Intrinsic Stacking Fault Energy Research Articles

Chemical short-range order enhances fracture toughness of medium entropy alloy CoCrNi

Using hybrid molecular dynamics and Monte Carlo simulations, we examine the role of lattice distortion (LD) and chemical short-range ordering (CSRO) on the development of defects ahead of a mode I crack in medium entropy alloy CoCrNi. We show that CSRO noticeably increases fracture toughness. The result can be explained by the effect of CSRO on lowering LD and increasing intrinsic stacking fault energy and the direct impact CSRO has on the energetic barriers for emitting partial dislocations and forming nanotwins from CoCr clusters on the crack tip. CSRO allows the nanotwin domains to further support inelastic deformation, such as dislocation glide and amorphization, leading to stable crack-tip plasticity and postponement of softening. These findings imply that the superior fracture toughness in CoCrNi can be attributed to the non-negligible CSRO that naturally exists.

Impact of Dilute Amounts of Fission Products on the Mechanical Behavior of Ni.

Fission products may interact with structural materials in various nuclear energy applications and cause their mechanical performance to deteriorate. Therefore, it is important to study the effects of different fission products on the mechanical properties of structural materials. In this work, nickel was chosen as a model structural material system and dilute amounts of uranium and fission product impurities X = (Tc, Te, Sb, Ce, Eu, and U) up to 4 at % were used. Density functional theory (DFT) calculations were utilized to assess the effects of these substitutional impurities on the elastic behavior of the metal. Additionally, DFT was used to investigate some aspects of plastic response by computing the generalized stacking fault energies on the {111} ⟨112⟩ slip system for all alloying elements and at varying distances away from the stacking fault plane. None of the dopants satisfied the Pugh or Pettifor criteria for embrittlement, and alloying with Tc led to a slight increase in the elasticity of nickel. The phenomenon of Suzuki segregation was observed for all alloying elements, and there was consequently a significant reduction in the intrinsic stacking fault energy. Finally, and based on the analysis of the stacking fault energies, dopants generally led to softening the nickel (except for Tc and Ce), and all of the dopants were correlated with a loss of ductility (except Eu). These findings may be useful to consider in the design of next-generation reactors and nuclear waste management systems.

Achieving ultra-strong and ductile CoNi-based FCC multi-principal element alloys via alloying with refractory Mo and W

FCC single-phase multi-principal element alloys (MPEAs) often suffer from insufficient strength, which limits their wide applications. Here a CoNi-based FCC MPEA (Co44Ni44Mo9W3, at. %) was designed by alloying with refractory Mo and W. The Co44Ni44Mo9W3 alloy possesses an ultrahigh yield strength of ∼1050 MPa and good ductility of ∼30 % at ambient temperature. The excellent mechanical properties were correlated to its superior lattice friction stress and grain boundary strengthening compared to most reported FCC MPEAs and conventional alloys. By density-functional theory calculations, such extraordinary mechanical properties were further attributed to its high lattice distortion, low intrinsic stacking fault energy and high unstable stacking fault energy due to the addition of Mo and W. Transmission electron microscopy investigations revealed that the high strength-ductility combination arises from the synergistic effect of planar slip bands, stacking faults and deformation nano-twins.

Short-range ordering mechanics in FCC materials

Short-range order (SRO) has a crucial impact on the mechanical strength of metallic alloys. Recent atomistic investigations defined an average SRO and attempted to correlate it with the yield strength. We propose that the local change in SRO upon slip advance must dictate the strengthening, and we elaborate the methodology to establish the “SRO change” on a slip plane considering the Wigner-Seitz cell. The model captures the variation of lattice resistance (Critical Resolved Shear Stress; CRSS) in the crystal as the SRO changes depending on the probability of neighboring atoms. The methodology was applied to Ni-V binary alloys for a wide range of compositions and stacking fault widths. Dislocation core widths were determined as a function of SRO and energy parameters (unstable and intrinsic stacking fault energies; γus, γisf). The complex variation of CRSS with compositional variations shows good agreement with limited experimental results. The compositions corresponding to the transition from partial to full dislocations at higher vanadium contents are found depending on the SRO and the intrinsic energy levels.

