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.

Artificial neural network for deciphering the structural transformation of condensed ZnO by extended x-ray absorption fine structure spectroscopy

Pressure-induced structural phase transitions play a pivotal role in unlocking novel material functionalities and facilitating innovations in materials science. Nonetheless, unveiling the mechanisms of densification, which relies heavily on precise and comprehensive structural analysis, remains a challenge. Herein, we investigated the archetypal B4 → B1 phase transition pathway in ZnO by combining x-ray absorption fine structure (XAFS) spectroscopy with machine learning. Specifically, we developed an artificial neural network (NN) to decipher the extended-XAFS spectra by reconstructing the partial radial distribution functions of Zn–O/Zn pairs. This provided us with access to the evolution of the structural statistics for all the coordination shells in condensed ZnO, enabling us to accurately track the changes in the internal structural parameter u and the anharmonic effect. We observed a clear decrease in u and an increased anharmonicity near the onset of the B4 → B1 phase transition, indicating a preference for the iT phase as the intermediate state to initiate the phase transition that can arise from the softening of shear phonon modes. This study suggests that NN-based approach can facilitate a more comprehensive and efficient interpretation of XAFS under complex in-situ conditions, which paves the way for highly automated data processing pipelines for high-throughput and real-time characterizations in next-generation synchrotron photon sources.

A first-principles study of the electronic, mechanical, vibrational, and optical properties of the zirconium carbide under high pressure

Zirconium carbide is a compound widely used in cutting tools, nuclear reactors, field emitter arrays and solar energy receivers; additionally, combined with other materials, it can be used in rocket technology and the aerospace industry. For this work was studied the effect of the high hydrostatic pressure on the electronic, mechanical, vibrational, and optical properties of the ZrC, from first principles calculations based on the Density Functional Theory. The calculated enthalpy and cohesive energy data show a B1 (NaCl) to B2 (CsCl) phase transition at 297 GPa. For the B1 phase, results for the calculated equilibrium lattice parameters, bands structure, electron and phonon densities of states, elastic moduli constants, entropy, enthalpy, Gibbs free energy, heat capacity, reflectivity, loss function, conductivity, and dielectric function are consistent with the available experimental and theoretical data. Our results for phonons show that the B1 phase is dynamically stable; in contrast, the B2 phase is not stable. Furthermore, when pressure is applied, the calculated density of electronic states shows that the C 2p-orbitals around the Fermi energy contribute significantly to the conduction band, turning the compound into a ductile the material, with a mixture of metallic and ionic-covalent bonds. On the other hand, the study of the mechanical properties of the B1 phase shows a highest mechanical resistance and maximum thermal absorption, above 356 K and 638 K, respectively; but these switch to higher temperatures as pressure is applied. Finally, the B1 phase of the ZrC is a good coating material and a photon detector at low frequencies in the UV region, but also at the visible and infrared regions; although, increasing the pressure, the values of the optical properties increase. The increase of the parameters’ values of the studied properties, as the pressure increases, indicates that the ZrC could be more efficient in a wider range of applications.

Temperature-dependent mechanical properties and elastocaloric effects of multiphase nanocrystalline NiTi alloys

We investigate the temperature-dependent mechanical properties and elastocaloric effects of different multiphase nanocrystalline NiTi alloys with grain sizes of 10 nm, 15 nm, 20 nm, 27 nm, 34 nm and 55 nm. These multiphase nanocrystalline NiTi alloys mainly consist of B2, B19′ and R phases and can undergo the thermally induced phase transition over a wide temperature range from 208 K to 353 K. Their superelastic deformation (loading to a strain of 4%) is contributed by combinations of the elastic deformation of B2 phase, the R → B2 phase transition, the reversible martensite reorientation and the B2 → R and B2/R → B19' phase transitions. Such complex deformation mechanism together with the microstructure evolution with temperature brings strong temperature-dependences of the mechanical properties and elastocaloric effects. As results, at the grain sizes of 15 nm ∼ 20 nm, the stress under a constant superelastic strain can show a significant V-shaped variation with temperature. At the grain size of 55 nm, the adiabatic temperature drop can even change from −8.5 K to −29 K ∼ −35.8 K as the ambient temperature rises from 293 K to 333 K. By comparison of the mechanical properties and elastocaloric effects of the different multiphase nanocrystalline NiTi alloys, it is found that the one with the grain size of 20 nm exhibits the best comprehensive cooling performances, which has a soft near-linear superelasticity (a moderate driving force), a very wide refrigeration temperature window (> 245 K) with considerable adiabatic temperature drops (∆Tmax= −17.1 K), and a good functional stability. This work provides an experimental basis for using the multiphase nanocrystalline NiTi alloys as solid-state refrigerants.

