B1-B2 Phase Transition Research Articles

Single-crystal elastic moduli, anisotropy, and the B1–B2 phase transition of NaCl at high pressures

Pressure dependences of the highest and lowest possible longitudinal sound velocities in single crystals of the B1 and B2 phases of NaCl were extracted from examination of their polycrystalline samples using the technique of time-domain Brillouin scattering. Based on the data collected up to 41 GPa, we largely extended the pressure range where single-crystal elastic moduli, Cij(P), and elastic anisotropy of the two cubic phases are measured, especially the experimental data for the B2 phase formed upon the reconstructive phase transition. The B1 phase of NaCl exhibits strong and growing anisotropy with increasing pressure, while that of the B2 phase is much weaker. Comparing with the previous experimental Cij(P) of other compounds exhibiting or expected to exhibit the B1–B2 phase transition, such as CaO, MgO, and (Mg1−x, Fex)O, we concluded that the transition is initiated by the shear instability due to violation of the Born stability criterion [C44(P)–P] > 0 and predicted the presently-not-verified transition pressures for MgO and (Mg1−x, Fex)O.

First-principles study of thermoelasticity and structural phase diagram of CaO

We present pressure $(P)$ and temperature $(T)$ variations of elastic and anisotropic properties, solid-solid (rocksalt, B1 to cesium chloride, B2) and solid-liquid structural phase transitions of CaO. We employed first-principles density functional theory supplemented with an anharmonic contribution to phonon dynamics. Good agreement is obtained for all properties up to the pressure and temperature range relevant to the Earth's mantle and outer core. Born elastic criteria are generalized for arbitrary stress to elaborate the structural phase diagram from a thermoelastic viewpoint. We propose a self-consistent computational scheme to incorporate the effect of thermal hysteresis into Lindemann's melting law. This improvised melting law exhibits quantitative agreement with reported findings for the high-$P$ melting curve. We find the triple point (i.e., the coexistence of B1, B2, and liquid phases) at 23 GPa and 4600 K. By examining the pressure-term included elastic properties, we can show that the solid-solid transition is mechanical in a pressure range of 0--200 GPa and temperature up to 3000 K. The softening of shear elastic constant ${C}_{44}$ drives the B1-B2 phase transition. This assertion is corroborated by examining the phonon dispersion curve and mode Gr\"uneisen parameter at different pressures for both B1 and B2 phases. The solid-liquid phase boundary can be treated accurately through the temperature-dependent thermodynamic Gr\"uneisen parameter. Furthermore, in this paper, we predict a negative melting slope $>140\phantom{\rule{0.28em}{0ex}}\mathrm{GPa}$ with a peak temperature of 7800 K, suggesting a smaller molar volume on the liquid side than that of the solid phase. This finding is supported by electronic band structure calculation. It is proposed that the hybridization of the empty $3d$ band of the cation with $s$ orbitals lowers the conduction band to cross the Fermi energy at the Brillouin zone center and leads the insulator-to-metal/semimetal phase transition $\ensuremath{\sim}200\phantom{\rule{0.28em}{0ex}}\mathrm{GPa}$. Different electronic states on solid and liquid sides make the liquid phase more compressible than the solid phase, eventually reducing the melting temperature with pressure.

Ab initio study of MgO under pressure using quasi-harmonic approximation

We examine the dependence of the Gibbs free energy and entropy on pressure and density along MgO isotherm 300 K. Some theoretical works have previously predicted a drastic drop of entropy along MgO isotherms by analyzing existing experimental data and extrapolating them to high pressures. We present first-principle calculations of thermodynamic properties of MgO under pressure using density functional theory and quasi-harmonic approximation. The robustness of our calculations is verified by comparing the calculated and experimental phonon dispersion curves. The comparison with available diamond anvil cell experimental data is also provided. Our estimate for the B1–B2 phase transition is in good agreement with other experimental and theoretical studies. However, our results for entropy along isotherm 300 K do not agree with previous theoretical estimates based upon the integration of thermal expansion coefficient and isothermal bulk modulus by volume.

Entropic Precursor for the B1–B2 Phase Transition of Crystalline Magnesium Oxide at 300 K

Calculations for MgO on a 300 K isotherm (as in the works of other authors) show that when compressed by 2–2.5 times, its absolute entropy falls sharply and tends to zero. A synergistic effect is then revealed: low values of entropy on the isotherm for MgO are a precursor of a phase transition that causes the entropy of the crystal to grow abruptly, eliminating the problem of zero entropy. A large group of diatomic solids of the NaCl type is identified that undergo similar phase transitions under compression.

