[Paper Review] Ab-initio free energies of liquid metal alloys: application to the phase diagrams of Li-Na and K-Na

Yang Huang, Michael Widom+1 more|arXiv (Cornell University)|May 18, 2021

Thermodynamic and Structural Properties of Metals and Alloys4 citations

TL;DR

This paper presents a first-principles method to compute absolute free energies of liquid metal alloys using ab-initio molecular dynamics (AIMD), combining simulated enthalpies with entropy derived from densities and pair correlation functions. The approach accurately predicts phase diagrams for Li-Na (showing a critical point and liquid-liquid phase separation) and K-Na (revealing a deep eutectic at 33% Na and 260 K), with strong agreement to experimental data, demonstrating a robust, computationally efficient route to absolute free energy in complex liquid systems.

ABSTRACT

Comparison of free energies between different phases and different compositions underlies the prediction of alloy phase diagrams. To allow direct comparison, consistent reference points for the energies or enthalpies are required, and the entropy must be placed on an absolute scale, yielding absolute free energies. Here we derive absolute free energies of liquids from ab-initio molecular dynamics (AIMD) by combining the directly simulated enthalpies with an entropy derived from simulated densities and pair correlation functions. As an example of the power of this method we calculate the phase diagrams of two binary alkali metal alloys, Li-Na and K-Na, revealing a critical point and liquid-liquid phase separation in the former case, and a deep eutectic in the latter. Good agreement with experimental data demonstrates the power of this simple method.

Motivation & Objective

• To develop a method for computing absolute free energies of liquid metal alloys from first principles, enabling direct comparison of thermodynamic stability across phases and compositions.
• To address the challenge of placing entropy on an absolute scale by deriving it from simulated densities and pair correlation functions, avoiding reliance on reference states or perturbation methods.
• To apply the method to predict phase diagrams of Li-Na and K-Na, two alkali metal systems with distinct phase behaviors, including critical points and eutectics.
• To validate the method against experimental data, ensuring accuracy in enthalpy, entropy, and free energy predictions for liquid metals.
• To demonstrate that finite-size effects and truncation in entropy (pair-level only) do not compromise predictive power for macroscopic phase behavior when combined with careful statistical analysis.

Proposed method

• The method computes absolute enthalpy from ab-initio molecular dynamics (AIMD) simulations at finite temperature, using the DFT-calculated energy as a reference point.
• Entropy is derived from the simulated radial distribution functions and densities using a pair-correlation-based approximation, enabling absolute entropy without relying on histogram or sampling methods.
• The total free energy G = H - TS is computed using the simulated enthalpy H and the derived entropy S, with T scaled to the simulation temperature.
• A modified Widom particle insertion method is used to compute chemical potentials and validate free energy consistency, though the main approach relies on direct thermodynamic integration via ensemble averaging.
• Hybrid Monte Carlo/Molecular Dynamics (MCMD) is employed to accelerate equilibration, especially for phase separation processes, by allowing discrete species swaps to enhance configurational sampling.
• Statistical errors are estimated by dividing simulation runs into segments and computing standard errors, with anticorrelation between H and -TS reducing uncertainty in G.

Experimental results

Research questions

• RQ1 Can absolute free energies of liquid metal alloys be computed directly from ab-initio molecular dynamics without relying on thermodynamic integration or perturbation theory?
• RQ2 To what extent can the entropy of a liquid metal be accurately approximated from pair correlation functions and density alone, without higher-order correlations?
• RQ3 Does the method correctly predict the phase behavior of Li-Na, including a critical point and liquid-liquid phase separation, in agreement with experiment?
• RQ4 Can the method accurately reproduce the deep eutectic in K-Na, including its composition and melting temperature, from first principles?
• RQ5 How do finite-size effects and truncation in the entropy expansion (pair vs. many-body) influence the prediction of phase boundaries in liquid alloys?

Key findings

• The method successfully computes absolute free energies of liquid metal alloys using only AIMD simulations of enthalpy, density, and pair correlation functions, avoiding the need for thermodynamic integration or reference states.
• For Li-Na, the predicted phase diagram shows a critical point at approximately 578 K and liquid-liquid phase separation, consistent with experimental observations, though simulation size effects lead to overestimation of the critical temperature.
• For K-Na, the method correctly predicts a deep eutectic at 33% Na and 260 K, matching experimental data, confirming the method’s accuracy for systems with strong mixing anomalies.
• The computed absolute entropies for pure liquid metals (Li, Na, K) agree well with NIST-JANAF tables, validating the entropy derivation method.
• Statistical errors on the free energy are estimated at ~0.4 meV/atom for K-Na at 473 K, indicating high precision despite finite sampling and system size.
• Finite-size effects cause premature phase separation in Li-Na above the critical point, especially in smaller cells (N=300), but the overall phase behavior remains qualitatively and quantitatively consistent with experiment when larger systems (N=500) are used.