B2 phase precipitation behavior in Ti–40Al–8Nb alloys during the hot deformation process

In this work, the B2 phase precipitation behavior in Ti–40Al–8Nb alloys with a (α2+γ) duplex microstructure during the hot deformation process was investigated. Results showed that even if the deformation temperatures, 1000 °C and 1050 °C, were much lower than the B2 phase precipitation temperature (1160 °C), obvious B2 precipitates were observed in the compressed samples. The characteristics of B2 precipitates were significantly dependent on the deformation condition, i.e., its grain size and phase content increased with the rise of deformation temperature and decrease of strain rate. The detailed analysis indicated that the B2 phase was derived from the α2→B2 phase transition under the mechanical-thermal coupling effect. The applied stress provides a driving force for the redistribution of Nb element in the deformed α2 phase and the preferable thermal conditions with an enhanced diffusion accelerate the enrichment of Nb element in local regions. Moreover, the precipitated B2 phase was thermodynamically unstable, and an inverse transition B2→α2 occurred during the post-annealing at 1050 °C.

Interatomic Potential for InP.

Classical modeling of structural phenomena occurring in InP crystal, for example plastic deformation caused by contact force, requires an interatomic interaction potential that correctly describes not only the elastic properties of indium phosphide but also the pressure-induced reversible phase transition B3↔B1. In this article, a new parametrization of the analytical bond-order potential has been developed for InP. The potential reproduces fundamental physical properties (lattice parameters, cohesive energy, stiffness coefficients) of the B3 and B1 phases in good agreement with first-principles calculations. The proposed interaction model describes the reversibility of the pressure-induced B3↔B1 phase transition as well as the formation of native point defects in the B3 phase.

Intermediate spin state and the B1−B2 transition in ferropericlase

Ferropericlase (fp), (Mg$_{1-x}$Fe$_x$)O, the second most abundant mineral in the Earth's lower mantle, is expected to be an essential component of super-Earths' mantles. Here we present an ab initio investigation of the structure and magnetic ground state of fp up to $\sim$ 3 TPa with iron concentrations (x$_{Fe}$) varying from 0.03 to 0.12. Calculations were performed using LDA+U$_{sc}$ and PBE exchange-correlation functionals to elucidate the pressure range for which the Hubbard U (U$_{sc}$) is required. Similar to the end-members FeO and MgO, fp also undergoes a B1 to B2 phase transition that should be essential for modeling the structure and dynamics of super-Earths' mantles. This structural transition involves a simultaneous change in magnetic state from a low spin (LS) B1 phase with iron total spin S=0 to an intermediate spin (IS) B2 phase with S=1. This is a rare form of pressure/strain-induced magnetism produced by local cation coordination changes. Phonon calculations confirm the dynamical stability of the iron B2-IS state. Free energy calculations are then carried out including vibrational effects and electronic and magnetic entropy contributions. The phase diagram is then obtained for low concentration fp using a quasi-ideal solid solution model. For x$_{Fe}$ > 0.12 this approach is no longer valid. At ultra-high pressures, there is an IS to LS spin state change in Fe in the B2 phase, but the transition pressure depends sensitively on thermal electronic excitations and on x$_{Fe}$.

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.

In situ XRD study on the phase transformations of the gas-atomized Ti-22Al-25Nb powder

In this paper, the phase transformations in the as-atomized Ti-22Al-25Nb powder were investigated by using in situ x-ray diffraction and differential scanning calorimetry. It was found that the as-atomized Ti-22Al-25Nb powder consists of metastable β phase at room temperature. The β phase is stable up to 550 ℃. Then, the O phase precipitates from the β phase matrix in the temperature range of 550 to 650 °C. The transition from O phase to α2 phase occurs from 850 to 1050 ℃. With further increasing temperature, the α2 to B2 phase transition takes place. The present work is valuable for designing and optimizing processing and annealing parameters of Ti-22Al-25Nb alloy parts fabricated from powders.

Evolution of the microstructure, electrical resistivity and microhardness during atomic ordering of cryogenically deformed Cu-47at.%Pd alloy

Abstract The kinetics of the A1→B2 phase transition in the cryogenically deformed Cu-47at.%Pd alloy has been compared with that both after room-temperature deformation and after quenching from high temperature. For this aim, the evolution of the microstructure, electrical properties and microhardness of the alloy during disorder→order transformation at 400 °C were studied. It was shown that annealing at 400 °C for 1 h led to the formation of a uniform ultrafine-grained ordered structure in the cryo-deformed alloy. In turn, the annealing duration of 1 h is not enough to finish the ordering process in the quenched sample. It was found that some volume of the ordered B2-phase was formed in the cryo-deformed Cu-47at.% Pd alloy after holding at room temperature for 0.5 year.

