Extrinsic Stacking Fault Energy Research Articles

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.

A novel simplified model for measuring the twinnability of face-centred-cubic metals

ABSTRACTTwinnability is a unique property describing the ease with which a metal plastically deforms by twinning relative to dislocation-mediated slip. Based on first-principles calculations, a simple and effective model, including two calculational supercells with three typical generalised stacking fault structures, is proposed to measure the twinnability of face-centred-cubic metals. Here, we investigated the interaction of alloying atoms with generalised stacking faults and their impact on the twinnability of aluminium alloys. It is found that the twin propensity of Al alloy increases with the increasing concentration of Sc and Ti, and a small increase with Y, while the addition of Sr, Zn, Sn and Ga exhibits opposite trends. It is predicted that twins will remain stable once they were formed in Al–Sc alloys on account of the small extrinsic stacking fault energy.

Doping effects on the stacking fault energies of the γ′ phase in Ni-based superalloys**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFB0701502).

The doping effects on the stacking fault energies (SFEs), including the superlattice intrinsic stacking fault and superlattice extrinsic stacking fault, were studied by first principles calculation of the γ′ phase in the Ni-based superalloys. The formation energy results show that the main alloying elements in Ni-based superalloys, such as Re, Cr, Mo, Ta, and W, prefer to occupy the Al-site in Ni3Al, Co shows a weak tendency to occupy the Ni-site, and Ru shows a weak tendency to occupy the Al-site. The SFE results show that Co and Ru could decrease the SFEs when added to fault planes, while other main elements increase SFEs. The double-packed superlattice intrinsic stacking fault energies are lower than superlattice extrinsic stacking fault energies when elements (except Co) occupy an Al-site. Furthermore, the SFEs show a symmetrical distribution with the location of the elements in the ternary model. A detailed electronic structure analysis of the Ru effects shows that SFEs correlated with not only the symmetry reduction of the charge accumulation but also the changes in structural energy.

An investigation concerning generalized stacking fault behavior of AlCoxCrFeNi (0.25 ≤ x ≤ 2) high entropy alloys: Insights from first-principles study

In current study, the generalized stacking fault curves for AlCoxCrFeNi (0.25 ≤ x ≤ 2) high entropy alloys have been successfully estimated to gain a better understanding on the deformation behavior (slip and twinning phenomena) utilizing first-principles study based on density functional theory. Through this method, four main generalized stacking fault energy parameters (unstable, intrinsic, unstable twinning and extrinsic stacking fault energies), the rivalry between twinning and dislocation mediated slip (crack tip twinning, grain boundary twinning, and critical twin stress) as well as the Rice-criterion were reported. It was found that dislocation mediated slip and martensitic transformation presumably overcome the plastic deformation as Co content increases. To further reveal the nature of strength and ductility, investigation of density of states and electron density difference were carried out to reflect how increasing Co content affect the strength and ductility. The above mentioned calculations provide a beneficial guideline for designing AlCoCrFeNi HEAs in relation with superior properties (special harmony between strength and ductility). Amidst all high entropy alloys in this study, AlCo2CrFeNi alloy exhibits a superior balance between ductility and strength.

Tunable stacking fault energies by tailoring local chemical order in CrCoNi medium-entropy alloys

High-entropy alloys (HEAs) are an intriguing new class of metallic materials due to their unique mechanical behavior. Achieving a detailed understanding of structure-property relationships in these materials has been challenged by the compositional disorder that underlies their unique mechanical behavior. Accordingly, in this work, we employ first-principles calculations to investigate the nature of local chemical order and establish its relationship to the intrinsic and extrinsic stacking fault energy (SFE) in CrCoNi medium-entropy solid-solution alloys, whose combination of strength, ductility, and toughness properties approaches the best on record. We find that the average intrinsic and extrinsic SFE are both highly tunable, with values ranging from -43 to 30 mJ⋅m-2 and from -28 to 66 mJ⋅m-2, respectively, as the degree of local chemical order increases. The state of local ordering also strongly correlates with the energy difference between the face-centered cubic (fcc) and hexagonal close-packed (hcp) phases, which affects the occurrence of transformation-induced plasticity. This theoretical study demonstrates that chemical short-range order is thermodynamically favored in HEAs and can be tuned to affect the mechanical behavior of these alloys. It thus addresses the pressing need to establish robust processing-structure-property relationships to guide the science-based design of new HEAs with targeted mechanical behavior.

