Peierls Stress Research Articles

Solid solution softening of Ti2AlC induced by alloying of boron

Solid solution softening is an unusual adjustment behavior that is attractive for material strength. In this paper, the effect of boron alloying on the strength of Ti2AlC is investigated by first-principles calculations. Our results show that the elastic modulus and ideal strength of Ti2AlC decrease overall due to alloying with boron, which indicates that solid solution softening occurs. Conversely, ductility and plasticity of Ti2AlC are greatly enhanced by alloying with boron. This phenomenon in Ti2AlC is mainly related to the reduction of Peierls stress and generalized stacking fault energies caused by alloying with boron. Our work provides an ideal candidate platform to study the solid solution softening effect in ceramics and provides theoretical guidance for engineering applications of MAX phase materials.

The influence of stress levels on the creep behavior of Ti–42Al–6Nb–0.05Y2O3 alloy

The paper studied the creep behavior of Ti–42Al–6Nb–0.05Y2O3 alloy. Short-term creep tests were performed at the temperature range of 750–900 °C and the stress range of 100–300 MPa. The results reveal that the stress exponent varies from 1.85 to 5.01 when the creep stress increases from 100 to 300 MPa at 850 °C. Interface sliding and dislocation climb are the main creep mechanisms at 100 and 300 MPa, respectively. Formation of intergranular cracks is the major cause of the failure above 150 MPa. Instead, under 100 MPa, nucleation of cracks along lamellar interfaces plays a dominant role in the rupture. There is a critical temperature at which the apparent activation energy (Qc) increases suddenly. For the lamellar alloy, the increase of Qc has a close association with the dislocation movement in minority α2 laths. Below the activation energy transition temperature (AETT), the deformation of α2 phase is mainly governed by a→ type dislocations. Whereas above the AETT, the activation of 2c→+a→ type dislocations plays a dominant role. Moreover, the AETT at 300 MPa is determined to be 800–850 °C, whereas that at 100 MPa is 850–900 °C. There is an increase of AETT with the decrease of creep stress. At the low stress (100 MPa), the AETT depends on lattice resistance rather than long-range internal stress, since the flow stress may be less than Peierls-Nabarro force for slipping of 2c→+a→ type dislocations, resulting in a high AETT.

Alkaline-Earth Metal Effects on Physical Properties of Ferromagnetic AVO3 (A = Ba, Sr, Ca, and Mg): Density Functional Theory Insights.

The effects of alkaline-earth metals on electronic, optical, thermodynamic, and physical properties of ferromagnetic AVO3 (A = Ba, Sr, Ca, and Mg) have been investigated by first-principles calculations within the GGA+U formalism based on density functional theory. The optimized structural parameters are in good agreement with the available experimental results that evaluate the reliability of our calculations. The cell and mechanical stability is discussed using the formation energy and Born stability criteria, respectively. The mechanical behaviors of AVO3 are discussed on the basis of the results of elastic constants, elastic moduli, Peierls stress, and Vickers hardness. The nature of the ductile–brittle transition of AVO3 compounds was confirmed by the values of Pugh’s ratio, Poisson’s ratio, and Cauchy pressure. The electronic band structures, as well as density of states, reveal the half-metallic behavior of BaVO3 and SrVO3. However, CaVO3 and MgVO3 exhibit spin-gapless and magnetic semiconductor characteristics, respectively. The microscopic origin of the transition from the half-metallic to semiconductor nature of AVO3 is rationalized using electronic properties. The presence of covalent, ionic, and metallic bonds in AVO3 compounds is found by the analysis of bonding properties. The single-band nature of half-metallic AVO3 is seen by observing hole-like Fermi surfaces in this study. Furthermore, the various thermodynamic and optical properties are calculated and analyzed. The refractive index suggests that AVO3 could be a potential candidate for applications to high-density optical data storage devices.

