Activation energy of homogeneous nucleation of Zr hydride: Density functional theory calculation

Considering the nucleation process of Zr hydrides as phase transformation from hexagonal closed-packed (HCP) to face-centered tetragonal (FCT) structure, we calculated the activation energy of the homogeneous nucleation process of Zr hydrides and atomic rearrangement during nucleation for Zr4H, Zr2H, ZrH and ZrH2 using density functional theory calculations and minimum energy path detection. At 0 K limit, although ZrH and ZrH2 have lower chemical potentials and are more energetically stable than Zr4H and Zr2H, the latter have lower activation energies for nucleation. At finite temperatures, the crossover of activation energies occurs around 300 K, where ZrH becomes the most possible candidate with the lowest activation energy. This was explained by the difference in the atomic rearrangement and change in phonon frequency during phase transformation.Akio Ishii, Activation energy of homogeneous nucleation of Zr hydride: Density functional theory calculation, Computational Materials Science, Volume 215, 2022, 111769, ISSN 0927-0256, https://doi.org/10.1016/j.commatsci.2022.111769

Morphology prediction of elastically interacting Zr hydride precipitates and cracks in α -Zr using atomistically informed Eshelby’s ellipsoidal inclusion

We propose an atomistically informed Eshelby’s inclusion analysis to investigate the morphology of secondary phases, which elastically interacted with each other through their respective local strain fields. Using the proposed method, we predict the morphology of -hydride precipitates and cracks, which interacted in the –Zr matrix. Planar cracks nucleate along the basal-normal -hydride disk. And at the crack tip, the prismaticnormal -hydride disk also nucleates depending on the stress condition around the crack, constructing the hydride-crack network. The findings contribute to the understanding of the fracture mechanism of Zr alloys, such as delayed hydride cracking, which is caused by Zr hydride.Ishii Akio. Morphology prediction of elastically interacting Zr hydride precipitates and cracks in α-Zr using atomistically informed Eshelby’s ellipsoidal inclusion. Computational Materials Science 231, 112568 (2023); https://doi.org/10.1016/j.commatsci.2023.112568

Ab initio morphology prediction of Zr hydride precipitates using atomistically informed Eshelby’s ellipsoidal inclusion

We energetically predicted the morphology of Zr hydride precipitates in a hexagonal close-packed (HCP) Zr matrix. Considering Zr hydride precipitates as ellipsoids, we used Eshelby’s ellipsoidal inclusions to calculate the elastic energy increment due to the presence of Zr hydride precipitates in the Zr matrix, in which the elastic anisotropy and inhomogeneity of the elastic constants between Zr and Zr hydride were considered. We compared the difference in the elastic energy increment between the ellipsoidal inclusions with different shapes: plates (mimicked by penny-shape ellipsoids), needles (mimicked by longitudinal ellipsoids) and sphere, and orientations to detect the stable structure with the minimum elastic energy increment. Eigenstrains of each Zr hydride and elastic constants of Zr hydrides and HCP Zr for Eshelby’s ellipsoidal inclusion analysis were determined using atomistic simulations based on a density functional theory calculation, achieving a parameter free abinitio morphology prediction. The morphology predictions were implemented for two cases: with and without shear components of eigenstrain (w/ and w/o shear). The 〈12̄10〉 longitudinal needle for the γ hydride (w/o shear) and plate (or disk) on the plane, which is 20° to 30° tilted about 〈12̄10〉-axis from basal plane (0001), for δ and ε hydrides (w/ shear) were successfully predicted as stable shapes and orientations of the precipitates under zero external stress conditions, qualitatively consistent with experimental observations. The external circumferential tensile stress on the basal plane reduces the elastic energy of [0001] parallel Zr hydride plates, which is also qualitatively consistent with the reoriented δ hydride precipitates observed in the experiment. On the other hand, predicted external stress for the reorientation of Zr hydride is quite high, around 10 GPa. This is inconsistent with experimental observation and further investigation is necessary. Generally, our predictions based on elasticity theory appear qualitatively consistent with experimental observations, suggesting an elastic origin of the morphology of Zr hydride precipitates in the HCP Zr matrix.Akio Ishii, Ab initio morphology prediction of Zr hydride precipitates using atomistically informed Eshelby’s ellipsoidal inclusion, Computational Materials Science, Volume 211, 2022, 111500, ISSN 0927-0256, https://doi.org/10.1016/j.commatsci.2022.111500