Structural modifications due to interface chemistry at metal-nitride interfaces.

Based on accurate first principles density functional theory (DFT) calculations, an unusual phenomenon of interfacial structural modifications, due to the interface chemistry influence is identified at two metal-nitride interfaces with strong metal-nitrogen affinity, Al/TiN {111} and Al/VN {111} interfaces. It is shown that at such interfaces, a faulted stacking structure is energetically preferred on the Al side of the interface. And both intrinsic and extrinsic stacking fault energies in the vicinity Al layers are negligibly small. However, such phenomenon does not occur in Pt/TiN and Pt/VN interfaces because of the weak Pt-N affinity. Corresponding to structural energies of metal-nitride interfaces, the linear elasticity analysis predicts characteristics of interfacial misfit dislocations at metal-nitride interfaces.

Planar fault energies of copper at large strain: A density functional theory study

We present density functional theory calculations of the extrinsic stacking fault energy γesf, twin fault energy γtf, and unstable stacking fault energy γusf of copper under large strains, up to ± 10%. The calculated values of γesf, γtf, and γusf for unstrained Cu are 41.8 mJ/m2, 20.2 mJ/m2, and 163.4 mJ/m2, respectively, in good agreement with experimental data and theoretical results. Four different types of strains are applied: (i) volumetric strain; (ii) uniaxial strain perpendicular to the fault plane; (iii) uniaxial strains parallel to the fault plane; and (iv) shear strains across the fault planes. We find that γesf, γtf, and γusf are strongly dependent on the magnitude and type of strain, challenging the common conception that they are constant material properties. The predicted strong strain dependencies provide useful insight into the deformation mechanisms of copper under high pressure and shock conditions and provide essential data to improve current Cu empirical potentials.

First-principles studies of defects, mechanical properties and electronic structure of Cr-based Laves phases

First-principles calculations have been performed to investigate the defects, mechanical properties and electronic structure of MCr 2 (M = Nb, Ti and Zr) Laves phases. The results show that the ternary additive of V preferentially substitutes the Cr site and Zr the Nb site in NbCr 2. W has a weak site preference on the Cr site in NbCr 2. The ternary site substitutions are related to the electronic structure of NbCr 2. Further calculations of the densities of states and charge density distribution of TiCr 2 show that a strong covalent bonding between the small atoms (Cr) along the Kagome net forms a tetrahedral electronic network, which is a common feature for the electronic structure in Laves phases. Mechanical properties, such as elastic constants, elastic moduli and stacking fault energies of ZrCr 2, were calculated additionally. The intrinsic and extrinsic stacking fault energies of ZrCr 2 are found to be 112 mJ m −2 and 98 mJ m −2, respectively.

Ab initio calculation of the phase stability, mechanical properties and electronic structure of ZrCr2 Laves phase compounds

Ab initio calculations have been used to investigate the phase stability, mechanical properties and electronic structure of ZrCr2 Laves phase compounds, based on the method of augmented plane waves plus local orbitals with the generalized gradient approximation. The calculated lattice constants for the C15, C36 and C14 structures are in good agreement with experimental values. The calculation of heats of formation showed that C15 is a ground-state phase, whereas C36 is an intermediate phase and C14 the high-temperature phase. The elastic constants and elastic moduli for the C15 structure were calculated systematically and compared with experiments and previous theoretical calculations. The intrinsic and extrinsic stacking fault energies are found to be 112 and 98 mJ m−2, respectively. The equilibrium separations between Schockley are also predicted using the calculated elastic moduli and stacking fault energies. Finally, the calculated electronic structures of these Laves phases are discussed based on these results.

