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 ab initio morphology prediction. The morphology predictions were implemented for two cases: with and without shear components of eigenstrain (w/ and w/o shear). The (1210) longitudinal needle for the y hydride (w/o shear) and plate (or disk) on the plane, which is 20? to 30? tilted about (1210)-axis from basal plane (0001), for delta and e 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 delta 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.

Automated summary

In this study, we energetically predicted the morphology of Zr hydride precipitates in a hexagonal close-packed Zr matrix using elasticity theory. We compared different shapes of ellipsoidal inclusions and successfully predicted the stable shapes and orientations of the precipitates, which were qualitatively consistent with experimental observations.