Energetics of heterogeneous Mg {101¯2} deformation twinning migration using an atomistically informed phase-field model

We have constructed an atomistically informed phase-field model for the quantitative energetic analysis of phase transformations. In our model, to describe the general phase transformation with a non-linear correlation between displacive and diffusive modes, we have defined two order parameters, γ and ϕ, which describe the lattice distortion (displacive mode) and shuffling (diffusive mode), respectively. Our method provides a way to introduce the energetics from atomistic simulations to the phase-field model, describes γ and ϕ in an atomic model, and derives phase-field parameters from the free energy calculated by atomistic simulation. As an application of our model, we used the energetics obtained from atomistic simulations using a density functional theory potential, and we calculated the free energy change during the heterogeneous {101¯2} twin migration of hexagonally close-packed (HCP) Mg, which can be considered as a lattice distortion and shuffling mixed phase transformation, by combining our phase-field model with the nudged elastic band method. The activation energy, and the critical nucleus size of the heterogeneous {101¯2} twin migration under a set stress were derived. The critical c-axis tensile stress (athermal stress), at which the activation energy becomes zero, is consistent with the experimental yield stress of {101¯2} for the twinning deformation of HCP Mg nanopillars in tensile tests. The critical nucleus size of the heterogeneous {101¯2} twin migration is on the range of nanometers under several hundred megapascals stress, which is consistent with the experimental observation of nanotwins.Akio Ishii, Energetics of heterogeneous Mg {101¯2} deformation twinning migration using an atomistically informed phase-field model, Computational Materials Science, Volume 183, 2020, 109907, ISSN 0927-0256, https://doi.org/10.1016/j.commatsci.2020.109907

Spatial and temporal heterogeneity of Kohlrausch–Williams–Watts stress relaxations in metallic glasses

We perform a molecular dynamics (MD) stress relaxation simulation for Zr50Cu40Al10 metallic glass to confirm that the time dependency of stress relaxation conforms with the Kohlrausch–Williams–Watts (KWW) equation, and to derive the temperature dependency of the Kohlrausch exponent βKWW. We also calculate local plastic deformation based on atomic strain, then discuss the morphology of relaxation and calculate the probability density of stress relaxation with respect to the characteristic time of relaxation from the number of deformed atoms. Afterward, we derive the time dependency of stress relaxation as a mode-averaged decay function, which expresses spatial and temporal heterogeneity. Both the results of simulation and calculation reproduce the KWW relaxation form and are in good agreement, confirming the spatially and temporally heterogeneous nature of KWW relaxation. The heterogeneity of the stress relaxation of metallic glass is determined by local stress changes caused by microscopic local plastic deformation.Akio Ishii, Spatial and temporal heterogeneity of Kohlrausch–Williams–Watts stress relaxations in metallic glasses, Computational Materials Science, Volume 198, 2021, 110673, ISSN 0927-0256, https://doi.org/10.1016/j.commatsci.2021.110673

Elastic investigation for the existence of B33 phase in TiNi shape memory alloys using atomistically informed Eshelby’s ellipsoidal inclusion

The existence of the B33 phase in TiNi alloys, which was reported to be a stable phase using density functional theory calculations but not confirmed experimentally, is controversial. Using Eshelby’s ellipsoidal inclusion, which was atomistically informed by density functional theory calculations, we investigated the existence of the B33 phase in the TiNi shape memory alloy. The calculated total strains of the heterogeneously nucleated B33 phase were similar to the eigenstrains of the B19’ phase, which were also calculated using density functional theory calculations. Considering the similarity of the atomic structures of B33 and B19’, this indicates that the B33 phase was elastically suppressed and changed to the B19’ phase by the original B2 matrix. We confirmed that the elastic inhomogeneity between the B2 matrix and B33 phase plays a role in this change.Ishii Akio. Elastic investigation for the existence of B33 phase in TiNi shape memory alloys using atomistically informed Eshelby’s ellipsoidal inclusion. Computational Materials Science, 218, 111954. https://doi.org/https://doi.org/10.1016/j.commatsci.2022.111954