Solid-state Nudged Elastic Band Method Research Articles

Development of a machine learning interatomic potential for exploring pressure-dependent kinetics of phase transitions in germanium.

We introduce a data-driven potential aimed at the investigation of pressure-dependent phase transitions in bulk germanium, including the estimate of kinetic barriers. This is achieved by suitably building a database including several configurations along minimum energy paths, as computed using the solid-state nudged elastic band method. After training the model based on density functional theory (DFT)-computed energies, forces, and stresses, we provide validation and rigorously test the potential on unexplored paths. The resulting agreement with the DFT calculations is remarkable in a wide range of pressures. The potential is exploited in large-scale isothermal-isobaric simulations, displaying local nucleation in the R8 to β-Sn pressure-induced phase transformation, taken here as an illustrative example.

Influence of External Conditions on the Black-to-Yellow Phase Transition of CsPbI3 Based on First-Principles Calculations: Pressure and Moisture

All-inorganic CsPbI3 perovskite has emerged as a promising candidate for next-generation solar cells. However, owing to the poor structural stability of black phase CsPbI3 perovskite at room temperature, it spontaneously transforms to the yellow, photoinactive, nonperovskite phase at room temperature, limiting further development of CsPbI3 perovskite solar cells. To better understand the mechanism driving such undesirable phase transformation, we examine the thermodynamics and kinetics associated with γ-to-δ phase transformation using density functional theory calculation. A solid-state nudged elastic band method was employed to find minimum energy pathways assuming a concerted solid-state phase transformation between these two phases. The gas molecules representing atmospheric (H2O, O2, and N2) and inert (Ar) ambient environments, as well as applied external pressure, were considered to examine the influence of external conditions on the black-to-yellow phase transition. Our calculation reveals that, with increasing pressure, the thermodynamic driving force for converting the γ-phase to the δ-phase increases, whereas a larger activation energy must be overcome for the phase transition to occur. We also investigate the moisture-induced phase transformation with an H2O molecule and its dissociated species (H+/OH–) and demonstrate that the reaction energy barriers can be significantly lowered in the presence of H2O or OH–. On the other hand, other nonpolar species (O2, N2, and Ar) have a negligible effect on the phase transformation kinetics, while they might reduce the thermodynamic driving force for the phase transformation and suppress the undesirable phase transformation. Our theoretical prediction could support recent observations that the γ-to-δ phase transformation occurs rapidly and catalytically in the presence of moisture, whereas in dry argon and dry oxygen atmospheres, the γ-CsPbI3 remains stable.

Phase stability and temperature effect in ScX (X=S, Se and Te) compounds

Based on first-principles calculations, the structural stability and temperature effect in ScX (X=S, Se and Te) compounds are studied with three typical structures of B1 (NaCl-type), hcp (NiAs-type) and β-hcp (inverse Li2O2-type). Their dynamic stability has been verified using phonon mode analysis and molecular dynamics simulations. From the total energy calculations, we find that the most stable ground state structures are B1 for ScS, and hcp for ScSe and ScTe, respectively. Moreover, structural stabilities at finite temperature are studied with the combination of phonon dependent dynamics analysis and first-principles calculations, which reveals a phase transition from hcp to B1 in ScSe around 230 K and a phase transition from hcp to β-hcp in ScTe around 460 K, in accordance with experimental findings. The energy barrier and pathway along the phase transformation from hcp to β-hcp ScTe are also calculated and analyzed by the solid-state nudged elastic band method.

Role of substituted atoms in stacking fault formation in long-period stacking ordered system

To study the formation mechanism of the long-period stacking ordered (LPSO) structures, the reaction pathways of solid–solid transformations from a hexagonal close-packed (HCP) structure to LPSO structures in Mg-Y-Zn alloys were calculated using the generalized solid-state nudged elastic band method. The energy increases along the transition from HCP to 18R, and the peak positions represent the activation energy for the transition. Y substitution hardly changes the activation energy but makes the 18R-type LPSO structure more stable than HCP. In contrast, Zn or Y + Zn substitution results in higher activation energy and makes the 18R-type LPSO structure less stable than HCP. The calculated results for 14H and 24R LPSO structures also show similar activation energy and LPSO stability to the HCP-18R transition. Therefore, Y substitution plays an important role in stabilizing the stacking faults in LPSO systems. For the microscopic mechanism, the volume dependence of the total energy in pure FCC and HCP Y were examined, and the result suggests that FCC-Y is stable than HCP-Y under pressure. Therefore, the effect of substitution of Y in HCP Mg can be explained by the characteristics of Y under the chemical pressure exerted by the small size of Mg lattice.

Nudged elastic band method for solid-solid transition under finite deformation

Solid-state nudged elastic band (SSNEB) methods can be used for finding solid-solid transition paths when solids are subjected to external stress fields. However, previous SSNEB methods may lead to inaccurate barriers and deviated reaction paths for transitions under stress and finite deformation due to an inaccurate evaluation of the external work contributions in enthalpies. In this paper, a finite deformation nudged elastic band (FD-NEB) method is formulated for finding transition paths of solids under finite deformation. Applications of FD-NEB to a phase transition of silicon from the diamond phase to the β-tin phase under uniaxial compression are presented. The results are compared with those from the generalized solid-state nudged elastic band method.