Theoretical study of CaO, CaS and CaSe via first-principles calculations

Abstract ab initio Calculations were performed to study the properties of CaO, CaS and CaSe alkaline earth chalcogenides in the B1 (NaCl) and B2 (CsCl) phases. The calculations were based on the density functional theory (DFT) within generalized gradient approximation (GGA). Results of structural properties (equilibrium lattice parameters, bulk moduli, its first pressure derivative) of both phases, and results of the properties of phase transition from B1 to B2 phase (transition pressure, compression ratio at the phase transition) were reported. Elastic properties of the B1 phase of these compounds, such as elastic constants C11, C12, and C44, shear modulus (G), Young's modulus (E), Poisson’s ratio (σ), Kleinman parameter (ξ), and anisotropy factor (A) were investigated at ambient conditions. The band structure and density of states were studied, too, for the B1 structure of these compounds. The results are in good agreement with the available experimental and other theoretical results.

Anelasticity of iron-aluminide Fe3Al type single and polycrystals

Mechanical spectroscopy and in situ neutron diffraction techniques were employed to study and interpret anelasticity in Fe-27 at.%Al single crystal (SC) and polycrystal (PC) alloys from room temperature to 600 °C. Thermally activated Zener relaxation was recorded in the temperature dependent internal friction (IF) curves for both SC and PC alloys upon heating and cooling. The reversible second-order D03 ↔ B2 phase transition studied by in situ neutron diffraction leads to a transient anelastic effect at ∼550 °C both upon heating and cooling. The transient peak temperature does not depend on measurement frequency, whereas the peak height is roughly proportional to the inverse frequency of measurements according to Landau's theory for the second order transitions. Calorimetry and magnetometry techniques recorded the same temperature range for the D03 ↔ B2 phase transition as mechanical spectroscopy and in situ neutron diffraction. The study of amplitude dependent internal friction (ADIF) revealed that the absolute value of maximum damping Qm−1 in the SC sample is about five times higher than that of in the PC sample at room temperature. The calculated value of internal stresses opposing magnetic domain wall motions for the PC sample is ∼1.5 times larger than that of for the SC sample, which corresponds to the detrimental influence of grain boundaries to magnetomechanical damping. By increasing the tightening force of torque wrench, a higher level of localized stress is induced to the sample, and the damping capacity (Qm−1) in single cantilever configuration of forced bending vibrations reduces monotonously.

Hysteresis and bonding reconstruction in the pressure-induced B3-B1 phase transition of 3C-SiC.

The determination of kinetic factors affecting phase metastability is crucial for the design of materials out of the ambient conditions. At a given temperature, the kinetic barrier associated with the reconstruction of the bonding network of a pressure-induced phase transition can be only overcome at pressures where the available vibrational energy of the system is equal or higher than the corresponding activation energy. Our work demonstrates that these pressures provide boundaries to hysteresis cycles that can be evaluated following a three-step computational strategy: (i) total energy electronic structure calculations, (ii) determination of vibrational contributions by means of a simple Debye model, and (iii) description of the energetic profile along the transition path in the framework of the martensitic approximation. In the 3C-SiC polytype, our results reveal that the high pressure rock-salt (B1) structure can not be quenched on release of pressure unless temperature is close to 0 K. The B1 phase transforms back to the low-pressure zinc blende (B3) polymorph at 300 K if pressure is below 30 GPa, in very good agreement with experimental observations. These results are supported by a full characterization of the B3-B1 energetic transition profile in terms of the chemical changes of the bonding network topologically analysed with the electron localization function.

Theoretical study of B3-to-B1 phase transition in ZnS

The pressure-induced phase transformation from B3 to B1 structures in ZnS using first-principle projector-augmented wave method is studied. To understand the nature and driving force behind the transition, the interesting properties in both phases, including enthalpy, phonon dispersion curves and elastic constants, are systematically investigated. The results show that the calculated transition pressure is within the range of 16.33 GPa to 19.04 GPa, which is in good agreement with the available experimental and theoretical data. The transition process can be viewed as the appearance and disappearance of very slight lattice distortion accompanied by the movement of Zn and S atoms along the [111] crystallographic axis. The physical driving force of the B3–B1 phase transition is confirmed to be a coupling effect between the mechanical instability of B3 phase under pressure and the softening acoustic phonon mode resulting from the pressure-induced lattice deformation. For B1 phase, it is further predicted that a new phase transition takes place at about 59.9 GPa.

