Solidification Morphology and Bifurcation Predictions with the Maximum Entropy Production Rate Model

Yaw Delali Bensah,J A Sekhar

doi:10.3390/e22010040

Yaw Delali Bensah, J A Sekhar

Open Access

https://doi.org/10.3390/e22010040

Copy DOI

Journal: Entropy	Publication Date: Dec 26, 2019
Citations: 5	License type: CC BY 4.0

Affiliation: University of Ghana, University of Cincinnati

Abstract

The use of the principle of maximum entropy generation per unit volume is a new approach in materials science that has implications for understanding the morphological evolution during solid–liquid interface growth, including bifurcations with or without diffuseness. A review based on a pre-publication arXiv preprint is first presented. A detailed comparison with experimental observations indicates that the Maximum Entropy Production Rate-density model (MEPR) can correctly predict bifurcations for dilute alloys during solidification. The model predicts a critical diffuseness of the interface at which a plane-front or any other form of diffuse interface will become unstable. A further confidence test for the model is offered in this article by comparing the predicted liquid diffusion coefficients to those obtained experimentally. A comparison of the experimentally determined solute diffusion constant in dilute binary Pb–Sn alloys with those predicted by the various solidification instability models (1953–2011) is additionally discussed. A good predictability is noted for the MEPR model when the interface diffuseness is small. In comparison, the more traditional interface break-down models have low predictiveness.

Highlights

The maximum entropy generation principle [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] has brought significant predictive capability to quantitative materials science
As the entropy generation is related to the gradients, it is possible that the maximum entropy production rate (MEPR) criterion may allow for a better estimate of the solute diffusion constant in binary alloys [18] that has proved elusive to predict by traditional models
During the one dimensional solidification of a pure metal or a binary molten alloy, which is at freezing temperature under a fixed temperature gradient and with constant interface velocity there is a loss of work potential from the dissipation of kinetic energy, giving rise to entropy generation rate density φmax (J m−3 K−1 s−1 ) is given by [1] in the region of the diffuse interface with dimensions ζ (m)

Summary

Introduction

The maximum entropy generation principle [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] has brought significant predictive capability to quantitative materials science. As the entropy generation is related to the gradients, it is possible that the MEPR criterion may allow for a better estimate of the solute diffusion constant in binary alloys [18] that has proved elusive to predict by traditional models This hypothesis is tested for dilute Pb–Sn alloys in this article. The appearance of a smooth-cellular or jagged morphology from a planar interface, especially for binary alloys, depends on the material composition, CO (wt% or mole/m3 ), velocity V (m/s) of the growing interface, and the temperature gradient GL (K/m) in the liquid and k, the non-dimensional solute partition coefficient These variables at the point of morphological instability are commonly subscripted with the symbol (c) to indicate a transition [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42]. Comparisons with the MEPR model are made

The MEPR Model

The CUT Model

The LST Model

Comparison with Experiments for the Diffusion Coefficient Prediction

Summary Discussions