Generalized Stacking Fault Energy Curves 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.

Coarse-grained molecular dynamic model for metallic materials

It is not yet straightforward to expand the time scale of molecular dynamics simulations in spite of recent progress in high-performance computing since time series of atomic motion cannot be parallelized easily. In this study, a novel coarse-grained molecular dynamic model is employed to scale up the time range of atomistic simulations for metallic materials. Basic mechanical and thermal properties of nickel including elastic constants, bulk modulus, shear modulus, Young modulus and melting point are well reproduced with the definition of the coarse-grained model. Moreover, it was found that single crystal plasticity occurring in the coarse-grained model compares very well with all-atom molecular dynamics simulations. This can be explained by the equality of the ratio in the generalized stacking fault energy curve between coarse-grained and all-atom models. Furthermore, a large-scale coarse-grained molecular dynamics simulation of the crystal growth was performed on the supercomputer as a practical example of the acceleration of simulation, in which a submicron-order crystal appears from the seed crystal in the undercooled melt. It is expected that the coarse-grained molecular dynamics method has a variety of applications in the future since it can handle calculations on such a large scale with relative ease.

Phase field modeling of dislocations and obstacles in InSb

We present a phase-field dislocation dynamics (PFDD) model informed by first-principle calculations to elucidate the competitive dislocation nucleation and propagation between the glide and shuffle sets in InSb diamond cubic crystal. The calculations are directly informed with generalized stacking fault energy curves on the (111) slip plane for both the “glide set,” with the smaller interplanar spacing, and the “shuffle set,” with the larger interplanar spacing. The formulation also includes elastic anisotropy and the gradient term associated with the dislocation core. The PFDD calculations show that under no stress the equilibrium structure of screw glide set dislocations dissociates into Shockley partials, while those of the shuffle set dislocations do not dissociate, remaining compact. The calculated dislocation core widths of these InSb dislocations agree well with the measured values for other semiconductor materials, such as Si and GaN. We find that a shuffle set dislocation emits from a dislocation source at an applied stress about three times smaller than that needed to emit leading and trailing partials successively on the glide set plane. Once the partial dislocations in the glide set are emitted, they propagate faster than the shuffle set perfect dislocation at the same stress level.

Mo and Ta addition in NbTiZr medium entropy alloy to overcome tensile yield strength-ductility trade-off

• The 0.1 M addition of Mo and Ta increased yield strength to 1060 ± 18 MPa without compromising ductility. • The improved ductility is attributed to lowered unstable stacking fault energy of {112}<111> slip system in NbTiZr(MoTa) x . • The MEAs in this study showed better wear resistance than traditional alloys. In this study, single-phase NbTiZr and NbTiZr(MoTa) 0.1 medium-entropy alloys (MEAs) were investigated for their use in biomedical implants. The alloys were prepared by arc melting, and were then cold-rolled, annealed, and characterized in terms of phase analysis, mechanical properties, fractography, and wear resistance. Both alloys showed a single body-centered cubic phase with superior mechanical, and tribological properties compared to commercially available biomedical alloys. Mo and Ta-containing MEAs showed higher tensile yield strength (1060 ± 18 MPa)) and higher tensile ductility (∼20%), thus overcoming the strength–ductility trade-off with no signs of transformation-induced plasticity, twinning, or precipitation. The generalized stacking fault energy (GSFE) calculations on the {112}<111> slip system by the first-principles calculations based on density functional theory showed that the addition of less than 0.2 molar fraction of Mo and Ta lowers the GSFE curves. This behavior posits the increase in ductility of the alloy by facilitating slips although strength is also increased by solid solution strengthening. The wear resistance of both alloys against hardened steel surfaces was superior to that of commercial biomedical alloys. Thus, we concluded that NbTiZr(MoTa) 0.1 MEA with good tensile ductility is a potential candidate for biomedical implants.

