Unstable Stacking Energy Research Articles

First-Principles Investigation of the Shear Properties and Sliding Characteristics of c-ZrO2(001)/α-Al2O3(11¯02) Interfaces

The ideal mechanical shear properties and sliding characteristics of c-ZrO2(001)/α-Al2O3(11¯02) interfaces are examined through simulated shear deformations using first-principles calculations. We investigate three types of interface models, abbreviated as O-, 2O-, and Zr- models, when shear displacements are applied along the <11¯01> and <112¯0> directions of their Al2O3 lattice. The theoretical shear strength and unstable stacking energy of the ZrO2/Al2O3 interfaces are discussed. In the process of the ZrO2/Al2O3 interfacial shear deformation, we find that the sliding of the ZrO2 atomic layers, accompanied by the shifting of Zr atoms and Al atoms near the interface, plays a dominant role; in addition, the ZrO2/Al2O3 interfaces fail within the ZrO2 atomic layer. Among the three models, the O- model exhibits the strongest shear resistance; whereas the Zr- model is the most prone to slip. Furthermore, their tensile and shear strengths are compared; moreover, their potential applications are provided.

Abnormally fast crack propagation induced by short-range ordering in iron-cobalt alloys: A combined experiments and molecular dynamics simulations

We experimentally found that FeCo21.5Cr0.2Ni0.8 alloy quenched from 500 °C, slightly above the order-disorder transition temperature, surprisingly exhibited an extreme impact brittleness. Impact fracture morphology observed by scanning electron microscope (SEM) showed that the impact brittleness was caused by the fast crack growth and poor local plasticity. Short-range ordered (SRO) structures were found in the sample quenched from 500 °C by high-resolution transmission electron microscope (HRTEM) characterizations, and the average SRO size is ~1.58 nm. We contribute the impact brittleness to the formation of SROs. Molecular dynamics (MD) simulations were carried out to reveal the SRO-induced embrittlement mechanism caused by fast crack propagation under high-speed loading. MD simulations showed SROs significantly inhibited the deformation plasticity near crack tips by suppressing the dislocation proliferation, dislocation slip, and twinning. Generalized stacking fault energy (GSFE) curves were calculated to evaluate the effect of SROs on antiphase boundary (APB) energies, unstable stacking energy γusf, and intrinsic stacking energy γisf. SROs were found to prominently increase the APB energies and γisfγusf, fully supporting the SRO-induced poor dislocation and twinning plasticity near crack tips in MD simulations. These findings revealed the potential SRO-induced impact brittleness and its embrittlement mechanism, and provide a design consideration for the engineering application of materials under impact loading.

Effect of sub-surface hydrogen on intrinsic crack tip plasticity in aluminium

ABSTRACTThe effects of sub-surface hydrogen and mixed mode loading on dislocation emission in aluminium are studied using a combination of techniques including crack simulations with an empirical interatomic potential, generalised stacking fault energy (GSF) calculations, with empirical interactions and Density Functional Theory, and the model by Rice which links the critical stress intensity factor to the unstable stacking energy. The crack orientation is and the loading is composed of a moderate traction along and a shear along , such that Shockley partials are emitted along the crack plane. The role of the relaxations around the H atoms and of the concentration of H in the glide plane, in the GSF calculation, is revealed by comparing Rice's model to the results of brute force simulations. The enhanced GSF is then calculated ab initio. The conclusion is a large decrease of the critical load to emit a dislocation, due to the displacement transverse to the glide direction. The effect of sub-surface hydrogen is negligible with respect to the mechanical one.

Modified Peierls–Nabarro dislocation equation for $$ \left\langle {\text{110}} \right\rangle {\{ 1\bar{1}0\} } $$ 110 { 1 1 ¯ 0 } dissociated superdislocations in perovskite CaSiO3

In the paper, we investigate the core width of superpartials and dissociated width of the 〈110〉{1–10} superdislocations in CaSiO3 perovskite under pressures of 30 and 100 GPa by using the modified P–N dislocation equation. Our results show that when taking into account the discrete effect correction, core width of superpartials and dissociated width become much wider, and both of them increase significantly with the increase of the superdislocation angle. Furthermore, it is found that the dissociated width and core width of superpartials are determined by value of the unstable stacking fault energy and antiphase boundary energy, which are independent of the position of unstable stacking energy. Interestingly, the Peierls stress of superpartials can be predicted by using the variational method to solve the modified P–N dislocation equation.

