Machine learning interatomic potential with DFT accuracy for general grain boundaries in α-Fe

Zhang L., Csányi G., van der Giessen E., Maresca F.

Machine learning interatomic potentials (ML-IAPs) enable quantum-accurate, classical molecular dynamics simulations of large systems, beyond reach of density functional theory (DFT). Yet, their efficiency and ability to predict systems larger than DFT supercells are not fully explored, posing a question regarding transferability to large-scale simulations with defects (e.g. dislocations, cracks). Here, we apply a three-step validation approach to body-centered-cubic iron. First, accuracy and efficiency are assessed by optimizing ML-IAPs based on four state-of-the-art ML packages. The Pareto front of computational speed versus testing root-mean-square-error (RMSE) is computed. Second, benchmark properties relevant to plasticity and fracture are evaluated. Their relative root-mean-square-error (Q) with respect to DFT is found to correlate with RMSE. Third, transferability of ML-IAPs to dislocations and cracks is investigated by using per-atom model uncertainty quantification. The core structures and Peierls barriers of screw, M111 and three edge dislocations are compared with DFT. Traction-separation curve and critical stress intensity factor (KIc) are also predicted. Cleavage on the pre-existing crack plane is found to be the zero-temperature atomistic fracture mechanism of pure body-centered-cubic iron under mode-I loading, independent of ML package and training database. Quantitative predictions of dislocation glide paths and KIc can be sensitive to database, ML package, cutoff radius, and are limited by DFT accuracy. Our results highlight the importance of validating ML-IAPs by using indicators beyond RMSE. Moreover, significant computational speed-ups can be achieved by using the most efficient ML-IAP package, yet the assessment of the accuracy and transferability should be performed with care.

Lin S., Casillas-Trujillo L., Tasnádi F., Hultman L., Mayrhofer P.H., Sangiovanni D.G., Koutná N.

AbstractMachine-learning interatomic potentials (MLIPs) offer a powerful avenue for simulations beyond length and timescales of ab initio methods. Their development for investigation of mechanical properties and fracture, however, is far from trivial since extended defects—governing plasticity and crack nucleation in most materials—are too large to be included in the training set. Using TiB2 as a model ceramic material, we propose a training strategy for MLIPs suitable to simulate mechanical response of monocrystals until failure. Our MLIP accurately reproduces ab initio stresses and fracture mechanisms during room-temperature uniaxial tensile deformation of TiB2 at the atomic scale ( ≈ 103 atoms). More realistic tensile tests (low strain rate, Poisson’s contraction) at the nanoscale ( ≈ 104–106 atoms) require MLIP up-fitting, i.e., learning from additional ab initio configurations. Consequently, we elucidate trends in theoretical strength, toughness, and crack initiation patterns under different loading directions. As our MLIP is specifically trained to modelling tensile deformation, we discuss its limitations for description of different loading conditions and lattice structures with various Ti/B stoichiometries. Finally, we show that our MLIP training procedure is applicable to diverse ceramic systems. This is demonstrated by developing MLIPs which are subsequently validated by simulations of uniaxial strain and fracture in TaB2, WB2, ReB2, TiN, and Ti2AlB2.

Jalolov F.N., Podryabinkin E.V., Oganov A.R., Shapeev A.V., Kvashnin A.G.

AbstractCalculating the elastic and mechanical characteristics of non‐crystalline solids can be challenging due to the high computational cost of ab initio methods and the low accuracy of empirical potentials. This paper proposes a computational technique for efficient calculations of mechanical properties of polycrystals, composites, and multi‐phase systems from atomistic simulations with high accuracy and reasonable computational cost. The calculated elastic moduli of polycrystalline diamond and their dependence on grain size are determined using a developed approach based on actively learned machine learning interatomic potentials (MLIPs). These potentials are trained on local fragments of the polycrystalline system, and ab initio calculations are used to compute forces, stresses, and energies. This technique allows researchers to perform extensive calculations of the mechanical properties of complex solids with different compositions and structures, achieving high accuracy and facilitating the transition from ideal (single crystal) systems to more realistic ones.

Ito K.

