Negative Stacking Fault Energy Research Articles

Atomic-Scale In Situ Observations of Reversible Phase Transformation Assisted Twinning in a CrCoNi Medium-Entropy Alloy.

Twinning is an important deformation mode of face-centered-cubic (FCC) medium- and high-entropy alloys, especially under extreme loading conditions. However, the twinning mechanism in these alloys that have a low or even negative stacking fault energy remains debated. Here, we report atomic-scale in situ observations of the deformation process of a prototypical CrCoNi medium-entropy alloy under tension. We found that the parent FCC phase first transforms into a hexagonal close-packed (HCP) phase through Shockley partial dislocations slipping on the alternate {111} planes. Subsequently, the HCP phase rapidly changes to an FCC twin band. Such reversible phase transformation assisted twinning is greatly promoted by external tensile loads, as elucidated by geometric phase analysis. These results indicate the previously underestimated role of the metastable HCP phase in nanotwin nucleation and early plastic deformations of CrCoNi alloys and shed light on microstructure regulation of medium-entropy alloys with enhanced mechanical properties.

Effect of stacking fault energy on B2 ZrCo phase transition and nanotwins formation in Zr54.5Co33.5Al12 alloy prepared by rapid solidification

Zr–Co–Al alloys are widely used due to their good biocompatibility and high-pressure properties. In the present work, the Zr54.5Co33.5Al12 alloy was prepared by rapid solidification. It has been found that the central region (b region) and the edge region (d region) have obvious changes in the microstructure, with the b region contains a large number of crystalline phases, and the d region can obviously observe the morphology of the amorphous state except a few dendrites. A certain amount of amorphous is contained in the d region as detected by XRD analysis. The fracture strength can undoubtedly reach up to 2031 MPa and the fracture strain is about 1.8 %. TEM analysis revealed the B2-to-B33 phase transition in the deformed alloy, and a significant number of nanotwins with a {111} <121> type of twin relationship were observed in the B33 ZrCo phase. Furthermore, the stacking fault energy (SFE) for varying applied stresses was calculated. From the calculation results, the negative SFE (about −41 mJ/m2) is beneficial to the B2-to-B33 phase transition, and it is known that twin thickness decreases with decreasing SFE.

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.

Composition-dependent transformation-induced plasticity in Co-based complex concentrated alloys

While the mechanically-induced martensitic transformation and transformation-induced plasticity (TRIP) effects have various known benefits, transformation of blocky martensite can also accelerate ductile damage nucleation and growth. Some complex-concentrated alloys (CCAs) with negative stacking-fault energy (SFE) demonstrate a rare faulting plasticity behavior with high strain hardening capability, that sets them apart from conventional low, positive SFE alloys that exhibit the TRIP effect. This study investigates the influence of dilute nitrogen on the TRIP mechanisms in a Co-rich CoCrNi CCA, and reveals, among other findings, that nitrogen interstitials can effectively reduce the extension of stacking faults and deformation-induced phase transformation, resulting in higher strain hardenability at early deformation levels and ductility. Thermodynamic calculations are coupled to various experimental analyses based on atom-probe tomography, scanning transmission electron microscopy, electron backscattered diffraction, electron-channeling contrast imaging, in situ high-energy synchrotron X-ray diffraction, and stress relaxation testing, to explore the origins of the observation. This work provides insights into the future design of CCAs with desirable TRIP, faulting plasticity, and mechanical properties.

Equilibrium versus non-equilibrium stacking fault widths in NiCoCr

First principles calculations in the NiCoCr medium-entropy alloy predict a negative stacking fault energy (SFE) at T=0 K, implying an infinite Shockley partial dissociation distance. Many experiments at room temperature (RT) show however a finite dissociation. This discrepancy has been suggested due to solute strengthening that prevents the partial separation. Here, atomistic simulations in a model NiCoCr alloy having a negative SFE show that solute strengthening can limit partial separation at T=0 K but, the solute-induced barriers are easily overcome at RT and time scales of only 1 ns. Under experimental conditions (time scales of hundreds of seconds and longer), solute pinning is therefore insufficient to limit dissociation. Finite partial separations are thus presumably due to a positive stacking fault free energy at RT or short-range-order effects. It is argued here that the former is more likely than the latter.