Insight into the stacking fault energy, dislocation, and thermodynamic properties of L12-Al3X(X[dbnd]Sc, Ti, V) intermetallics from first-principles calculations

The dislocation and thermodynamic properties of L12-Al3X(XSc, Ti, V) intermetallics were studied based on first-principles calculations. The computed stacking fault energies indicate the energy barrier for dislocation formation in Al3Sc is higher than that of Al3Ti and Al3V. Also, the negative anti-phase boundary(APB) energy for Al3V suggests the formation of APB is energetically favored, and this finding is further evidenced by electron localization function(ELF) and densities of states(DOS). Moreover, the computed Peierls energies and Peierls stress suggest the movement of edge dislocation is easier than screw dislocation in Al3Sc, Al3Ti, and Al3V. Further, the < 110 > (111) screw dislocation of Al3Sc and the < 110 > (111) edge dislocation of Al3V is the most difficult and easiest to move in all the studied systems, respectively. It is consistent with the computed ideal shear stress(τiss) for Al3Sc, Al3Ti, and Al3V. Moreover, we speculated the Al3Sc and Al3Ti in aluminum alloy may possess a better strengthening effect in comparison with Al3V. Finally, the thermodynamic properties of Al3Ti was found less dependent on temperatureare than that of Al3Sc and Al3V, the Al3Ti can serve as a better candidate for improving the heat resistance of aluminum alloys.

Core structure and Peierls barrier of basal edge dislocations in Ti[formula omitted]AlC[formula omitted] MAX phase

In the MAX phase, the nucleation and motion of basal dislocations dominate the plastic deformation at room temperature. Therefore, information on the dislocation core properties and energy barrier for dislocation glide is essential to understand their plasticity. Dislocations in MAX phases are mainly 〈a〉-type basal edge dislocations (b=a/3[112̄0]) and can glide in the basal plane (typical slip) or form kink bands depending on the load direction and crystal orientation owing to the strong plastic anisotropy. In this study, we determined the core structure, Peierls barrier, and corresponding stress of a/3(0001)[112̄0] edge dislocations in Ti3AlC2 MAX phase by multiple computational approaches using the semidiscrete variational Peierls–Nabarro method, density functional theory, and classical bond-order-potential-based molecular statics calculations. The a/3[112̄0] basal edge dislocation was dissociated into two Shockley partial dislocations with a 2–2.5b-wide stacking fault in between. These partial dislocations glide between the Ti(4f) and Al atomic layer. For straight dislocation motion, the Peierls barrier was single-humped and the corresponding Peierls stress was estimated to be approximately 182 MPa.

Intrinsic freedom of dislocation structures and Peierls stress oscillation

When the continuous translation symmetry breaks, a continuous mode splits into two distinct discrete modes with different energies. Based on the fully discrete Peierls model, it is found that stability of such discrete modes for dislocations can be tuned by the stacking fault energy of a slip system. As the stacking fault energy changes continuously, the stable dislocation structure transforms periodically and the Peierls stress varies oscillatorily. Furthermore, at the transformation point, the lattice resistance nearly vanishes and thus the dislocation can almost move freely.

Influence of Carbon and Oxygen on the Core Structure and Peierls Stress of Screw Dislocation in Molybdenum

The plasticity and hardness of metals are largely dependent on how dislocation interacts with solute atoms. Here, taking bcc molybdenum (Mo) as the example, the interaction of interstitial solutes carbon (C) and oxygen (O) with screw dislocation, and their influences on the dislocation motion, have been determined using first-principles calculations and thermodynamic models. Due to the incompact atomic structure and variation of electronic states in the dislocation core, C and O will segregate from the bulk system to the dislocation region. Notably, the presence of C/O at the dislocation induces the reconstruction of the core structure, from an easy-core to hard-core configuration. This originates from the fact that the hard-core structure provides a larger available volume at the interstitial site than the easy-core structure and, thus, facilitates the dissolution of C and O. More importantly, the addition of C/O in the dislocation significantly increases the Peierls stresses and double-kink formation enthalpies of screw dislocation in Mo, from 1.91 GPa and 1.18 eV for C/O-free dislocation to 5.63/4.69 GPa and 1.77/1.58 eV for C/O-saturated dislocation. Therefore, these interstitial solutes have a pinning effect on the dislocation motion, and this effect becomes stronger with higher segregating levels. This work reveals the profound effect of interstitial solutes on the properties of the dislocation core and provides a fundamental factor to account for the interstitial solutes-related phenomena in bcc metals.

Core structure and Peierls stress of the 90° dislocation and the 60° dislocation in aluminum investigated by the fully discrete Peierls model

The core structure, Peierls stress and core energy, etc. are comprehensively investigated for the 90° dislocation and the 60° dislocation in metal aluminum using the fully discrete Peierls model, and in particular thermal effects are included for temperature range 0 ≤ T ≤ 900 K. For the 90° dislocation, the core clearly dissociates into two partial dislocations with the separating distance D ∼ 12 Å, and the Peierls stress is very small σ p < 1 kPa. The nearly vanishing Peierls stress results from the large characteristic width and a small step length of the 90° dislocation. The 60° dislocation dissociates into 30° and 90° partial dislocations with the separating distance D ∼ 11 Å. The Peierls stress of the 60° dislocation grows up from 1 MPa to 2 MPa as the temperature increases from 0 K to 900 K. Temperature influence on the core structures is weak for both the 90° dislocation and the 60° dislocation. The core structures theoretically predicted at T = 0 K are also confirmed by the first principle simulations.

