Generalized Planar Fault Energy Research Articles

Understanding phase stability and deformation mechanisms of zirconium under high pressures from generalized stacking fault energy curves: A first-principles study

The mechanical properties of metals are strongly depend on their phase structures, in this work, to understand the phase stability and deformation mechanisms of zirconium(Zr) under high pressures, the generalized planar fault energy(GPFE) curves based on first-principles calculations are utilized to illustrate the deformation processes of α-Zr at high pressures. Firstly, it is found the prismatic slip system is more prominent toward α-Zr at zero pressure, while the slips based on basal plane undertake the main participant during the deformation processes of α-Zr at high pressures. Meanwhile, based on the basal slip, α-Zr phase containing the pre-existing stacking fault is found more favorable to generate twin fault instead of FCC fault at zero pressure; However, the deformation twinning is overwhelmed by the HCP-to-FCC transformation for the α-Zr when the external pressure is higher than 10.4 GPa. It is thus speculated that the slips of partial dislocations for forming FCC fault based on the basal plane (0001) act as a contributing participant during the phase transition processes of Zr under high-pressure. Additionally, the computed elastic constants and the HCP-to-FCC allotropic transformation under specified conditions have revealed the metastable nature of FCC Zr in comparison with HCP Zr.

The complexity of [formula omitted] twin interface structure and energetics in HCP materials

The quest for a deeper understanding of the mechanical properties of HCP alloys has been an ongoing effort. Due to the lack of a sufficient number of slip systems, twin nucleation and migration originate as a substantial plastic deformation mechanism in HCP metals. The paper uncovers the energetics and atomistic mechanism of the {112¯1}〈112¯6〉 which is one of the most prominent twin modes in HCP materials that has not been fully understood. In view of corrugated {112¯1}interfaces, the positioning of lattice/motif atoms needs to be clarified. First, we establish the initial twin boundary (TB) structure unambiguously via the lattice offsets resulting in volume invariancy and correct relative positioning of the twin variants. Secondly, the TB migration mechanism is determined from a crystallographic (zero net shuffle, Σs→=0) and energetic standpoints (minimum energy path). The Generalized Planar Fault Energy (GPFE) curves are calculated for Ti, Hf, Mg, and Zr. Such GPFE curves for this twin mode are calculated for the first time, and point to unusually high unstable energies (300-850 mJ/m2), and low migration barriers (<60 mJ/m2) for twinning accompanied with large shuffle magnitudes, |s→|, comparable to the Burger's vector (|s→|≅be>0.44Å).

Atomistic insights into silver-indium solid solution softening mechanism for microelectronics packaging

Silver-indium solid solution is the key material in advancing low-temperature/pressure solid-state technology for electronics packaging, due to its rare solid solution softening (SSS) phenomenon. In this work, the critical resolved shear stress (CRSS) for slip, ideal shear strength and critical twinning stress of silver-indium disordered solid solutions were systematically evaluated by the generalized planar fault energy (GPFE) analysis, using first-principles modelling. Compared with others, Ag-based metals have much lower ideal shear strength and critical twinning stress, whereas the CRSS for slip of silver-indium solid solutions decreases with the increases of indium content, therefore exhibiting a general trend of softening behaviors. For the first time, the electronic origin of silver-indium SSS mechanism has been unveiled, where the modification of its GPFE structure was the fundamental cause for the reduction of CRSS for slip, critical twinning stress and the corresponding SSS phenomenon. As confirmed by transmission electron microscopy, this work presents a new design criterion for the next-generation solid-state bonding materials development.

Effects of rare-earth elements on twinning deformation of Al alloys from first-principles calculations

Effects of rare-earth (RE = Ce, Dy, Er, Ho, La, Tb, and Yb) elements on twinning deformation of Al alloys are studied using first-principles calculations. The influence rules of RE atoms doped at the first nearest neighbor layer on the generalized planar-fault energy curves are analyzed, and the interaction energies of RE atoms in various atomic layers of stacking fault configurations are studied. On the basis of the improved twinning criterion formula and uniform distribution model, the influence rules of RE solute concentration on twinnability at the crack tip, at the grain boundary, and inside the grain of Al alloys are further analyzed. Results show that RE elements can evidently decrease the minimum energy barriers of dislocation nucleation and motion, and La and Ce atoms have significant effects on promoting dislocation nucleation and motion. Ce and La atoms can promote twinning deformation at the crack tip. Except for the La atom, the remaining RE atoms inhibit twinning deformation at the grain boundaries, and La atom at high concentrations is beneficial to promote twinning deformation at the grain boundaries. RE atoms (Dy, Er, Ho, La, Tb, and Yb) for twinning deformation inside Al alloy grains exhibit slight effect. Nevertheless, the Ce atom can greatly promote twinning deformation inside the grains when the solute concentration is in the range of 5%–7.1%, and the twinning ability decreases with the increase in solute concentration again. This work takes the lead in revealing the mechanism of twinning deformation by considering the interactions between RE atoms and generalized faults, which provides valuable guidance for exploiting high-performance Al–RE alloys.

