Prediction of average spacing for constrained cellular/dendritic growth

Since 1990, it has been gradually understood that there exists an allowable range of cellular/dendritic spacings during unidirectional solidification. The lower and upper limits of the allowable range are very sharp at the same current growth condition, while the average spacing for cellular/dendritic arrays depends on the history of variation of solidification parameters. The present work puts forward a novel numerical model to predict the ultimate average spacing for constrained cellular and dendritic growth, according to the characteristics of unsteady-state evolution of cellular and dendritic arrays. Our analysis considering the history-dependent selection of the average spacing for cellular/dendritic arrays, we find - with no adjustable parameters - good agreement with experimental results obtained in different alloys and in different velocity histories.