Peierls–Nabarro modeling of twinning dislocations in fcc metals

Metals with fcc structure may exhibit deformation twinning under specific conditions, which is an interesting but somewhat elusive aspect of their deformation behavior. It is well acknowledged that the phenomenon occurs through the activities of twinning partial dislocations. However, the lack of a comprehensive understanding of their fundamental properties obstructs the development of detailed multiscale plasticity models for the fcc metals. Here, we explore the core-structures and lattice friction of twinning partials through atomistically informed numerical modeling. To this end, we choose four fcc crystals with widely differing stacking fault energies. Using the semi-discrete variational Peierls–Nabarro model with non-local and surface corrections, we compute the core-widths and Peierls stresses of edge and screw twinning dislocations. In particular, the alternate-shear mode of twinning has been considered in addition to the regular layer-by-layer mechanism. In the former case, the stable disregistry energy of the middle layer is observed to be significantly less than the unsheared configuration, which is enough to overcome the Peierls barrier spontaneously. This study also highlights the significance of incorporating the correction terms, the absence of which may lead to significant inaccuracy in estimating the intrinsic lattice resistance of the twinning partials.

Shock wave study of precipitation hardening of beryllium copper

Based on three series of planar impact tests performed on beryllium copper samples, having thickness 0.25–6 mm, individual contributions of beryllium clusters (in the as quenched supersaturated solid solution), Guinier-Preston zones (GP, formed following ageing at 300°C for 26 min) and metastable γ" precipitates (crystallizing after 400 min ageing at 300°C) to the strength of alloy were quantified along with corresponding activation volumes. These data being coupled with Transmission Electron Microscopy evaluation of geometry and statistics of GP and γ" precipitates, made determination of the resistance τp to dislocation motion (Peierls stress) of the lattices of these particles possible. The great difference between values measured in these two cases, namely 3.7 GPa for GP and 1.4 GPa for the γ" precipitates may be considered as an additional confirmation of the fact that in these two cases the strengthening occurs due to different phases.

The effect of impurities on stacking fault energy and dislocation properties in γ-TiAl

The dislocation properties of γ-TiAl are systematically investigated under the effect of impurities with semi-discrete variational Peierls-Nabarro (SDVPN) model. The impurities prefer to locating at the first layer below the stacking fault plane along 1/2<112‾] which is attributed to the local effect between stacking fault and impurities by local energy scheme analysis. The dislocation dissociation width of γ-TiAl is 1.58 Å, which shows a compact core character and is well consistent with that by atomic simulation and experimental observation. Negligible changes occur in the dislocation dissociation width as C or O is doped, while the dislocation does not even dissociate with N or H addition. The Peierls stress is reduced and the dislocation mobility is improved by N, H, and O, while C takes an opposite effect. The improved dislocation mobility with H is consistent with the enhanced dislocation mobility by H in experiments, while the improved dislocation mobility with O in calculation excludes the dislocation pinning effect of oxygen in solution.

Drastic Oscillation of Peierls Stress from Peierls-Nabarro Model Calculation and its Remedy

Drastic Oscillation of Peierls Stress from Peierls-Nabarro Model Calculation and its Remedy

Constructing Machine-learned Interatomic Potentials for SiC: MD Analyses of Dislocation

In Molecular Dynamics (MD), the motion of atoms is calculated based on the interatomic potential, which is a mathematical model of the interatomic interaction. Recently, some types of machine-learning interatomic potentials (ML-IAPs) are being proposed, which will reproduce adequately results of first-principles calculation without any empirical assumption or data. First-principles calculations should be avoided for large simulation models, such as edge dislocations, due to its high calculation costs. However, it is expected for ML-IAPs to analyze crystalline defects in large systems with the same accuracy as first-principles calculations. In this research, SNAP, which is one of ML-IAPs, was created for silicon carbide with cubic crystalline structure (3C-SiC), and it was examined on the reproducibility when it is applied to MD computation. It is confirmed that the SNAP we built from scratch has higher reproducibility than any empirical one in terms of lattice constant, elastic modulus, and bulk modulus. The edge dislocation cores properly moved along the predicted slip plane of 3C-SiC. In addition, the Peierls stress estimated by SNAP agrees well with that of covalent materials which is usually high.