First-principles studying the properties of oxygen in vanadium: Thermodynamics and tensile/shear behavior

Employing the first-principles simulation, we investigate the energetics of oxygen (O) and the influence of O on the mechanical behaviors of vanadium. O atom prefers to occupy the octahedral interstitial site with the solution energy of −4.942 eV. Along the [100] direction, the ideal tensile strength of vanadium doped with an O occupying the octahedral interstitial site is 17.4 GPa, which can be reduced by ∼8.9% compared to 19.1 GPa of pure vanadium. This demonstrates that impurity O has a large effect on the tensile strength of vanadium. We further calculate the generalized fault energies including the unstable stacking energy (γus) and the cleavage energy (γcl) in pure vanadium and O-vanadium system in the most preferable {110}<111> slip system. The cleavage energy can be decreased from 1.705 J/m2 of pure vanadium to 1.681 J/m2 of O-vanadium system and simultaneously the unstable stacking energy can be increased from 0.308 J/m2 of pure vanadium to 0.325 J/m2 of O-vanadium system. The ratio of γcl/γus alters from 5.536 to 5.172 and can be thus decreased by 6.57%. This means that the ductility of vanadium will significantly decrease owing to the appearance of impurity O.

Behaviors of alloying element titanium in vanadium: From energetics to tensile/shear deformation

Using first-principles simulation, we investigate the effect of alloying element titanium (Ti) on the mechanical properties of vanadium (V). The ideal tensile strengths of Ti1.85V98.15 and Ti6.25V93.75 alloys in the [100] direction are 18.6GPa and 17.5GPa, respectively. These values are, respectively, reduced by 2.6% and 8.4% in comparison with 19.1GPa of pure V. This suggests that such alloying effect of Ti on the tensile strength of V appears to be relatively large. The generalized fault energies have been calculated including the unstable stacking energy (γcl) and the cleavage energy (γcl) in a pure V and Ti0.35V99.65 alloy along the most preferable {110}〈111〉 slip system. Ti can decrease γcl from 1.705J/m2 to 1.704J/m2 and simultaneously increase γus from 0.308J/m2 to 0.311J/m2 in comparison with the pure V. The ratios of γcl/γus for the pure V and Ti0.35V99.65 alloy are 5.536 and 5.479, respectively. The value is decreased by 1.03%, meaning that the ductility of dilute Ti0.35V99.65 alloy can be slightly reduced in comparison with that of the pure V.

Influence of Re on the propagation of a Ni/Ni3 Al interface crack by molecular dynamics simulation

The influence of Re on the propagation of a (0 1 0)[1 0 1] crack in the Ni/Ni3Al interface, including crack propagation velocity, crack-tip shape, and dislocation emission, is investigated using a molecular dynamics method with a Ni–Al–Re embedded-atom-method potential. The propagation velocity of the crack noticeably decreases at 5 K when 3 or 6 at% Re atoms are added into the Ni matrix. At 1033 K, the crack tip becomes blunter and emission of dislocations becomes easier with Re addition, owing to the larger bond strength between Re and Ni atoms. Furthermore, we calculate the unstable stacking energy (γus), surface energy (γs), and adhesion work (Wad) of the interface. When Re atoms are randomly doped into a Ni matrix, γs/γus increases correspondingly. This means that Re addition decreases brittleness and improves ductility. The calculation also shows that γus is not affected by Re–Ni atomic interaction, and that Re–Re atomic interaction has some effect on γus. In addition, Wad increases with Re addition, and a small increase in Wad results in a larger decrease in crack velocity. This indicates that Re–Ni atomic interaction restrains crack propagation velocity at low temperature.

