Statistical learning for evaluation of crystal growth in low-melting alloy droplets with application to quasicrystal-forming Ti–Zr–Ni alloys

The evaluation of the crystal growth in undercooled alloy melts is essential for investigations of their solidification behavior. Low-melting alloy systems usually exhibit little self-illumination and cinematography is not often feasible. A time-temperature data based statistical learning approach is presented to evaluate the crystal growth in an undercooled droplet, where a spatial geometry-informed, errors-in-variables probabilistic model is developed based on the prediction of the dendrite growth paths. The preferable growth mechanism and growth velocities can be evaluated from statistical model selection and parameter estimation. Based only on the pyrometry data of two Ti–Zr–Ni alloys, a bulk growth mechanism is justified and the growth velocities in both the stable C14 phase and metastable icosahedral phase are able to be measured and statistically interpreted. (paper)