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

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 $\le$ X $\le$ 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.

References in corpus (10)

• A constitutive law for dense granular flows
• Coherency strain and the kinetics of phase separation in LiFePO4
• py4DSTEM: a software package for multimodal analysis of four-dimensional scanning transmission electron microscopy datasets
• Learning Constitutive Relations using Symmetric Positive Definite Neural Networks
• Demonstration of a novel focusing small-angle neutron scattering instrument equipped with axisymmetric mirrors
• Constitutive Relation for Nonlinear Response and Universality of Efficiency at Maximum Power for Tight-Coupling Heat Engines
• Interplay of phase boundary anisotropy and electro-autocatalytic surface reactions on the lithium intercalation dynamics in Li${}_X$FePO${}_4$ platelet-like nanoparticles
• Exploring physics of ferroelectric domain walls via Bayesian analysis of atomically resolved STEM data
• Image Inversion and Uncertainty Quantification for Constitutive Laws of Pattern Formation
• Building Free Energy Functional from Atomically-Resolved Imaging: Atomic Scale Phenomena in La-doped BiFeO3

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