Modified Embedded‐Atom Method Potentials for the Plasticity and Fracture Behaviors of Unary HCP Metals

AbstractModified embedded‐atom method (MEAM) potentials have been widely used in molecular dynamics (MD) simulations to describe the interatomic interactions in metallic systems. However, conventional MEAM potentials are almost exclusively fit to a limited number of key single‐value properties, limiting the predictability of MD simulations, especially for complex hexagonal‐close‐packed (HCP) metals with multiple slip systems. Here, three MEAM potentials for unary HCP metals (Mg, Co, and Ti) are fit to conventional target properties, as well as continuous‐energy curves and their gradients obtained from density‐functional theory calculations. These targets include the lattice parameters, cohesive energy, elastic constants, and surface energies as well as the cohesive energy curve, basal plane decohesion energy curve, and generalized stacking fault energy curves for basal, prismatic, pyramidal I, and pyramidal II planes. These interatomic potentials demonstrate excellent reproduction of relevant properties and enable accurate MD simulations of volumetric and plastic deformations, as well as fracture in Mg, Co, and Ti HCP metals. Importantly, the interatomic potentials demonstrate better performance than all existing EAM/MEAM potentials readily available from the literature.

Effect of alloying elements on stacking fault energies and twinnabilities in high‐entropy transition‐metal carbides

AbstractTwinning is a fundamental mechanism behind the simultaneous increase in the strength and ductility of high‐entropy alloys. Similar approaches may contribute to the remarkable improvements of the mechanical properties of high‐entropy ceramics. In this study, the stacking fault energies (SFEs) and twinnabilities of a novel category of ZrNbTa‐based high‐entropy transition‐metal carbides (HETMCs) are investigated in terms of their generalized stacking fault energy curves (γ‐curves) via first‐principle calculations. The γ‐curves show that dislocation nucleation in ZrNbTa‐based HETMCs occurs more easily than that of unary transition metal (TM, TM = Zr, Nb, Ta, Hf, Ti, V) carbides. When a pre‐existing intrinsic stacking fault (ISF) is considered, C‐ vertices (TM‐ mirror) twinning fault (TF) more likely forms and TF may be more stable than ISF. The stable SFEs of C‐ vertices ISF and TF decrease with the addition of Hf, Ti, and V atoms to (ZrNbTa)C owing to the severe local lattice distortion. The calculated barrier energies and twinnabilities further indicate that twinning is possible for the selected ZrNbTa‐based HETMCs. Theoretical twinnabilities (τa) decrease in the following sequence: (ZrNbTa)C &gt; (ZrNbTaHfTi)C &gt; (ZrNbTaHf)C &gt; (ZrNbTaHfTiV)C. Thus, the addition of Hf, Ti, and V atoms to (ZrNbTa)C may decrease the twinning probability. This study may be used as a guide for the design of twinning‐induced plasticity HETMCs with excellent mechanical properties.

Modeling twin boundary structures in body centered cubic transition metals

The twin boundary structures in the BCC transition metals are determined by analyzing twin boundary generalized stacking fault energy curves and complete structural relaxation of the twinned crystals utilizing both interatomic potentials and density functional theory calculations. In contrast to the crystallographic description of twin elements in BCC metals, the pure reflection twin boundary structure has been found to be unstable in all seven metals considered. Instead, this work identifies three possible metastable twin boundary structures that are distorted forms of the pure reflection twin boundary structure and isosceles twin boundary structure previously proposed: a distorted reflection, distorted isosceles, and scalene structures. The DFT simulations reveal that the stability and energetic preference to form these structures differs between the Group 5 and Group 6 BCC metals despite having the same structure and general type of bonding. This work ates how these equilibrium structures and their relative stability affect the commonly reported twinning generalized stacking fault energy curves and explain why these curves (as previously computed) always have cusps.

Asymmetric equilibrium core structures of pyramidal-II 〈c+a〉 dislocations in ten hexagonal-close-packed metals

The structures of pyramidal-II $\ensuremath{\langle}c+a\ensuremath{\rangle}$ dislocations, one of the most important defects in structural hexagonal-close-packed (HCP) metals, have not been fully characterized for many of the HCP metals in use today. Here, we employ ab initio informed phase-field dislocation dynamics to determine the minimum energy structure of pyramidal $\left\{\overline{1}\overline{1}22\right\}\ensuremath{\langle}11\overline{2}3\ensuremath{\rangle}$ dislocations in ten HCP metals, including Be, Co, Mg, Re, Ti, Zn, Cd, Hf, Y, and Zr. As input for the simulations, we calculate, using first-principles density functional theory, the $\left\{\overline{1}\overline{1}22\right\}$ generalized stacking fault energy (GSFE) curves for all ten metals. From these calculations, it is found that magnetism in Co is necessary for achieving a local minimum in the GSFE curve. We observe in simulations that edge and screw character dislocations split into two partials separated by a low-energy intrinsic stacking fault. The splitting distance is shown to scale inversely with the local minimum energy normalized by the product of its shear modulus and Burgers vector. Interestingly, some HCP metals exhibit an asymmetric structure, with either unequal partial Burgers vectors or widths, in contrast to the symmetric configuration expected from linear elastic dislocation theory. We explain these structures by properties of the local maxima in their GSFE curves. Metals with larger degrees of elastic anisotropy result in dislocations with larger splitting distances than would be expected under the commonly used assumption of elastic isotropy. These findings on the sizes and asymmetry in the structures of pyramidal-II $\ensuremath{\langle}c+a\ensuremath{\rangle}$ dislocations are fundamental to understanding how these dislocations glide and interact or react with other defects when these metals are mechanically strained.

