Generalized Stacking Fault Energy Surfaces Research Articles

Interatomic force fields for zirconium based on the embedded atom method and the tabulated Gaussian Approximation Potential

The accuracy of interatomic interaction potentials–also known as force fields–is the main factor determining the physical soundness of classical molecular dynamics (MD) simulations. Here, we present a multi-objective framework to generate embedded-atom-method (EAM) force fields using ab initio data. The EAM force fields were tuned via particle swarm optimization to capture the non-linear association between atomic structures and system energies. Using this framework, 95 standard EAM force fields for zirconium were developed and 45 physical features for each developed force field were tracked. Principal component analysis (PCA) was performed to provide insights into the compromises that must be made when generating EAM force fields. Of note, by assigning large fitting weights to generalized stacking fault energy (GSFE) surfaces, there exist EAM force fields with properly positioned minima on prismatic GSFE surfaces and containing no spurious minima in basal GSFE surfaces. However, while standard EAM force fields achieved this without explicitly taking the angular dependence of atomic interactions into account, they led to a severe mismatch between other important physical properties and benchmarks. Hence, we also constructed two machine-learned tabulated Gaussian approximation potentials (tabGAP) with an additional three-body term, which successfully tackled the aforementioned issue and exhibit acceptable prediction accuracy across many physical properties (lattice parameters, elastic properties, dimer potential energies, melting temperatures, phase stability, point defect formation energies, point defect migration energies, and free surface energies) of Zr. Remarkably, its computational efficiency is only 6 times slower than standard EAM force fields.

A Set of Moment Tensor Potentials for Zirconium with Increasing Complexity.

Machine learning force fields (MLFFs) are an increasingly popular choice for atomistic simulations due to their high fidelity and improvable nature. Here we propose a hybrid small-cell approach that combines attributes of both offline and active learning to systematically expand a quantum-mechanical (QM) database while constructing MLFFs with increasing model complexity. Our MLFFs employ the moment tensor potential formalism. During this process, we quantitatively assessed the structural properties, elastic properties, dimer potential energies, melting temperatures, phase stability, point defect formation energies, point defect migration energies, free surface energies, and generalized stacking fault (GSF) energies of Zr as predicted by our MLFFs. Unsurprisingly, the model complexity has a positive correlation with prediction accuracy. We also find that the MLFFs were able to predict the properties of out-of-sample configurations without directly including these specific configurations in the training dataset. Additionally, we generated 100 MLFFs of high complexity (1513 parameters each) that reached different local optima during training. Their predictions cluster around the benchmark DFT values, but subtle physical features such as the location of local minima on the GSF energy surface are washed out by statistical noise.

Statistical modeling of the effect of chemical inhomogeneity on incipient plasticity in complex concentrated alloys

In recent years, complex concentrated alloys (CCAs), also referred to as medium- or high-entropy alloys, have attracted substantial research interest due to their excellent mechanical properties including high strength, ductility, and toughness. It is known that the chemical inhomogeneity of CCAs gives rise to spatial variations in local properties such as the generalized stacking fault energy (GSFE) surface, which in turn affect their mechanical properties, but how such an inhomogeneity affects dislocation nucleation and incipient plasticity remains largely unknown and unexplored. Here, we develop a physics-informed statistical model for incipient plasticity in CCAs by combining elasticity theory for dislocation nucleation and statistical modeling of nanoindentation. Our model connects a material's fundamental properties to the statistics of incipient plasticity and is validated by the excellent agreement with the statistical data from molecular dynamics simulations of nanoindentation of CrCoNi CCA samples. By accounting for the spatial variation in the local generalized stacking fault energy surface in CCAs, our model captures the key difference in the nanoindentation-induced incipient plasticity response of CCAs compared with a conventional metal (fcc Cu) and also reproduces the trends across CCA samples with different degrees of short-range ordering. Our model also reveals a critical length scale for the underlying GSFE fluctuations which controls the overall statistics of incipient plasticity during nanoindentation of CCAs, which reflects the critical loop size of the underlying dislocation nucleation mechanism.