Measurements of thermal conductivity across the B1-B2 phase transition in NaCl

We present measurements of the pressure dependence of thermal conductivity for high pressure phases of KCl and NaCl using the laser-heated diamond anvil cell (LHDAC) and a 3D finite element model for heat flow. Temperature measurements are made in the LHDAC of KCl in the B2 phase, from 15 GPa to 24 GPa, and of NaCl from 14 GPa to 43 GPa, across the B1-B2 phase transition. The measurements are forward modeled, using the geometry and material properties of the cell as inputs, solving for the change in thermal conductivity between pressure steps. The results for B2 KCl indicate increasing thermal conductivity over the experimental pressure range and give dlnκdlnρ=3.75 ± 0.9. For NaCl, thermal conductivity increases in the B1 and B2 phases, dlnκdlnρ=1.6 ± 0.5 and dlnκdlnρ=2.9 ± 0.8, respectively. Our results constrain the reduction in thermal conductivity across the NaCl B1-B2 transition to 37% ± 7%.

Strength and texture of sodium chloride to 56 GPa

The strength and texture of sodium chloride in the B1 (rocksalt) and B2 (cesium chloride) phases were investigated in a diamond anvil cell using synchrotron X-ray diffraction in a radial geometry to 56 GPa. The measured differential stresses within the Reuss limit are in the range of 0.2 GPa for the B1 phase at pressure of 24 GPa and 1.6 GPa for the B2 phase at pressure of 56 GPa. A strength weakening is observed near the B1-B2 phase transition at about 30 GPa. The low strength of NaCl in the B1 phase confirms that it is an effective pressure-transmitting medium for high-pressure experiments to ∼30 GPa. The B2 phase can be also used as a pressure-transmitting medium although it exhibits a steeper increase in strength with pressure than the B1 phase. Deformation induces weak lattice preferred orientation in NaCl, showing a (100) texture in the B1 phase and a (110) texture in the B2 phase. The observed textures were evaluated by viscoplastic self-consistent model and our results suggest {110}⟨11¯0⟩ as the slip system for the B1 phase and {112}⟨11¯0⟩ for the B2 phase.

B1-B2 phase transition mechanism and pathway of PbS under pressure.

Experimental studies at finite Pressure-Temperature (P-T) conditions and a theoretical study at 0 K of the phase transition in lead sulphide (PbS) have been inconclusive. Many studies that have been done to understand structural transformation in PbS can broadly be classified into two main ideological streams-one with Pnma and another with Cmcm orthorhombic intermediate phase. To foster better understanding of this phenomenon, we present the result of the first-principles study of phase transition in PbS at finite temperature. We employed the particle swarm-intelligence optimization algorithm for the 0 K structure search and first-principles metadynamics simulations to study the phase transition pathway of PbS from the ambient pressure, 0 K Fm-3m structure to the high-pressure Pm-3m phase under experimentally achievable P-T conditions. Significantly, our calculation shows that both streams are achievable under specific P-T conditions. We further uncover new tetragonal and monoclinic structures of PbS with space group P21/c and I41/amd, respectively. We propose the P21/c and I41/amd as a precursor phase to the Pnma and Cmcm phases, respectively. We investigated the stability of the new structures and found them to be dynamically stable at their stability pressure range. Electronic structure calculations reveal that both P21/c and I41/amd phases are semiconducting with direct and indirect bandgap energies of 0.69(5) eV and 0.97(3) eV, respectively. In general, both P21/c and I41/amd phases were found to be energetically competitive with their respective orthorhombic successors.

Vacancies in MgO at ultrahigh pressure: About mantle rheology of super-Earths

First-principles calculations are performed to investigate vacancy formation and migration in the B2 phase of MgO. Defect energetics suggest the importance of intrinsic non-interacting vacancy pairs, even though the extrinsic vacancy concentration might govern atomic diffusion in the B2 phase of MgO. The enthalpies of ionic vacancy migration are generally found to decrease across the B1-B2 phase transition around a pressure of 500 GPa. It is shown that this enthalpy change induces a substantial increase in the rate of vacancy diffusion in MgO of almost four orders of magnitude (∼104) when the B1 phase transforms into the B2 phase with increasing pressure. If plastic deformation is controlled by vacancy diffusion, mantle viscosity is expected to decrease in relation to this enhanced diffusion rate in MgO across the B1-B2 transition in the interior of Earth-like large exoplanets. Our results of atomic relaxations near the defects suggest that diffusion controlled creep viscosity may generally decrease across high-pressure phase transitions with increasing coordination number. Plastic flow and resulting mantle convection in the interior of these super-Earths may be therefore less sluggish than previously thought.

