl, but that the local structure in molten KCl must be changed by compression. According to a molecular-dynamics simulation, this change of S(Q) can be explained by a continuous increase in the coordination number of the nearest-neighbor ions in molten KCl with pressure.

Electronic and structural properties of alkaline-earth oxides under high pressure.

The linear muffin-tin-orbital method in its tight-binding representation is used to calculate the band structures and to investigate the structural phase stability of MgO, CaO, and SrO under high pressures. The calculated equilibrium properties agree well with the experimental data. In CaO and SrO, the B1-B2 transition occurs at 557 and 317 kbar, respectively, which are in agreement with the experimental observations. For MgO the transition from the B1 to B2 phase is found to occur at a very high pressure of 1975 kbar. The electronic band structures at normal and at high pressures and the variation of fundamental band gaps as a function of pressure are calculated.

A topological transition of B1-KOH-T1I-B2 type AgCl under high pressure

A new B1–B2 transition with two intermediate phases was observed in AgCl in the pressure and temperature range up to 17.5 GPa and 500 °C by the X-ray powder diffraction method in situ. One intermediate phase has the KOH type structure, which is stable in the pressure range between about 8 and 12 GPa. The other has the T1I type structure which is stable up to 17 GPa at room temperature. The T1I type phase transforms to the B2 type phase at 17 GPa and 200 °C. We demonstrate that these four structures can be described systematically using a common monoclinic cell, and the cell parameters change continuously from the B1 to B2 structures. A topological mechanism by a simple deformation is proposed to explain these transformations, in which the [110] and [11̄0] directions of the B1 structure correspond to the [100] and [01̄1] of the B2 structure, respectively.

Low- and high-pressure ab initio equations of state for the alkali chlorides.

We have carried out ab initio perturbed ion calculations in the rocksalt (B1) and cesium chloride (B2) phases of the alkali (A) chloride (ACl) crystals. Zero temperature (T), and pressure (P) lattice energies and equilibrium distances are computed with errors less than 5%. From static calculations, zero-T equations of state (EOS) are reported in the ranges 0\char21{}80 GPa for LiCl, 0\char21{}60 GPa for NaCl and KCl, 0\char21{}10 GPa for RbCl, and 0\char21{}5 GPa for CsCl. The experimental data enable us to perform a critical test of the performance of a theoretical methodology; we place particular emphasis on (a) the comparison between calculated and experimental trends and (b) the consistency with the behavior observed in real materials. We have found that our theoretically modeled solids obey the Vinet universal EOS and match the experimental behavior in temperature-scaled EOS diagrams. We have also analyzed the phase stability of the ACl crystals from a thermodynamic point of view. The hydrostatic pressure necessary to produce the B1-B2 phase transition is calculated to decrease with the cation size, in agreement with the experimental observation. Our predicted value of the (not yet measured) B1-B2 transition pressure for LiCl is close to 80 GPa. Finally, our calculations based on the combined kinetic-thermodynamic model proposed by Li and Jeanloz for the NaCl transition phase [Phys. Rev. B 36, 474 (1987)] predict that the hysteresis pressure range of the B1-B2 transition decreases from LiCl to RbCl.

A High-Pressure Test of Birch's Law

The compressional wave velocities of polycrystalline NaCl and KCl have been measured to over 17 gigapascals, with the use of Brillouin scattering and the diamond anvil cell. This pressure corresponds to 40% compression for NaCl and 60% compression for KCl (including the volume change across the B1-B2 transition). The data obey Birch's Law, which predicts that the velocity of each material is linear with density, except across the B1-B2 phase transition in KCl. This deviation from Birch's Law can be rationalized in terms of an interatomic potential model wherein the vibrational frequencies of the nearest neighbor bonds decrease when going to the eight-coordinated B2 structure from the six-coordinated B1 structure.

Measurement of the B1-B2 transition pressure in NaCl at high temperatures.

