Peierls Barrier Research Articles

First-principles study on the mechanical properties of interstitial solid solution Aluminum–Boron alloy

The sputtering Al-B alloy film exhibits a unique growth structure and a high strengthening efficiency. In this study, the first-principles method was used to investigate the effect of addition B element on the mechanical properties of Al-B alloys, including the elastic properties, anisotropy, ideal shear strength, generalized stacking fault energy (GSFE), and dislocation core. Results indicate that the solid solution of B slightly decreases the elastic modulus of the alloy and decreases the ideal shear strength. Thus, the anisotropic tendency weakens, GSFE substantially increases, and the Peierls stress and Peierls barrier energy substantially increase. Therefore, the introduce of B has little effect on the intrinsic properties of the alloy, but the interstitial solid solution of B greatly increases the dislocation initiation energy, which limits the initiation and movement of dislocation, and has an important contribution to the strengthening effect.

Analyzing the cross slip motion of screw dislocations at finite temperatures in body-centered-cubic metals: molecular statics and dynamics studies

The plasticity of body-centered-cubic metals at low temperatures is substantially determined by the screw-dislocation kinetics. Because the core of screw dislocations in these metals has a non-planar structure, its motion is complex. For example, although density functional theory predicts slip on a {110} plane, the actual slip plane at elevated temperatures differs from the prediction. In this work, we explored state-of-the-art atomistic modeling methods and successfully reproduced the transition of the slip plane through a temperature increase. We then devised an algorithm to analyze the activation of dislocation jump over the Peierls barrier and discovered a possible origin of this unexpected phenomenon: thermal fluctuation leads to the kink-pair nucleation for cross slip jumps with no transition of the dislocation core structure.

The effects of solid solution and oxide dispersion alloying on the viscoelastic behavior of Au alloy thin films

The effects of solid solution and oxide dispersion alloying on viscoelastic relaxation behavior of Au alloy films were investigated by using gas pressure bulge testing in the temperature range of 20–80 °C. Three sets of 500 nm thick films were fabricated for the study: nominally pure Au, Au-V solid solution alloys with V concentration ranging from 0.89 to 5.4 at% V, and a Au-V2O5 nanoparticle dispersion alloy with a V concentration of 5.4 at%. The residual stress, unrelaxed plane strain modulus, and normalized time-dependent effective modulus were determined as a function of alloy type and temperature. Both alloying approaches resulted in a refined grain size that was thermally stable. As expected, the fractional modulus decay measured after 3 h was greater at higher temperatures for all cases. Solid solution strengthening and dispersion strengthening were both effective at reducing the 3-h modulus decay, and the Au-V2O5 films showed the largest resistance to relaxation at all temperatures studied. Activation energy analysis reveals a value of approximately 0.11 eV, matching the Peierls barrier height, for pure Au and the two alloys. The results are consistent with a viscoelastic stress relaxation mechanism based on reversible dislocation bowing, weak solid solution hardening through elastic solute/dislocation interactions, and strong dislocation pinning associated with oxide nanoparticles.

Interactions between bare and protonated Mg vacancies and dislocation cores in MgO

Water can be incorporated into the lattice of mantle minerals in the form of protons charge-balanced by the creation of cation vacancies. These protonated vacancies, when they interact with dislocations, influence strain rates by affecting dislocation climb, pinning the dislocation, and, potentially, by altering the Peierls barrier to glide. We use atomic scale simulations to investigate segregation of Mg vacancies to atomic sites within the core regions of dislocations in MgO. Energies are computed for bare and $$V_{{{\text{Mg}}}}^{\prime \prime }$$ protonated Mg vacancies occupying atomic sites close to ½ 〈110〉 screw dislocations, and ½ 〈110〉 {100} and ½ 〈110〉 {110} edge dislocations. These are compared with energies for equivalent defects in the bulk lattice to determine segregation energies for each defect. Mg vacancies preferentially bind to ½ 〈110〉 {100} edge dislocations, with calculated minimum segregation energies of − 3.54 eV for and − 4.56 eV for $${\text{2H}}_{{{\text{Mg}}}}^{{\text{x}}}$$ . The magnitudes of the minimum segregation energies calculated for defects binding to ½ 〈110〉 {110} edge or ½ 〈110〉 screw dislocations are considerably lower. Interactions with the dislocation strain field lift the threefold energy degeneracy of the $${\text{2H}}_{{{\text{Mg}}}}^{{\text{x}}}$$ defect in MgO. These calculations show that Mg vacancies interact strongly with dislocations in MgO, and may be present in sufficiently high concentrations to affect dislocation mobility in both the glide- and climb-controlled creep regimes.