Dependency of grain boundary dislocation network configuration on generalized stacking fault energy surface in FCC metals

We use a microscopic phase-field (MPF) model, incorporating the generalized stacking fault energy (GSFE) surfaces (i.e., the γ-surface) as inputs, to investigate systematically the evolution of dislocation network configurations at low-angle pure twist grain boundaries (GBs) in six face-centered cubic (FCC) metals (Ag, Cu, Rh, Ir, Pd and Pt) that have different GSFE surfaces. The equilibrium configurations of GB dislocation networks are obtained via the interplay between the crystalline energy and the elastic strain energy during the energy minimization process. It was found that for {111} twist GBs, though the geometrically necessary dislocations (GNDs) of the screw type are observed, they can be either full or partial ones depending on the GSFE surfaces of the above metal systems. The areas of the staking faults regions formed between partial dislocations are quantitatively characterized as a function of the magnitude of the stacking fault energy, the elastic modulus and the GB misorientation angle. A fast-acting model for predicting the geometric characteristics of the GB dislocation networks is developed based directly on the material properties and GB misorientation, which is validated by its applications to another two metal systems (Au and Ni) with the same GB.

Tensile deformation behavior and generalized stacking fault energy surface of γ-Fe23C6 by atomistic modelling

To investigate the fatigue behavior of steel or Ni-based superalloy, it is necessary to identify the mechanism of crack initiation and non-uniform deformation by studying the mechanical properties of M23C6 carbides. The effects of temperature, vacancies, and void on the mechanical properties of M23C6 (M = Fe) carbides are investigated by the molecular dynamics method. Furthermore, in order to identify the slip system which is the most conductive to dislocation activity for M23C6 type carbides, based on the generalized stacking fault energy (GSFE) model of Fe23C6, the three-dimensional GSFE surface is calculated. The results show that Fe23C6 is more prone to cleavage fracture along the [110] direction than along the [100] and the [111] directions at the same temperature; the void size has a great effect on the tensile stress curve of Fe23C6 along the [100] direction but has little effect on the tensile stress curve along [110] and [111] directions. The slip of Fe23C6 on the (111) plane tends to follow the [11 2‾] direction, and Fe23C6 is more likely to produce the dislocation structure on the (111) plane than on the (110) plane.

Effect of Sn on Generalized Stacking Fault Energy Surfaces in Zirconium and its Hydrides

Effect of Sn on Generalized Stacking Fault Energy Surfaces in Zirconium and its Hydrides

Machine learning for metallurgy III: A neural network potential for Al-Mg-Si

High-strength metal alloys achieve their performance via careful control of the nucleation, growth, and kinetics of precipitation. Alloy mechanical properties are then controlled by atomic scale phenomena such as shearing of the precipitates by dislocations. Atomistic modeling to understand the operative mechanisms requires length and timescales far larger than those accessible by first-principles methods. Here, a family of Behler-Parinello neural network potentials (NNPs) for the Al-Mg-Si system is developed to enable quantitative studies of Al-6xxx alloys. The NNP is trained on metallurgically important quantities computed by first-principles density function theory (DFT) leading to high-fidelity predictions of intermetallic compounds, elastic constants, dilute solid-solution energetics, precipitate/matrix interfaces, Al stacking fault energies, antisite defect energies, and other quantities. The generalized stacking fault energy surfaces for the three prevalent ${\ensuremath{\beta}}^{\ensuremath{'}\ensuremath{'}}$ precipitate compositions in peak-aged Al-6xxx are then computed with the NNP, and are validated by DFT computations at key points. A preliminary examination of early stage clustering kinetics and energetics in Al-6xxx is then made, showing the formation of low-energy Mg-Si structures and the trapping of vacancies in these clusters. The NNP thus shows significant transferability across structures, making it a powerful approach for chemically accurate simulations of metallurgical phenomena in Al-Mg-Si alloys.

Ab-Initio Investigation of Planar Defects in <i>Immm</i>-Ni <sub>2</sub>(Cr,Mo,W) Strengthened HAYNES 244 Alloy

The Immm-Ni2(Cr,Mo,W) body centered orthorhombic (BCO) intermetallic phase, denoted as γ´´´, is the primary strengthening phase in commercial Ni-base HAYNES® 242® and 244® alloys. Due to the relatively low symmetry and six crystallographic variants precipitating in the face-centered cubic solid solution γ matrix, the deformation mechanisms are expected to be complex, and a myriad of planar defects are predicted to be observed on the close-packed {013} and {110} planes, which are nearly co-planar to the matrix {111} plane. We find that these defects include those analogous to the γ´-Ni3Al phase: superlattice intrinsic stacking faults, antiphase boundaries, and complex stacking faults. We determined these planar defect energies and generalized stacking fault energy surfaces utilizing ab-initio density functional theory calculations. The γ´´´ {013} and {110} planes exhibited comparable planar defect energies but showed drastically different dislocation shear pathways due to the lower symmetry of the orthorhombic phase. We observed that the addition of W increased the fault energies significantly, which could correspond to the observed increase in yield strength of 244 alloy over that of 242 alloy.

