Superlattice Intrinsic Stacking Fault Energy Research Articles

Effects of alloying elements on the super-lattice intrinsic stacking fault energy and ideal shear strength of Ni3Al crystals

The effects of alloying elements (Re,W,Ti,Ta,andMo) on the super-lattice intrinsic stacking fault energy and ideal shear strength (σmax) of Ni3Al crystals at 0 K was studied through first-principles calculation. The calculated formation enthalpy of point defects reveals that single solute atoms (i.e., Re,W,Ti,Ta,andMo) tend to occupy the Al site, while solute–solute complex defects (i.e., Re-Re, Re-W, Re-Mo, Re-Ta, Re-Ti, W-Mo, W-Ta, W-Ti, Mo-Ta, Mo-Ti, and Ta-Ti) tend to occupy the Al-Al site. The addition of single solute atom can increase the unstable stacking fault energy and ideal shear strength (σmax) of perfect Ni3Al crystals. Therefore, the doping of a single solute atom is beneficial for the creep strengthening of Ni3Al crystals. Compared with the doping of W,Ti,Ta,andMo, the doping of Re can more effectively impede the nucleation and movement of dislocations of Ni3Al crystals. Through the careful comparison of the creep properties of Ni3Al crystals with solute–solute complex defects, a conclusion can be drawn that the doping of alloy elements W and Re exhibit similar strengthening effects on the creep properties of Ni3Al crystals. W can be preliminarily predicted to replace part of Re in Ni3Al crystals without affecting creep properties. In addition, comprehensive evaluation reveals that the weak interaction between solute–solute complex defects should improve the strengths of Ni3Al crystals to a certain extent.

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.

When a defect is a pathway to improve stability: a case study of the L12 Co3TM superlattice intrinsic stacking fault

Effect of solutes of transition metals (TM = Cr, Fe, Hf, Mn, Mo, Nb, Ni, Pt, Rh, Ru, Re, Ta, Ti, V, W, Y and Zr) on the local phase transition between the L12 and D019 structures in superlattice intrinsic stacking fault (SISF) of Co3TM has been investigated. All the models employed herein, i.e. (1) the SISF-containing supercell, (2) the axial nearest-neighbor Ising (ANNI) model, and (3) both the L12- and D019-containing (L12 + D019) supercell, yield the same result regarding the stability of SISF in L12-type Co3TM. In the view of bonding charge density, the atomic and electronic basis of local D019 phase transition in the SISF fault layers of Co3TM are revealed. Especially, the negative SISF energy predicted by the L12 + D019 model suggests that both the SISF fault layers (i.e. the local D019 structure) and the L12 phase of Co3TM can be stabilized through a coupling interaction between the fault layers and the solutes, paving a pathway to stabilize Co-base superalloys via Co3TM precipitate. Moreover, the consist results of ESISF via the ANNI model with the classical SISF-supercell method utilized in first-principles calculations supports the approach to efficiently distinguish various planar faults and predict their corresponding energies, such as SISF, superlattice intrinsic stacking fault, anti-phase boundaries, and so on.

Temperature Effects on the Elastic Constants, Stacking Fault Energy and Twinnability of Ni3Si and Ni3Ge: A First-Principles Study

The volume versus temperature relations for Ni 3 Si and Ni 3 Ge are obtained by using the first principles calculations combined with the quasiharmonic approach. Based on the equilibrium volumes at temperature T, the temperature dependence of the elastic constants, generalized stacking fault energies and generalized planar fault energies of Ni 3 Si and Ni 3 Ge are investigated by first principles calculations. The elastic constants, antiphase boundary energies, complex stacking fault energies, superlattice intrinsic stacking fault energies and twinning energy decrease with increasing temperature. The twinnability of Ni 3 Si and Ni 3 Ge are examined using the twinnability criteria. It is found that their twinnability decrease with increasing temperature. Furthermore, Ni 3 Si has better twinnability than Ni 3 Ge at different temperatures.