The phase boundary and kinetics of the B1-B2 transition in NaCl are documented between 298 and 670 K by visual observation into an externally heated diamond cell. We find an equilibrium (reversed) transition pressure ${P}_{\mathrm{tr}=26.8}$ GPa at room temperature, with a Clapeyron slope ${\mathrm{dP}}_{\mathrm{tr}/\mathrm{dT}=\mathrm{\ensuremath{-}}8.9}$ MPa/K at elevated temperatures; the corresponding entropy change is 7.4 J/mol K. An apparent activation energy of 5.3 kJ/mol is obtained from the observed decrease in transition hysteresis with temperature. Previous determinations of the NaCl B1-B2 transition pressure have been biased upward by 3 GPa or more due to kinetic hindrances. Extrapolating our results to 0 K, however, we find good agreement (\ensuremath{\sim}12% difference) with the transition pressure derived from ab initio pseudopotential calculations.

Thermal effects at the B1–B2-transition of potassium bromide

Measurements of the thermal diffusivity and observations of the latent heat are used to investigate the mechanism of the pressure-induced B1–B2-transition of potassium bromide. The latent heat is delivered in the form of a series of pulses. From the observation of the thermal diffusivity and the appearance of the pulses it follows that there is coexistence range of 0.15 GPa width which is smaller than the hysteresis width of 0.6 GPa. Different domains in the single crystal are transformed one after the other. All observations indicate a martensitic character of the transition.

Mechanism of B1-B2 transition of ionic crystals under pressure

Under pressure the B1 structure of alkali halides transforms to the B2 structure. There is a preferred orientation relation between these two structures. Lattice-dynamically, the TA[100] mode of B1 structure becomes unstable under pressure. It is shown that this instability is caused by the repulsive term which increases under pressure and is weakened by deformation of the TA[100] mode. Discussions on thermodynamics are given; there is no difference between the Gibbs and the internal energies for lattice-dynamical studies, but for finite deformation what must be dealt with is the Gibbs free energy.

B1-B2 Transition in Calcium Oxide from Shock-Wave and Diamond-Cell Experiments

Volume and structural data obtained by shock-wave and diamond-cell techniques demonstrate that calcium oxide transforms from the B1 (sodium chloride type) to the B2 (cesium chloride type) structure at 60 to 70 gigapascals (0.6 to 0.7 megabar) with a volume decrease of 11 percent. The agreement between the shockwave and diamond-cell results independently confirms the ruby-fluorescence pressure scale to about 65 gigapascals. The shock-wave data agree closely with ultrasonic measurements on the B1 phase and also agree satisfactorily with equations of state derived from ab initio calculations. The discovery of this B1-B2 transition is significant in that it allows considerable enrichment of calcium components in the earth's lower mantle, which is consistent with inhomogeneous accretion theories.

The high pressure phase transitions in KF and RbF

The high pressure B1 ⇹ B2 transitions in KF at ~ 40 kbar and RbF at ~ 30 kbar have been studied using hydrostatic X-ray diffraction. No other transitions have been observed. The addition of the ΔV V for these transitions to the already existing body of literature on B1–B2 transitions in alkali halides permits an extension of Pauling's theory to larger values of radius ratios. It also permits the modified Born criterion for predicting phase transitions to be further verified. Values of ionic radii for 8 coordination we suggest are 1.33 Å for F −, 1.84 Å for Cr −, 2.00 Å for Br − and 2.27 Å for I −.

Isothermal equation of state for sodium chloride by the length-change-measurement technique

The change in length of a 1-m-long NaCl single crystal has been determined as a function of hydrostatic pressure up to 7.5 kbar and at temperatures of 29.5 and 40.4 °C, to an accuracy of 500 Å using a Fabry-Perot–type He-Ne laser interferometer. The best values of the isothermal bulk modulus and its pressure derivative at atmospheric pressure and at 29.5 °C are B0=237.7±0.3 kbar, B′0 =5.71±0.25, and B″0=−0.10±0.05 kbar−1, respectively. These are the averages of the values obtained by a least-squares fit of several different equations of state to the present isothermal data. From these low-pressure measurements along, it is not possible to conclude which one of these equations provides a better fit to the data than the others. However, when other high-pressure data are taken into account, it appears that Keane’s equation best represents the measurements. When Keane’s equation is fitted to the data, and the published lattice parameter of NaCl at the Bi-III-V transition and at the NaCl B1-B2 transition are used, the respective transition pressures are found to be 75.8 kbar, within 1.2 kbar of the presently accepted value and 262 kbar, respectively. Considering the precision of the experiment the values of B0, B′0, and B″0 represent the best measurements so far. The determination of B″0 isothermally represents the first measurement of its kind.