Modified embedded-atom method potentials for the plasticity and fracture behaviors of unary fcc metals

The predictability of molecular dynamics simulations on the plasticity and fracture behaviors of metals is critically dependent on the accuracy of the employed interatomic potential. Here we present an approach to fitting modified embedded-atom method (MEAM) interatomic potentials to several key properties obtained from first-principles calculations and literature data that govern the continuous mechanistic processes in pure unary fcc Ni, Al, and Cu metals. Along with the commonly used lattice and elastic properties, our MEAM potentials are fitted to the cohesive energy curve, the decohesive energy curve, and the generalized stacking fault energy curve, which are the key properties governing the lattice response to volumetric, fracture, and shear deformations. We further demonstrate that these potentials are able to accurately predict the experimental values for a range of other mechanically relevant properties. Importantly, the potentials presented here outperform all existing EAM/MEAM interatomic potentials readily available from the literature and thus enable more accurate simulations of plasticity and fracture behavior of unary fcc metals.

Simultaneous twinning and microband formation under dynamic compression in a high entropy alloy with a complex energetic landscape

High entropy alloys (HEAs) have been the subject of significant research in recent years due in part to their excellent mechanical properties and unique microstructure. Chemical disorder in these alloys is thought to lead to a complex energetic environment that affects the nucleation and movement of dislocations. In this study the development of deformation substructures is assessed in the Cantor HEA (CoCrFeMnNi) due to quasistatic and dynamic compression. Scanning and transmission electron microscopy (SEM/TEM) techniques are used to image and quantify dislocation density. When increasing the strain rate from 10−3 s−1 to 5000 s−1 we observe an increase in the overall dislocation density which leads to the formation of deformation twins. Further at a rate of 8000 s−1, both deformation twins and microbands become operative plasticity modes, which are usually associated with different extremes of stacking fault energy. To relate this plastic response to chemical disorder, atomistic calculations are used to compute the generalized stacking fault energy curve and approximate the temperature dependence of the intrinsic stacking fault energy for the Cantor alloy, which reveals significant local variation in these critical energetic parameters associated with dislocation and twinning behaviors.

Effect of Cr on the generalized stacking fault energy of impure doped Ni (111) surface: a first-principles study

In the present work, a systematic analysis of the microscopic plastic deformation mechanism and mechanical properties of interstitial impurities (H, O, N, S, and P) and Ni doped, or not doped, with Cr, was conducted based on generalized stacking fault energy curves generated via first-principles calculations. Focus has been put on the effects of Cr on plastic deformation for Ni doped interstitial impurities, upon the GPFE curve, with the aim to investigate the effects of Cr on the deformation mode and mechanical properties for doped Ni systems. It is found that a solid solution of Cr caused the tendency of partial dislocation in Ni. The evaluation of the Rice criterion reveals that Cr tends to decrease the ductility in Ni, and it cannot reverse interstitial H promoting the probability of cleavage fracture in Ni, while increases the ductility of O, P and S doped Ni, particular in O doped Ni, due to increasing the value of ductility D remarkably, so possibly changes the tendency of cleavage fracture. Besides, the solid solution of Cr is beneficial in promoting the dissociation of dislocation into fragments more easily in Ni, and enhances dislocation nucleation, while O, N, and S impurities have a slower rate of partial dislocation emission in Ni when interacting with Cr. Furthermore, Cr promotes the probability of twinning in Ni, and probably switches the deformation mechanism of H doped Ni from dislocation mediated slipping to twinning. Our study provides important insights toward the understanding and control of dislocation dynamics in doped Ni.