In the development of high-strength steels for carbon neutrality, it is important to control grain boundary (GB) segregation in paramagnetic γ-Fe. Recently, many studies have been performed in this direction using first-principles calculations; however, in most of them, γ-Fe was treated as nonmagnetic (NM). In the present study, the effect of magnetism on GB segregation in γ-Fe was investigated by systematically calculating and comparing the GB segregation of nine transition-metal alloying elements using NM γ-Fe and γ-Fe with the magnetic structure of the antiferromagnetic double-layer (AFMD)—a simple approximation of paramagnetism. It was found that AFMD γ-Fe, which has lattice constants and elastic properties similar to those of paramagnetic γ-Fe, can reproduce the GB segregation in paramagnetic γ-Fe well, whereas NM γ-Fe significantly overestimates the GB segregation tendency or leads to qualitatively incorrect conclusions. This study clarifies the importance of magnetism in γ-Fe using first-principles calculations and demonstrates an interesting relationship between metallurgical phenomena and magnetism.

Zhang S., Meng F., Fu R., Ogata S.

Artificial neural network potentials (NNPs) have emerged as effective tools for understanding atomic interactions at the atomic scale in various phenomena. Recently, we developed highly transferable NNPs for α-iron and α-iron/hydrogen binary systems (Physical Review Materials 5 (11), 113606, 2021). These potentials allowed us to investigate deformation and fracture in α-iron under the influence of hydrogen. However, the computational cost of the NNP remains relatively high compared to empirical potentials, limiting their applicability in addressing practical issues related to hydrogen embrittlement. In this work, building upon our prior research on iron-hydrogen NNP, we developed a new NNP that not only maintains the excellent transferability but also significantly improves computational efficiency (more than 40 times faster). We applied this new NNP to study the impact of hydrogen on the cracking of iron and the deformation of polycrystalline iron. We employed large-scale through-thickness {110}〈110〉 crack models and large-scale polycrystalline α-iron models. The results clearly show that hydrogen atoms segregated at crack tips promote brittle-cleavage failure followed by crack growth. Additionally, hydrogen atoms at grain boundaries facilitate the nucleation of intergranular nanovoids and subsequent intergranular fracture. We anticipate that this high-efficiency NNP will serve as a valuable tool for gaining atomic-scale insights into hydrogen embrittlement.

Zhang L., Csányi G., van der Giessen E., Maresca F.

AbstractThe prediction of atomistic fracture mechanisms in body-centred cubic (bcc) iron is essential for understanding its semi-brittle nature. Existing atomistic simulations of the crack-tip under mode-I loading based on empirical interatomic potentials yield contradicting predictions and artificial mechanisms. To enable fracture prediction with quantum accuracy, we develop a Gaussian approximation potential (GAP) using an active learning strategy by extending a density functional theory (DFT) database of ferromagnetic bcc iron. We apply the active learning algorithm and obtain a Fe GAP model with a converged model uncertainty over a broad range of stress intensity factors (SIFs) and for four crack systems. The learning efficiency of the approach is analysed, and the predicted critical SIFs are compared with Griffith and Rice theories. The simulations reveal that cleavage along the original crack plane is the atomistic fracture mechanism for {100} and {110} crack planes at T = 0 K, thus settling a long-standing issue. Our work also highlights the need for a multiscale approach to predicting fracture and intrinsic ductility, whereby finite temperature, finite loading rate effects and pre-existing defects (e.g., nanovoids, dislocations) should be taken explicitly into account.

Wagih M., Schuh C.A.

Grain boundaries control a wide variety of bulk properties in polycrystalline materials, so simulation methods like density functional theory are routinely used to study their structure-property relationships. A standard practice for such simulations is to use compact, high-symmetry (coincident site lattice) boundaries as representatives of the much more complex polycrystalline grain boundaries. In this letter, we question this practice by quantitatively comparing the spectra of atomic sites and properties amongst grain boundaries. We show, using solute segregation as an example property, that highly symmetric tilt boundaries (with Σ values less than 10) will fail to capture polycrystalline grain boundary environments, and thus lead to incorrect quantitative and qualitative insights into their behavior.

Dösinger C., Hodapp M., Peil O., Reichmann A., Razumovskiy V., Scheiber D., Romaner L.

