Nudged-elastic band method with two climbing images: finding transition states in complex energy landscapes

The nudged-elastic band (NEB) method is modified with concomitant two climbing images (C2-NEB) to find a transition state (TS) in complex energy landscapes, such as those with serpentine minimal energy path (MEP). If a single climbing image (C1-NEB) successfully finds the TS, C2-NEB finds it with higher stability and accuracy. However, C2-NEB is suitable for more complex cases, where C1-NEB misses the TS because the MEP and NEB directions near the saddle point are different. Generally, C2-NEB not only finds the TS but guarantees that the climbing images approach it from the opposite sides along the MEP, and it estimates accuracy from the three images: the highest-energy one and its climbing neighbors. C2-NEB is suitable for fixed-cell NEB and the generalized solid-state NEB (SS-NEB).Comment: 3 pages, 4 figure

Coexistence pressure for a martensitic transformation from theory and experiment: revisiting the bcc-hcp transition of iron under pressure

The coexistence pressure of two phases is a well-defined point at fixed temperature. In experiment, however, due to non-hydrostatic stresses and a stress-dependent potential energy barrier, different measurements yield different ranges of pressure with a hysteresis. Accounting for these effects, we propose an inequality for comparison of the theoretical value to a plurality of measured intervals. We revisit decades of pressure experiments on the bcc - hcp transformations in iron, which are sensitive to non-hydrostatic conditions and sample size. From electronic-structure calculations, we find a bcc - hcp coexistence pressure of 8.4 GPa. We construct the equation of state for competing phases under hydrostatic pressure, compare to experiments and other calculations, and address the observed pressure hysteresis and range of onset pressures of the nucleating phase.Comment: 8 pages, 1 figure, 202 citation

Revealing the nature of antiferro-quadrupolar ordering in Cerium Hexaboride: CeB6_6

Cerium-hexaboride (CeB$_6$) f-electron compound displays a rich array of low-temperature magnetic phenomena, including `magnetically hidden' order, identified as multipolar in origin via advanced x-ray scattering. From first-principles electronic-structure results, we find that the \emph{antiferro-quadrupolar} (AFQ) ordering in CeB$_{6}$ arises from crystal-field splitting and yields band structure in agreement with experiments. With interactions of $p$-electrons between Ce and B$_{6}$ being small, the electronic state of CeB$_{6}$ is suitably described as Ce(4$f^{1}$)$^{3+}$(e$^{-}$)(B$_{6}$)$^{2-}$. The AFQ state of orbital spins is caused by an exchange interaction induced through spin-orbit interaction, which also splits J=5/2 state into $\Gamma_{8}$ ground state and $\Gamma_{7}$ excited state. Within the smallest antiferromagnetic (111) configuration, an orbital-ordered AFQ state appears during charge self-consistency, and supports the appearance of `hidden' order. Hydrostatic pressure (either applied or chemically induced) stabilizes the AFM (AFQ) states over a ferromagnetic one, as observed at low temperatures.Comment: 6 pages, 4 figure

Mixed valency and site-preference chemistry for cerium and its compounds: A predictive density-functional theory study

Cerium and its technologically relevant compounds are examples of anomalous mixed valency, originating from two competing oxidation states—itinerant Ce4+ and localized Ce3+. Under applied stress, anomalous transitions are observed but not well understood. Here we treat mixed valency as an “alloy” problem involving two valences with competing and numerous site-occupancy configurations. We use density-functional theory with Hubbard U (i.e., DFT+U) to evaluate the effective valence and predict properties, including controlling the valence by pseudoternary alloying. For Ce and its compounds, such as (Ce,La)2(Fe,Co)14B permanent magnets, we find a stable mixed-valent α state near the spectroscopic value of νs=3.53. Ce valency in compounds depends on its steric volume and local chemistry. For La doping, Ce valency shifts towards γ-like Ce3+, as expected from steric volume; for Co doping, valency depends on local Ce-site chemistry and steric volume. Our approach captures the key origins of anomalous valency and site-preference chemistry in complex compounds

Intrinsic magnetic properties in R(Fe1−xCox)11TiZ(R=Yand Ce;Z=H,C,and N)

To guide improved properties coincident with reduction of critical materials in permanent magnets, we investigate via density functional theory (DFT) the intrinsic magnetic properties of a promising system, R(Fe1−xCox)11TiZ with R=Y, Ce and interstitial doping (Z=H,C,N). The magnetization M, Curie temperature TC, and magnetocrystalline anisotropy energy K calculated in local density approximation to DFT agree well with measurements. Site-resolved contributions to K reveal that all three Fe sublattices promote uniaxial anisotropy in YFe11Ti, while competing anisotropy contributions exist in YCo11Ti. As observed in experiments on R(Fe1−xCox)11Ti, we find a complex nonmonotonic dependence of K on Co content and show that anisotropy variations are a collective effect of MAE contributions from all sites and cannot be solely explained by preferential site occupancy. With interstitial doping, calculated TC enhancements are in the sequence of N\u3eC\u3eH, with volume and chemical effects contributing to the enhancement. The uniaxial anisotropy of R(Fe1−xCox)11TiZ generally decreases with C and N; although, for R=Ce, C doping is found to greatly enhance it for a small range of 0.