Discovering High-Strength Alloys via Physics-Transfer Learning

TL;DR

A data-driven framework that leverages neural networks trained on force field simulations to understand crystal plasticity physics is proposed, predicting Peierls stress from material parameters derived via density functional theory computations, which are otherwise computationally intensive for direct dislocation modeling.

Abstract

Predicting the strength of materials requires considering various length and time scales, striking a balance between accuracy and efficiency. Peierls stress measures material strength by evaluating dislocation resistance to plastic flow, reliant on elastic lattice responses and crystal slip energy landscape. Computational challenges due to the non-local and non-equilibrium nature of dislocations prohibit Peierls stress evaluation from state-of-the-art material databases. We propose a data-driven framework that leverages neural networks trained on force field simulations to understand crystal plasticity physics, predicting Peierls stress from material parameters derived via density functional theory computations, which are otherwise computationally intensive for direct dislocation modeling. This physics transfer approach successfully screen the strength of metallic alloys from a limited number of single-point calculations with chemical accuracy. Guided by these predictions, we fabricate high-strength binary alloys previously unexplored, utilizing high-throughput ion beam deposition techniques. The framework extends to problems facing the accuracy-performance dilemma in general by harnessing the hierarchy of physics of multiscale models in materials sciences.

Figures (5)

• Figure 1: Predictions of Peierls stress and uncertainties quantification.(a) The vast metastable materials space and potential high-strength materials. (b, c) Compared to equilibrium properties (e.g., elastic constants), the measurement or calculations of materials’ non-equilibrium properties (e.g., material strength) have larger deviations. (d) Crystal plasticity (CP) and key parameters of critical resolved shear stress (CRSS). (e, f) PT framework transfers the physics from low-fidelity force field models to chemically accurate first-principles methods, effectively addressing the trade-off between accuracy and computational expense.
• Figure 2: Material strength screening using PT approach.(a) Stress-strain ($\sigma$-$\epsilon$) curves under uniaxial tension along the $[100]$ direction of Cu. The elastic constants ($Y$) are determined as the slope obtained from single-point calculations. (b) The $\gamma$ surface calculated on the $\{111\}$ plane using MLFFs. The $\gamma$ surface can be fitted by Fourier series on single-point calculations (marked in panel (b) as scatter points). (c) The scheme to integrate mesoscale physics into the computational material databases with first-principles accuracy. (d) The material strength database constructed by PT learning, which covers $88$ elements across the periodic table. (e) High-strength material screening from the extensive space of metastable materials in GNoME. (f) The distribution of $\tau_{\rm P}$ in the material strength database. (g) High-strength materials screened using PT learning and the corresponding yield strengths ($\sigma_{\rm Y}$) reported in experiments (extracted from MatWeb ross2013metallic).
• Figure 3: PT screening and experimental fabrication of high-strength, metastable alloys.(a) The metastable binary Cu-Ti, Al-Ti, and Al-Mo alloys with higher strength are screened out. (b) Schematic diagram of the experimental fabrication of metastable alloys using the ion beam deposition (IBD) approach. (c) The Cu-Ti alloy film prepared experimentally has a Ti content ranging from 14 at% to 22 at%. (d) The stress-strain curves obtained from microcolumn compression tests for metastable fcc solid solution ($\rm Cu_{17}Ti_{3}$, $\rm Cu_{5}Ti$, $\rm Al_{4}Ti$), and $\rm Cu_{4}Ti$ glass. (e) The heightened dislocation density, as determined by the inverse fast Fourier transform (IFFT) of transmission electron microscopy (TEM) images following deformation, elucidates the deformation mechanism of dislocation glide within the metastable crystal. (f) The screened and fabricated metastable crystal materials ($\rm Cu_{17}Ti_{3}$, $\rm Al_{4}Ti$) using the PT approach and high-throughput experiments demonstrate superior strength in contrast to an extensive array of materials reported in contemporary literature, encompassing Cu- and Al-based alloys, metallic glasses, as well as intermetallic compounds zhang2019FEDwang2022MSEAmao2018MSEAli2020JACsarma2008MSEAjiang2012JEMwang2005JNCSli2018AM. For $\rm Cu_{4}Ti$, although the PT approach identifies it as a high-strength alloy crystal, glassy structures are produced in experiments due to constraints associated with IBD.
• Figure 4: Physical insights from latent space feature analysis.(a) The underlying physics of the data can shape the structures and latent space of the well-trained neural network. (b,c) The neural networks of PT learning possess smaller parameter magnitudes (b) and a lower activation rate of neurons (c) compared to 'statistical learning' with inputs of lattice constants, elastic constants, and the $\gamma$ surface. In comparison, PT learning also includes the average atomic strain for the physics of solid solution strengthening. The standard deviation, reported in the error bars, is calculated from $10$ independently trained neural networks. (d) The differences in physics mechanisms and parameter deviations can be reflected in the latent space of neural networks. (e) For the scenarios with the same physical mechanisms but differing parameters, the locations of activated neurons in the latent space are consistent, whereas the intensities of their activation vary. (f) In scenarios where the underlying physical mechanisms differ, additional neurons are activated in the latent space, and the difference in activation magnitudes at the same activation positions becomes more pronounced. (g) Distilling physics by analyzing the relationship between active neurons in the latent space and the data. (h) The strong correlation between the principal eigenvalues of the activated neurons in the latent variable space and the physics of crystal plasticity.
• Figure : (g, h) PT framework predicts Peierls stress with high accuracy and efficiency. The PT predictions are closely aligned with the outcomes of DFT and MLFF calculations, with a difference below $48.91\%$, while the results obtained using EAM models deviate substantially from the DFT predictions, with a discrepancy of $221.27\%$(g). The PT approach also reduces the computational time notably by statistical inference, in comparison with atomistic simulations using DFT, MLFFs, or EAM (h). (i-n) PT predictions for different slip systems ( (i): fcc, (k): bcc, (m): hcp). The PT predictions show good consistency compared to MLFF simulation results (with errors $e = 12.55\%$, $48.09\%$, $4.30\%$ for Cu $\{111\}\langle\overline{1}10\rangle$, Fe $\{110\}\langle111\rangle$, Ti $\{10\overline{1}0\}\langle11\overline{2}0\rangle$ in prediction, respectively), and superior accuracy compared to EAM ($e = 33.07\%$, $72.02\%$, $13.89\%$ ( (j), (l), (n)), respectively). (o) Uncertainty quantification shows that the PT predictions eliminate physical and system uncertainties. 'L' denotes the large-supercell system with $\sim 0.8\times 10^{6}$ atoms ($160~\rm{nm} \times2~\rm{nm}\times40~\rm{nm}$). (p) Uncertainty decomposition shows that the inference errors are smaller compared to the physical and system uncertainties. The standard deviation is reported in the error bars.