Unstable Stacking Fault Energy Research Articles

Theoretical prediction of texture requirements for improving the intrinsic cleavage crack resistance of BCC Fe

Based on the classical Rice model of crack tip dislocation emission, the present article provides a theoretical prediction of suitable grain orientations (texture components) in a rolled polycrystalline BCC Fe plate which can improve the overall resistance to cleavage crack propagation. Besides, the beneficial effect of alloying additions on further improvement in the intrinsic crack resistance of the steel is also discussed pertaining to the role of unstable stacking fault energy.

Modeling the improved hydrogen embrittlement tolerance of twin boundaries in face-centered cubic complex concentrated alloys

With increasing interest in hydrogen as an alternative fuel, there is a need to develop structural alloys with improved resistance to hydrogen embrittlement (HE) for application in the new hydrogen economy. Complex concentrated alloys (CCAs), which include high entropy alloys and their derivatives, medium entropy alloys, are a new class of structural materials, some of which have reported improved HE resistance. While some studies have suggested that the improved HE resistance in CCAs with the face-centered cubic (fcc) crystal structure may be due to the high density of nanotwins within them, a detailed mechanistic understanding is yet to be developed. Towards that end, following the approach of Zhou, Tehranchi and Curtin, we employ a density functional theory-informed Griffith–Rice model22This type of model has also been referred to in the literature as the Rice–Thomson model. In this work, we refer to it as the Griffith–Rice model to reflect that the concept of unstable stacking fault energy was introduced into the model due to Rice (1992). to predict the ductile or brittle response of a crack tip interacting with twin boundaries (TBs) in a model fcc CCA, CrCoNi, both in the absence of and presence of hydrogen. Both the model and molecular dynamics simulations predict that TBs in fcc alloys are not inherently more susceptible to HE than the bulk matrix, and could in fact improve HE resistance by retarding cracks while promoting dislocation emission along the TB. Thus, designing fcc CCAs with a high density of nanotwins or utilizing gradient nanotwinned structures could be a way forward for realizing alloys with high HE resistance.

Tuning chemical short-range order for simultaneous strength and toughness enhancement in NiCoCr medium-entropy alloys

The pursuit of enhancing strength and toughness remains a critical endeavor in the field of structural materials. This study explores two distinct strategies to overcome the traditional strength-toughness trade-off. Specifically, we manipulate the chemical composition and short-range order (SRO) of the NiCoCr medium-entropy alloy, which has shown remarkable fracture toughness in recent experiments. Utilizing molecular dynamics simulations, we uncover nano-scale deformation mechanisms during crack propagation. Our findings highlight that optimizing the SRO degree leads to improvements in both atomic scale strength and toughness defined as the area underneath stress-strain curves from MD simulations. In contrast, a trade-off between strength and toughness persists when only manipulating the Ni content in the NiCoCr alloy. Based on the simulation results, we establish a strong correlation between toughness, strength, surface energies, and unstable stacking fault energies. These factors are influenced by the chemical composition and SROs in NiCoCr, with SROs acting as strong obstacles to dislocations, thereby contributing to additional strength. The exceptional toughness of NiCoCr with SRO arises from a synergy of intrinsic and extrinsic mechanisms, including dislocation glide, nanobridging during nanovoid coalescence and zigzag crack path. It is found that, in the presence of SRO, intrinsic toughening mechanisms usually associated with crack tip blunting and dissipation can also facilitate the onset of extrinsic toughening mechanisms of nanobridging and zig-zag crack path associated with nanovoid formation and coalescence. This study emphasizes the importance of tailoring SRO in designing materials with enhanced strength and toughness.

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.