Magneto-structural transformations via a solid-state nudged elastic band method: Application to iron under pressure.

We extend the solid-state nudged elastic band method to handle a non-conserved order parameter, in particular, magnetization, that couples to volume and leads to many observed effects in magnetic systems. We apply this formalism to the well-studied magneto-volume collapse during the pressure-induced transformation in iron-from ferromagnetic body-centered cubic (bcc) austenite to hexagonal close-packed (hcp) martensite. We find a bcc-hcp equilibrium coexistence pressure of 8.4 GPa, with the transition-state enthalpy of 156 meV/Fe at this pressure. A discontinuity in magnetization and coherent stress occurs at the transition state, which has a form of a cusp on the potential-energy surface (yet all the atomic and cell degrees of freedom are continuous); the calculated pressure jump of 25 GPa is related to the observed 25 GPa spread in measured coexistence pressures arising from martensitic and coherency stresses in samples. Our results agree with experiments, but necessarily differ from those arising from drag and restricted parametrization methods having improperly constrained or uncontrolled degrees of freedom.

Migrations of pentagon-heptagon defects in hexagonal boron nitride monolayer: the first-principles study.

The first-principles calculations are employed to study the migrations of pentagon-heptagon (5-7) defects in hexagonal boron nitride monolayer (h-BN). A type of grain boundaries, consisted of 5-7 defects, is constructed on the basis of experimental observations. With the absorption of a pair of atoms, one 5-7 defect in the grain boundary migrates apart by one unit cell and afterward migrates again through the bond rotation. It is also found that the two migrations could be replaced by one single step when the pair of absorbed atoms is located at another specific site in the same heptagon. Energy barriers and reaction paths for the migrations of 5-7 defects in h-BN by the bond rotation are theoretically investigated by the standard nudged elastic band method and the generalized solid-state nudged elastic band method. To elucidate the difference between the bond rotation process of the 5-7 defects with N-N bonds and those with B-B bonds, a couple of typical 21.7° grain boundaries with either N-N or B-B bonds are investigated. It is shown that the energy barrier of the migration of defects with N-N bonds is lower than that with B-B bonds in this type of grain boundaries.

Nature of the metal-insulator transition inNbO2

We report a theoretical study of the structural phase transition and associated metal-to-insulator transition in $\mathrm{Nb}{\mathrm{O}}_{2}$ within density functional theory using the transition state theory as formulated in the generalized solid-state nudged elastic band method. Consistent with prior experimental work, we demonstrate that niobium dimerization is primarily driven by soft modes at the P point of the rutile Brillouin zone. In light of our results, it appears that the metal-to-insulator transition in $\mathrm{Nb}{\mathrm{O}}_{2}$ is driven by a second-order structural transition of the Peierls type.

Mechanism of the CaIrO3post-perovskite phase transition under pressure

Recent experiments have shown that the perovskite to post-perovskite phase transformation in CaIrO${}_{3}$ occurs more readily at room temperature when a shear stress is applied as compared to isotropic pressure. To understand this mechanistically, we have calculated the minimum-energy pathway of the phase transition with density functional theory under different pressure conditions with the generalized solid-state nudged elastic band method. Our results reveal that shear stress significantly lowers the barrier and stabilizes the product state while isotropic pressure initially raises the barrier and only reduces the barrier at pressures above 90 GPa. The nonmonotonic change in barrier with isotropic pressure is explained in terms of an increase in the activation volume under low pressure and a decrease under high pressure.

Communication: From graphite to diamond: Reaction pathways of the phase transition

Phase transitions between carbon allotropes are calculated using the generalized solid-state nudged elastic band method. We find a new reaction mechanism between graphite and diamond with nucleation characteristics that has a lower activation energy than the concerted mechanism. The calculated barrier from graphite to hexagonal diamond is lower than to cubic diamond, resolving a conflict between theory and experiment. Transitions are calculated to three structures of cold compressed graphite: bct C4, M, and Z-carbon, which are accessible at the experimentally relevant pressures near 17 GPa.

A generalized solid-state nudged elastic band method

A generalized solid-state nudged elastic band (G-SSNEB) method is presented for determining reaction pathways of solid-solid transformations involving both atomic and unit-cell degrees of freedom. We combine atomic and cell degrees of freedom into a unified description of the crystal structure so that calculated reaction paths are insensitive to the choice of periodic cell. For the rock-salt to wurtzite transition in CdSe, we demonstrate that the method is robust for mechanisms dominated either by atomic motion or by unit-cell deformation; notably, the lowest-energy transition mechanism found by our G-SSNEB changes with cell size from a concerted transformation of the cell coordinates in small cells to a nucleation event in large cells. The method is efficient and can be applied to systems in which the force and stress tensor are calculated using density functional theory.