The Competition Between Deformation Twinning and Dislocation Slip in Deformed Face-Centered Cubic Metals

The competition between deformation twinning and dislocation slip underpins the evolution of mesoscale plasticity in face-centered cubic materials. While competition between these mechanisms is known to be related to the critical features of the generalized planar fault energy landscape, a physical theory that tracks competition over extended plasticity has yet to emerge. Here, we report a methodology to predict the mesoscale evolution of this competition in deformed crystals. Our approach implements kinetic Monte Carlo simulations to examine fault structure evolution in face-centered cubic metals using intrinsic material parameters as inputs. These results are leveraged to derive an analytical model for the evolution of the fault fraction, fault densities and partitioning of plastic strains among deformation mechanisms. In addition, we define a competition parameter that measures the tendencies for deformation twinning and dislocation slip. In contrast to previous ‘twinnability’ parameters, our derivation considers deformation history when examining mechanism competition. This contribution therefore extends the reach of deformation twinning theory beyond incipient nucleation events. These products find direct applications in work hardening and crystal plasticity models, which have previously relied on phenomenological relations to predict the mesoscale evolution of deformation twin microstructures.

Formula omitted] Twin interface structure and energetics in HCP materials

This study systematically analyzes the {101¯2} twin in Hexagonally Close Packed (HCP) materials. Despite several propositions over 50 years, the Twin Boundary (TB) structure and twinning mechanism remain a debated topic, precluding determination of twinning energy barriers. This debate is resolved via Crystallographic Analytical Methods (CAM), Molecular Statics (MS) simulations in HCP Ti and Density Functional Theory (DFT) calculation of the Generalized Planar Fault Energy (GPFE) curve for several HCP materials. The {101¯2} crystallographic plane is “corrugated” comprising of two non-coincident sub-planes of lattice-sites (L-plane) and motif-sites (M-plane), causing ambiguity in determining the TB structure. This study resolves this ambiguity by establishing an energy-minimizing lattice-offset between the twin and matrix. At this offset, the TB forms by relaxation of both sub-planes into coincidence on a common atomic plane. A crystallographic calculation of this offset is proposed, extendable to non-single-lattice structures, in general. The twinning mechanism is determined, obtaining a shear-shuffle partition clarifying the motion of lattice and motif atoms. Nudged Elastic Band (NEB) simulations verify the mechanism along with disconnection-mediated migration of the twin. The GPFE is calculated for the first time in literature, to the best of our knowledge, revealing energy barriers for twin nucleation and migration. An absence of correlation of the unstable twinning energy barrier against twinning shear, Burgers vector magnitude or cohesive energy is shown, emphasizing the irreplaceability of the calculated barriers for predictive twinning models. Thus, a thorough clarification of the {101¯2} twinning mode is proposed, converging on the correct TB structure, twinning mechanism and energy barriers.

Core-structure and lattice friction of twinning dislocation in platinum

Only the coarse-grained fcc metals with low stacking fault energies have a high propensity to deformation twinning; however, nanocrystalline metals with high SFEs may also show deformation twinning with different twinning nucleation paths. Contrary to the convectional twinning routes, a new alternate-shear mechanism for nucleation of twins in nanocrystalline platinum has recently been proposed, though very little information is available regarding the fundamental parameters of the twinning dislocations involved there. In the present study, we examine the core-structure and lattice resistance of these twinning dislocations by employing an integrated approach of atomistic simulations and the variational Peierls Nabarro model. Exploring the core-width and the Peierls stresses of the twinning dislocations is critical in connecting the atomistic scale model to the mesoscale model. Here, we employ the fully anisotropic elasticity formalism and a robust optimization protocol to solve the variational problem. A two-dimensional generalized planar fault energy with negative SFE is obtained in this scheme, and the near-field elastic displacement is estimated.