Temperature Dependences of Mechanical Properties and Fracture Features of Low-Activation Ferritic-Martensitic EK-181 Steel in a Temperature Range from – 196 to 720°C

The features of the microstructure, structural-phase transformations, and regularities of the change in the short-term mechanical properties of low-activation 12% chromium ferritic-martensitic steel EK-181 together with the features of its plastic deformation and fracture by the active stretching method in a temperature range from–196 to 720°C are investigated. The high efficiency of dispersive hardening by nanoscale particles V(C, N) provides a weak temperature dependence of the steel strength properties with increasing temperature from 20 to 450°C. A significant increase in the temperature dependence of the steel yield strength is observed in the ductile-to-brittle transition interval (below T ~ 20°C). In a temperature range from–196 to 720°С, the change in the plasticity regularities and the mode of steel fracture are closely related to the features of the temperature dependence of the yield stress and ultimate tensile strength. In the region of temperatures above 0°С (up to ~450°С), these features are determined by the weak temperature dependence of the value of dispersion hardening by nanoscale vanadium carbonitride particles; in the temperature range below 0°С, they are determined by a strong temperature dependence of the thermally activated mobility of dislocations in the crystalline relief (the Peierls barrier, solid solution of impurities).

Slip of shuffle screw dislocations through tilt grain boundaries in silicon

In this paper, molecular dynamics (MD) simulations of the interaction between tilt grain boundaries (GBs) and a shuffle screw dislocation in silicon are performed. Results show that dislocations transmit into the neighboring grain for all GBs in silicon. For Σ3,Σ9 and Σ19 GBs, when a dislocation interacts with a heptagon site, it transmits the GB directly. In contrast, when interacting with a pentagon site, it first cross slips to a plane on the heptagon site and then transmits the GB. The energy barrier is also quantified using the climbing image nudged elastic band (CINEB) method. Results show that Σ3 GB provides a barrier for dislocation at the same level of the Peierls barrier. For both Σ9 and Σ19 GBs, the barrier from the heptagon sites is much larger than the pentagon sites. Since the energy barrier for crossing all the GBs at the heptagon sites is only slightly larger than the Peierls barrier, perfect screw dislocations cannot pile up against these GBs. Furthermore, the critical shear stress averaged over the whole sample for the transmission through the Σ9 and Σ19 GBs is almost twice on heptagon site for initially equilibrium dislocation comparing with dislocations moving at a constant velocity.

A theoretical investigation of the glide dislocations in the sphalerite ZnS

The 90° and 30° partial glide dislocations in ZnS are investigated theoretically in the framework of the fully discrete Peierls model and first-principles calculation. It is found that there are four types of equilibrium cores for each kind of partial glide dislocation, which are named as the O-Zn-core, the B-Zn-core, the O-S-core, and the B-S-core, according to their geometrical feature and atomic ingredient at the core. For the 90° partial dislocation, the O-Zn-core (double-period core) and the B-S-core (single-period core) are stable. The Peierls barrier heights of the O-Zn-core and the B-S-core are about 0.03 eV/Å and 0.01 eV/Å, respectively. For the 30° partial dislocation, the O-Zn-core (double-period core) and the B-Zn-core (single-period core) are stable and their Peierls barrier heights are approximately the same as that of the O-Zn-core of the 90° partial dislocation. The Peierls stress related to the barrier height is about 800 MPa for the 90° partial dislocation with the B-S-core. The existence of unstable equilibrium cores enables us to introduce the concept of the partial kink. Based on the concept of the partial kink, a minimum energy path is proposed for the formation and migration of kinks. It is noticed that the step length in kink migration is doubled due to the core reconstruction.

The Effect of Al and V Solutes on Dislocation Motion in Titanium Alloys: A First-Principles Study

The deformation mode of some titanium (Ti) alloys differs from that of pure Ti because of the presence of a secondary phase and alloying elements in the α-phase. Herein, we investigated the effect of Al and V solutes as typical additive elements on the dislocation motion in Ti alloys using density functional theory (DFT) calculations. Calculations of the stacking fault (SF) energy in all possible slip planes indicated that both Al and V solutes reduce the SF energy in the basal plane and the Al solute especially increases the SF energy in the prismatic plane, making the energy for slip motion in different planes more comparable. To clarify the energy differences between various dislocation core structures, we evaluated all possible core structures and motion in various slip planes. The energy difference between most stable pyramidal and prismatic cores is very small (22.8 meV/b), whereas that between the prismatic and basal cores is larger (127 meV/b), thereby preventing dislocation motion in the basal plane in pure Ti. However, the Peierls barrier for motion in the basal plane is not as high (15 meV/b) if the dislocation exists in the basal core. Direct calculations for the dislocation core around solutes revealed that both Al and V solutes facilitate dislocation motion in the basal plane by reducing the energy difference between the core structures while these solutes have a reverse trend for the interaction energy with the dislocation core.