Ultrahigh grain boundary strengthening ability of VCoNi medium entropy alloy

Tensile tests of VCoNi medium-entropy alloy with different grain sizes were conducted at 77 K, 194 K and 293 K. The results show that the grain boundary strengthening ability characterized by the Hall-Petch slope of the alloy increases with decreasing temperature and is evidently higher than that of FCC pure metals, CuAl alloys, and some common FCC high-entropy alloys/medium-entropy alloys at room temperature. A new model correlated to intrinsic stacking fault energy and lattice friction stress is derived to describe the high grain boundary strengthening ability. The high grain boundary strengthening ability and its temperature dependence of the VCoNi medium-entropy alloy are mainly attributed to the high lattice friction stress of the VCoNi alloy. The findings provide a possibility for designing the single-phase FCC medium-entropy alloy with ultra-high yield strength and considerable plasticity.

Negative stacking fault energy in FCC materials-Its implications

Recent atomistic simulations on medium entropy alloys uncovered the possibility of negative intrinsic stacking fault energies (SFEs), which suggest infinite stacking fault widths (SFWs). However, experimental measurements of SFWs in the same alloys have shown that SFWs are finite, which contradicts the classical derivations based on force balance. To address this contradiction, we develop an advanced treatment employing atomistic lattice and continuum theories that produce finite SFW solutions corresponding to negative SFEs. The idea is based on energy minimization, where the finite SFW corresponds to the first local minimum in the energy landscape. By exploring combinations of intrinsic and unstable fault energies, we identify regimes in which solutions for finite SFWs exist for thousands of hypothetical materials. Elastic moduli and lattice constants also impact the results, with lower moduli and smaller lattice constants expanding the negative stacking fault energy domain corresponding to finite SFWs. Additionally, the study has revealed a distribution of SFEs due to possible chemical heterogeneities within the alloy, resulting in variations in SFWs within the same material. The work underscores the capabilities of the theory for SFW and CRSS (Critical Resolved Shear Stress) determination for medium to high entropy alloys in agreement with experiments.

Impact of alloying elements on generalized stacking fault energy and twinning of Ag-based alloys

The creep strength of Ag-based alloys can be remarkably enhanced through the formation of twin structures. In this study, the effects of alloying elements, including Sn, In, Zn, Cu, Zr, Ni, Ir, Cr, and W, on the formation enthalpy of point defects and the generalized stacking fault energy of Ag-based alloys were investigated using first-principles calculations. The formation enthalpy of point defects serves as a measure of the difficulty of alloying element doping in Ag-based alloys. Calculation results shows that the ability of alloying element doping to form point defects follows the order of Sn > In > Zn > Cu > Zr > Ni > Ir > Cr > W. The generalized stacking fault energy along the [112‾](111) slip direction in Ag-based alloys characterizes the competition between dislocation slip and twinning. As the formation enthalpy of point defects increases, the intrinsic stacking fault energy increases, leading to a decrease in twinning tendency. Once the formation enthalpy of point defects corresponding to the alloying element exceeds 1 eV, the intrinsic stacking fault energy and twinning tendency remain relatively unchanged. Comprehensive analysis shows that alloying elements Sn and In effectively reduce the intrinsic stacking fault energy and promote twinning, which aligns with the behavior observed in commonly used Ag–Sn–In electrical contact materials.

First-principle exploration for RE solid-solution influence on Ni mechanical properties

Rare earth element (abbreviated as RE) doped nickel alloy is very attracted for the neutron shielding application for excellent neutron absorption and good mechanical behavior. RE solid-solution influence on Ni alloy mechanical properties has been comprehensively investigated by first-principles calculations in this work. The elastic constant and generalized stacking fault energy analysis indicate that RE substitutional solution would decrease the mechanical strength (For example, bulk modulus: BNi = 198.9 GPa, BNi31RE = 174.7 ∼ 189.8 GPa, Young's modulus: ENi = 242 GPa, ENi31RE = 183.1 ∼ 226.1 GPa and shear modulus: GNi = 93.25 GPa, GNi31RE = 69.05 ∼ 86.88 GPa) while increase the plastic deformation (intrinsic stacking fault energy: γis,Ni52 = 137.1 mJ/m2, γis,Ni51RE = 57.69 ∼ 94.17 mJ/m2 and critical intrinsic stress: τcrit,Ni52 = 31.08, τcrit,Ni51RE = 13.89 ∼ 20.00). Furthermore, the influence has a correlation with atomic radii difference Δr/rNi (the bigger difference is, the greater influence is), which is due to that hybridization strength and bonding strength decreases as Δr/rNi increases. The work provide a theoretical guidance for RE doped nickel alloys plastic deformation promotion.