Sulfur-induced embrittlement of nickel: a first-principles study

We study the embrittlement of Ni due to the presence of S impurities, considering their effect in the bulk and at grain boundaries (GBs). For bulk Ni, we employ Rice's theory based on generalized-stacking-fault energetics and the unstable stacking energy criterion. We use first-principles density-functional-theory calculations to determine the ductility parameter D = γs/γus, the ratio of the surface energy γs to the unstable stacking energy γus, for bulk Ni with substitutional S impurities. Similar arguments based on Rice's theory for the mechanical properties of GBs are invoked. We study the Σ5(0 1 2) GB with interstitial S impurities, in which case D is defined as the ratio of the work of separation Ws and the unstable stacking energy γus, to model the competition between grain decohesion and shear-induced plastic deformation due to grain boundary sliding (GBS). The presence of S impurities is found to increase the value of D by ∼40% in bulk Ni, but reduces it by over 80% for the GB. These results support earlier suggestions that embrittlement of Ni by S impurities is related to their effect on GBs. We further calculate relevant tensile and shear stresses to study the expected fracture mode and find that intergranular crack propagation accommodated by GBS is inhibited in the system considered here.

Dislocation emission from a crack under mixed mode loading studied by molecular statics

The dislocation emission surface in (k I, k II, k III) space is calculated by means of atomistic simulations for the {111}⟨110⟩ crack in Al. For each relevant combination of loading mode, the precise nature of the dislocations and of the emission process are determined. When appropriate, the analytic formulas proposed by Rice are used by calculating the unstable stacking energy including the effect of the mixed mode loading. Quantitative agreement with the full atomistic calculation is found in the case where dislocations glide in the crack plane. This clearly identifies when and how ab initio data can be introduced in the calculation.

Shear strength and sliding behavior of Ni/Al2O3 interfaces: A first-principle study

Abstract

Stacking faults in B2-structured magnesium alloys from first principles calculations

The stacking faults of 17 B2-structured magnesium alloys have been studied systematically by means of first-principles calculations. After structure optimization and stability analysis, the generalized stacking fault energy surfaces for two possible slip planes {001} and {110} have been calculated using a super-cell tilling technique, and the main feature of generalized stacking fault energy surfaces was analyzed. Then the most likely slip directions were determined, and the stable and unstable stacking energies were obtained. The dissociation of perfect dislocation was further discussed. The electronic structures were also investigated to reveal the underlying mechanism for stability and stacking faults.

Effect of Sn and Nb on generalized stacking fault energy surfaces in zirconium and gamma hydride habit planes

We have investigated the effects of Sn and Nb on dislocation properties in a Zr lattice to elucidate the role of these alloying elements in hydride nucleation processes. According to experimental observations, γ-hydride habit planes are close to the prismatic plane in pure Zr and close to the basal plane in Zircaloy. Dislocation loops are observed around hydride precipitates, implying they play a part in hydride formation. Our ab initio generalized stacking-fault energy calculations showed remarkable effects of Sn on unstable-stacking energy and stacking-fault energy: these parameters for basal slip were considerably reduced while those for prismatic slip were increased in the presence of Sn. These results suggest selective stabilization and enhancement of dislocation spreading in the basal plane, promoting possible elementary processes of hydride precipitation with basal habit plane, i.e. screw-dislocation spreading and edge-dislocation emission in the basal plane.

Ab initio study on plane defects in zirconium–hydrogen solid solution and zirconium hydride

