Machine-Learning Force Fields for Metallic Materials: Phase Transformations and Deformations
LI Zhishang, ZHAO Long, ZONG Hongxiang(), DING Xiangdong
State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China
Cite this article:
LI Zhishang, ZHAO Long, ZONG Hongxiang, DING Xiangdong. Machine-Learning Force Fields for Metallic Materials: Phase Transformations and Deformations. Acta Metall Sin, 2024, 60(10): 1388-1404.
A comprehensive understanding of the microscopic mechanisms underlying phase transitions and deformations in metallic materials is crucial for developing new materials that meet the nation's essential needs. Molecular dynamic simulation techniques, particularly those powered by machine-learning molecular force fields, are emerging as potent tools for unraveling atomic-scale phenomena. In this study, recent advancements in machine-learning molecular force fields were reviewed to investigate metallic phase transitions and deformations. First, the fundamental principles and evolution of machine-learning molecular force fields were introduced. Then, the phase transformation and deformation of metals were examined, providing insights into the kinetics of phase transitions and microscopic mechanisms. Finally, the challenges faced by current machine-learning molecular force fields in studying metallic phase transformations and deformations were identified, and a glimpse into future research directions was discussed.
Fig.1 Schematic of machine-learning force fields (MLFFs)[32-34] (i, j, k represent three different atoms; rij denotes the distance between atom i and atom j; rik denotes the distance between atom i and atom k; θjik represents the angle formed by the central atom i with atoms k and j)
Fig.2 Schematic of the DeepMD model. The frame in the box is an enlargement of a deep neural network (DNN). The relative positions of all neighbors with respect to atom i, i.e., { Rij }, is first converted to descriptor matrix { Dij }, then passed to the hidden layers to compute Ei[66] (E—total energy)
Fig.3 Schematic of graph-based atomic descriptor. The initial graph is represented by the set of atomic attributes V = {vi }, bond attributes E = {(ek, rk, sk )}, and global state attributes u. In the first update step, the bond attributes are updated. Information flows from atoms that form the bond, the state attributes, and the previous bond attribute to the new bond attributes. Similarly, the second and third steps update the atomic and global state attributes, respectively, by information flow among all three attributes. The final result is a new graph representation[75] (vi is an atomic attribute vector for atom i in a system; ek is the bond attribute vector for bond k, rk and sk are the atom indices forming bond k; MEGNet—MatErials Graph Network)
Fig.4 Trade-offs between accuracy and cost among different types of MLFFs. All potentials except EAM4 were refitted to the same tungsten data set. Computational costs were benchmarked with a 128-atom bcc-tungsten supercell[83] (EAM—embedded atom method; GAP—Gaussian approximation potential; SNAP, qSNAP—spectral neighbor analysis potential (SNAP) and its quadratic variant, respectively; MTP—moment tensor potential; DFT—density functional theory; LJ—Lennard-Jones function; RMSE—root-mean-squared error; RMSF—root-mean-square-fluctuation; σE—the range of the ground truth value of RMSE; σF—the range of the ground truth value of RMSF)
Fig.5 Application of MLFFs in dislocation dynamics of conventional metallic materials under quasi-static loading condition (a) screw dislocation core of bcc-Fe (τ—shear stress, a—Peierls valleys spacing, b—Burgers vector modulus)[90] (b) atoms at the dislocation core during a simulation snapshot, evidencing dislocation glide by kink-pair mechanism[90] (c) stress-dependent reaction path of the interaction between an incoming 1/2<110> screw dislocation and the semi-coherent Ni/Ni3Al interface with a preexisting interfacial dislocation[91] (d) variation of energy barrier as a function of the external stress for the first and second interacting stages[91]
Fig.6 Application of MLFFs in dislocation dynamics of high entropy alloys under qausi-static loading condition (a) expansion of dislocation loop in Ni16.67Co16.67Fe36.67Ti30 high-entropy alloys (HEAs) under shear stress τxy = 600 MPa at T = 300 K[94] (t—the duration of the simulation) (b) variation of velocity as a function of shear stress for both edge and screw dislocations at T = 300 K in Ni16.67Co16.67Fe36.67Ti30 HEAs[94] (c) dislocation line with cross-slip locking viewed from the y and z directions[93] (d110—interplanar spacing of the 110 crystal plane) (d, e) CSRO effects on screw dislocation velocity (d) and edge dislocation velocity (e) vs stress dependency at 1800 K (CSRO—chemical short-range order)[93]
Fig.7 Application of MLFFs in the mechanical behavior of nanocrystalline alloys[97] (a) a polycrystalline model for the quaternary NbMoTaW multi-principal element alloys (MPEA) with atoms colored according to the common neighbor analysis algorithm to identify different structure types (cyan: bulk bcc; orange: grain boundary (GB)) (b) the same polycrystalline model after random initialization with equimolar quantities of Nb, Mo, W, and Ta. Atoms are colored by elements (c) snapshot of polycrystalline model after hybrid Monte Carlo/molecular dynamics (MC/MD) simulations
Fig.8 Application of MLFFs in dislocation dynamics of conventional metallic materials (a) width of dislocation core as a function of the shock velocity in the elemental metals and bcc HEAs[98] (b) phase diagram of dislocation core and spatial distribution of local shear modulus (Gatom)[98] (c) microstructure of a Zr-10Nb (atomic fraction, %) single crystal at t = 12 ps in response to [001] β shock loading[99] (TB—twin boundary)
Fig.9 Application of MLFFs in phase transition of zirconium (a) predicted phase diagram of pure Zr as a function of pressure and temperature[106] (b) snapshots of the phase transformation processes in [0001] α shocked Zr single crystals with different piston velocities[104] (Insets show the neiborhood information of the atoms before and after the transformation. They correspond to the hcp and bcc structures, respectively) (c) typical microstructure evolution of β-Zr during cooling at pressure P = 0 GPa and P = 8.0 GPa using the present machine-learning (ML) potential[106]
Fig.10 Application of MLFFs in phase transition of Zr-Nb alloy[108] (a) MD simulation of the Zr-10Nb single crystal showing the formation of local interlayer twists (LITs) (b) temperature-pressure phase diagram of Zr-Nb alloys from MD simulations
Fig.11 Application of MLFFs in phase transition of the high-pressure solid alkali metal potassium (a) forcefield simulated phase diagram of potassium[118] (b) top view and side view of the incommensurate host-guest (HG) structure K-III (a, b, c—lattice constants) (c) correlation along the chains, showing long-range oscillatory order at 250 K (blue) and exponentially decaying short-ranged order at 750 K (red)[118](—the intrachain correlation function, Δz(cg)—the difference in the z-directional displacement between atoms, expressed as multiples of the guest lattice constant) (d, e) typical microstructure evolution of bicrystalline KIII-fcc upon isothermal annealing at 16 and 21 GPa[117] (Blue boxes outline the presence of disordered regions)
Fig.12 Application of MLFFs in phase transition of the liquid alkali metal potassium (a) heat capacity (cp ) at different temperatures varies with pressure[120] (b) normalized diffusion constant vs pressure for selected temperatures (D—diffusion constant) [120] (c) radial distribution functions (RDFs) g(r) at selected pressures and 650 K (d) heat map of distribution of coordination numbers vs pressure at 650 K[120] (e) electron localization function (ELF) values at 2, 16, and 26 GPa are shown in the RGB scale from 0 (blue) to 0.70 (red), with 0.35 (green) [120]
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