Assessing the magnetic order dependent γ-surface of Cr-Co-Ni alloys

In order to efficiently explore the nearly infinite composition space in multicomponent solid solution alloys for reaching higher mechanical performance, it is important to establish predictive design strategies using computation-aided methods. Here, using ab initio calculations we systematically study the effects of magnetism and chemical composition on the generalized stacking fault energy surface (γ-surface) of Cr-Co-Ni medium entropy alloys and show that both chemistry and the coupled magnetic state strongly affect the γ-surface, consequently, the primary deformation modes. The relations among various stable and unstable stacking fault energies are revealed and discussed. The present findings are useful for studying the deformation behaviors of Cr-Co-Ni alloys and facilitate a density functional theory based design of transformation-induced plasticity and twinning-induced plasticity mechanisms in Cr-Co-Ni alloys.

First-principles study of the ternary effects on the plasticity of upgamma -TiAl crystals

We studied the effects of important ternary elements, such as Cr, Nb, and V, on the plasticity of upgamma -TiAl crystals by calculating the point defect formation energy and the change in the generalized stacking fault energy (GSFE) surface from first-principles calculations. For all three elements, the point defect formation energies of the substitutional defects are lower in the Ti site than in the Al site, which implies that substitution on the Ti site is energetically more stable. We computed the GSFE surfaces with and without a substitutional solute and obtained the ideal critical resolved shear stress (ICRSS) of each partial slip. The change in the GSFE surface indicates that the substitution of Ti with Cr, Nb, or V results in an increase in the yield strength because the ICRSS of the superlattice intrinsic stacking fault (SISF) partial slip increases. Interestingly, we find that Cr substitution on an Al site could occur owing to the small difference between the substitutional defect formation energies of the Ti and Al sites. In that case, the reduction of ICRSSs of the SISF partial slip and twinning would lead to improved twinnability. We discuss the implications of the computational predictions by comparing them with experimental results in the literature.

Designing Transformation-Induced Plasticity and Twinning-Induced Plasticity Cr-Co-Ni Medium Entropy Alloys: Theory and Experiment

In order to efficiently explore the nearly infinite composition space in multicomponent solid solution alloys, it is important to establish predictive design strategies and use computation-aided methods. In the present work, we demonstrated the density functional theory calculations informed design routes for realizing transformation-induced plasticity (TRIP) and twinning-induced plasticity (TWIP) in Cr-Co-Ni medium entropy alloys (MEAs). We systematically studied the effects of magnetism and chemical composition on the generalized stacking fault energy surface (γ-surface) and showed that both chemistry and the coupled magnetic state strongly affect the γ-surface, consequently, the primary deformation modes. Based on the calculated effective energy barriers for the competing deformation modes, we constructed composition and magnetism dependent deformation maps at both room and cryogenic temperatures. Accordingly, we proposed various design routes for achieving desired primary deformation modes in the ternary Cr-Co-Ni alloys. The deformation mechanisms predicted by our theoretical models are in nice agreement with available experimental observations in literature. Furthermore, we fabricated two non-equiatomic Cr-Co-Ni MEAs possessing the designed TWIP and TRIP effects, showing excellent combinations of tensile strength and ductility.

Modified Generalized Stacking Fault Energy Surface of II–VI Ionic Crystals from Excess Electrons and Holes

Electron and hole carriers are ubiquitous in semiconductors and play an important role in determining the electronic properties that are essential in biolabeling and electronic device applications....

Density functional theory calculations of generalized stacking fault energy surfaces for eight face-centered cubic transition metals

In this work, we use density functional theory to calculate the entire generalized stacking fault energy (GSFE) surface for eight transition metals with a face-centered cubic structure: Ag, Au, Cu, Ir, Ni, Pd, Pt, and Rh. Analysis of the ⟨112⟩ GSFE curves finds that the displacements corresponding to the unstable stacking fault energy are larger than the ideal value for all eight metals except Ag and Cu. Over the entire surface, Pt is found to not possess well-defined local maxima or minima, suggesting spreading in favor of dissociation of the dislocation core, unlike the other seven metals. Our calculations also reveal that at a large ⟨112⟩ displacement, where atoms on two {111} adjacent planes are aligned, an anomalous local minimum occurs for Ir and Rh. The oddity is explained by relatively large, localized atomic displacements that take place in the two metals to accommodate the alignment that do not occur in the other six metals. In addition to the fully calculated surfaces, we characterize a continuous 11-term Fourier-series function, which provides a particularly excellent representation of the GSFE surfaces for Ag, Au, Cu, Ni, and Pd.