Tailoring short-range order and dislocation evolution in Cr–Co–Ni medium-entropy alloys: A molecular dynamics study

The research community has recently been captivated by the atomic-scale short-range order observed in high- and medium-entropy alloys. However, significant challenges persist in improving the mechanical performance through manipulation of the short-range order. Herein, molecular dynamics simulations are employed to establish the correlation between this ordering and the chemical composition for the Cr–Co–Ni medium-entropy alloys. It is demonstrated that atomic-scale clustering can be tailored through adjusting the chemical composition. Particularly, it can be promoted by decreasing the content of elements that do not participate in the clusters. The short-range ordering plays a significant role in affecting the dislocation evolution and tensile properties. Reducing the tendency to form Cr–Co clusters yields enhanced strengthening due to the increased local unstable stacking fault energy. Increasing the tendency to form Ni–Ni clusters instead results in enhanced strain hardening due to the high sessile dislocation density impeding the movement of dislocations. These findings unveil the crucial role of chemical composition on short-range ordering and have significant implications on the design of high-performance high- and medium-entropy alloys.

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.

High-ductility Mg-9Li-1Zn-2Gd-1.2Mn alloy prepared via traditional hot extrusion

The dual-phase Mg-9Li-1Zn-2Gd-1.2Mn alloys were prepared by traditional hot extrusion at 200 °C, 250 °C, and 300 °C, respectively. The microstructure of as-extruded Mg-9Li-1Zn-2Gd-1.2Mn alloy is remarkably refined, and the mechanical properties are significantly improved compared with the as-cast alloy. The Mg-9Li-1Zn-2Gd-1.2Mn alloy extruded at 200 °C exhibits the best comprehensive mechanical properties among the alloys with the yield strength (YS), ultimate tensile strength (UTS), and elongation to failure (εef) are 141 MPa, 166 MPa, and 57%, respectively. The dispersed second phases and Zn segregation along the grain boundary inhibit the growth of recrystallized grains and reduce the grain size, contributing to high ductility. Then, the unstable stacking fault energy of {0001}<11 2‾ 0> slip system (γusf(basal)) and surface energy of {0001} plane (γs(basal)) in Mg and Mg-Li-Gd-Zn supercells are characterized by first-principles calculation. The results indicated that the value of γusf(basal) decreased from 259 mJ/m2 to 249 mJ/m2, while the value of γs(basal) increased from 537 mJ/m2 to 597 mJ/m2. The lower γusf(basal) promotes the initiation of basal slip and higher γs(basal) leads to a lower cracking tendency, revealing the ductility improvement by adding Li, Zn, and Gd elements. This work provides an effective strategy to prepare high-ductility Mg-Li alloys.

Twinning behavior and thermoelectric performance of Cu2SnS3

With the perfect and orderly atomic arrangement, nanotwins could effectively scatter mid- and low-frequency phonons while minimizing the scattering for carriers, beneficial for enhancing the thermoelectric properties of materials. To unlock these features, we explored the twin structural characteristics in Cu2SnS3 and found that nanotwins formed along [100] direction on the glide-set plane, and further delved into the mechanism of twin formation and found that twinning possessed a lower nucleation barrier than the slipping. In addition, we reduced the unstable stacking fault energy in the stacking stage and amplified the probability of twin formation by introducing Se atoms at the S sites. In spite of more nanotwins, a slight increase in carrier mobility was realized, leading to a maximum power factor of 5.5 μW cm−1 K−2 at 773 K for the Cu2SnS2Se material. Meanwhile, the lattice thermal conductivity across the entire temperature range was effectively reduced due to the introduction of nanotwins and SeS points defects, which is approximately 0.46 W m−1 K−1 at 773 K for Cu2SnS2Se. Further optimization of the power factor was realized by utilizing a high-efficient doping strategy via introducing Sn vacancies. The carrier concentration became significantly augmented while minimizing ionized impurities scattering, giving rise to an exceptionally high power factor of 8.2 μW cm−1 K−2 and a highly-ranked thermoelectric figure of merit of 0.98 at 773 K for Cu2Sn0.99S2Se. Our work demonstrates an intriguing route towards the high thermoelectric performance of Cu2SnS3 through the introduction of nanotwins as well as high-efficient doping techniques.