On the faulting and twinning mediated strengthening and plasticity in a γʹ strengthened CoNi-based superalloy at room temperature

Microscopic defects and their mutual interactions are fundamentally important in deciding the load carrying capacity of structural materials. In this context, the present work reports an unprecedented precipitate shearing mechanism in CoNi-based superalloys at room temperature where L12 ordered γʹ precipitates are embedded within a disordered CoCrNi-rich matrix. A combined electron channelling contrast imaging (ECCI) and scanning transmission electron microscopy (STEM) analysis revealed stacking fault (SF) and SF coupled nano-twin formation that rendered a significant work hardening rate. The observed twinning induced plasticity (TWIP) effect correlates with an excellent combination of yield strength, ultimate tensile strength (UTS) and plasticity of 910 ± 30 MPa, 1360 ± 40 MPa and ∼ 18.5 (%), respectively, as exhibited by the peak aged Co-30Ni-12Cr-7Al-4Ti-2Nb-0.006B alloy at room temperature. Rigorous center of symmetry (COS) analysis on atomic resolution STEM images from the deformed samples unambiguously establishes precipitate shearing via single a/6⟨112⟩{111} partial dislocations resulting in twin formation, succeeding the intrinsic stacking fault (ISF) and complex stacking fault (CSF) of γ and γʹ, respectively. Through thermodynamic and first principles density functional theory calculations, it is demonstrated that the experimentally observed deformation mechanism is directly correlated with the negative stacking fault energy of γ matrix and low CSF energy of the γʹ precipitates. Based on these new findings, the present work demonstrates the flexibility of tuning the composition of CoCrNi containing superalloys to widen the alloy spectrum for designing alloys with improved properties.

Impact of chemical short-range order on radiation damage in Fe-Ni-Cr alloys

Chemical short-range order (CSRO), as a nanoscale atomic feature, has been found to significantly alter material properties in various alloys. Here, we use Fe-Ni-Cr alloys to demonstrate how CSRO affects defect properties and radiation behavior, based on extensive molecular dynamics simulations. Statistically significant results are obtained as a function of dose for three CSRO levels. The random solution as an energetically unfavorable state (negative stacking fault energy) shows the strongest tendency to enable diffusion, while a high CSRO degree scenario generally reduces the effective defect diffusivity due to trapping effects, leading to distinct defect dynamics. Notably, in the high-CSRO scenario, interstitial clusters are Cr-rich and interstitial loops preferentially reside in/near the Cr-rich CSRO domains. Also, CSRO is dynamically evolving in a decreasing or increasing manner upon irradiation, reaching a steady-state value. These new understandings suggest the importance of incorporating the effect of CSRO in investigating radiation-driven microstructural evolution.

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.

Suzuki hardening and segregation in Co0.95Cr0.8Fe0.25Ni1.8Mo0.475 high-entropy alloys

A Co0.95Cr0.8Fe0.25Ni1.8Mo0.475 high-entropy alloy was heavily cold-rolled and subsequently aged at 773 K. Aging-induced Suzuki hardening was observed. High-angle annular dark-field scanning transmission electron microscopy imaging and the corresponding energy dispersive X-ray spectroscopy elemental distribution mapping suggested the enrichment of Co atoms at stacking faults (SFs), which pinned down partial dislocations and enhanced the resistance of the alloy to plastic deformation. Furthermore, the enrichment of Co and Mo atoms at SFs was observed in a low dislocated, strain-aged specimen. The significant difference in the SF density of the specimens led to difference in segregation. The local stacking fault energy (SFE) with the segregation of Co and Mo atoms was calculated as −30.6 mJ/m2 at the aging temperature. The negative SFE did not restrict the SF expansion, indirectly resulting in the formation of wide SFs.

Theory of transformation-mediated twinning.

High-density and nanosized deformation twins in face-centered cubic (fcc) materials can effectively improve the combination of strength and ductility. However, the microscopic dislocation mechanisms enabling a high twinnability remain elusive. Twinning usually occurs via continuous nucleation and gliding of twinning partial dislocations on consecutive close-packed atomic planes. Here we unveil a completely different twinning mechanism being active in metastable fcc materials. The transformation-mediated twinning (TMT) is featured by a preceding displacive transformation from the fcc phase to the hexagonal close-packed (hcp) one, followed by a second-step transformation from the hcp phase to the fcc twin. The nucleation of the intermediate hcp phase is driven by the thermodynamic instability and the negative stacking fault energy of the metastable fcc phase. The intermediate hcp structure is characterized by the easy slips of Shockley partial dislocations on the basal planes, which leads to both fcc and fcc twin platelets during deformation, creating more twin boundaries and further enhancing the prosperity of twins. The disclosed fundamental understanding of the complex dislocation mechanism of deformation twinning in metastable alloys paves the road to design novel materials with outstanding mechanical properties.

