[Paper Review] Determining fluid-crystal phase boundaries for a binary hard-sphere mixture using direct-coexistence simulations

Rinske M. Alkemade, Alessandro Salo+2 more|arXiv (Cornell University)|Jan 8, 2026

Material Dynamics and Properties0 citations

TL;DR

Extends direct-coexistence methods to stoichiometric binary crystals to accurately determine fluid–crystal phase boundaries in a binary hard-sphere mixture and analyzes how crystal-plane choice affects accuracy.

ABSTRACT

Determining fluid-crystal phase boundaries via direct-coexistence methods can be challenging due to the fact that the simulation box can introduce crystal strain. Recently, a direct-coexistence approach was developed which allows one to easily identify the equilibrium strain-free fluid-crystal coexistence in monodisperse systems. Here, we show that this approach can be readily extended to binary mixtures forming stoichiometric binary crystals, allowing accurate and efficient determination of the phase boundaries. Moreover, we examine how the choice of crystal plane in contact with the fluid affects the accuracy of the phase boundary determination. The method is easy to implement and does not require prior knowledge of the binary fluid's equation of state. These results further establish the method as a robust and practical tool for accurately determining fluid-crystal phase boundaries.

Motivation & Objective

• Extend direct-coexistence to binary mixtures forming stoichiometric crystals.
• Determine fluid–crystal phase boundaries for a binary hard-sphere mixture with q=0.58.
• Assess how crystal orientation relative to the fluid influences boundary accuracy and sampling efficiency.
• Show that the method does not require the binary fluid equation of state (EOS).
• Compare direct-coexistence results with previous free-energy predictions and analyze sources of systematic shifts.

Proposed method

• Use event-driven molecular dynamics in the NVT ensemble to simulate binary hard-sphere mixtures.
• Perform direct-coexistence with an elongated box ensuring a fluid–crystal interface perpendicular to the long axis.
• Measure the normal pressure Pzz and undeformed crystal pressure PUD to locate unstrained coexistence by matching Pzz with PUD.
• Monitor and align the fluid composition profile chi(z) along the interface to extract the coexisting fluid composition chi^F.
• Allow the fluid to exchange particles with the crystal at the interface, yielding the coexistence composition automatically.
• Explore multiple crystal orientations (FCC(A), FCC(B), AB2, AB13) and quantify the impact of orientation on interfacial stiffness and sampling efficiency.

Experimental results

Research questions

• RQ1 Can the direct-coexistence approach for unstrained fluid–crystal coexistence be reliably extended to stoichiometric binary crystals?
• RQ2 What are the fluid–crystal phase boundaries for the binary hard-sphere mixture with size ratio q=0.58?
• RQ3 How does the choice of crystal plane/orientation at the fluid interface affect the accuracy and efficiency of boundary determination?
• RQ4 Do direct-coexistence results align with or differ from previous free-energy predictions for binary hard-sphere mixtures, and why?
• RQ5 What is the role of composition fluctuations in the coexisting fluid during the direct-coexistence process?

Key findings

• Direct-coexistence simulations yield accurate fluid–crystal phase boundaries for the binary mixture with q=0.58.
• Phase boundaries obtained are consistently below the Eldridge–Madden–Frenkel (EMF) free-energy predictions for several crystal types.
• Using a more accurate monodisperse-like EOS (KLM) brings agreement with direct-coexistence results, revealing BMCSL underestimates coexistence pressure.
• Crystal-plane orientation strongly affects interfacial stiffness; rotated orientations can yield a smoother, wider interface and better sampling (notably AB2 and AB13).
• The AB2 and AB13 coexistence data show that finite-size and slow sampling can occur due to large unit cells and slow crystal growth/shrinkage, requiring longer simulations.
• A small but finite region exists where fluid–FCC(B) coexistence is stable, as shown in the phase diagram.