Hydrogen embrittlement of zirconium alloys is one of the main causes of the mechanical degradation of the fuel cladding in light water reactors, and has therefore been extensively studied. Although various conjectures have been proposed as the origin of such embrittlement, it is not known which one plays the most important role: the brittle nature of the hydride, micro-crack nucleation by interaction of hydride precipitates with dislocations or void nucleation at the interface between hydride precipitates and zirconium matrix. The purpose of the present study was to elucidate the origin of the embrittlement by investigating the fracture properties of the hydride. We have evaluated the surface energy γ S and unstable stacking energy γ US of Zr–H systems by using ab initio calculations. The ductile/brittle behavior of the hydride is discussed based on the difference between γ S and γ US among the hydride, pure zirconium and hydrogen solid solution. For the solid solution at a H/Zr ratio less than 0.5 we obtained a monotonous decrease by 15–34% and 50–100% in γ S and γ US, respectively, from those in pure zirconium, indicating a reduction in both brittleness and ductility. Thus, hydrogen-induced embrittlement of the hcp Zr matrix was not confirmed. On the other hand, for the hydride we obtained a 25% smaller γ S and a 200–300% larger γ US than those in pure zirconium. This indicates that zirconium hydride has an extremely brittle nature due to the synergistic effect of a small γ S, implying easy generation of a fracture surface, and large γ US, implying a difficulty in dislocation motion, compared with pure zirconium. Furthermore, Rice’s ductile/brittle parameter D was 1.4 in the δ-hydride, indicating that it undergoes brittle fracture more easily than iridium, known as an extremely brittle material. These results seem sufficient to attribute hydrogen embrittlement of zirconium alloys substantially to the brittle nature of the hydride.

A systematic investigation of stacking faults in magnesium via first-principles calculation

The stacking faults of crystal magnesium have been studied systematically by means of first-principles calculation within the generalized gradient approximation (GGA). The generalized stacking fault (GSF) energy surfaces for four kinds of basal stacking faults as well as other non-basal stacking faults in the prismatic and pyramidal planes have been gained using a supercell approach with the supercell tilling technique. The most likely slip directions for the formation of these stacking faults in the corresponding slip plane were determined, and the generalized stacking fault energy curves along the most likely slip directions were derived, then the stable and unstable stacking energies were obtained and discussed. The present results are helpful for further investigation of dislocations and the correlative mechanical properties.

Dislocation formation and twinning from the crack tip in Ni3Al: molecular dynamics simulations

The mechanism of low-temperature deformation in a fracture process of L12 Ni3Al is studied by molecular dynamic simulations. Owing to the unstable stacking energy, the [01̄1] superdislocation is dissociated into partial dislocations separated by a stacking fault. The simulation results show that when the crack speed is larger than a critical speed, the Shockley partial dislocations will break forth from both the crack tip and the vicinity of the crack tip; subsequently the super intrinsic stacking faults are formed in adjacent {111} planes, meanwhile the super extrinsic stacking faults and twinning also occur. Our simulation results suggest that at low temperatures the ductile fracture in L12 Ni3Al is accompanied by twinning, which is produced by super-intrinsic stacking faults formed in adjacent {111} planes.

Study of hardness and deformation of brittle materials with a density functional theory

We investigated controlling parameters of hardness in brittle materials by exploring the correlation between hardness and shear mode cracking. Density functional theory was used to calculate the unstable stacking energies (shear resistance to irreversible deformation) and the surface energies (tension resistance to fracture) for comparison. We found that both the unstable stacking energies and the surface energies had a monotonic relationship with hardness in Ge, Si, 3C-SiC, cBN, and diamond. In particular, both the relationship between hardness and the unstable stacking energy and the relationship between hardness and surface energy are better characterized as power law than linear relationships. Moreover, the surface energy has a better correlation with hardness than the unstable stacking energy. Both the theoretical stress for a crack to form and the stress intensity factor for a crack to propagate, which depend on surface energies, have better correlation with hardness than the stress intensity factor for a crack to emit a dislocation, which depends on unstable stacking energies. The implication of these results for fracture and deformation mechanism during hardness measurement is also discussed.