Atomic level simulations of the phase stability and stacking fault energy of FeCoCrMnSi high entropy alloy

High entropy alloys (HEAs) have many promising properties beneficial to advanced technologies. However, their underlying deformation mechanisms are largely unclear. So, as a first step, we have developed a modified embedded atom method potential for FeCoCrMnSi alloys to study such mechanisms. We predict the phase stability, chemical short-range ordering (CSRO), and stacking fault energy (SFE) of a specific alloy system using molecular dynamics (MD) and hybrid Monte-Carlo and molecular dynamics (MC/MD) simulation techniques. Room temperature MD simulations showed that both the potential energy and free energy of the single phase ε-hcp alloy is marginally more stable than the γ-fcc phase alloy, which resulted in a large, negative SFE. However, the room temperature MC/MD simulation showed an opposite trend where the γ-fcc phase was found to be more stable than the ε-hcp phase, and this resulted in a small, positive SFE. The prediction of the lower energy γ-fcc phase and resultant SFE agreed well with the experimentally reported SFE and phase stability for the Fe40Co20Cr15Mn20Si5 HEA, illustrating the importance of CSRO. Also, the calculated basal SFE of the hcp phase was close to that of the fcc phase. Therefore, the MC/MD implementation is crucial for the proper prediction of the phase stability and structural evolution in this HEA system. Many previous studies showed the ability of hybrid MC/MD technique to obtain consistent structural and configurational information of different alloy systems. The current work illustrates the potential of accelerating HEA materials development by utilizing computational methods based on the MC/MD technique which can reduce time and cost associated with experimental methods.

Interactions between screw dislocation and twin boundary in high-entropy alloy: A molecular dynamic study

The interaction between dislocations and twin boundaries plays an important role in the plastic deformation of high-entropy alloys (HEAs), in which deformation twinning mechanisms are highly active. However, research concerning the twinning-induced strengthening in HEAs is lacking, especially atomistic studies. Therefore, molecular dynamics (MD) simulations are performed to elucidate the interaction mechanisms between the screw dislocation and the coherent twin boundary in the CoNiCrFeMn HEA and pure Ni. Dislocation transmission across the twin boundary is observed as the only mode in the CoNiCrFeMn HEA and pure Ni. However, the Shockley partial dislocations cannot simultaneously constrict on the twin boundary in the CoNiCrFeMn HEA because of the nanoscale segment detrapping mechanism related to the statistical fluctuation of chemical ordering, different from that in pure Ni. To quantify the interaction mechanism, generalized stacking fault energies and lattice friction are considered for predicting the interaction mode in the CoNiCrFeMn HEA. A new material parameter that considers the negative stacking fault energy and large lattice friction stress is proposed for the CoNiCrFeMn HEA.

Defect dynamics and uniaxial tensile deformation of equi and non-equi-atomic configuration of multi-elemental alloys

In this article, molecular dynamics and statics-based simulations were carried out to study the effect of equi-atomic and non-equi-atomic compositions of multi-elemental alloys on defect dynamics and tensile deformation. High and medium entropy alloy configurations were subjected to uni-axial tensile loading, and deformation governing mechanism was identified with the help of dislocation extraction algorithm and common neighbour analysis. Due to low or negative stacking fault energy, phase transformation from FCC to HCP in conjunction with solid solution hardening was identified as the governing mechanism for the plastic deformation in most of the multi-elemental alloys. Atomistic snapshots of simulation box containing deformed configurations of medium and high entropy alloys also show heterogenous nucleation, pinning of dislocations, cross channelling of twin boundaries. It was predicted that in alloys with higher Cr content twinning and stacking fault is prominent mode of deformation. Nudged elastic band algorithm was used to predict the vacancy migration energies in each of the atomistic configurations. The results presented in the article are in qualitatively in agreement with the experimental results, and higher fidelity simulations helps in developing better understanding about the plastic deformation in equi and non-equi-atomic composition of multi-elemental alloys.

Can experiment determine the stacking fault energy of metastable alloys?

