Wave number selection in rapid solidification processes in one dimension

¹ Department of Materials Science and Engineering, Guangdong Technion-Israel Institute of Technology Shantou, Guangdong 515063, China
² State Key Laboratory of Rolling and Automation (RAL), Northeastern University - Shenyang 110819, China
³ Guangdong Provincial Key Laboratory of Materials and Technologies for Energy Conversion, Guangdong Technion-Israel Institute of Technology - Shantou, Guangdong 515063, China
⁴ Technion, Israel Institute of Technology - Haifa 32000, Israel

Received: 12 August 2025
Accepted: 8 October 2025

Abstract

The wave number of the periodic solid phase selected by a fast invading front into an unstable uniform liquid phase had been studied in the context of solidification models at constant undercooling. However, in technologically important rapid solidification processes, the temperature typically becomes a spatially varying field and is strongly affected by latent heat release at the solidification front. It is important to examine the predictive capability of the marginal stability theory in the rapid solidification process. This work explores the wave number selection behavior in rapid solidification processes in one dimension based on numerical simulations of the phase field crystal model. It is found that the selected wave number is strongly affected by the latent heat generated at the solidification front. The marginal stability theory, although it is formulated for systems with uniform temperature, still gives a good prediction of the selected wave number as a function of the solid-liquid interface velocity in various solidification conditions examined in this work.