Methods to evaluate the twin formation energy: comparative studies of the atomic simulations and in-situ TEM tensile tests

Deformation twinning, one of the major deformation modes in a crystalline material, has typically been analyzed using generalized planar fault energy (GPFE) curves. Despite the significance of these curves in understanding the twin nucleation and its effect on the mechanical properties of crystals, their experimental validity is lacking. In this comparative study based on the first-principles calculation, molecular dynamics simulation, and quantitative in-situ tensile testing of Al nanowires inside a transmission electron microscopy system, we present both a theoretical and an experimental approach that enable the measurement of a part of the twin formation energy of the perfect Al crystal. The proposed experimental method is also regarded as an indirect but quantitative means for validating the GPFE theory.

Modeling the interface structure of type II twin boundary in B19′ NiTi from an atomistic and topological standpoint

This study addresses fundamental quandaries in the understanding of Type II twin interface in B19′ NiTi. A combined atomistic-topological approach is proposed to resolve a longstanding debate on the interface structure, affirming the hypothesis of a semi-coherent ledged geometry comprising of disconnected terraces. Atomic registry across the terrace is shown to require interface coherence strains. The twinning plane is shown to be a non-crystallographic virtual boundary separating the strained twin variants. Consequently, the issue of lattice offset arises and is addressed by an atomistic evaluation of interface energetics upon parametric variation of an offset parameter. Required atomic movements for migration of the terrace are established from a crystallographic analysis of the strained interface structure, and validated by a Molecular Statics (MS) simulation of the twin migration segment in the Generalized Planar Fault Energy (GPFE) curve. The GPFE calculation estimates a twinning partial magnitude consistent with an earlier ab initio prediction. This twinning partial serves as a “perfect” interface dislocation which, along with the coherence strain, feed into a topological model causally explaining the known irrational indices of the effective Twin Boundary (TB). A complete mechanistic picture of diffusionless TB migration is presented, the importance of which is discussed.

Effect of solute redistribution on twinnability of twins at a crack tip in Al alloys

The twinnability of twins at a crack tip in Al-X (X = Zn, Li, Ge, Mg, Au, Ag Si, Cu, Sc, Sr, Y, Rb, Zr and La) have been investigated within the framework of the generalized planar fault energy curves by using first-principles calculations. It is found that concentration distribution of solute atom is a key factor affecting the twinnability. Solute atoms under Fermi–Dirac distribution would lead to a greater influence in twinnability than uniform distribution. For most Al alloys, twinnability almost keeps stable, which directly explains the rarity of twins produced in Al alloys. It is significant that the twinnabilities of Al-X (X = Sr, Rb and La) increase continuously with the increasing concentration of Sr, Rb and La atoms. Our results indicate that the atomic size effect plays an important role in the change of twinnability, and atoms whose radius is more than 1.3 times of Al would have more obvious effects on twinnability.

Atomistic Energetics and Critical Twinning Stress Prediction in Face and Body Centered Cubic Metals: Recent Progress

This paper recounts recent advances on the atomistic modeling of twinning in body-centered cubic (bcc) and face-centered cubic (fcc) alloy. Specifically, we have reviewed: (i) the experimental evidence of twinning-dominated deformation in single- and multi-grain microstructures, (ii) calculation of generalized planar fault energy (GPFE) landscapes, and (iii) the prediction of critical friction stresses to initiate twinning-governed plasticity (e.g., twin nucleation, twin–slip and twin–twin interactions). Possible avenues for further research are outlined.

Twinnability of Al–Mg alloys: A first-principles interpretation

Al–Mg alloys are considered to have potentials to form twins during deformation because Mg can reduce the intrinsic stacking fault energy γISFE of Al. Nevertheless, twinning has rarely been found in Al–Mg alloys even subjected to various severe plastic deformation (SPD) techniques. In order to probe the twinning propensity of Al–Mg alloys, first-principles calculations were carried out to investigate the effects of Mg and vacancies on the generalized planar fault energy (GPFE) of Al. It is found that both Mg and vacancies exhibit a Suzuki segregation feature to the stacking fault, and have the influence of decreasing the γISFE of Al. However, γISFE does not decrease and the twinnability parameter τa of Al does not increase monotonically with increasing Mg concentration in the alloy. On the basis of τa evaluated from the calculated GPFE of Al–Mg alloys, we conclude that deformation twinning is difficult for Al–Mg alloys even with a high content of Mg. Besides, the decrease of γISFE caused by the introduction of Mg and vacancies is supposed to have the effect of improving the work-hardening rate and facilitating the formation of band structures in Al–Mg alloys subjected to SPD.