First-principles computations of mechanical properties of Ni2Cr and Ni2Mo

Nickel-based alloys are being considered for use as the outer container of the waste package for the disposal of high-level nuclear waste. During fabrication processes and long-term storage, Ni-based alloy outer containers can undergo microstructural changes due to the formation of Ni2Cr, Ni2Mo, and Ni2(Cr, Mo), which are ordered orthorhombic (oI6) phases whose mechanical properties are unknown because of fabrication difficulties. To circumvent the experimental limitation, a first-principles quantum-mechanical code based on the full-potential linearized augmented plane-wave (FLAPW) method was used to compute the elastic constants and the theoretical stress-strain curves of Ni2Cr and Ni2Mo. The theoretical mechanical properties were then correlated with charge-density distributions of the stressed oI6 unit cell to identify the critical conditions at the onset of fracture. Using first-principles results as material input, the unstable stacking energy and the Peierls-Nabarro (P-N) barrier energy were computed and used to estimate the tensile ductility and fracture toughness of Ni2Cr and Ni2Mo. The influences of the elastic anisotropy and slip vector on dislocation mobility in Ni2Cr and Ni2Mo are identified and contrasted to those in MoSi2 with a tetragonal (tI6) crystal structure.

Alloying effects on the fracture toughness of Nb-based silicides and Laves phases

Nb-based in situ composites are characterized by a large volume fraction of silicides and Laves phase particles in an Nb solid solution matrix. The intermetallic hard particles can adversely affect the fracture resistance of the composites. Recent work has shown that certain alloy additions can improve the fracture resistance of Nb-based silicides, Laves phases and the Nb solid solution. In this paper, the effects of alloy additions on the fracture toughness of Nb-based silicides and Laves phases are summarized. Theoretical calculations have been performed to determine the influence of alloy additions on the bond order, unstable stacking energy, and the Peierls–Nabarro energy for selected slip systems in the intermetallics. The theoretical results will be used in conjunction with experimental data to elucidate the possible roles of alloy additions in the slip process and the fracture resistance in Nb-based silicides and Laves phases and to compare the observed behaviors against those in Ti-based silicides and Laves phases.

Mechanistic models for the activation volume and rate sensitivity in metals with nanocrystalline grains and nano-scale twins

This paper describes mechanistic models that seek to rationalize experimentally determined low values for the activation volume associated with the high strain rate sensitivity of nanocrystalline metals. We present models for the emission of partial or perfect dislocations from stress concentrations at a grain boundary or twin boundary. The emission of deformation twins is likewise examined as a competing mechanism to perfect dislocation emission. The approach illustrates the important roles of both the intrinsic stacking fault energy and the unstable stacking energy. We find that the models lead to estimates of activation volumes in the range 3 − 10 b 3 for truly nanocrystalline metals. Activation volumes are found to increase monotonically with increasing grain size. The findings are found to be in accord with available experimental evidence in both a quantitative and qualitative manner. Deficiencies in the available experimental evidence are noted, specifically in the context of explaining some of the difficulties in comparing theoretical predictions to experimental observation.

Linking electronic and dislocation parameters to fracture resistance in Nb–Ti–Cr alloys and Laves phases

The possible linkage of electronic and bonding variables to material parameters that describe dislocation nucleation, dislocation mobility, and the fracture resistance of metals and intermetallics is investigated in this paper. Using appropriate analytical methods, the effects of the number of d + s electrons per atom on the unstable stacking energy and the Peierls–Nabarro (P–N) barrier energy are computed for Nb–Ti–Cr solid solution alloys, Laves phase, and in-situ composites. Comparison of model computations with previously published experimental data reveals that the number of d + s electrons/atom exerts significant effects on the P–N barrier energy and the fracture toughness of the solid solution alloys, but has little effect on the unstable stacking energy, P–N barrier energy, and fracture toughness of the Laves phases. For in-situ composites, the electronic effects stem mainly from those exerted through the solid solution phase. A systematic investigation of the various components that contribute to P–N barrier energy indicates that the electronic effect is a manifestation of the influence of the charge density on the anisotropic shear modulus in the slip plane and direction, which in turn affects the lattice phase angle, the P–N barrier energy, dislocation mobility, and ultimately the fracture resistance. Ti addition in Nb–Ti–Cr alloys reduces the charge density, the anisotropic shear modulus, and the P–N barrier energy; the reductions enhance the dislocation mobility and improve the fracture toughness. In contrast, Cr addition increases the charge density, the anisotropic shear modulus, and the P–N barrier energy; these increases diminish the dislocation mobility and reduce the fracture toughness.