Effects of short range ordering on the generalized stacking fault energy and deformation mechanisms in FCC multiprincipal element alloys

Equiatomic FCC CrCoNi, VCoNi and CrCoNiFeMn exhibit distinctly different deformation mechanisms where twinning is prevalent in CrCoNi and CrCoNiFeMn, but not in VCoNi. Extant density-functional theory (DFT) calculations show that all 3 alloys possess similarly low/negative intrinsic stacking fault energies (SFEs) and thus high twinnability in random-solute states, which obviously contradicts experimental observations. Here, the mean and local generalized SFE-lines (γ-lines) are systematically determined using DFT in all 3 alloys with special quasirandom structure (SQS) and Monte Carlo (MC) simulation optimized structures. Linear elasticity with DFT-based γ-lines predicts wide core separations and twinnabilities higher than elemental FCC metals in all 3 alloys with SQS. During MC simulations, chemical short range ordering (SRO) is formed, with VCoNi exhibiting the strongest SRO, followed by CrCoNi and CrCoNiFeMn. SRO always raises the mean intrinsic SFE relative to that in base SQS configurations. The average increase scales linearly with the magnitude of the SRO, resulting in moderate, large and drastic increases in CrCoNiFeMn, CrCoNi and VCoNi, respectively. Furthermore, SRO has strong effects on the intrinsic and extrinsic SFEs, but weaker effects on the unstable SFEs, leading to disparate dislocation and twinning behaviour. In SRO-saturated states, CrCoNi and CrCoNiFeMn retain high twinnability comparable to Ag, while VCoNi has narrow core separations similar to Al and twinnability lower than all elemental FCC metals. The DFT-based γ-lines and mechanics-based prediction not only reveal SRO effects on GSFE, dislocation and twinning, but also shed light on the physical origin of the different deformation mechanisms in these alloys.

N-body potential for simulating lattice defects and diffusion in copper

We present a new classical interatomic potential for molecular dynamics simulations of copper. The potential was developed within the N-body approach, which, in addition to pair and many-body interactions, can take into account three-body ones with the required precision. Our potential accurately predicts a wide range of properties of copper: structural, elastic, point and planar, and thermal such as melting point. The latter is essential for the proper reproduction of the homologous temperature and comparison of the calculated results with the corresponding experimental data, such as diffusion coefficients. The potential predicts the intrinsic stacking fault energy within the range of experimental measurements, which indicates its ability to correctly describe the deformation behavior of copper. In this work, we performed simulations of lattice and grain-boundary diffusion of copper with our potential. It shows a moderate overestimation of the lattice diffusivity with a deviation less than one order of magnitude. To simulate the grain boundary diffusion, we built a general-type grain boundary employing the original method. The calculated grain-boundary diffusivity is in remarkable agreement with the literature data and almost coincides with them at higher temperatures in the considered temperature range. The constructed potential can be effectively used for molecular dynamics simulations of defect properties and diffusion phenomena and composing the interatomic potentials within the N-body approach for alloys containing copper.