Quantum effects on dislocation motion from ring-polymer molecular dynamics

Quantum motion of atoms known as zero-point vibration was recently proposed to explain a long-standing discrepancy between theoretically computed and experimentally measured low-temperature plastic strength of iron and possibly other metals with high atomic masses. This finding challenges the traditional notion that quantum motion of atoms is relatively unimportant in solids comprised of heavy atoms. Here we report quantum dynamic simulations of quantum effects on dislocation motion within the exact formalism of Ring-Polymer Molecular Dynamics (RPMD). To extend the reach of quantum atomistic simulations to length and time scales relevant for extended defects in materials, we implemented RPMD in the open-source code LAMMPS thus making the RPMD method widely available to the community. We use our RPMD/LAMMPS approach for direct calculations of dislocation mobility and its effects on the yield strength of α-iron. Our simulation results establish that quantum effects are noticeable at temperatures below 50 K but account for only a modest (≈13% at T = 0 K) overall reduction in the Peierls barrier, at variance with the factor of two reduction predicted earlier based on the more approximate framework of harmonic transition state theory. Our results confirm that zero-point vibrations provide ample additional agitation for atomic motion that increases with decreasing temperature, however its enhancing effect on dislocation mobility is largely offset by an increase in the effective atom size, an effect known as quantum dispersion that has not been accounted for in the previous calculations.

Numerical Simulation of the Movement of Frenkel–Kontorova Dislocations in Aluminum Single Crystals at Low Temperatures

The motion of Frenkel–Kontorova dislocations in the single crystals of aluminum at low temperatures has been studied, by means of the computer simulation. It is shown that the dislocation movement is realized by the quantum tunneling of the kinks of dislocations through the Peierls barriers. It is shown that the action of the Peierls high barrier is analogous to the action of low temperatures, and if the Peierls barrier overcome, the dislocation moves unevenly, accelerating under the action of the Peierls barrier and slowing down after overcoming the Peierls barrier. Based on the numerical experiment, the mean free path of dislocation, the distance between the Peierls potential barriers and the width of the Peierls barrier are calculated. The computed values correspond to the real values.

Variational construction of positive entropy invariant measures of Lagrangian systems and Arnold diffusion

We develop a variational method for constructing positive entropy invariant measures of Lagrangian systems without assuming transversal intersections of stable and unstable manifolds, and without restrictions to the size of non-integrable perturbations. We apply it to a family of $2\frac{1}{2}$ degrees of freedom a priori unstable Lagrangians, and show that if we assume that there is no topological obstruction to diffusion (precisely formulated in terms of topological non-degeneracy of minima of the Peierls barrier), then there exists a vast family of ‘horseshoes’, such as ‘shadowing’ ergodic positive entropy measures having precisely any closed set of invariant tori in its support. Furthermore, we give bounds on the topological entropy and the ‘drift acceleration’ in any part of a region of instability in terms of a certain extremal value of the Fréchet derivative of the action functional, generalizing the angle of splitting of separatrices. The method of construction is new, and relies on study of formally gradient dynamics of the action (coupled parabolic semilinear partial differential equations on unbounded domains). We apply recently developed techniques of precise control of the local evolution of energy (in this case the Lagrangian action), energy dissipation and flux.

Direct observation of recombination-enhanced dislocation glide in heteroepitaxial GaAs on silicon

We use an electron beam to induce and directly observe dislocation glide in strained GaAs thin films on silicon substrates at room temperature using electron channeling contrast imaging (ECCI). Plastic behavior in this brittle material is kinetically facilitated by a lowering of the Peierls barrier for glide due to recombination of cathodogenerated electron-hole pairs at dislocations. The high residual strain in the GaAs film provides the overall driving force for motion. The dynamics of a variety of previously inaccessible dislocation interactions are studied by tracking individual threading dislocations with high spatial and temporal resolution. The ECCI technique has an inherently high resolution and was conducted in a convenient scanning electron microscope environment. The results and methods described in this Rapid Communication provide insight into dislocation-filtering processes and failure mechanisms in technologically important III-V devices on silicon, as well as other mismatched heteroepitaxial systems.

