[Paper Review] Data-Driven Prediction of Complex Crystal Structures of Dense Lithium

Xiaoyang Wang, Zhenyu Wang+7 more|arXiv (Cornell University)|Feb 8, 2023

Machine Learning in Materials Science4 citations

TL;DR

This study combines swarm-intelligence-based global structure search with machine learning potentials to predict four new complex crystal phases of dense lithium with unit cells up to 192 atoms, all energetically competitive with known phases near the melting minimum (40–60 GPa). The predicted mP160, oP192, oP48, and tI20 structures exhibit near-degenerate Gibbs free energies with experimental phases, offering strong candidates for the newly observed crystalline phases in lithium under high pressure and finite temperature.

ABSTRACT

Lithium (Li) is a prototypical simple metal at ambient conditions, but exhibits remarkable changes in structural and electronic properties under compression. There has been intense debate about the structure of dense Li, and recent experiments offered fresh evidence for new yet undetermined crystalline phases near the enigmatic melting minimum region in the pressure-temperature phase diagram of Li. Here, we report on an extensive exploration of the energy landscape of Li using an advanced crystal structure search method combined with a machine learning approach, which greatly expands the scale of structure search, leading to the prediction of four complex Li crystal phases containing up to 192 atoms in the unit cell that are energetically competitive with known Li structures. These findings provide a viable solution to the newly observed yet unidentified crystalline phases of Li, and showcase the predictive power of the global structure search method for discovering complex crystal structures in conjunction with accurate machine-learning potentials.

Motivation & Objective

• To resolve the long-standing ambiguity in the crystal structures of dense lithium near its melting minimum, where experimental data remain inconclusive due to amorphous phases and sample degradation.
• To explore the complex energy landscape of lithium under high pressure and finite temperature, where multiple shallow minima challenge conventional stability assessments.
• To demonstrate the predictive power of integrating advanced global optimization with machine learning potentials for discovering complex, large-unit-cell crystal structures in strongly correlated materials.
• To provide thermodynamically consistent predictions of phase stability by calculating Gibbs free energies using thermodynamic integration with deep potential molecular dynamics.

Proposed method

• Employed a swarm-intelligence-based global structure search algorithm to explore the potential energy surface of lithium across a wide range of high-pressure and finite-temperature conditions.
• Utilized deep learning potentials (DPMD) trained on density functional theory data to enable accurate and efficient free energy calculations for large supercells with up to 192 atoms.
• Applied thermodynamic integration (TI) via deep potential molecular dynamics to compute Gibbs free energies of competing phases with high precision, including anharmonic and nuclear quantum effects.
• Calculated free energy differences relative to the cI16 phase using both harmonic approximations (FD and DFPT) and anharmonic corrections (TI), with error estimation from DP uncertainty and statistical fluctuations.
• Used a multi-scale approach combining ab initio calculations, machine learning potentials, and statistical thermodynamics to assess relative stability across the P-T phase diagram.
• Validated predictions by comparing free energy trends with experimental X-ray diffraction data from rapid-compression experiments, particularly in the 45–70 GPa range.

Experimental results

Research questions

• RQ1 What are the stable crystal structures of dense lithium near the melting minimum (40–60 GPa), where experimental data show ambiguous diffraction peaks?
• RQ2 How do the Gibbs free energies of newly predicted complex phases compare with those of experimentally observed phases like oC88 and cI16 at finite temperatures?
• RQ3 To what extent do anharmonic effects and nuclear quantum effects influence the relative stability of competing lithium phases in this pressure range?
• RQ4 Can machine learning potentials combined with global optimization reliably predict large-unit-cell crystal structures in strongly correlated metals like lithium?
• RQ5 What is the thermodynamic origin of the observed phase coexistence and near-degeneracy in the energy landscape of dense lithium?

Key findings

• The mP160 phase is the most promising candidate below 50 GPa, showing nearly degenerate Gibbs free energy with cI16 and liquid phases at 50 GPa and 250 K, where other phases are dynamically unstable.
• The oP48 phase exhibits superior thermodynamic stability compared to both the predicted oP192 and experimentally observed oC88 phases at 55 GPa, with free energy lower than oC88 above ~110 K.
• At 65 GPa, the oP48 and tI20 phases have lower free energies than oC88 above 110 K and 160 K, respectively, indicating their potential to be the true ground states in this region.
• The predicted oP192 phase is dynamically stable only at 55 GPa and shows lower free energy than oC88, suggesting it may be a transient or metastable phase in the transition path.
• The Gibbs free energy differences between competing phases are within 2 meV/atom at 50 GPa and 250 K, indicating a flat energy landscape with high sensitivity to P-T history and experimental conditions.
• The entire energy landscape near the melting minimum is characterized by multiple shallow local minima, with several phases (including mP160, oP48, oP192, tI20) competing within a few meV/atom window, explaining the experimental difficulty in unambiguous phase assignment.