Segregation of solutes to grain boundaries (GBs) is an important process having a large impact on mechanical properties of metallic alloys. In this work, we show how accurate density functional theory (DFT) calculations can be combined with machine learning methods to obtain reliable GB segregation energies with significantly lower computational efforts compared to a full ab initio approach. First we compare various descriptor sets with respect to their efficiency in predicting segregation energies for arbitrary GB types. Second, we demonstrate that active learning can be employed to optimize the initial training set obtained by DFT calculations. The methodology is applied to the GB segregation of Re in a WRe alloy, which is a well-studied system of technological relevance.

Wang F., Yang Z., Li F., Shao J., Xu L.

A machine learning force field for predicting the bcc–hcp phase transitions of iron, demonstrates good performance with DFT calculations, offering new insights and approaches for materials science and solid-state physics research.

Podryabinkin E., Garifullin K., Shapeev A., Novikov I.

Nowadays, academic research relies not only on sharing with the academic community the scientific results obtained by research groups while studying certain phenomena but also on sharing computer codes developed within the community. In the field of atomistic modeling, these were software packages for classical atomistic modeling, and later for quantum-mechanical modeling; currently, with the fast growth of the field of machine-learning potentials, the packages implement such potentials. In this paper, we present the MLIP-3 package for constructing moment tensor potentials and performing their active training. This package builds on the MLIP-2 package [Novikov et al., “The MLIP package: moment tensor potentials with MPI and active learning,” Mach. Learn.: Sci. Technol., 2(2), 025002 (2020)], however, with a number of improvements, including active learning on atomic neighborhoods of a possibly large atomistic simulation.

Li C., Lu S., Divinski S., Vitos L.

Grain boundary energy (GBE) and its temperature dependence in body-centered cubic (bcc) metals are investigated using ab initio calculations. We reveal a scaling relationship between the GBEs of the same grain boundary structure in different bcc metals and find that the scaling factor can be best estimated by the ratio of the low-index surface energy. Applying the scaling relationship, the general GBEs of bcc metals at 0 K are predicted. Furthermore, adopting the Foiles’s method which assumes that the general GBE has the same temperature dependence as the elastic modulus c44 [Scr. Mater., 62 (2010) 231–234], the predicted general GBEs at elevated temperatures are found in good agreement with available experimental data. Reviewing two experimental methods for determining the general GBEs, we conclude that the two sets of experimental GBEs for bcc metals correspond to different GB structural spaces and differ by approximately a factor of 2. The present work puts forward an efficient methodology for predicting the general GBEs of metals, which has the potential to extend its application for homogeneous alloys without strong segregation of the alloying element and facilitates GB engineering for advanced alloy design.

Ito K., Tanaka Y., Tsutsui K., Sawada H.

Hydrogen embrittlement caused by hydrogen segregation at grain boundaries (GBs) is the most serious issue in the development of high-strength steels, but the mechanisms behind this process are still not well understood. The GB segregation behavior of hydrogen in body-centered cubic (bcc)-Fe polycrystals was comprehensively analyzed based on the interatomic potentials derived from first-principles calculations. Considering that the atomic structure of GBs is almost independent of the grain size, the GBs in polycrystals were modeled as nano-polycrystalline GBs with random orientations. The segregation energies of hydrogen for ∼17 million interstitial sites in this GB model were calculated. From these segregation energies, the effective segregation energy for the polycrystalline GB at thermal equilibrium under various temperature and hydrogen content conditions were determined, and the validity of the calculation method was verified by comparing the results with experimental data. The relationship between the segregation energy of hydrogen at each segregation site and the surrounding local atomic environment was used to identify the major hydrogen segregation sites at the atomic level, and the changes in the crystal structure near the GB that dominated segregation were clarified. The effective segregation energies at the polycrystalline GBs were in the range of −0.48 to −0.42 eV, which are in good agreement with the experimentally reported binding energy of hydrogen at GBs of bcc-Fe polycrystals (−0.52 eV). The major hydrogen segregation sites were octahedral sites with Voronoi volumes larger than 7.0 Å3, and the segregation energy was mainly due to the uniaxially distorted crystal structure in the short-axis direction of octahedral sites. Our findings and the developed calculation method contribute to the understanding of the hydrogen segregation behavior and hydrogen embrittlement mechanism in polycrystalline metallic materials.