The Third-Order Elastic Constants and Mechanical Properties of 30° Partial Dislocation in Germanium: A Study from the First-Principles Calculations and the Improved Peierls–Nabarro Model

The elastic constants, core width and Peierls stress of 30° partial dislocation in germanium has been investigated based on the first-principles calculations and the improved Peierls–Nabarro model. Our results suggest that the predictions of lattice constant and elastic constants given by LDA are in better agreement with experiment results. While the lattice constant is overestimated at about 2.4% and most elastic constants are underestimated at about 20% by the GGA method. Furthermore, when the applied deformation is larger than 2%, the nonlinear elastic effects should be considered. And with the Lagrangian strains up to 8%, taking into account the third-order terms in the energy expansion is sufficient. Except the original γ—surface generally used before (given by the first-principles calculations directly), the effective γ—surface proposed by Kamimura et al. derived from the original one is also used to study the Peierls stress. The research results show that when the intrinsic−stacking−fault energy (ISFE) is very low relative to the unstable−stacking−fault energy (USFE), the difference between the original γ—surface and the effective γ—surface is inapparent and there is nearly no difference between the results of Peierls stresses calculated from these two kinds of γ—surfaces. As a result, the original γ—surface can be directly used to study the core width and Peierls stress when the ratio of ISFE to the USFE is small. Since the negligence of the discrete effect and the contribution of strain energy to the dislocation energy, the Peierls stress given by the classical Peierls–Nabarro model is about one order of magnitude larger than that given by the improved Peierls–Nabarro model. The result of Peierls stress estimated by the improved Peierls–Nabarro model agrees well with the 2~3 GPa reported in the book of Solid State Physics edited by F. Seitz and D. Turnbull.

Glide Mobility of a-Type Edge Dislocations in Aluminum Nitride by Molecular Dynamics Simulation.

Classical molecular dynamics simulations are performed to investigate the motion of a-type edge dislocations in wurtzite aluminum nitride (AlN). The nucleation and propagation of kinks are observed via the dislocation extraction algorithm. Our simulation results show that the nucleation energy of the kink pair in AlN is 1.2 eV and that the migration energy is 2.8 eV. The Peierls stress of the 1/3⟨112̅0⟩{101̅0} edge dislocation at 0 K is 15.9 GPa. The viscous motion of dislocations occurs when τ > τp, and the dislocation velocity is inversely proportional to the temperature and directly proportional to the applied stress. Below room temperature, the value of the critical resolved shear stress (CRSS) on the prismatic plane is the lowest, which suggests that the dislocation mobility on the prismatic plane is the easiest. The CRSS on the pyramidal plane is always the highest at all temperatures, which suggests that pyramidal slip is the hardest among these three slip systems.

High-throughput exploration of the composition-dependent elasto-plastic properties in Co–Ni–W system

Co–Ni–W alloys are widely employed in aviation aerospace and power industries, and their elasto-plastic property data are very useful for the design and development of novel alloys. Electron probe microanalysis and nanoindentation tests were performed on 7 groups of Co–Ni–W diffusion couples annealed at 1373 K for 120 h, and a home-made MATLAB program based on the reverse analysis algorithms was used to obtain the composition-dependent elasto-plastic property data in a wide composition space of Co–Ni–W system. And the databanks of Young’s modulus, hardness, and yield stress over the whole face-centered cubic phase zone were then obtained by using machine learning approach. Subsequently, bulk and shear moduli of Co–Ni–W alloys were extrapolated from the experimental Young’s modulus and the constant Poisson’s ratio. Moreover, Peierls stresses varied with the compositions were calculated with the aid of shear modulus data to analyze the dislocation motion in the Co–Ni–W lattices. This work reveals the construction of composition-dependent elasto-plastic property databanks for multicomponent alloys, and the results indicate that Co–(0–7.8) at% Ni–(9.1–9.5) at% W alloys have high moduli and high hardness.