Mechanical properties of aluminum through electronic- and atomic-scale simulations

Implementing the integrated computational materials engineering methodology in modeling plastic deformation processes and associated phenomena can provide a unique opportunity for a deeper study of material behavior at smaller scales and result in more precise and accurate predictions. This study presents a multiscale modeling framework linking two different length scales – namely, the electronic and the atomic scale – to investigate the mechanical properties of pure aluminum (Al) and to achieve the required parameters and information for higher scales. At the electronic scale, the elastic properties and interfacial energies for aluminum were garnered from density functional theory simulations to calibrate the modified embedded atom method (MEAM) potentials required for atomic simulations. The calculation for the generalized stacking fault energy resulted in an intrinsic stacking fault energy of 185.5 mJ/m2. Using the parameter calculated at the electronic scale as well as the MEAM potential parameters, the edge dislocation mobility of aluminum from molecular dynamics simulations was calculated at the atomic scale (nano). A drag coefficient of 7.3 × 10−5 Pa s was computed at 300 K. The dependency of the drag coefficient on the temperature was also studied, and the results showed that the velocity linearly depended on τ/T up to 0.4 MPa/K.

Theoretical investigation on fundamental properties of glide partial in CdTe based on lattice theory of dislocation

The core structure and Peierls stress of 30° partial dislocation are researched on the basis of lattice theory of dislocation to further recognize the mechanical properties of CdTe. The surface effect and elastic strain energy missed in classical PN model have been considered in calculations. In addition, the influences of γ- surface fitting on estimation of core width and Peierls stress are analysed. Research results indicate that the rectification of surface effect to dislocation fundamental properties is more evident for narrower dislocations. Since the intrinsic stacking-fault energy(SFE) of CdTe is far lower than the unstable SFE, the difference between the results calculated by using original and effective γ- surface is negligible. More extensive, for crystal whose SFE satisfies the condition mentioned, the original γ- surface can be used for investigation of dislocation properties directly. The deviation of fitted γ- surface from the numerical result will result in non-negligible influence on the estimated result of Peierls stress, and affect the analysis of metastable state. The core width and Peierls stress are about 0.64∼0.73b and 1∼2GPa, respectively. The research results are useful for better understanding and utilization of semiconductor CdTe.

Ab initio study of the effect of interstitial alloying on the intrinsic stacking fault energy of paramagnetic γ-Fe and austenitic stainless steel

Intrinsic stacking fault energy (SFE) values of γ-Fe and AISI 304 austenitic stainless steels were determined as a function of carbon and nitrogen content using ab initio calculations. In contrast to previous investigations, the analysis was conducted incorporating the paramagnetic state to account for the magnetic constitution of real austenitic stainless steels. The effect of finite temperature was partially accounted for by performing ab initio calculations at the experimental volumes at room temperature. Including paramagnetism in γ-Fe increases the SFE of non-magneticγ-Fe by ∼385 mJ.m–2. Interstitial alloying of non-magneticγ-Fe causes a linear increase in intrinsic stacking fault energy with interstitial content. In comparison, interstitial alloying of paramagneticγ-Fe increases the SFE at only about half the rate. The SFE of paramagnetic interstitial-free AISI 304 is within the range of -12 to 0 mJ.m–2 and only deviates slightly from the SFE of paramagneticγ-Fe. It follows a similar, albeit flatter linear dependency on the interstitial content compared to γ-Fe. Both γ-Fe and γ-AISI 304 were found to be metastable in their interstitial-free condition and are stabilized by interstitial alloying. The possible effect of short range ordering between interstitials and Cr on the SFE was discussed. The calculated threshold nitrogen content necessary to stabilize austenite in AISI 304 is in good agreement with experimental investigations of deformation microstructures in dependence of the nitrogen content. Finally, the calculated negative SFE values of AISI 304 were reconciled with experimentally determined positive SFE values using a recent method that accounts for the kinetics of stacking fault formation.

Effects of alloying elements on the super-lattice intrinsic stacking fault energy and ideal shear strength of Ni3Al crystals