Tight-binding calculations of stacking energies and twinnability in fcc metals

We calculate the material properties needed to evaluate the tendency of a face-centered-cubic (fcc) metal to plastically deform by forming crystallographic twins as opposed to dislocation-mediated slip. We refer to this property as the twinnability of the metal. We use a formulation for twinnability derived from a coupling of continuum mechanics with an atomistic stress-slip relation. The essential quantities for evaluating the twinnability are elastic constants, which are measurable experimentally, and energies for various stacking sequences of the fcc (111) planes. These stacking sequences include the intrinsic stacking fault configuration as well as the unstable-stacking energy and unstable-twinning energy configurations which can only be determined computationally. We use a tight-binding model to evaluate the necessary stacking energies, as well as the extrinsic stacking fault energy and twin-boundary energy, for eight fcc metals. The accuracy of the tight-binding parameters is established by comparing them with first-principles values obtained through an extensive study of the literature. The results of the literature survey are included in the paper as a resource for the reader. We show that the ranking of these metals in order of twinnability agrees with available experimental results. We reproduce the low incidence of deformation twinning in Al, and explain it in terms of the material parameters using an approximation to the twinnability expression. We also predict that Pd, which has not been studied experimentally, should twin as easily as Cu.

Extrinsic stacking faults and twinning in hadfield manganese steel single crystals

University of Paderborn, Lehrstuhl fu¨r Werkstoffkunde, D-33095 Paderborn, Germany(Received June 26, 2000)(Accepted in revised form August 21, 2000)Keywords: Twinning; Austenite; Solid solution strengthening; Dislocation mobility; Extrinsicstacking faultsIntroductionExtrinsic stacking faults (SFs) have not been commonly observed in fcc materials. In some specialoccasions, pairs of extrinsic-intrinsic SFs are reported in the low stacking fault energy (SFE) copper andsilver alloys [1]. However, extrinsic SFs can form in elemental and compound semiconductors withprior multiple slip activation [2]. The basic driving factors for the extrinsic extension of partialdislocations in these materials are: a) the different mobility of partial dislocations because of theinherent crystal structure [3], b) lower extrinsic stacking fault energy [4], c) high applied stress levelsbecause of predeformation and low temperatures. The purpose of this work is to demonstrate extrinsicSFs in certain crystallographic orientations in a low SFE steel.Hadfield steel is an fcc material (g

First-principles calculation of stacking fault and twin boundary energies of Cr2Nb

Abstract The stacking fault and twin boundary energies of C15 Cr2Nb are calculated by the first-principles local-density-functional approach. It is found that the intrinsic and extrinsic stacking fault energies are 116 and 94mJm−2, respectively, and the twin boundary energy is 39mJm−2. The lower extrinsic stacking fault energy is consistent with the fact that the C36 structure has a lower energy than the C14 structure. The calculated stacking fault energies at 0K are larger than the experimental values available in the literature. The equilibrium separations between Shockley partials based on the calculated elastic constants and stacking fault energies are also calculated.

Elastic properties and stacking fault energies of Cr 2Ta

The elastic moduli, stacking fault and twin boundary energies of C15 Cr 2Ta are calculated by first-principles local-density-functional approach. Similarly to the case of Cr 2Nb, Cr 2Ta is characterized by a low twin boundary energy (33 mJ/m 2). On the other hand, the intrinsic and extrinsic stacking fault energies are found to be 88 and 83 mJ/m 2, respectively. Using the results of elastic constants and stacking fault energies, we predict the equilibrium separation between Shockley partials. The results of Cr 2Ta are compared with those of Cr 2Nb.

Evaluation of the extrinsic and intrinsic stacking-fault energies of GaP

Abstract Stacking-fault double ribbons have been observed by transmission electron microscopy in undoped GaP films grown on Si. Values of the extrinsic and intrinsic stacking-fault energies of 40.5 ± 3 mJ m−2 and 43.4 ± 2 mJ m−2, respectively, were obtained from measurements of the widths of the individual ribbons. The ratio of the intrinsic to extrinsic stacking-fault energy was found to be 1.07 ± 0.05.