Stacking fault energy (SFE) plays an important role in deformation mechanisms and mechanical properties of face-centered cubic (fcc) metals and alloys. In many concentrated fcc alloys, the SFEs determined from density functional theory (DFT) calculations and experimental methods are found having opposite signs. Here, we show that the negative SFE by DFT reflects the thermodynamic instability of the fcc phase relative to the hexagonal close-packed one; while the experimentally determined SFEs are restricted to be positive by the models behind the indirect measurements. We argue that the common models underlying the experimental measurements of SFE fail in metastable alloys. In various concentrated solid solutions, we demonstrate that the SFEs obtained by DFT calculations correlate well with the primary deformation mechanisms observed experimentally, showing a better resolution than the experimentally measured SFEs. Furthermore, we believe that the negative SFE is important for understanding the abnormal behaviors of partial dislocations in metastable alloys under deformation. The present work advances the fundamental understanding of SFE and its relation to plastic deformations, and sheds light on future alloy design by physical metallurgy.

Electron localization governed plasticity in nanotwinned metals beyond the Hall-Petch type limit

While nanotwinned metals have been widely reported to show a strengthening-softening transition as the twin spacing decreases below a critical size, which is similar to the Hall-Petch limit in nanocrystalline materials, a recent study has suggested that some nanotwinned high entropy alloys (HEAs) could show continuous strengthening as long as the twin spacing decreases. Here we investigate the physical origin of the contrasting plasticity in nanotwinned face-centered-cubic (FCC) metals beyond the Hall-Petch type limit by using atomistic simulations based on density functional theory. Our results indicate that the degree of electron localization among atoms at the FCC sites and the stacking faults, which have a hexagonal-closed-packed (HCP) structure, governs the plasticity in nanotwinned metals with extremely fine twin spacing. Specifically, metals whose electrons are more localized at FCC atoms than those at stacking faults, such as conventional FCC metals, are associated with positive stacking fault energy and accordingly detwinning and strengthening-to-softening transition beyond the Hall-Petch type limit. In contrast, metals in which electrons are more localized at stacking faults than at FCC sites as found in some HEAs exhibit negative stacking fault energy and continuous strengthening by the unconventional FCC-to-HCP martensite transformation when the Hall-Petch type limit is reached. This work provides a new microscopic aspect from the electron properties to understand the macroscopic mechanical behavior of nanotwinned FCC metals which can shed some light on designing novel complex alloys.

Can Experiment Determine the Stacking Fault Energy of Metastable Alloys?

Stacking fault energy (SFE) plays an important role in deformation mechanisms and mechanical properties of face-centered cubic (fcc) metals and alloys. In metastable fcc alloys, the SFEs determined from density functional theory (DFT) calculations and experimental methods often have opposite signs. Here, we show that the negative SFE by DFT reflects the thermodynamic instability of the fcc phase relative to the hexagonal close-packed one; while the experimentally determined SFEs are restricted to be positive by the models behind the indirect measurements. We argue that the common models underlying the experimental measurements of SFE fail in metastable alloys. In various concentrated solid solutions, we demonstrate that the SFEs obtained by DFT calculations correlate well with the primary deformation mechanisms observed experimentally, showing a better resolution than the experimentally measured SFEs. Furthermore, we believe that the negative SFE is important for understanding the abnormal behaviors of partial dislocations in metastable alloys under deformation. The present work advances the fundamental understanding of SFE and its relation to plastic deformations, and sheds light on future alloy design by physical metallurgy.

Phase transformation assisted twinning in a face-centered-cubic FeCrNiCoAl0.36 high entropy alloy

The FeNiCoCr-based high entropy alloys (HEAs) exhibit excellent mechanical properties, such as twin-induced plasticity (TWIP) and phase transformation plasticity (TRIP) that can reach a remarkable combination of strength and ductility. In the present work, the face-centered-cubic (FCC) single-crystal FeNiCoCrAl0.36 HEAs were studied, using the density functional theory (DFT) combined with the phonon calculation to estimate the stacking fault energies, temperature-dependent phase stabilities of different structures. And the kinetic Monte Carlo (kMC) was used to predict the substructures evolution based on the transition state energies obtained from DFT calculations. We proposed two different formation paths of nano-twins in this Al-composited HEA and found that short-range hexagonal-close-packed (HCP)-stacking could occur in this HEA. The DFT calculations suggest that this HEA has negative stacking fault energy (SFE), HCP formation energy, and twin-formation energy at 0 K. Phonon calculations indicate that at the finite temperature, the competing FCC/HCP phase stability and propensity for twinning make it possible to form HCP-like twin boundaries. The kMC simulations suggest that under deformation, TWINs could form within the HCP laths which differs from the study of others. With the great agreement of results from kMC simulations and experiments, this twin-hcp laminated substructure formation path offers a new concept of designing TWIP HEAs containing tunable twin structures with HCP and TWIN lamellae structures, which could result in better mechanical properties of HEAs.