First-principles investigation of the micromechanical properties of fcc-hcp polymorphic high-entropy alloys

High-entropy alloys offer a promising alternative in several high-technology applications concerning functional, safety and health aspects. Many of these new alloys compete with traditional structural materials in terms of mechanical characteristics. Understanding and controlling their properties are of the outmost importance in order to find the best single- or multiphase solutions for specific uses. Here, we employ first-principles alloy theory to address the micro-mechanical properties of five polymorphic high-entropy alloys in their face-centered cubic (fcc) and hexagonal close-packed (hcp) phases. Using the calculated elastic parameters, we analyze the mechanical stability, elastic anisotropy, and reveal a strong correlation between the polycrystalline moduli and the average valence electron concentration. We investigate the ideal shear strength of two selected alloys under shear loading and show that the hcp phase possesses more than two times larger intrinsic strength than that of the fcc phase. The derived half-width of the dislocation core predicts a smaller Peierls barrier in the fcc phase confirming its increased ductility compared to the hcp one. The present theoretical findings explain a series of important observations made on dual-phase alloys and provide an atomic-level knowledge for an intelligent design of further high-entropy materials.

Understanding thermally-activated glide of [formula omitted] screw dislocations in UO2 – A molecular dynamics analysis

As shown experimentally, the interplay between screw and edge dislocations in uranium dioxide (UO2) determines the low-temperature plasticity in this material. For the latter, neither the mobility of screw dislocations nor the mechanisms of their glide had been assessed – up until now. It is particularly interesting to evaluate the mobility of 1/2〈110〉{110} screw dislocations, supposedly the least mobile in UO2 due to the allegedly extremely high Peierls barrier of their motion. To address this issue, molecular dynamics simulations of dislocation glide are conducted on Lomonosov/MVS-10P supercomputers with LAMMPS software, and post-processing is done using DXA/OVITO. Under changing temperature and stress, the following variations of thermally-activated glide are found: nucleation and expansion of double kinks, formation and recombination of 1/6〈112〉 Shockley partials, self-pinning and production of debris, formation of sessile 1/3〈111〉 Frank loops. Velocity function of 1/2〈110〉{110} dislocations calculated at temperatures T=500–2000 K and shear stresses σ=10–1000 MPa shows a weak temperature dependence and becomes higher than the velocity of 1/2〈110〉{001} edge dislocations at temperatures T<1250 K.

Microband induced plasticity and the temperature dependence of the mechanical properties of a carbon-doped FeNiMnAlCr high entropy alloy

The uniaxial mechanical properties of the high entropy alloy (HEA) Fe40.4Ni11.3Mn34.8Al7.5Cr6 doped with 1.1 at.% C have been determined for both the as-cast and recrystallized states at temperatures from 77 to 973 K. Very high yield strengths were obtained at 77 K of 928 MPa for the as-cast HEA and 1037 MPa for the recrystallized HEA. The yield strength decreased sharply to 293 K and more slowly to 973 K, where it was ~200 MPa [11] in both conditions. The lattice friction stress, which results from the increase of the Peierls barrier, was the major contributor to the large yield strength at 77 K. On the other hand, the grain boundaries lose their strengthening ability at a high temperature, which largely accounts for the sharp drop in yield strength of the fine-grained (5 μm) recrystallized HEA at 973 K. The elongation to failure was highest at 293 K and 673 K with the lowest values at 77 K. Transmission electron microscopy was used to study the effects of temperature on the deformation mechanisms of the HEAs, especially the temperature dependence of the microband-induced plasticity effect. At temperatures ranging from 77 K to 673 K microbands form in the as-cast HEA, while dislocation clusters were observed in the recrystallized HEA over this temperature range. Only tangled dislocations were found at 973 K for both the as-cast and recrystallized HEA due to thermally-activated deformation.

Polyacetylene: Myth and Reality.

Polyacetylene, the simplest and oldest of potentially conducting polymers, has never been made in a form that permits rigorous determination of its structure. Trans polyacetylene in its fully extended form will have a potential energy surface with two equivalent minima. It has been assumed that this results in bond length alternation. It is, rather, very likely that the zero-point energy is above the Peierls barrier. The experimental studies that purport to show bond alternation are reviewed and shown to be compromised by serious experimental inconsistencies or by the presence, for which there is considerable evidence, of finite chain polyenes. In this view, addition of dopants results in conductivity by facilitation of charge transport between finite polyenes. The double minimum potential that necessarily occurs for polyacetylene, if viewed as the result of elongation of finite chains, originates from admixture of the 11Ag ground electronic state with the 21Ag excited electronic singlet state. This excitation is diradical (two electron) in character. The polyacetylene limit is an equal admixture of these two 1Ag states making theory intractable for long chains. A method is outlined for preparation of high molecular weight polyacetylene with fully extended chains that are prevented from reacting with neighboring chains.