Origin of gamma surface asymmetries in body-centered cubic refractory high entropy alloys

In this study, we develop an understanding of the effect of high stacking fault elements in the γ-surfaces and twinnability of NbMoTaW refractory High Entropy Alloy (HEA) using first-principles density functional theory calculations. γ-surfaces developed low energy pathways leading to asymmetries by controlling the concentration of high stacking fault energy elements in the HEA. This effect was correlated to the strength of specific solid-state pair interactions using the projected crystal orbital Hamilton population analysis, and they were found to be weak except for W-Mo and W-Ta. Since the interactions involving Tungsten are stronger than the other interactions, stacking fault and twin formation are less likely to happen near tungsten-rich portions of the alloy. This suggests the formation of tungsten-deficient twin boundaries in NbMoTaW which will further improve the ductility of the system. Stable twin fault energy as low as 522 mJ/m2 is reported for the equimolar random atomic configurations of the HEA system. The ratio between twin boundary migration energy and the difference in unstable stacking fault energies (γTBMΔus) was found to be as low as 0.13 suggesting deformation twinning can happen in the HEA system. Vibrational analysis of the alloy system has indicated that tungsten and tantalum contribute to the acoustic phonon frequencies of the HEA. Fundamental insights from this study will help in engineering high entropy alloys with high strength and ductility.

Impact of local chemical ordering on deformation mechanisms in single-crystalline CuNiCoFe high-entropy alloys: a molecular dynamics study

High-entropy alloys (HEAs), composed of multiple constituent elements with concentrations ranging from 5% to 35%, have been considered ideal solid solution of multi-principal elements. However, recent experimental and computational studies have demonstrated that complex enthalpic interactions among constituents lead to a wide variety of local chemical ordering (LCO) at lower temperatures. HEAs containing Cu typically decompose by forming of Cu-rich phases during annealing, thus affecting mechanical properties. In this study, CuNiCoFe HEA was chosen as a model with a tendency for Cu segregation at low temperatures. The formation of LCO and its impact on the deformation behaviors in the single-crystalline CuNiCoFe HEA were studied via molecular dynamics simulations. Our results demonstrate that CuNiCoFe HEA decomposes by Cu clustering, in agreement with prior experimental and computational studies, owing to insufficient configuration entropy to compete against the mixing enthalpy at lower temperatures. A softening in ultimate stress in the LCO models was observed compared to the random solid solution models. The softening is due to the lower unstable stacking fault energy, which determines the nucleation event of dislocations, thereby rationalizing the dislocation nucleation in the Cu-rich regions and the softening of the overall ultimate strength in the LCO models. Additionally, the inhomogeneous FCC–BCC transformation is closely associated with concentration inhomogeneity. CuNiCoFe HEA with LCO can be regarded as composites, consisting of clusters with different properties. Consequently, concentration inhomogeneity induced by LCO profoundly impacts the mechanical properties and deformation behaviors of the HEA. This study provides insights into the effect of LCO on the mechanical properties of CuNiCoFe HEAs, which is crucial for developing HEAs with tailored properties for specific applications.

Influence of alloying elements on various properties of face-centered-cubic iron

Austenitic stainless steel 316 L, a typical face-centered-cubic (FCC) iron alloy, demonstrates great potential as structural materials in nuclear plant. However, liquid metal (Pb and Bi) embrittlement (LME) constitutes the major bottlenect in its wide application. In this work, first-principles calculations are conducted to reveal the influences of Cr, Mo, Ni, Pb, and Bi on magnetic property, surface energy, stacking fault energy, ductility, as well as electronic structure of FCC Fe under the magnetic ground state of antiferromagnetic double layer (AFMD). It is discovered that the addition of Ni could considerably increase the ductility of FCC Fe, while the effects of Cr and Mo on the increase of ductility of FCC Fe seem much smaller. On the contrary, both Pb and Bi significantly reduce the ductility of FCC Fe. Such a large decrease is mainly attributed to the more reduction of surface energy than that of unstable stacking fault energy as well as a more directional and weaker chemical bonding. The derived results could provide insight into the influence of alloying elements on the various properties of FCC Fe.