First-Principles Modeling of the Temperature Dependence for the Superlattice Intrinsic Stacking Fault Energies in L1$$_2$$ Ni$$_{75-x}$$X$$_x$$Al$$_{25}$$ Alloys

Stronger and more resistant alloys are required in order to increase the performance and efficiency of jet engines and gas turbines. This will eventually require planar faults engineering, or a complete understanding of the effects of composition and temperature on the various planar faults that arise as a result of shearing of the $$\gamma ^\prime $$ precipitates. In the current study, a combined scheme consisting of the density functional theory, the quasi-harmonic Debye model, and the axial Ising model, in conjunction with a quasistatic approach is used to assess the effects of composition and temperature of a series of pseudo-binary alloys based on the $$({\mathrm{Ni}}_{75-x}{\mathrm{X}}_{x}){\mathrm{Al}}_{25}$$ system using distinct relaxation schemes to assess observed differences. Our calculations reveal that the (111) superlattice intrinsic stacking fault energies in these systems decline modestly with temperature between $$0\,$$ K and $$1000\,$$ K.

First-principles modeling of superlattice intrinsic stacking fault energies in Ni3Al based alloys

High-throughput quantum mechanics based simulations have been carried out to establish the change in lattice parameter and superlattice intrinsic stacking fault (SISF) formation energies in Ni3Al-based alloys using the axial Ising model. We had direct access to the variation in SISF energies due to finite compositional change of the added ternary transition metal (TM) element through constructing large supercells, which was equally necessary to account for chemical disorder. We find that most added TM ternaries induce an important quasi-linear increase in the SISF energy as a function of alloying composition x. The most pronounced increase corresponds to Fe addition, while Co addition decreases the SISF energy monotonically. Our results shed light on the role played by TM elements on strengthening L12 Ni3Al precipitates against stacking fault shear. The data are of high importance for designing new Ni-based superalloys based on computational approaches.

Tuning planar fault energies of Ni3Al with substitutional alloying: First-principles description for guiding rational alloy design

We determine effects of substitutional alloying, at Al or Ni sublattice, with 3d, 4d and 5d series of transition elements on the energies of anti-phase boundary (APB), superlattice intrinsic stacking fault (SISF) and unstable stacking fault (USF) of Ni3Al using first-principles density functional theoretical calculations. We show that USF and APB energies are maximal for the systems wherein elements having half-filled d-orbitals are substituted at the Al site. Analysis of the data on alloys studied reveals a correlation between SISF and APB energies, which along with d-orbital occupancy can be useful as descriptors in rational design of improved Ni-Al alloys.

First‐principles calculations of thermodynamic properties and planar fault energies in Co3X and Ni3X L12 compounds

AbstractWe do Density Functional Theory based total‐energy calculations of the phase in X and X compounds, X being a transition metal element. The lattice parameters, magnetic moments and formation enthalpies are determined and compared with the available experimental data. The (111) superlattice intrinsic stacking fault energy (SISF), a crucial factor affecting materials strength and their mechanical behavior, is calculated using the axial interaction model. We have applied the quasiharmonic Debye model in conjunction with first‐principles in order to establish the temperature dependence of the lattice parameters and the (111) SISF energies. We investigate our prediction of a low formation enthalpy in the system Ni −25 at.%Zn by doing auxiliary simulations for the fcc random alloy at the composition 25 at.%Zn. Our simulations indicate that the elements Ti, Zr, Hf, Nb, and Ta can help stabilizing the promising and extremely important alloy.

Stacking fault energy, yield stress anomaly, and twinnability of Ni3Al: A first principles study**Project supported by the National Natural Science Foundation of China (Grant Nos. 11104361 and 11304403) and the Fundamental Research Funds for the Central Universities, China (Grant Nos. CQDXWL2014003 and CDJZR14328801).

Using first principles calculations combined with the quasiharmonic approach, we study the effects of temperature on the elastic constants, generalized stacking fault energies, and generalized planar fault energies of Ni3Al. The antiphase boundary energies, complex stacking fault energies, superlattice intrinsic stacking fault energies, and twinning energies decrease slightly with temperature. Temperature dependent anomalous yield stress of Ni3Al is predicted by the energy-based criterion based on elastic anisotropy and antiphase boundary energies. It is found that p increases with temperature and this can give a more accurate description of the anomalous yield stress in Ni3Al. Furthermore, the predicted twinnablity of Ni3Al is also decreasing with temperature.