(TiZrNbTa)-Mo high-entropy alloys: Dependence of microstructure and mechanical properties on Mo concentration and modeling of solid solution strengthening

In this work, the evolution of microstructure and fundamental mechanical properties with Mo concentration in the arc-melted (TiZrNbTa)100-xMox (0 ≤ x ≤ 20) high-entropy alloys (HEAs) are investigated. The arc-melted (TiZrNbTa)100-xMox alloys structurally consist of two bcc phases. The change in volume fractions of two phases in the microstructure is insignificant with Mo concentration, at levels of ∼75% for bcc1 and ∼25% for bcc2. The increases in microhardness and Young's modulus of the alloys linearly scale with Mo concentration. To compromise the strength and ductility, the (TiZrNbTa)90Mo10 exhibits an optimal combination of stiffness (E = 137 GPa), compressive yield strength (σy = 1370 MPa) and deformability (εp ≈ 25%). In addition, it is indicated that dislocation widths in bcc lattice of refractory HEAs are insensitive to the alloying complexity, reflecting that the Peierls barrier is excluded as a predominant factor of strengthening. Furthermore, a simple model is proposed to reveal the solid solution hardening (SSH) in bcc refractory HEAs, in which the solid solutions are treated as an imposition of distortion-free and distorted lattices. By applying this model to archived refractory HEAs, the predicted yield strength agrees well with experimentally measured values. It provides a simple empirical tool used for predicting the strength of bcc refractory HEAs and to assist new alloy design.

Analysis of the Motion of Frenkel-Kontorova Dislocations in Single Crystals of Aluminum with Allowance for the Peierls Barrier

The regularities of the motion of a one-dimensional Frenkel-Kontorova dislocation in pure aluminum at helium temperatures are studied. Computer simulation was carried out using the sine Gordon equation, written in dimensionless variables. It is proven that when the transition to dimensionless variables the discreteness of the model is preserved. The dependence of the true values of stresses on deformation in the Euler variables, as well as the velocity distribution of the dislocation fragments along the coordinate for successive instants of time, are obtained. It is shown that under these conditions dislocation motion is realized by quantum tunneling of the dislocation bends. The quantum-mechanical estimate confirms the possibility of quantum tunneling of the kink of dislocations in aluminum at low temperatures.

Ab initio investigation on the slip preference of 〈a〉-dislocations in hexagonal metals and alloys

Slip preference is investigated via ab initio calculations in hexagonal metals, Be, Mg, Ti, Zn and Zr, as well as alloyed Mg and Ti. In general, the unstable stacking fault energy, γus, which is relevant with the Peierls barrier, plays the key role in determining slip preference. In the materials studied, slip is preferred on the plane that possesses a lower γus. Detailed studies indicate that γus, determined by the directionality of electron bonding, is primarily relevant to the c/a ratio. In alloyed Mg and Ti, alloying varies the c/a ratio, but due to different dependences of γus on c/a, certain alloying elements significantly affect 〈a〉-slip preference in Mg, while alloying exhibits negligible influence on 〈a〉-slip preference in hexagonal Ti.

The effect of temperature on the elastic precursor decay in shock loaded FCC aluminium and BCC iron

This article offers a comprehensive experimental and theoretical study of the causes of thermal hardening in FCC Al and BCC Fe at high strain rates, with the aim to shed light on important mechanisms governing deformation and failures in materials subjected to shocks and impacts at very high strain rates. Experimental evidence regarding the temperature dependence of the dynamic yield point of FCC Al and BCC Fe shock loaded at 107 s−1 is provided. The dynamic yield point of Al increases with temperature in the range 125K–795K; for the same loading and temperate range, the dynamic yield point of BCC Fe remains largely insensitive. A Multiscale Discrete Dislocation Plasticity (MDDP) model of both Fe and Al is developed, leading to good agreement with experiments. The importance of the Peierls barrier in Fe is highlighted, showing it is largely responsible for the temperature insensitivity in BCC metals. The relevance of the mobility of edge components in determining the plastic response of both FCC Al and BCC Fe at different temperatures is discussed, which leads to developing a mechanistic explanation of the underlying mechanisms leading to the experimental behaviour using Dynamic Discrete Dislocation Plasticity (D3P). It is shown that the main contributing factor to temperature evolution of the dynamic yield point is not the mobility of dislocations, but the temperature variation of the shear modulus, the decrease of which is correlated to the experimental behaviour observed for both FCC Al and BCC Fe.