New understanding of one-dimensional thermal glide of a nano-sized prismatic dislocation loop in bcc iron: an atomic scale study

Vacancy-type prismatic dislocation loops (PDLs) can be formed directly through cross-slip mechanisms of screw dislocations or via the accumulation and transformation of high-density vacancy-type defects. The concentration of vacancy-type defects in body-centered cubic (BCC) iron can be increased through plastic deformation and in the presence of hydrogen. Nano-sized PDLs can act as high-speed vacancy transport in BCC iron, causing embrittlement. Based on molecular dynamics simulations, this study comprehensively analyzes the one-dimensional diffusion of vacancy-type PDLs composed of 37–169 vacancies (V37-V169) at temperatures ranging from 100 to 1000 K. The activation energy of diffusion increased with decreasing PDL size for small loops (V37–V61) but remained almost constant for larger loops (>V91). This behavior was found to be associated with the tensile stress produced by the opposing edge dislocation segment in the loop where the distance is closer for a smaller PDL. That is, the tensile stress along the slip direction of edge dislocation causes the unstable stacking fault energy to increase, and the change of dislocation core structure further contributes to an increase in the activation energy for the diffusion of PDL. In contrast, an external compressive stress reduces the activation energy and pre-exponential factor of diffusion in small PDLs, as exemplified in V37 PDL.

The precipitation tendency and stacking fault energy of Al-modified ultra-super ferritic stainless steels: An experimental and first-principles study

Super ferritic stainless steels (SFSS) are prone to the precipitation of multiple brittle second phases, increasing the production difficulty and restricting their applications. In this study, Al is added to super ferritic stainless steel to facilitate industrial production with controlled precipitation of brittle phases. The precipitation and recrystallization of the Al-modified super ferrite stainless steel are investigated through experimental and first principles approaches. It is found the addition of Al can inhibit σ-phase and promote the precipitation of Laves phase. It also increases the surface energy of BCC-Fe and reduces the unstable stacking fault energy, leading to an increase in the ductility of the SFSS. The results provide theoretical guidance for further improvements of mechanical properties of Al-modified ultra-super ferrite stainless steel.

Improving the strength and ductility of magnesium alloys by Sc alloying: An experimental and first-principles study

Mg–Sc alloys have great application potential due to the positive effect of Sc on improving corrosion resistance and mechanical properties. In this work, the effects of Sc content on the strength and ductility of Mg-xSc (x=0, 1, 2, 3 at.%) alloys were investigated by experiments and first-principles calculations. The results indicate that, with the increase of Sc content, the hardness, strength, and ductility of the alloys increase significantly. The improvement of strength is attributed to the solid solution strengthening and grain size refinement effect. The addition of Sc reduces the prismatic unstable stacking fault energy of the alloys, thereby promoting the activation of stacking faults and <c+a> dislocations, resulting in the significant improvement of ductility. The mechanism of the enhanced ductility of Mg-xSc solid solution alloys is revealed, which provides guidance for designing high-performance Mg alloys.

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.

On the influence of enthalpy of formation on lattice distortion and intrinsic ductility of concentrated refractory alloys

Valence electron concentration (VEC), atomic size difference (δ), and Pugh’s ratio (B/G) are a few of the empirical parameters widely used to design ductile refractory alloys. Here, we used the intrinsic ductility parameter (D), which is the ratio of surface energy (γs) and unstable stacking fault energy (γusfe), to design ductile refractory alloy. We found that the D correctly captures the experimentally observed ductility in concentrated refractory alloys. Here, we studied the enthalpy of formation (ΔEf), lattice distortion, and D of 9 refractory metals and 36 equiatomic refractory alloys using density functional theory simulations. We found that the ΔEf strongly influences the D of concentrated refractory alloys. The positive ΔEf and δ lead to large lattice distortion in concentrated refractory alloys. However, we did not find a strong correlation between lattice distortion and D in the presently studied alloys. We found that the success of VEC and Pugh’s ratio in designing ductile refractory alloys has a strong dependence on the underlying ΔEf of the alloy. We have developed a bottom-up method, which drastically reduces the number of alloys to be studied, to design ductile concentrated refractory alloys that can be thermodynamically stable.