Kinetics of the B1-B2 phase transition in KCl under rapid compression

Kinetics of the B1-B2 phase transition in KCl has been investigated under various compression rates (0.03–13.5 GPa/s) in a dynamic diamond anvil cell using time-resolved x-ray diffraction and fast imaging. Our experimental data show that the volume fraction across the transition generally gives sigmoidal curves as a function of pressure during rapid compression. Based upon classical nucleation and growth theories (Johnson-Mehl-Avrami-Kolmogorov theories), we propose a model that is applicable for studying kinetics for the compression rates studied. The fit of the experimental volume fraction as a function of pressure provides information on effective activation energy and average activation volume at a given compression rate. The resulting parameters are successfully used for interpreting several experimental observables that are compression-rate dependent, such as the transition time, grain size, and over-pressurization. The effective activation energy (Qeff) is found to decrease linearly with the logarithm of compression rate. When Qeff is applied to the Arrhenius equation, this relationship can be used to interpret the experimentally observed linear relationship between the logarithm of the transition time and logarithm of the compression rates. The decrease of Qeff with increasing compression rate results in the decrease of the nucleation rate, which is qualitatively in agreement with the observed change of the grain size with compression rate. The observed over-pressurization is also well explained by the model when an exponential relationship between the average activation volume and the compression rate is assumed.

Role of 5f electrons in the structural stability of light actinide (Th-U) mononitrides under pressure.

Pressure induced structural sequences and their mechanism for light actinide (Th-U) mononitrides were studied as a function of 5f-electron number using first-principles total energy and electronic structure calculations. Zero pressure lattice constants, bulk module and C11 elastic module vary systematically with 5f-electron number implying its direct role on crystal binding. There is a critical 5f-electron number below which the system makes B1-B2 and above it B1-R3̄m-B2 structural sequence under pressure. Also, the B1-B2 transition pressure increases with increasing 5f-electron number whereas an opposite trend is obtained for the B1-R3̄m transition pressure. The ascending of N p anti-bonding states through the Fermi level at high pressure is responsible for the structural instability of the system. Above the critical 5f-electron number in the system a narrow 5f-band occurs very close to the Fermi level which allows the system to lower its symmetry via band Jahn-Teller type lattice distortion and the system undergoes a B1-R3̄m phase transition. However, below the critical 5f-electron number this mechanism is not favorable due to a lack of sufficient 5f-state occupancy and thus the system undergoes a B1-B2 phase transition like other ionic solids.

Pressure induced phase transition in CeN with NaCl–type structure

We have expressed the Gibbs free energy for CeN compound as a function of pressure and charge transfer through improved interaction potential model (IIPM). The lattice energy in it has been represented by an IIPM which include Coulomb interaction, three body interaction, polarizability effect and overlap repulsive interaction. The phase transition pressure and relative compression reveal that this compound shows a B1-B2 phase transition and this approach are found to be the experimental data in future. The phase transition pressures and volume collapses obtained from this model show a generally good agreement with available results.

The Pressure Induced B1-B2 Phase Transition of CdO

In this paper, the structural, elastic and thermodynamic properties of CdO under di erent pressure range have been reported. An extended interaction potential model (including the zero point energy e ect) has been used for this study. Phase transition pressures are associated with a sudden collapse in volume. At compressed volume, the present oxide is found in cesium chloride (CsCl) phase. The calculated second order elastic constants and their various combinations have been reported in di erent pressure range. The calculated values have been compared with available results. Our values have been found in good agreement with existing ndings.

Induced changes in vibrational properties of NaH and KH under hydrostatic pressure

The pressure induced phase transition from the NaCl to CsCl structure in NaH and KH has been investigated by means of first-principles calculations, and density functional linear-response theory. A pressure-induced soft-acoustic phonon mode is identified at 30GPa, and 7.5GPa for NaH and KH respectively. Phonon calculations suggest that the pressure induced instabilities of the transverse acoustic modes at the [ε00], and [εε0] directions are responsible for the phase transition of NaH and KH. Furthermore charge density analysis shows that there is charge transfer from the alkali ion to hydrogen (i.e., Na→H, K→H) inducing B1–B2 phase transition.