Ab initio-informed phase-field modeling of dislocation core structures in equal-molar CoNiRu multi-principal element alloys

In this work, selecting the equal-molar CoNiRu multi-principal element alloy (MPEA) as a model material, we study dislocation core structures starting from first principles. We begin by sifting through all possible configurations to find those corresponding to elastic stability and energetically favored face-centered cubic (fcc) phases and, then, for these configurations, employ a phase field-based model to predict the extent of dislocations lying within them. The main findings are that for the fcc phase, (i) large variations in atomic configuration for the same chemical composition can cause significant changes in the generalized stacking fault energy surface and (ii) the dispersion in defect fault energies are chiefly responsible for substantial variations in the intrinsic stacking fault (ISF) widths of screw and edge dislocations. For instance, positive the ISF energy can vary by 10 times, with the lower values correlated with entirely Ni and Ru atoms and higher values with only Co and Ru atoms across the slip plane. Variations in lattice parameter and stiffness tensor accompany local differences in atomic configuration are also taken into account but shown to play a lesser role. We find that the dislocation can experience profound variations (3–7-fold changes) in its associated ISF width along its line, with the screw dislocation experiencing a greater variation than the edge dislocation (6.02–43.22 Å for the screw dislocation, and 19.6–62.62 Å for the edge dislocation). We envision that the ab initio-informed phase-field modeling method developed here can be readily adapted to MPEAs with other chemical compositions.

Characteristics of atomic elastic stiffness at GSF energy surface, edge and screw dislocation cores in fcc, bcc and hcp metals

Basic characteristics of 6 × 6 matrix of atomic elastic stiffness (AES), Bija=Δσia/Δεj, or the deformation resistance at each atom point, are discussed first in static analyses of generalized stacking fault (GSF) energy surface for 8 fcc, 4 bcc and 4 hcp metals with Zhou’s EAM potential. For hcp metals, the stress–strain peak along the GSF path exactly coincides with the point where the AES loses the resistance showing negative 1st eigenvalue ηa(1), or the solution of BijaΔεj=ηaΔεi=Δσia; however, all fcc and 2 bcc (Mo and W) never have negative ηa(1) along the GSF path. Fe and Ta transiently show ηa(1) < 0 while they also have positive ηa(1) at the GSF energy peak. Then we performed MD simulations of edge and screw dislocation dipoles in a periodic slab cell of typical elements of fcc, bcc and hcp; and discussed the eigenvalue and the corresponding eigenvector {Δεxx, Δεyy, Δεzz, Δγyz, Δγzx, Δγxy} of the dislocation cores. As expected from the results of the GSF analyses, dislocation cores in fcc Ni have no ηa(1) < 0 atoms, even in their glide process under external shear loading. Bcc Fe and hcp Co definitely have ηa(1) < 0 atoms in the dislocation cores and their migration direction can be visualized by the maximum shear direction of the strain tensor of the corresponding eigenvector.

Predicting grain boundary structure and energy in BCC metals by integrated atomistic and phase-field modeling

We predict structure and energy of low-angle (11¯0) pure twist grain boundaries (GBs) in five BCC transition metals (β-titanium, molybdenum, niobium, tungsten, and tantalum) using a combination of atomistic and microscopic phase-field (MPF) modeling. The MPF model takes as inputs solely the generalized stacking fault energy surfaces (i.e., the γ-surface) and elastic constants obtained from the atomistic simulations. Being an energy-based method, the MPF model lifts the degeneracy of the geometric models in predicting GB structures. For example, the multiple indefinite solutions offered by the Frank-Bilby equation are shown to converge to exactly the same equilibrium structure. It predicts a transition of the equilibrium GB structure from a pure screw hexagonal network (Mo and W) to mixed hexagonal networks (Nb and Ta) to a rhombus network (β-Ti) of dislocations. Parametric simulation studies and detailed analyses of the underlying dislocation reactions that are responsible for the formation of the rhombus and hexagonal structures reveal a close correlation between material properties (including the elastic anisotropic ratio and the local curvature on the γ-surface) and the GB structure and energy in BCC metals. This integrated approach allows one to explore, through high throughput calculations, the potential to tailor the structure and energy of special GBs in BCC metals by alloying.