Simultaneous Twinning and Microband Formation Under Dynamic Compression in a High Entropy Alloy with a Complex Energetic Landscape

High entropy alloys (HEAs) have been the subject of significant research in recent years due in part to their excellent mechanical properties and unique microstructure. Chemical disorder in these alloys is thought to lead to a complex energetic environment that affects the nucleation and movement of dislocations. In this study we assess the development of deformation substructures in the Cantor HEA (CoCrFeMnNi) due to quasistatic and dynamic compression. Scanning and transmission electron microscopy (SEM/TEM) techniques are used to image and quantify dislocation density. When increasing the strain rate from 10-3 s-1 to 5000 s-1 we observe an increase in the overall dislocation density which leads to the formation of deformation twins. Further at a rate of 8000 s-1, both deformation twins and microbands become operative plasticity modes, which are usually associated with different extremes of stacking fault energy. To relate this plastic response to chemical disorder, atomistic calculations are used to compute the generalized stacking fault energy curve and approximate the temperature dependence of the intrinsic stacking fault energy for the Cantor alloy, which reveals significant local variation in these critical energetic parameters associated with dislocation and twinning behaviors.

Atomic-level calculations and experimental study of dislocations in InSb

Plastic deformation in InSb single crystals is governed by the motion of dislocations. Since InSb has a diamond cubic lattice, it possesses two sets of slip planes: a shuffle set and a glide set. Transmission electron microscopy analysis of deformed bulk single crystals shows that, at low temperatures (&amp;lt;20 °C), dislocations have narrow cores, while at higher temperatures, they have extended cores. However, it remains unclear to which slip plane set these dislocations belong. In this paper, by combining experiments and atomic-level calculations, we show that dislocations with narrow and extended cores, respectively, belong to the shuffle and glide sets. The conclusion is reached by calculating the generalized stacking fault energy curves and ideal shear stresses using density functional theory calculations and the intrinsic stacking fault width associated with dislocations using atomistic simulations. It is also found that while the shuffle set dislocations are easier to activate at lower temperatures, dislocations on the glide set become dominant at higher temperatures.

Modeling of solute hydrogen effect on various planar fault energies

The strength, plasticity and ductility-brittleness transition of metals are often governed by various planar fault energies. Due to interactions between the solute hydrogen (H) and the planar faults, the planar fault energies are heavily affected in the H-charged metals. An accurate quantitative description of the H-affected planar fault energies is essential for us to understand correctly the H-induced plasticity mechanism in metals. In this paper, a reliable atomistic modeling method is s2uggested to calculate quantitatively the effect of solute H on four frequently-used fault energies. The computed results show that solute H can increase the unstable stacking fault energy but decrease the other three, and the fault energies are linearly related to the equilibrium hydrogen concentration up to 0.020. In addition, the generalized stacking fault energy curves of the H-charged Ni in the <112> and <110> directions are also computed to construct the γ-surfaces. Finally, the influence of pre-stress on the unstable and stable stacking fault energies is discussed in detail. These quantitative results are helpful to understand the dislocation/twin-dominated plastic mechanisms in the H-charged metals and to develop the H-affected discrete dislocation dynamic (DDD) and crystal plasticity (CP) algorithms.

Alloying effects on the plasticity of magnesium: comprehensive analysis of influences of all five slip systems

Low plasticity has been a major issue for the application of Mg alloys. Here, based on the generalized stacking fault energy curves and Arrhenius equation, we systematically study alloying effects on the stacking fault energies and the activation probability of basal and non-basal 〈a〉, and pyramidal 〈c + a〉 slip systems in twenty-one Mg alloys. Our results reveal that activation of 〈c + a〉 slip systems on pyramidal II plane can significantly improve the plasticity. For example, Ca is found to promote the activation probability of this slip system by one order of magnitude and dramatically improve the plasticity of Mg.

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

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

Plastic deformation in zinc-blende AlN under nanoindentation: A molecular dynamics simulation

Using molecular dynamics (MD) simulations, we studied the mechanical response and nanostructure evolution of aluminum nitride with zinc-blende structure (zb-AlN). The defect types and structural evolutions as well as the formation and propagation of prismatic loops were discussed. The generalized stacking fault energy (GSFE) was also calculated to explain the glide of dislocations. It showed that perfect dislocations with Burgers vectors b = 1/2〈1 1 0〉 and Shockley partial dislocations with b = 1/6〈1 1 2〉 occur simultaneously for the indentation on (1 1 0) and (1 1 1) planes. The indentation force-depth (P-h) curve exhibits great compliance compared with that determined by the Hertz theory in the elastic phase. And the first three main drops on the P-h curve are related to dislocation nucleation and expansion. Moreover, a “lasso”-like formation mechanism of prismatic loops was found and the GSFE curves were also analyzed to assess the dislocation slips in zb-AlN. It was found that the dominant dislocation is of shuffle-set with Burgers vector b = 1/2 〈1 1 0〉, by comparing the GSFE along 111<1¯10> with that along 111<112¯>.