Interaction of extended dislocations with nanovoid clusters

Voids of nanoscale dimensions in irradiated metals can act as obstacles to dislocation motion and cause strengthening. In this work, nanovoid strengthening and the influences of void size, void spacing and material properties, such as stacking fault energies, on dislocation bypass mechanisms are investigated using Phase Field Dislocation Dynamics, a three-dimensional mesoscale model that predicts the minimum energy pathway taken by discrete dislocations. A broad range of face centered cubic metals (copper, nickel, silver, rhodium, and platinum) and nanovoid sizes and spacings are treated, altogether spanning void size–to–dislocation stacking fault width ratios from less than unity to ten. Material γ-surfaces, calculated from ab initio methods, are input directly into the formulation. The analysis reveals that the critical bypass stress scales linearly with the linear void fraction, effective isotropic shear modulus, and ratio of the intrinsic to unstable stacking fault energies. With only a few exceptions, the critical stress is controlled by the stress required for the leading partial to impinge the voids (to move within range of the attractive image stress field of the void). When the void diameter is nearly an order of magnitude greater than the stacking fault width, the mechanism determining critical strength shifts to the stress for the dislocation to breakaway after partially cutting the void. This situation corresponds to that treated by line tension models and is realized here for Pt, with a sub-nanometer stacking fault width.

Simulated nanoindentation into single-phase fcc Fe_{x}Ni_{1-x} alloys predicts maximum hardness for equiatomic stoichiometry

We investigate by molecular dynamics simulation the mechanical behavior of concentrated alloys under nanoindentation for the special example of single-phase fcc Fe_{x}Ni_{1-x} alloys. The indentation hardness is maximum for the equiatomic alloy, x=0.5. This finding is in agreement with experimental results on the strength of these alloys under uniaxial strain. We explain this finding with the increase of the unstable stacking fault energy in the alloys towards x=0.5. With increasing Fe content, loop emission from the plastic zone under the indenter becomes less pronounced and the plastic zone features a larger fraction of screw dislocation segments; simultaneously, the length of the dislocation network and the number of atoms in the stacking faults generated in the plastic zone increase. However, the volume of twinned regions in the plastic zone is highest for the elemental solids and decreases for the alloys. This feature is explained by the fact that twinning proceeds by the glide of dislocations on adjacent parallel lattice planes; this concerted motion is less efficient in the alloys. Finally, we find that surface imprints show increasing pile-up heights with increasing Fe content. The present results will be of interest for hardness engineering or generating hardness profiles in concentrated alloys.

Multi-scale investigation of short-range order and dislocation glide in MoNbTi and TaNbTi multi-principal element alloys

Refractory multi-principal element alloys (RMPEAs) are promising materials for high-temperature structural applications. Here, we investigate the role of short-range ordering (SRO) on dislocation glide in the MoNbTi and TaNbTi RMPEAs using a multi-scale modeling approach. Monte carlo/molecular dynamics simulations with a moment tensor potential show that MoNbTi exhibits a much greater degree of SRO than TaNbTi and the local composition has a direct effect on the unstable stacking fault energies (USFEs). From mesoscale phase-field dislocation dynamics simulations, we find that increasing SRO leads to higher mean USFEs and stress required for dislocation glide. The gliding dislocations experience significant hardening due to pinning and depinning caused by random compositional fluctuations, with higher SRO decreasing the degree of USFE dispersion and hence, amount of hardening. Finally, we show how the morphology of an expanding dislocation loop is affected by the applied stress.

Solid solution softening in single crystalline metal nanowires studied by atomistic simulations

Solid solution strengthening is a common method used in physical metallurgy to increase the strength of metals. However, it is also possible for solute atoms to reduce the strength of metals, known as the solid solution softening effect. In this paper, atomistic simulations were carried out using molecular dynamics and Monte Carlo simulations to explore the softening phenomenon in single crystalline metal nanowires (MNWs) of different alloy systems. It was found that, for single crystalline MNWs, softening is more prominent than strengthening when solute atoms are introduced, which contrasts with the solid solution strengthening that is usually observed in bulk metals. The reduction of unstable stacking fault energy, increase in atomic size misfit, and solute clustering are responsible for this phenomenon, as they facilitate the surface dislocation nucleation in the alloyed nanowires. Additionally, while the nanowire diameter, orientation, surface segregation, and chemical short-range ordering all influence the yield strength, they do not alter the overall softening trend. It is assumed that the softening mechanisms uncovered in this paper are applicable to metallic structures whose yielding is determined by dislocation nucleation.