Phase Transformation Assisted Twinning in Face-Centered-Cubic FeCrNiCoAl &lt;sub&gt;0.36&lt;/sub&gt;

The FeNiCoCr-based high entropy alloys (HEAs) exhibit excellent mechanical properties, such as twin-induced plasticity (TWIP) and phase transformation plasticity (TRIP) that can reach a remarkable combination of strength and ductility. In this work, the face-centered-cubic (FCC) single-crystal FeNiCoCrAl0.36 HEAs were studied, using the density functional theory (DFT) combined with the phonon calculation to estimate the stacking fault energies, temperature-dependent phase stabilities of different structures. And the kinetic Monte Carlo (kMC) is used to predict the substructures evolution based on the transition state energies obtained from DFT calculations. We proposed two different formation paths of nano-twins in this Al-composited HEA and found that short-range hexagonal-close-packed (HCP)-stacking could occur in this HEA. DFT calculations suggest that this HEA has negative stacking fault energy, HCP formation energy, and twin-formation energy at 0 K. Phonon calculations represent that at the finite temperature, the competing FCC/HCP phase stability and propensity for twinning makes it possible to form HCP-like twin boundaries. The kMC simulations suggest that under deformation, HCP substructures could form followed by twins which differs to the study of others. With the great agreement of results from kMC simulations and experiments, this twin-formation path offers a new concept of designing TWIP HEAs containing tunable twin structures with HCP and TWIN lamellae structures, which results in better mechanical properties of HEAs.

Deformation-induced phase transformation in a Co-Cr-W-Mo alloy studied by high-energy X-ray diffraction during in-situ compression tests

Nickel-free Co-Cr-W-Mo alloys exhibit a very low or even negative stacking fault energy, and therefore a pronounced tendency towards a deformation-induced phase transformation of the metastable face-centered cubic (fcc) γ-phase to the hexagonal close-packed (hcp) low-temperature ε-phase. In order to analyze the phase transformation in-situ and to correlate it to an external strain, compression tests between 30 °C and 400 °C were performed in a deformation dilatometer simultaneously to high-energy X-ray diffraction. Hence, the elastic strains of the fcc unit cell during compression, the external loads for the onset of the phase transformation and the temperature-dependency could be determined. In the parent fcc γ-phase, the evolution of an 101 fiber texture as well as texture inheritance effects and a distinct variant selection could be observed. Further, for the investigated alloy composition it is demonstrated that the continuum concepts of i) a structural stretch tensor and ii) an invariant plane strain perfectly agree with the widely-accepted nucleation theory of ε-martensite formation in Co-Cr alloys via Shockley partial dislocations on every second {111}γ plane. Both, the observed transformation texture as well as crystallographic transformation strains reveal the importance of shear stresses in this system.

Thermal spin fluctuations in CoCrFeMnNi high entropy alloy

High entropy alloys based on 3d transition metals display rich and promising magnetic characteristics for various high-technology applications. Understanding their behavior at finite temperature is, however, limited by the incomplete experimental data for single-phase alloys. Here we use first-principles alloy theory to investigate the magnetic structure of polymorphic CoCrFeMnNi in the paramagnetic state by accounting for the longitudinal spin fluctuations (LSFs) as a function of temperature. In both face-centered cubic (fcc) and hexagonal close-packed (hcp) structures, the LSFs induce sizable magnetic moments for Co, Cr and Ni. The impact of LSFs is demonstrated on the phase stability, stacking fault energy and the fcc-hcp interfacial energy. The hcp phase is energetically preferable to the fcc one at cryogenic temperatures, which results in negative stacking fault energy at these conditions. With increasing temperature, the stacking fault energy increases, suppressing the formation of stacking faults and nano-twins. Our predictions are consistent with recent experimental findings.