First-principles study of crystallographic slip modes in \u03c9-Zr

We use first-principles density functional theory to study the preferred modes of slip in the high-pressure ω phase of Zr. The generalized stacking fault energy surfaces associated with shearing on nine distinct crystallographic slip modes in the hexagonal ω-Zr crystal are calculated, from which characteristics such as ideal shear stress, the dislocation Burgers vector, and possible accompanying atomic shuffles, are extracted. Comparison of energy barriers and ideal shear stresses suggests that the favorable modes are prismatic 〈c〉, prismatic-II langle 10bar{1}0rangle and pyramidal-II 〈c + a〉, which are distinct from the ground state hexagonal close packed α phase of Zr. Operation of these three modes can accommodate any deformation state. The relative preferences among the identified slip modes are examined using a mean-field crystal plasticity model and comparing the calculated deformation texture with the measurement. Knowledge of the basic crystallographic modes of slip is critical to understanding and analyzing the plastic deformation behavior of ω-Zr or mixed α-ω phase-Zr.

Mechanism and energetics of 〈c + a〉 dislocation cross-slip in hcp metals

Hexagonal close-packed (hcp) metals such as Mg, Ti, and Zr are lightweight and/or durable metals with critical structural applications in the automotive (Mg), aerospace (Ti), and nuclear (Zr) industries. The hcp structure, however, brings significant complications in the mechanisms of plastic deformation, strengthening, and ductility, and these complications pose significant challenges in advancing the science and engineering of these metals. In hcp metals, generalized plasticity requires the activation of slip on pyramidal planes, but the structure, motion, and cross-slip of the associated [Formula: see text] dislocations are not well established even though they determine ductility and influence strengthening. Here, atomistic simulations in Mg reveal the unusual mechanism of [Formula: see text] dislocation cross-slip between pyramidal I and II planes, which occurs by cross-slip of the individual partial dislocations. The energy barrier is controlled by a fundamental step/jog energy and the near-core energy difference between pyramidal [Formula: see text] dislocations. The near-core energy difference can be changed by nonglide stresses, leading to tension-compression asymmetry and even a switch in absolute stability from one glide plane to the other, both features observed experimentally in Mg, Ti, and their alloys. The unique cross-slip mechanism is governed by common features of the generalized stacking fault energy surfaces of hcp pyramidal planes and is thus expected to be generic to all hcp metals. An analytical model is developed to predict the cross-slip barrier as a function of the near-core energy difference and applied stresses and quantifies the controlling features of cross-slip and pyramidal I/II stability across the family of hcp metals.

Impact of local magnetism on stacking fault energies: A first-principles investigation for fcc iron

A systematic ab initio study of the influence of local magnetism on the generalized stacking fault energy (GSFE) surface in pure fcc iron at 0 K has been performed. In the calculations we considered ferro- and antiferro- (single- and double-layer) magnetic order of local moments as well as their complete disorder, corresponding to paramagnetic (PM) state. We have shown that local magnetism is one of the most important factors stabilizing austenitic structure in iron (with respect to more stable at 0 K hcp) and that the perturbation of magnetic structure by the formation of stacking fault is a short-range effect. Local magnetism also strongly influences the GSFE surface topology and, therefore, the material's plasticity by reducing the energetic barriers that need to be overcome to form the intrinsic stacking fault (ISF) or return from the ISF structure to fcc. The influence of atomic relaxations on such barriers is moderate and does not exceed 15%. In addition, a methodology to evaluate the PM ISF energy using a superposition of the ISF energies obtained for ordered magnetic structures is proposed to overcome computational impediments arising when dealing with disorder in the PM state. The complications of the proposed methodology together with the ways to overcome them are also discussed.

Generalized stacking fault energies in the basal plane of triclinic molecular crystal 1,3,5-triamino-2,4,6-trinitrobenzene (TATB)

Molecular dynamics and molecular statics simulations were used to investigate dislocation glide in the basal plane (i.e. the – plane, where , and define the edge vectors of the unit cell) of -triamino--trinitrobenzene (TATB) using generalized stacking fault energy surfaces (-surfaces). Triclinic symmetry and molecular packing arrangement result in two glide plane types for the same glide plane normal. The unstable stacking fault energies () are less than at K and atm, indicating easy dislocation glide. Glide in the and – directions is preferred compared to the direction at atm. A stable stacking fault is predicted in the – direction at atm and 5 GPa. A compound twin with energy is predicted to be stable in the basal plane. Unequal values of about the stable stacking fault in the and – traces indicate an asymmetric barrier to dislocation glide. High pressure ( GPa) results in an increase in the values. The extremely small barriers to twinning and dislocation glide might be sources for observed second-harmonic generation in the nominally centrosymmetric crystal.