Ahmadian, A., Scheiber, D., Zhou, X., Gault, B., Romaner, L., Kamachali D., R., Ecker, W., Dehm, et. al.

AbstractThe embrittlement of metallic alloys by liquid metals leads to catastrophic material failure and severely impacts their structural integrity. The weakening of grain boundaries (GBs) by the ingress of liquid metal and preceding segregation in the solid are thought to promote early fracture. However, the potential of balancing between the segregation of cohesion‐enhancing interstitial solutes and embrittling elements inducing GB de‐cohesion is not understood. Here, the mechanisms of how boron segregation mitigates the detrimental effects of the prime embrittler, zinc, in a Σ5 [001] tilt GB in α‐Fe (4 at.% Al) is unveiled. Zinc forms nanoscale segregation patterns inducing structurally and compositionally complex GB states. Ab initio simulations reveal that boron hinders zinc segregation and compensates for the zinc‐induced loss in GB cohesion. The work sheds new light on how interstitial solutes intimately modify GBs, thereby opening pathways to use them as dopants for preventing disastrous material failure.

Yokoi T., Matsuura M., Oshima Y., Matsunaga K.

An artificial neural network (ANN) potential for Al, trained with density-functional-theory (DFT) data, is constructed to accurately predict lattice vibrational properties and thermodynamics of grain boundaries (GBs) in Al. The ANN potential is demonstrated to accurately predict not only atomic structures and energetics of the GBs at 0 K but also partial phonon densities of states and vibrational entropies, even for GBs absent in the training data sets. In addition, their total potential energies and atomic forces by DFT at elevated temperatures up to 800 K can also be well reproduced by molecular dynamics with the ANN potential. In contrast, a modified embedded atom method (MEAM) potential shows larger errors in phonon frequencies and atomic forces for atoms at GBs, as well as in the bulk, than the ANN potential. The MEAM potential is thus likely to be inadequate to quantitatively predict thermodynamic properties of GBs, particularly at high temperature. The present ANN potential is also applied to systematically examine thermodynamic stability of asymmetric tilt GBs. It is predicted that for the \ensuremath{\Sigma}9 system, the GB free-energy profile as a function of inclination angle exhibits a cusp at elevated temperatures, due to its larger vibrational entropies of asymmetric tilt GBs than those of \ensuremath{\Sigma}9 symmetric tilt GBs.

Zhang S., Li J., Peng Z., Liu S., Huang F., Liu J.

Hydrogen embrittlement (HE) is a major problem that restricts the application of ultra-high strength hot stamping steels. This paper proposes a novel strategy for against HE via Ta–Mo multi-microalloying, and systematically analyzes the synergistic effects of Ta and Mo. The results show that a major fraction of Ta and a small fraction of Mo generated high-density semicoherent nanosized (Ta, Mo) C precipitates and further refined the prior-austenite-grain/martensite structure. Ta–Mo multi-microalloying resulted in significantly higher precipitate and grain boundary (GB)-induced H trap densities and a higher H trapping capacity of the precipitates than Ta alloying, thereby reducing the H diffusivity. Additionally, Ta–Mo alloying significantly increased the HE resistance through the following mechanisms: (i) Ta–Mo hindered H enrichment at the GBs by providing numerous additional H traps and increasing the GB cohesive strength through Mo segregation, inhibiting hydrogen-enhanced decohesion (HEDE); and (ii) Ta reduced the proportion of Σ3 boundaries, Mo increased the binding force of Σ3 boundaries, and (Ta, Mo) C precipitates hindered the H–dislocation interactions, suppressing hydrogen-enhanced localized plasticity (HELP). In summary, Ta–Mo multi-microalloying combines the advantages of Ta and Mo and synergistically hinders the HELP and HEDE, thereby significantly increasing the HE resistance.

Meng F., Li J., Shinzato S., Matsubara K., Geng W., Ogata S.

Lejček P., Šob M.