ASW first principles calculation of the intrinsic and extrinsic stacking fault energies in aluminum

The ASW method is applied for the first principles calculation of the stacking fault energies in aluminum. In the procedure the stacking faults are placed in a supercell which is repeated periodically. By choosing the supercell large enough (eight and ten atomic layers for intrinsic and extrinsic stacking fault energy calculations) so that the interaction between faults in neighbouring cells can be omitted, the energy of one stacking fault is calculated. The calculated stacking fault energies of aluminum Γ ISF =154 erg cm 2 and Γ ESF =138 erg cm 2 are in good agreement with the estimated value, Γ ( A1 )=163 erg cm 2 , from experiments.

Observation of double ribbons in GaAs and AlGaAs

Abstract Stacking-fault double-ribbons have been observed in GaAs; a compound semiconductor. Values for the extrinsic and intrinsic stacking-fault energies of 41·2±5 mJm−2 and 46·5±6 mJm−2, respectively, were obtained from the widths of the stacking-fault ribbons. The ratio of the intrinsic to extrinsic stacking-fault energy is found to be 1·13±0·08.

Defects and Interfaces in GaAs Grown on Si

AbstractThe characterization of semiconductor epilayers by electron microscopy has revealed many different defects in the epilayer. Observations on three representative examples from GaAs epilayers grown on Si are presented. Double-ribbons, which are formed as a result of dislocation interactions near the heterojunction, have been used to determine the intrinsic and extrinsic stacking-fault energies in GaAs. Inverted stacking-fault pyramids have been observed which have nucleated in the epilayer and grown outward to the surface. Finally, differences in the growth rates of different twins are recorded by using AlGaAs layers to preserve the growth surface at various stages during epilayer growth.

Extrinsic and intrinsic nodes in the gamma prime phase of a single crystal superalloy

Transmission Electron Microscopy has been used to examine the interaction of superdislocations to form nodes and networks in the γ′ phase of the cold deformed and annealed single crystal superalloy, SRR99. The formation of these “super nodes” is traced through various metastable configurations to form, eventually, extended “super nodes” which contain superlattice stacking faults. Several dislocations interacting are observed to form networks of such nodes having alternately intrinsic and extrinsic character. The extrinsic supernodes are found to be larger than the intrinsic supernodes with the implication that the superlattice extrinsic stacking fault energy is lower than the superlattices intrinsic fault energy.

The generation of point defects during the oxidation of silicon

Abstract Oxidation of silicon is known to cause the climb of faulted defects and to influence the rate of impurity diffusion. These effects have been related to the. generation of excess point defects at the oxidizing interface. The paper describes experiments designed to determine the point defect concentrations at the oxidizing interface using the loop annealing technique. The loops were initially introduced into silicon slices by ion-implantation and annealing and then the growth or shrinkage of the loops was measured in thin foils following annealing treatments using oxidizing or non-oxidizing atmospheres. Vacuum annealing caused loop shrinkage from which the coefficient of self-diffusion and the extrinsic stacking fault energy were determined. These values are in good agreement with values obtained by other techniques. Comparison of these shrinkage rates with the growth rates obtained during an oxidizing anneal enabled the ratio of the interstitial concentration at the oxidizing interface to the bulk...

Direct TEM determination of intrinsic and extrinsic stacking fault energies of silicon

Abstract The intrinsic and extrinsic stacking fault energies of silicon have been determined from images of double ribbons obtained using the weak–beam method of electron microscopy. The ribbons occurred in distorted regions of small–angle twist boundaries on {111} planes prepared by welding. The results are compared with values obtained from isolated dislocations in the screw and edge orientation in the same sample, which were found to be consistently lower than the values obtained from double ribbons. It is found that, contrary to other recent work, the ratio γMin γMex is actually only ∼ 14% greater than unity.