The effects of alloying elements (Re,W,Ti,Ta,andMo) on the super-lattice intrinsic stacking fault energy and ideal shear strength (σmax) of Ni3Al crystals at 0 K was studied through first-principles calculation. The calculated formation enthalpy of point defects reveals that single solute atoms (i.e., Re,W,Ti,Ta,andMo) tend to occupy the Al site, while solute–solute complex defects (i.e., Re-Re, Re-W, Re-Mo, Re-Ta, Re-Ti, W-Mo, W-Ta, W-Ti, Mo-Ta, Mo-Ti, and Ta-Ti) tend to occupy the Al-Al site. The addition of single solute atom can increase the unstable stacking fault energy and ideal shear strength (σmax) of perfect Ni3Al crystals. Therefore, the doping of a single solute atom is beneficial for the creep strengthening of Ni3Al crystals. Compared with the doping of W,Ti,Ta,andMo, the doping of Re can more effectively impede the nucleation and movement of dislocations of Ni3Al crystals. Through the careful comparison of the creep properties of Ni3Al crystals with solute–solute complex defects, a conclusion can be drawn that the doping of alloy elements W and Re exhibit similar strengthening effects on the creep properties of Ni3Al crystals. W can be preliminarily predicted to replace part of Re in Ni3Al crystals without affecting creep properties. In addition, comprehensive evaluation reveals that the weak interaction between solute–solute complex defects should improve the strengths of Ni3Al crystals to a certain extent.

Reconciling experimental and theoretical stacking fault energies in face-centered cubic materials with the experimental twinning stress

Stacking fault energy and twinning stress are thought to be closely correlated. All currently available models predict a monotonous decrease in twinning stress with decreasing stacking fault energy and depart from the assumption that the intrinsic stacking fault energy has a positive value. Opposite to this prediction, for medium- and high-entropy alloys the twinning stress was shown to increase with decreasing SFE. Additionally, for metastable materials, first principles methods predict negative intrinsic stacking fault energy values, whilst experimentally determined values are always positive. In the present communication, it is postulated that the twinning stress scaled by the Burgers vector bridges the difference between intrinsic and experimentally measured stacking fault energy. The assumption is tested for Cu-Al alloys, for pure metals and for medium- and high-entropy alloys and, for the first time, provides a consistent quantitative interpretation of data for both alloys with positive and negative stacking fault energy.

Insights into plastic deformation mechanisms of austenitic steels by coupling generalized stacking fault energy and semi-discrete variational Peierls-Nabarro model

The generalized stacking fault energy (GSFE) is a key parameter to determine the plastic deformation mechanisms of austenitic steels. However, the underlying physics why the GSFE can affect the plastic deformation behaviors remains unclear. In this paper, the plastic deformation mechanisms of austenitic steels with different carbon (C) additions were investigated by coupling the GSFE with the semi-discrete variational Peierls-Nabarro (P–N) model. The internal mechanisms behind the P–N stress and plastic deformation were explained at atomic scale. It is found that the positions and contents of C atoms affect the GSFE of austenite, and thus regulate plastic deformation behaviors of austenitic steels by influencing dislocation core structure. As exemplified that with 4 ​at.%C in austenite, the intrinsic stacking fault energy increases from −433 to −264 mJ/m2, and the stacking fault width increases to 6.62b from 4.72b of FCC-Fe with b being the Burgers vector. This corresponds to the plastic deformation mechanism dominated by the ε martensitic transformation with the lattice changing from FCC to HCP. With increasing C contents to 8 ​at.%, the intrinsic stacking fault energy of austenite increases to −9.01 mJ/m2, while the stacking fault width decreases to 6.03b. The plastic deformation tends to proceed via the mechanical twinning mode. The present investigation establishes a solid foundation for clarifying the plastic deformation mechanisms of austenitic steels from the perspective of the dislocation core structure.

Atomic scale simulations of [formula omitted] symmetric incoherent twin boundaries in gold

The crystalline defects may play an important role in the improvement of the properties of materials. This is the case of twin boundaries which improve the mechanical properties. Σ3{111} coherent twin boundaries (CTBs) and Σ3{112} symmetric incoherent twin boundaries (ITBs) are two defects studied in this work. Atomistic simulations with four interatomic potentials commonly used in the literature and density functional theory have been used to characterize in detail these two defects in gold. The results show that the excess volumes introduced by twin boundaries strongly depend on the potential. After the ITB relaxation, a portion of 9R phase is formed. This phase is rotated from the face centred cubic (fcc) phase through an angle α which has been determined. The 9R phase formation energy γform has been quantified through atomic scale simulations. We put forward a model to calculate this formation energy γform as a function of the intrinsic stacking fault energy γISF and the excess volume. This model shows that the interaction energy between ISFs is much larger for the Ackland and Baskes potentials than for the Foiles and Grochola potentials. Furthermore, the elastic deformation ɛxx produced in the system to ensure consistency between the 9R phase and the fcc phase is computed. It allows us to discuss the width of the 9R phase in terms of γform and elastic energy and not uniquely in terms of γISF, as previously done in the literature.