A first-principles study of the effect of Ta on the superlattice intrinsic stacking fault energy of L12-Co3(Al,W)

New Co-based alloys containing a L12 reinforcement phase display exceptional high-temperature properties. Early research has shown that the quaternary alloy Co-8.8Al-9.8W-2Ta (at.%) has a high-temperature strength comparable to single-crystal Ni-based superalloys above 1200 K. Associated with high strength is an unusual high density of intrinsic stacking faults within the γ′ precipitates. In this work, Density Functional Theory, the Axial Next Nearest Neighbor Ising model and Special Quasi-random Structures have been used to calculate the stacking fault energy of L12-Co3(Al,W) and the effect of small Ta additions on the stacking fault energy. The model predicts a superlattice intrinsic stacking fault energy of 90–93 mJ/m2, which increases up to 30% when one Ta atom is substituted on the Al/W sub-lattice. This effect can be explained by considering d-band effects resulting from the addition of Ta.

First—principles study of stacking fault energies in Ni3Al intermetallic alloys

The first-principles method based on the projector augmented wave method within the generalized gradient approximation was employed to calculate the superlattice intrinsic stacking fault (SISF) and complex stacking fault (CSF) energies of the binary Ni3Al alloys with different Al contents and the ternary Ni3Al intermetallic alloys with addition of alloying elements, such as Pd, Pt, Ti, Mo, Ta, W and Re. The results show that the energies of SISF and CSF increase significantly with increase of Al contents in Ni3Al. Addition of Pd and Pt occupying the Ni sublattices does not change the SISF and CSF energies of Ni3Al markedly in comparison with the Ni–23.75Al alloy. While addition of alloying elements, such as Ti, Mo, Ta, W and Re, occupying the Al sublattices dramatically increases the SISF and CSF energies of Ni3Al. The results suggest that the energies of SISF and CSF are dependent both on the Al contents and on the site occupancy of the ternary alloying element in Ni3Al intermetallic alloys.

On the core structure of ⟨112] edge dislocations in γ-TiAl

Weak-beam image simulations have been carried out using the CUFOUR programme of a ] edge dislocation in γ-Ti–50 wt% Al, dissociated into three ⟨112] partial dislocations bounding superlattice intrinsic stacking-fault (SISF) and superlattice extrinsic stacking-fault (SESF) ribbons of equal width. The simulations included one of the two core configurations of the composite Shockley partial dislocation found by Kumar et al. to explain their observed image contrast, and two others that involve dissociation into stair-rods. These latter simulated images cannot be distinguished from those for the model proposed by Kumar et al. for the composite Shockley dislocation and therefore account for the observed image contrast equally well. The claim of these workers that configurations consisting of stair-rod dislocations can be ruled out is not substantiated. The core structures involving sessile stair-rod dislocations explain the locked nature of the edge dislocation. The values found by Kumar et al. for the true separation between the pairs of partial dislocations have been used to calculate (on anisotropic elasticity theory) the SISF and SESF energies to be 123 ± 10 mJ m−2.

Anomalous Strengthening Mechanism in NbSi2-Based Silicide Single Crystals

ABSTRACTAnomalous strengthening behavior of NbSi2-based silicide single crystals with C40 structure was examined focusing on the effect of substitutional alloying elements and the formation of a solute dragging atmosphere. After pre-straining to 1% at temperatures between 600 and 1600°C, single crystals were deformed at 400°C to examine the effects of dislocation sources and segregation of solute atoms around dislocations. The stress amplitude of yield drop was derived by the segregation of solute atoms at the superlattice intrinsic stacking fault (SISF) between two superpartials. Introduction of dislocation sources by pre-straining remarkably improved fracture strain, but the segregation of solute atoms around dislocations during pre-straining at higher temperatures induced a rapid drop of fracture strain. Change in the SISF energy by static and dynamic aging was observed to obtain evidence of segregation of solute atoms at the SISF between two superpartials.