Compression of mineral barite, BaSO4: a structural study

The aim of this paper is to contribute to a better understanding of the behaviour of mineral barite, BaSO4, at high pressures, particularly the recently reported phase transition at 27 GPa to a new structure type. For this purpose, we will focus on the evolution of its BaS cation array with pressure, which will additionally allow for a rational description of the structure. When the initial Pnma barite structure transforms into the also orthorhombic P212121 structure, no change in the coordination number of Ba or S atoms occurs ([SO4] tetrahedra and [BaO12] dodecahedra). However, the second coordination sphere presents an increase of neighbour atoms and a decrease of the Ba–S distances. This rearrangement of atoms is related to the Buerger's mechanism of the B1–B2 phase transition for the BaS cation array, confirming that cations (second neighbours) do not arrange in an arbitrary way.

Structural phase transition and elastic properties of cerium chalcogenides at high pressure

The structural and elastic properties of cerium chalcogenides (CeZ, Z = S, Se, Te) under high pressure have been investigated by using the potential model considered up to third nearest neighbor interaction. The computed values of B1-B2 phase transition pressure, equation of state (compression curve), bulk modulus, its first order pressure derivative and elastic constants in the case of cerium chalcogenides agree well with the experimental results. The present study shows the anomalous behavior of cerium chalcogenides in comparison to the alkaline earth chalcogenides, due to the presence of Kondo effect and reentrant valence behavior of Ce in cerium chalcogenides.

Pressure-induced B1-B2 phase transition in AgX: revisited

Pressure-induced B1-B2 phase transition in Ag<i>X</i>: revisited

A Walk on the Chemical Landscape: The Role of B33 along the B1–B2 Phase Transition in RbF and NaBr

AbstractA comparative atomistic study of the high‐pressure polymorphism in crystalline RbF and NaBr is presented. For RbF a pair potential is developed from coarse‐graining DFT‐LDA calculations. The results clearly indicate the intermediate role of structural motifs of B33 type. In RbF it appears as an interfacial motif, in NaBr B33 phase grows larger from an initial inset within the pristine B1 structure, highlighting the role of chemical reactivity and smooth reactivity trends in high‐pressure experiments.

The pressure induced B1–B2 phase transition of alkaline halides and alkaline earth chalcogenides. A first principles investigation

In this work, we considered the pressure induced B1–B2 phase transition of AB compounds. The DFT calculations were carried out for 11 alkaline halides, 11 alkaline earth chalcogenides and the lanthanide pnictide CeP. For both the B1 and the B2 structures of each compound, the energy was calculated as a function of the cell volume. The transition pressure, the bulk moduli and their pressure derivatives were obtained from the corresponding equations of state. The transition path of the Buerger mechanism was described using roots of the transition matrix. We correlated the computed enthalpies of activation to some structure defining properties of the compounds. A fair correlation to Pearsons hardness of the ions was observed.

Pressure-induced phase transition and elastic properties of barium chalcogenides

Two-body, Born–Mayer type potential considered up to the third nearest-neighbor interaction have been used to investigate the B1–B2 phase transition and elastic properties of barium chalcogenides at high pressure. The computed values of B1–B2 phase transition pressure, equation of state (compression curve), bulk modulus, and its first-order pressure derivative are given along with the available experimental and other theoretical values. This study supports the Born's stability criterion and shows that the third nearest-neighbor interaction has an important role to predict the B1–B2 phase transition pressure in barium chalcogenides.

Atomistic In Situ Investigation of the Morphogenesis of Grains during Pressure‐Induced Phase Transitions: Molecular Dynamics Simulations of the B1–B2 Transformation of RbCl

The mechanistic details of the pressure-induced B1-B2 phase transition of rubidium chloride are investigated in a series of transition path sampling molecular dynamics simulations. The B2→B1 transformation proceeds by nucleation and growth involving several, initially separated, nucleation centers. We show how independent and partially correlated nucleation events can function within a global mechanism and explore the evolution of phase domains during the transition. From this, the mechanisms of grain boundary formation are elaborated. The atomic structure of the domain-domain interfaces fully support the concept of Bernal polyhedra. Indeed, the manifold of different grain morphologies obtained from our simulations may be rationalized on the basis of essentially only two different kinds of Bernal polyhedra. The latter also play a crucial role for the B1→B2 transformation and specific grain boundary motifs are identified as preferred nucleation centers for this transition.