Temperature dependent stacking fault free energy profiles and partial dislocation separation in FCC Cu

The generalized stacking fault energy profile is fundamental to models of metal plasticity and thus a key parameter for alloy design. However, to account for thermal vibrations, models require the stacking fault free energy profile, but current methods can only calculate metastable intrinsic stacking faults. We show how the full stacking fault free energy profile can be calculated using PAFI, a linear scaling method that fully accounts for anharmonic thermal vibrations. Applying our approach to empirical and machine learning potentials for FCC Cu, we show via direct comparison with molecular dynamics simulations that accounting for temperature effects is essential to predict the statistics of partial dislocation separations. The machine learning potential gives quantitative agreement with available density functional theory data on the intrinsic stacking fault energy, whilst additionally returning the unstable stacking fault, a key parameter for predicting ductile fracture.

High-Throughput Predictions of the Stabilities of Multi-Type Long-Period Stacking Ordered Structures in High-Performance Mg Alloys.

The effects of 44 types of elements on the stabilities of I1-constitute multi-type long-period stacking-ordered (LPSO) structures in Mg alloys, such as 4H, 6H, 8H, 9R, 12H, 15R, and 16H phases, are systematically investigated by first-principle high-performance calculations. The intrinsic stacking-fault energies (ISFEs) and their increments are calculated along with the formation enthalpies of solute atoms, and interaction energies between solute atoms and LPSO structures. The results suggest that the 15R phase is the easiest to form and stabilize among these LPSO structures, and 44 types of solute atoms have different segregation characteristics in these LPSO structures. A high temperature inhibits structural stabilizations of the LPSO phases, and these alloying elements, such as elements (Sb, Te, and Cs) for 4H; elements (S, Fe, Sb, and Te) for 6H, 8H, 9R, 15R, and 16H; and elements (S, Sb, and Te) for 12H, can effectively promote the stability of LPSO structures at high temperatures. S and Fe atoms are the most likely to promote the stabilities of the 16H structure with regard to other LPSO phases, but the Fe atom tends to inhibit the stabilities of 4H and 12H structures. This work can offer valuable references to further study and develop high-performance Mg alloys with multi-type LPSO structures.

Atomic origins of the plastic deformation micro-mechanisms of γ/γ’ FeCoNiAlTi high-entropy alloys

The γ/γ’ FeCoNiAlTi high-entropy alloys (HEAs) break the strength-ductility trade-off and possess an excellent combination of strength and ductility. However, lack of atomic-level understanding of plastic deformation behaviors restricts the exploration of full capacities of the FeCoNiAlTi HEAs. By computing the generalized stacking fault energies (GSFEs) of the γ and γ’ phases, the relationships between planar stacking faults and work-hardening capacities, and the effect of chemical concentration and grain orientation on the deformation mechanisms were explored in depth for the FeCoNiAlTi HEAs. Our results demonstrate that the multicomponent nature lowers the GSFEs of the matrix but enhances those of the precipitate to achieve the strength-ductility balance of the HEA. An active factor (ε) defined as γisf/γapb (γisf: intrinsic stacking fault energy, γapb: anti-phase boundary energy) was introduced to bridge activation of microbands (MBs) and planar stacking faults in the γ/γ’ alloys. Tuning a suitable low ε around 0.2 is an efficient strategy for acquiring the extended MBs-induced plasticity. Analyzing the individual/synergetic contribution of the principal elements to the GSFEs-related properties, we find that increasing the amount of Co and Ti promotes the strength-ductility balance and facilitates the MB activation by altering the GSFEs of both γ and γ’. Based on our comprehensive analysis, it is concluded that raising the Co/Fe ratio or lowing the Al/Ti ratio benefits the achievement of the desired mechanical properties of the FeCoNiAlTi HEA.