Combined effect of Mg and vacancy on the generalized planar fault energy of Al

By first-principles calculations, a systematic study has been undertaken to investigate the combined effect of vacancies and Mg impurities on the generalized planar fault energy (GPFE) of pure Al. It was predicted that introduction of a single vacancy at the stacking fault plane can decrease the GPFE and enhance twinning propensity of Al. Furthermore, vacancies were shown to exhibit a natural/activated Suzuki segregation feature towards the intrinsic/extrinsic stacking fault of Al, respectively. Along with an increasing vacancy content localized near the deformation plane a noticeable decrease in the intrinsic stacking fault energy γISFE was obtained, which potentially may induce more split-up of dislocations into partials. However, a further increase of twinnability (based on the predicted GPFE curves) with increasing vacancy concentration was not found. More interestingly, we discovered a coupled Suzuki segregation behavior of Mg solutes and vacancies towards the intrinsic stacking fault of Al. A systematic analysis of the twinnability parameter τa on basis of the modified GPFE curves under the influence of Mg solutes and vacancies clearly demonstrates the general difficulty of deformation twinning of Al-Mg alloys. Moreover, a decreased γISFE with Mg alloying as well as with the presence of vacancies may serve, at least partially, to explain the high work-hardening rate and the formation of band structures in Al-Mg alloys processed by severe plastic deformation (SPD).

Impurity effect of Mg on the generalized planar fault energy of Al

Generalized planar fault energy (GPFE) curves are widely used to evaluate the deformation behavior of metals and alloys. In the present work, a systematic analysis of the microscopic plastic deformation mechanism of face-centered cubic Al in comparison to Cu was conducted based on GPFE curves generated via first-principles calculations. Focus has been put on the effects of Mg impurities in terms of local concentration and local atomic arrangement nearby the deformation plane, upon the GPFE curve of Al, with the aim to investigate the twinnability of Al–Mg alloys subjected to plastic deformation. It is found that Mg exhibits a Suzuki segregation feature to the stacking fault of Al, either intrinsic or extrinsic. Mg atoms residing in the stacking fault plane can decrease the intrinsic stacking fault energy γ ISFE and enhance the twinning propensity of Al. However, the γ ISFE value does not decrease monotonically with increasing Mg concentration in the alloy, and a continuous twinnability increase with increasing Mg content is not observed. It is also seen that different local concentrations and atomic configurations of Mg atoms in the vicinity of deformation plane could yield a large variation of γ ISFE and the twinning propensity of Al. It is proposed that Mg alloying cannot substantially enhance the twinning propensity of Al alloys.

Critical Stresses for Twinning, Slip, and Transformation in Ti-Based Shape Memory Alloys

We investigate the effect of Nb and Ta contents on the (i) critical resolved shear stress (CRSS) for the β − α″ transformation, (ii) the CRSS for austenite slip, and (iii) the CRSS for twin nucleation in martensite (α″ phase) that govern shape memory and superelasticity in Ti-based alloys. The critical stresses for slip and twinning are achieved with a modified Peierls Nabarro formalism utilizing generalized stacking fault energy and the generalized planar fault energy (GPFE), respectively, obtained from first-principles density functional theory (DFT) calculations. During the calculation of the twinning stress, we show the importance of the shuffling process in stabilizing and lowering the GPFE curve. Similarly, the transformation stress is obtained with heterogeneous martensite nucleation mechanism incorporating the energy barriers associated with the transformation process. Here, we point to the role of dislocations in the shuffling process during the early stage of transformation. We show that the increase of Ta content raises the CRSS more effectively for the case of slip compared to twinning or transformation. The slip stress and twin stress magnitudes increase with an increase in the unstable fault energy $$\left( {\gamma_{\text{us}} } \right)$$ and unstable twinning fault energy $$\left( {\gamma_{\text{ut}} } \right),$$ respectively. In summary, as the Ta composition increases, the difference between martensite/austenite slip resistance and the transformation/twinning stress widens showing the efficacy of Ta alloying additions.

