Correlative image learning of chemo-mechanics in phase-transforming solids

TL;DR

This paper introduces a physics-constrained image learning framework to determine chemo-mechanical laws at the nanoscale in phase-transforming solids, validated on battery materials, revealing composition-strain relations and residual strain visualization.

Contribution

The work presents a novel, generalizable method combining correlative microscopy and data-driven learning to uncover constitutive laws in heterogeneous solids, including inside unstable regions.

Findings

Uncovered the composition-eigenstrain relation in Li$_X$FePO$_4$ across all compositions.

Validated Vegard's law at the nanoscale.

Visualized residual strain fields and their origins in dislocations.

Abstract

Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (e.g., due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids. In this work, we developed a generalizable, physically-constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional scanning transmission electron microscopy and X-ray spectro-ptychography images. We demonstrated this approach on Li$_X$FePO$_4$, a technologically-relevant battery positive electrode material. We uncovered the functional form of composition-eigenstrain relation in this two-phase binary solid across the entire composition range (0 $\leq$ X $\leq$ 1), including inside the thermodynamically-unstable miscibility gap. The learned relation directly validates Vegard's law of linear response at the nanoscale. Our physics-constrained data-driven approach directly visualizes the residual strain field (by removing the compositional and coherency strain), which is otherwise impossible to quantify. Heterogeneities in the residual strain arise from misfit dislocations and were independently verified by X-ray diffraction line profile analysis. Our work provides the means to simultaneously quantify chemical expansion, coherency strain and dislocations in battery electrodes, which has implications on rate capabilities and lifetime. Broadly, this work also highlights the potential of integrating correlative microscopy and image learning for extracting material properties and physics.