Composition Design of Shape Memory Ceramics based on Gaussian Processes

We present a Gaussian process machine learning model to predict the transformation temperature and lattice parameters of ZrO$_2$-based ceramics. Our overall goal is to search for a shape memory ceramic with a reversible transformation and low hysteresis. The identification of a new low hysteresis composition is based on design criteria that have been successful in metal alloys: (1) $\lambda_2 = 1$, where $\lambda_2$ is the middle eigenvalue of the transformation stretch tensor, (2) minimizing the max$|q(f)|$, which measures the deviation from satisfying the cofactor conditions, (3) high transformation temperature, (4) low transformational volume change, and (5) solid solubility. We generate many synthetic compositions, and identify a promising composition, 31.75Zr-37.75Hf-14.5Y-14.5Ta-1.5Er, which closely satisfies all the design criteria based on predictions from machine learning. However, differential thermal analysis reveals a relatively high thermal hysteresis of 137{\deg}C for this composition, indicating that the proposed design criteria are not universally applicable to all ZrO$_2$-based ceramics. We also explore reducing tetragonality of the austenite phase by addition of Er$_2$O$_3$. The idea is to tune the lattice parameters of austenite phase towards a cubic structure will increase the number of martensite variants, thus, allowing more flexibility for them to accommodate high strain during transformation. We find the effect of Er$_2$O$_3$ on tetragonality is weak due to limited solubility. We conclude that a more effective dopant is needed to achieve significant tetragonality reduction. Overall, Gaussian process machine learning models are shown to be highly useful for prediction of compositions and lattice parameters, but the discovery of low hysteresis ceramic materials apparently involves other factors not relevant to phase transformations in metals.