Alloying Mg with Gd and Y: Increasing both plasticity and strength

The addition of rare elements to Mg enhances mechanical behavior via solution and precipitation strengthening mechanisms. To provide fundamental insight into the underlying mechanisms, we apply density-functional theory (DFT) calculations to systematically study the generalized planar fault energy (GPFE) for pure Mg and its alloys with Gd, Y, and Gd–Y. Special attention is focused on the {0001}〈11¯00〉 basal and {11¯00}〈112¯0〉 prismatic slip systems. Our results show that the addition of Gd and Y in Mg significantly reduces the magnitude of GPFE, in particular for the {11¯00}〈112¯0〉 prismatic slip system. The analysis of the charge density distribution reveals that the predicted reduction in GPFE can be primarily attributed to a decrease of shear resistance between the slip planes. Based on the criterion for the anisotropy of the dislocation mobility and disembrittlement parameter, we demonstrate that alloying Mg with Gd and Y yields lower resistance to slip and hence an improvement in plasticity. Our results also suggest that the strength and plasticity of the Mg–Gd–Y system can be simultaneously enhanced due to charge transfer between Mg and alloying atoms.

Temperature-Dependent Generalized Planar Fault Energy and Twinnability of Mg Microalloyed with Er, Ho, Dy, Tb, and Gd: First-Principles Study

The generalized planar fault energies, Rice criterion ductility, and twinnability of pure Mg and Mg-RE (RE = Er, Ho, Dy, Tb, and Gd) alloys at different temperature have been investigated using density functional theory. It is shown that all the fault energies and twinnability in the same materials decrease with increasing temperature. However, the ductility has the opposite change trend. On the other hand, alloying rare earth elements will generally decrease the fault energies and increase the ductility and twinnability of Mg at different temperature. It is interesting to note that alloying larger atomic radius will enhance the ductility of Mg more easily and alloying smaller radius will make twinning tendency of Mg more easily. Finally, the electron structure further reveals the underlying mechanisms for the reduction of fault energies with the addition of rare earth elements.

Quasicontinuum Analysis of Dislocation Propagation during Nanocontact

Multiscale simulations using the quasicontinuum (QC) method with the embedded-atom method (EAM) potential are performed to investigate the process of nanocontact including sliding and subsequent withdrawal between Ni tip and Au substrate. The multiscale model reveals that deformation twinning in Au substrate is induced not only by the sheer stress but also by the adhesive stress. Combining with the generalized planar fault energy (GPF) curve of Au, the underlying formation mechanism of deformation twinning is studied in detail. During the withdrawal process, the dislocation degeneration and the vacancy evolution are observed.

Modeling of pseudotwinning in Fe3Ga

Pseudotwinning is an important deformation mechanism that can produce reversible deformations similar to the shape memory phenomenon. Pseudotwinning merits further consideration from a modeling viewpoint as it could open new frontiers for discovery of alloys with recoverability of deformation. In this study, we focus on the Fe3Ga (D03 and L12 lattices) with atomistic simulations. We present a pseudotwin nucleation model based on the generalized planar fault energy from first-principles calculations. The minimization of the total energy at the mesoscale associated with pseudotwin nucleation leads to determination of the twinning stress. The low energy barriers and twinning stress demonstrate that pseudotwinning in D03 Fe3Ga is a possible deformation mode, but pseudotwinning is unlikely to occur in L12 Fe3Ga due to the significantly high energy barrier and twinning stress. The predicted twinning stress is compared with experimental measurements, and the results show very good agreement. Hence, we suggest that the results provide a quantitative methodology to understanding and determining pseudotwinning in ordered alloys.

The generalized planar fault energy, ductility, and twinnability of Al and Al—RE (RE = Sc, Y, Dy, Tb, Nd) at different temperatures: A first-principles study

The genearlized planar fault energies of Al and Al—RE (RE = Sc, Y, Dy, Tb, Nd) alloys have been investigated using first-principles methods combined with a quasiharmonic approach. The stacking fault energies, unstable stacking fault energies, and unstable twinning energies decrease slightly with increasing temperature. The ductility parameter D, the relative barrier difference δutus, and the twinnability τa of Al and Al—RE alloys at different temperatures have been determined. It is found that the ductilities of Al and Al alloys are nearly the same and the ductilities increase slightly with increasing temperature. The RE alloying elements make twinning more likely and the twinnabilities of Al and Al alloys decrease with increasing temperature.