Studying the phase transition, thermal expansion, and heat capacity of technetium mononitride by first-principles calculations

The pressure-induced B3⿿B1 phase transition and some interesting thermodynamic properties for B3 structure of ideal stoichiometric technetium mononitride (TcN) have been studied systematically by first-principles calculations. It is found that TcN has a B3 ground-state phase at zero pressure and the transition pressure from B3 to B1 structure determined by the energy vs volume curves is about 35GPa. Through the quasi-harmonic Debye model, the dependences of thermal expansion coefficient, constant-volume heat capacity, and constant-pressure heat capacity of TcN with B3 phase on temperature up to 1600K are successfully predicted at 0, 10, 20 and 35GPa pressures, respectively.

Atomic origin of the spin-polarization of the Co2FeAl Heusler compound

Using synchrotron x-ray techniques, we studied the Co2FeAl spin-polarization state that generates the half-metallicity of the compound during an A2 (low-spin) → B2 (high-spin) phase transition. Given the advantage of element specificity of x-ray techniques, we could fingerprint the structural and magnetic cross-reactions between Co and Fe within a complex Co2FeAl structure deposited on a MgO (0 0 1) substrate. X-ray diffraction and extended x-ray absorption fine structure investigations determined that the Co atoms preferably populate the (1/4,1/4,1/4) and (3/4,3/4,3/4) sites during the development of the B2 phase. X-ray magnetic spectroscopy showed that although the two magnetic elements were ferromagnetically coupled, they interacted in a competing manner via a charge-transfer effect, which enhanced Co spin polarization at the expense of Fe spin polarization during the phase transition. This means that the spin-polarization of Co2FeAl was electronically dominated by Fe in A2 whereas the charge transfer turned the dominance to Co upon B2 formation. Helicity-dependent x-ray absorption spectra also revealed that only the minority state of Co/Fe was involved in the charge-transfer effect whereas the majority state was independent of it. Despite an overall increase of Co2FeAl magnetization, the charge-transfer effect created an undesired trade-off during the Co–Fe exchange interactions, because of the presence of twice as many X sites (Co) as Y sites (Fe) in the Heusler X2YZ formula. This suggests that the spin-polarization of Co2FeAl is unfortunately regulated by compromising the enhanced X (Co) sites and the suppressed Y (Fe) sites, irrespective of the development of the previously known high-spin-polarization phase of B2. This finding provides a possible cause for the limited half-metallicity of Co2FeAl discovered recently. Electronic tuning between the X and Y sites is necessary to further increase the spin-polarization, and likely the half-metallicity as well, of the compound.

Crystal behavior of potassium bromate under compression.

We report on high-pressure angle-dispersive X-ray diffraction data up to 15 GPa and ab initio total-energy calculations up to 242 GPa for KBrO3. No phase transition was found below 15 Pa in contrast to previously reported data. Its experimental bulk modulus in the quasi-hydrostatic regime is B0 = 18.8 (9) GPa with a bulk modulus pressure derivative B'0 = 8.2 (4). However, according to our ab initio calculations, KBrO3 significantly reduces its rhombohedral distortion via small cooperative movements of the atoms and the structure progressively approaches the cubic symmetry, where the KBr subarray would adopt a topology similar to that of the corresponding B2-type bromide. This rearrangement of atoms is directly related to the Buerger's mechanism of the B1-B2 phase transition for halides, confirming that cations (second neighbors) do not arrange in an arbitrary way. The O atoms forming the [BrO3] pyramidal units move smoothly with pressure to the center of the [K8] cube faces, where electron localization function calculations present their maxima in other B2-type compounds, eventually adopting the perovskite-type structure at P ≃ 152 GPa. Our data on KBrO3 has been compared with chemically substituted isostructural halates, providing new insights on the compressibility of this family of compounds.

Dielectric properties of anti-ferroelectric B2 phase of bent core liquid crystal

A phenomenological theory of the dielectric properties in the vicinity of the isotropic to anti-ferroelectric B2 phase transition in banana shaped molecules is developed. The temperature, pressure and frequency dependences of the complex dielectric permittivity in the B2 phase are calculated and comparison is made with experimental data reported by us earlier. The proposed model describes well, the isotropic-B2 phase boundary and the behavior of permittivity in the B2 phase.

A Theoretical Investigation of the Effect of Pressure on the Structural, Elastic and Mechanical Properties of ZnS Crystals

Structural, elastic, and mechanical properties of blende-type zinc sulfide (bt-ZnS) were investigated under pressures up to 20 GPa. Unlike previous theoretical calculations, an existing mixed-type interatomic potential was applied with geometry optimization calculations. B3 → B1 phase transition pressure was obtained as 17 GPa under zero pressure and temperature. Pressure dependence of typical cubic elastic constants, bulk, shear and Young moduli, elastic wave velocities, Kleinman parameter, static and high-frequency dielectric constants of bt-ZnS were also obtained. Overall, our results for the considered parameters of bt-ZnS are in good agreement with experiments and better than those of several available theoretical data.