Dislocation dissociations and fault energies in Ni 3Al alloys doped with palladium

Dislocation structures in polycrystalline Ni 3A1 alloy doped with palladium deformed at room temperature have been investigated by transmission electron microscopy. The structure consists mainly of dislocations dissociated into a/2<0 1 1> super partials bounding an anti-phase boundary (APB). Dislocations dissociated into a/3<112> super Shockley partials bounding a superlattice intrinsic stacking fault (SISF) were often observed. The majority of the SISFs are truncated loops, i.e. the partials bounding the SISF are of similar Burgers vector. These faulted loops are generated from APB-coupled dislocations, according to a mechanism for formation of SISFs proposed by Suzuki et al. (Suzuki K, Ichihara M, Takeuchi S. Acta Metall 1978;26:183) and recently modified by Chiba et al. (Chiba A, Hanada S. Philos Mag 1994;69:751). The APB energies for {111} and {100} slip planes are measured to be 144±20 and 102±11 mJ/m 2, respectively, and the SISF energy has been estimated to be 12 mJ/m 2 in this alloy. It is concluded that the dislocation structure in Ni 74.5Pd 2Al 23.5 alloy deformed at room temperature is similar to that in binary Ni 3Al and the difference in fault energies between these two alloys is small. Thus, it seems unlikely that the enhancement of ductility of Ni 74.5Pd 2Al 23.5 results from only such a small decrease of the ordering energy of the alloy. SISF bounding dislocations also have no apparent influence on the ductilization of Ni 74.5Pd 2Al 23.5 alloy.

Temperature dependence of dislocation structure of L12–Al3Sc

Superdislocations in Al 3 Sc deformed at various temperatures were observed by TEM (transmission electron microscopy). Emphasis was placed on the low temperature range. Below room temperature, dislocations in pile ups dissociated into two a/3<112> superpartials separated by a SISF (superlattice intrinsic stacking fault). At 77 K, triple dislocation nodes separated by SISF were observed. SISF energies estimated from the separation width of superpartial dislocations are 170 mJ m −2 at 77 K, 230 mJ m −2 at 210 K and 290 mJ m −2 at 293 K. The experimentally determined temperature dependence of dissociation mode in Al 3 Sc is similar to that of Co 3 Ti reported previously. Taking into account the results of the above TEM observations and also of strength measurements, the dislocation structure in L1 2 –Al 3 Sc is discussed.

Planar fault energies and sessile dislocation configurations in substitutionally disordered Ti-Al with Nb and Cr ternary additions

Abstract Variations in planar fault energies, generated by changes in alloy composition, can influence thermally activated processes which govern plasticity in intermetallic alloys. Predicting variations in defect energy as a function of alloy composition would aid both alloy design and the interrogation of models of yield stress. In this paper, layered Korringa-Kohn-Rostoker coherent potential approximation calculations are reported for the superlattice intrinsic stacking fault (SISF) and antiphase-boundary (APB) energies in binary and ternary Ti-Al alloys. The planar fault energies were calculated over a range of alloy composition: (Ti1−xAlx)1−y My with 0·48 ≤ × ≤ 0·51, 0·00 ≤ y ≤ 0·02 and M = Cr, NB. For the Ti-rich alloys, ternary additions up to 4at.% were also considered. APB (010) energies were calculated for the binary alloy while the SISF and APB (111) energies were calculated for all the binary and ternary alloys. The compositions Ti50Al50 and (Ti50Al50)1−yCry have the maximum defect energies for this range of alloy compositions. Cr additions appear to have little influence on the defect energies of the Ti-rich alloys, while slightly reducing the APB (111) in the Al-rich alloys. The defect energies for the Nb alloys are reduced relative to the binary alloys, with the fault energies increasing monotonically with increasing Al concentration. The variation in defect energies, both trends and magnitude, are used with anisotropic elasticity theory to estimate the forces needed to produce two possible 〈101]{111} superdislocation glide barriers. Also, the anisotropic elastic energy of the nonplanar equilibrium superdislocations are compared. The formation of 〈101] {111} superdislocations with portions on cross-slip octahedral planes is favoured over cross-slip onto the cube plane for conservative estimates of the planar fault energies and applied stress. These results suggest that alloy designers can expect only moderate improvements in the high-temperature yield stress, because of the formation of 〈101] {111} superdislocation barriers, with changes in alloy composition.