{110} planar faults in strained bcc metals: Origins and implications of a commonly observed artifact of classical potentials

Large-scale atomistic simulations with classical potentials can provide valuable insights into microscopic deformation mechanisms and defect-defect interactions in materials. Unfortunately, these assets often come with the uncertainty of whether the observed mechanisms are based on realistic physical phenomena or whether they are artifacts of the employed material models. One such example is the often reported occurrence of stable planar faults (PFs) in body-centered cubic (bcc) metals subjected to high strains, e.g., at crack tips or in strained nano-objects. In this paper, we study the strain dependence of the generalized stacking fault energy (GSFE) of {110} planes in various bcc metals with material models of increasing sophistication, i.e., (modified) embedded atom method, angular-dependent, Tersoff, and bond-order potentials as well as density functional theory. We show that under applied tensile strains the GSFE curves of many classical potentials exhibit a local minimum which gives rise to the formation of stable PFs. These PFs do not appear when more sophisticated material models are used and have thus to be regarded as artifacts of the potentials. We demonstrate that the local GSFE minimum is not formed for reasons of symmetry and we recommend including the determination of the strain-dependent (110) GSFE as a benchmark for newly developed potentials.

Micropillar compression deformation of single crystals of Mo5SiB2 with the tetragonal D8l structure

The deformation behavior of single crystals of Mo5SiB2 (so-called T2 phase) with the tetragonal D8l structure has been investigated by micropillar compression at room temperature as a function of crystal orientation and specimen size. The dissociation scheme and glide plane (actual atomic layers) of the identified dislocations have been investigated both experimentally through atomic-resolution scanning transmission electron microscopy imaging of their core structures and theoretically by first-principles calculations of the relevant generalized stacking fault energy curves. Although plastic flow is observed only above 1500 °C even for single crystals in the bulk form, plastic flow is observed at room temperature in a wide range of crystal orientation in the micropillar form, and three different slip systems, (001)<100>, {110}<11¯0> and {01¯1}<111>, are identified to be operative in Mo5SiB2 at room temperature. Although (001)<100> slip was predicted by calculation in the past, the other two slip systems are identified for the first time. The values of critical resolved shear stress (CRSS) for the three slip systems are extremely high all exceeding 2 GPa. The CRSS value for each slip system increases with the decrease in the specimen size, following the inverse power-law relationship with an exponent much smaller than those reported for FCC and BCC metals. The <100> dislocation on (001) and the <11¯0> dislocation on {110} are observed to dissociate into two collinear partials on their slip plane, while the 1/2<111> dislocation on {01¯1} does not make any apparent dissociation, all of which are consistently confirmed by experiment and theoretical calculation.

Effect of β-stabilizer elements on stacking faults energies and ductility of α-titanium using first-principles calculations

The effect of W, Mo, V, Ta, and Nb, five common β-stabilizing substitutional elements, on α-Ti stacking fault energy has been studied using first principle calculations. The generalized stacking fault energy (GSFE) curves have been determined for different concentrations of β-stabilizers at the fault plane using supercells with up to 360 atoms. Both basal and prismatic slip systems with the stable (γSF) and unstable (γUSF) stacking faults and twinning fault energies were determined. All the alloying elements reduce the stacking fault energy for Ti for both basal and prismatic slip. At higher concentration of 25 at. % of V, Ta, and Nb at the slip plane, the basal slip becomes more favorable than the prismatic slip in Ti. Ti-Mo and Ti-W systems also show a significant shift in the GSFE curve towards a higher shear deformation strain along 〈011¯0〉 due to the change in bond character between Ti and those two elements. Using Rice criterion, which employs γS/γUSF ratio to estimate ductility, we show that all the alloying elements likely improve the ductility of α-Ti with Ti-25 at. % Nb exhibiting the most ductile behavior. However, according to the Tadmor and Bernstein model, all the alloying elements considered here do not improve the partial dislocation emission or the twinning propensity in spite of decreasing the stacking fault energies for α-Ti and. Hence, a better empirical model that incorporates changes in the character of directional bonding upon alloying is needed to estimate how alloying influences ductility in hcp metals.