Low temperature deformation mechanisms of polycrystalline CoZr and Co39Ni11Zr50 B2-type intermetallic compounds

The B2-type intermetallic compounds CoZr and Co39Ni11Zr50 were deformed in tension at low temperatures. While CoZr is ductile down to 4 K, Co39Ni11Zr50 becomes brittle below 125 K due to a martensitic phase transformation. Thermal activation analysis shows that CoZr follows the Cottrell-Stokes law indicating forest dislocation cutting as the dominant rate-controlling deformation mechanism, similar to face-centered cubic metals. The moderate ductility of both intermetallic compounds at low temperatures may qualitatively be related to a significant metallic character of bonding giving rise to a low Peierls stress estimated for primary {110}<100> slip and most likely also leads to an easier activation of secondary {110}<110> slip which was proven by transmission electron microscopy. Secondary slip is necessary for the fulfillment of the von Mises criterion for homogeneous plastic deformation of polycrystalline materials. The present results generalize the findings made on the ductile rare earth intermetallics YAg and YCu and, therefore, may help to search for other ductile systems in the broad class of intermetallic compounds.

On the origin of internal obstacles to dislocation glide in single-phase NiFe random alloys

Over the past decade, a new class of unconventional alloys, where several constitutive elements are presented in close to equal concentrations, is considered as promising structural materials in many applications. Properties and behavior of many concentrated solid solution alloys (CSSAs) under different conditions, including mechanical loading, differs from that of conventional alloys and has been the subject of intensive studies by different techniques. A key feature of these materials is that there is no clear distinction between solute and solvent species of atoms, which is the conventional approach to considering dislocation motion in alloys. To understand this regime, we have recently reported on the glide of a screw dislocation glide in a simple equiatomic NiFe alloy and reported the two-mode character. At low applied stress, the dislocation motion is similar to a glide through a field of obstacles. In this paper, we report the results of a detailed study on the nature of these internal obstacles. We demonstrate that these are not conventional localized “obstacles” but is the result of significantly different energies of instantaneous dislocation configurations over the alloy bulk. The strong pinning positions are associated with composition changes in the partial dislocation cores, while observing no significant composition changes along the stacking faults. Local energies can vary significantly, as demonstrated using simulations of short-periodicity dislocation lines. Therefore, the critical stress to move a dislocation under such conditions is not a constant Peierls stress but represents a wide spectrum of barriers between different non-straight valleys that the dislocation line accommodates in the bulk at particular stress/strain conditions.

The core characteristics and Peierls stress of dislocations in {110} plane of B2–AlY

AlY alloys have many advantages and are widely used; nevertheless, few studies have been conducted on their mechanical properties. Dislocations strongly affect the properties of such materials, and therefore, the study of their core structure is fundamental to understanding their mechanical properties. In this study, we investigated the dislocation core characteristics of B2–AlY in the {110} plane through a truncated approximation method. The results show that the core width of an edge dislocation in the <111> direction is more significant than those in the <110> and <100> directions. This proves that the slip system of AlY is in the <110> {110} direction. In addition, we evaluated the dissociation widths of two partial dislocations, based on which the <111> superdislocation can be decomposed. The Peierls stress and the Peierls energy of the Burgers vectors in the <100>{110}, <110>{110}, and <111>{110} directions are also investigated. Our results show that as the dislocation angle increases, the elastic strain energy, misfit energy, Peierls energy, and Peierls stress decrease.

Temperature-dependent hardening contributions in CrFeCoNi high-entropy alloy

We studied the deformation behavior of CrFeCoNi high-entropy alloy by in situ neutron diffraction at room temperature, intermediate low temperature of 140 K, low temperatures of 40 K (no serrated deformation) and 25 K (with massive serrations). The evolution of lattice strain and texture along different grain orientations provided distinct insights into deformation behavior at low temperatures. The in situ data showed an early activation of stacking faults and a higher stacking fault probability with decreasing test temperature. The stacking fault probability reached ∼4.7% at low temperatures. The dislocation density at 40 and 25 K evolved similarly and had a very high value of ∼9.2 × 1015 m−2. However, twin fault probability at 25 K (∼6%) was higher than that at 40 K (∼5%). The samples at 40 and 25 K deformed uniformly and lacked any necking region, thus imparting an excellent ductility of ∼58%. The contributions from different deformation mechanisms to the yield strength and strain hardening have been estimated. The athermal contributions to the yield strength were ∼183 MPa at all temperatures, while the Peierls stress increased significantly at low temperatures (from 148 MPa at room temperature to 493 MPa at 25 K). Dislocations contributed to ∼94% strain hardening at room temperature. Although the dislocation strengthening remained the major hardening mechanism at very low temperatures, the planar faults contribution increased steadily from 6% at room temperature to 28% at 25 K.