The dislocation structure in L12ordered alloy Ni3Ge

Abstract The dislocation structure in polycrystalline Ni3Ge deformed at room temperature has been studied transmission electron microscopy. The structure consists mainly of screw 〈110〉 dislocations and superlattice intrinsic stacking fault (SISF)-coupled partial dislocations. A few dislocations are present as antiphase boundary (APB)-coupled partials. Two kinds of SISF partial dislocation are observed: SISF pairs with dissimilar Burgers vectors and SISF pairs with antiparallel Burgers vectors. The energies of the APBs on {111} and {001} planes have been estimated to be 169 and 148 mJ m−2 respectively, and the SISF energy has been measured to be between 15 and 30 mJ m−2. Dissimilar SISF partials appeared to be formed the dissociation of a segment of a segment of a perfect dislocation, confirming a mechanism for SISF formation first suggested by Pak, Saburi and Nenno in 1976. Anomalous yield stress behaviour in the low-temperature region (below room temperature) is attributed mainly to mechanism(s) based on...

Crack-tip dislocations and fracture behavior in Ni 3Al and Ni 3Si

The ideal Griffith energies and the critical stress intensity factors for three cleavage modes are determined from the calculated elastic constants and surface energies. The propensity for crack tip deformation is estimated on the basis of the calculated antiphase boundary (APD), complex stacking fault and superlattice intrinsic stacking fault energies and the anisotropic coupling effect on dislocation mobility, i.e. non-Schmid effects. It is shown that while the calculated Griffith energy of Ni 3 Si is larger than that of Ni 3Al, dislocation emission from a crack tip is easier and dislocation mobility is higher in Ni 3Al than in Ni 3Si. When a crack is loaded in a mixed mode (K I + K III), emission of a super-Shockley partial from the crack trailing extended SISF is predicted and confirmed by in situ straining transmission electron microscopy observations of Ni 3Al.

Electronic structure of planar faults in TiAl

The mechanical behavior of intermetallic alloys is related to the mobility of the dislocations found in these compounds. Currently the effect of bonding on dislocation core structure and its influence on deformation behavior is not well understood. However, the unusual properties of these materials, such as the anomalous temperature dependence of flow stress observed in TiAl, are derived in part from the aspects of bonding that determine dislocation mobility. Several recent studies have suggested a particular relationship between directional bonding in TiAl and dislocation mobility. To understand better the flow behavior of high temperature intermetallics, and as a step toward bridging the gap between electronic structure and flow behavior, we have calculated the electronic structure of various planar faults in TiAl. The self consistent electronic structure has been determined using a layered Korringa Kohn Rostoker (LKKR) method which embeds the fault region between two semi-infinite perfect crystals. Calculated defect energies in stoichiometric TiAl agree reasonably well with other theoretical estimates, though overestimating the experimental (111) anti-phase boundary (APB) energy, found for Ti46Al54. We approximate the energy of the (111) APB for the Al-rich stoichiometry by calculating the energy of Al antisites near that defect plane. The calculated (111)APB energy decreases by 6% in going from stoichiometric TiAl to Ti46Al54. The overall hierarchy of fault energies is found to be associated with the number of crystal bond states that are disrupted by the introduction of the fault plane. However, the hierarchy of fault energies is inconsistent with the traditionally accepted ordering. Changes in bonding taking place in the vicinity of the planar defects are illustrated through the density of states and charge density plots. A three body atomistic model is introduced to parameterize the bonding observed in TiAl. The L10 lattice (c/a = 1.00), within a second nearest neighbor three body model, yields a (111)APB energy which is the sum of the complex and superlattice-intrinsic stacking fault energies.

High-Resolution TEM Observations of Superdislocations in Ni&lt;SUB&gt;3&lt;/SUB&gt;(Al, Ti)

End-on images of dislocations in Ni 3 (Al, Ti) single crystals deformed at 683 and 293 K were observed by high-resolution transmission electron microscopy. They showed a superlattice intrinsic stacking fault (SISF) type of dissociation on a {111} plane and an antiphase boundary (APB) type of dissociation on a {001} plane. SISF and APB energies were calculated to be 133 and 560 mJ/m 2 , respectively, using an isotropic elasticity theory, and they were compared with the other results obtained by field ion microscopy, weak-beam technique and high-resolution electron microscopy