[Paper Review] Interfacial instability of a planar interface and diffuseness at the solid-liquid interface for pure and binary materials

Yaw Delali Bensah, J. A. Sekhar|arXiv (Cornell University)|May 17, 2016

Solidification and crystal growth phenomena38 references3 citations

TL;DR

This paper proposes the Maximum Entropy Production Rate (MEPR) principle as a unifying framework to predict interfacial instability and diffuse interface behavior during solidification in pure and binary materials. By identifying the interface configuration that maximizes entropy production, the model quantitatively predicts diffuse interface thickness, pseudo-atomic layer count, and transitions from planar to non-planar morphologies (facet or cellular) across varying solidification velocities and temperature gradients—offering the first predictive breakdown conditions for binary alloys where prior models failed.

ABSTRACT

Topographical and diffuse interface reconfigurations occur with a change in the solidification rate. In this article we pursue the hypothesis that the interface configuration during solidification is determined by the rate of entropy production in the region between a rigorous solid and rigorous liquid phase. We posit that when an interface begins to migrate, there are several stable configurations that are possible. These include atomistically-planar, diffuse-planar, facet non-planar and cellular non-planar. The configuration and topographical condition that affords the maximum entropy production rate (MEPR) yields the most stable interface configuration. The principle of MEPR is applied to (1) describe atomistically smooth and diffuse interfaces, (2) provide quantitative results for the diffuse interface thickness and the number of pseudo-atomic layers in the interface region, and (3) predict the transition from planar to a non-planar facet or non-facet cellular morphology as a function of solidification velocity or temperature gradient. Numerous experimental investigations spanning over sixty years have failed to comprehensively validate any of the existing solid-liquid interface (SLI) growth instability models. With the MEPR model, for the first time, breakdown conditions are predicted with a fair degree of accuracy for a number of binary alloys where no previous theoretical model had predictability. The model considers steady state solidification at close-to and far-from equilibrium conditions.

Motivation & Objective

• To explain interfacial instability and diffuse interface formation during solidification using thermodynamic principles.
• To address the long-standing lack of predictive models for solid-liquid interface (SLI) growth instabilities across pure and binary systems.
• To identify the stable interface configuration as the one maximizing entropy production rate (MEPR).
• To quantitatively predict diffuse interface thickness and number of pseudo-atomic layers.
• To predict the transition from planar to non-planar (facet or cellular) morphologies as a function of solidification velocity and temperature gradient.

Proposed method

• The Maximum Entropy Production Rate (MEPR) principle is applied to identify the most thermodynamically stable interface configuration during solidification.
• Steady-state solidification conditions are analyzed under both close-to-equilibrium and far-from-equilibrium regimes.
• The model considers the rate of entropy production in the interfacial region between rigid solid and liquid phases.
• Interface configurations—atomistically-planar, diffuse-planar, facet non-planar, and cellular non-planar—are evaluated for entropy production rate.
• The model derives quantitative expressions for diffuse interface thickness and pseudo-atomic layer count based on MEPR maximization.
• Waveform analysis is incorporated to refine predictions of morphological transitions.

Experimental results

Research questions

• RQ1 What determines the stable configuration of a solid-liquid interface during solidification—planar, diffuse, facet, or cellular?
• RQ2 How can the thickness of the diffuse interface and the number of pseudo-atomic layers be quantitatively predicted?
• RQ3 What conditions trigger the transition from planar to non-planar (facet or cellular) morphologies during solidification?
• RQ4 Can the MEPR principle predict breakdown conditions for solidification instabilities in binary alloys where prior models failed?
• RQ5 How does the entropy production rate vary across different interface morphologies under varying solidification velocities and temperature gradients?

Key findings

• The MEPR principle successfully predicts the transition from planar to non-planar morphologies (facet or cellular) as a function of solidification velocity and temperature gradient.
• The model provides quantitative predictions for diffuse interface thickness and the number of pseudo-atomic layers in the interfacial region.
• For the first time, the model predicts breakdown conditions in binary alloys with fair accuracy, where previous theoretical models lacked predictability.
• The model is valid under both close-to-equilibrium and far-from-equilibrium solidification conditions.
• The inclusion of waveform analysis improves the accuracy of morphological transition predictions.
• The results are consistent with experimental observations across a range of materials, validating the MEPR-based framework.