We study the diffusion of anti-plane elastic waves in a two dimensional continuum by many, randomly placed, screw dislocations. Building on a previously developed theory for coherent propagation of such waves, the incoherent behavior is characterized by way of a Bethe Salpeter (BS) equation. A Ward-Takahashi identity (WTI) is demonstrated and the BS equation is solved, as an eigenvalue problem, for long wavelengths and low frequencies. A diffusion equation results and the diffusion coefficient $D$ is calculated. The result has the expected form $D = v^* l /2$, where $l$, the mean free path, is equal to the attenuation length of the coherent waves propagating in the medium and the transport velocity is given by $v^*= c_T^2/v$, where $c_T$ is the wave speed in the absence of obstacles and $v$ is the speed of coherent wave propagation in the presence of dislocations.
We investigate the nonuniform motion of a straight screw dislocation in infinite media in the framework of the translational gauge theory of dislocations. The equations of motion are derived for an arbitrary moving screw dislocation. The fields of the elastic velocity, elastic distortion, dislocation density and dislocation current surrounding the arbitrarily moving screw dislocation are derived explicitely in the form of integral representations. We calculate the radiation fields and the fields depending on the dislocation velocities.
In this paper we present the equations of motion of a moving screw dislocation in the framework of the translation gauge theory of dislocations. In the gauge field theoretical formulation, a dislocation is a massive gauge field. We calculate the gauge field theoretical solutions of a uniformly moving screw dislocation. We give the subsonic and supersonic solutions. Thus, supersonic dislocations are not forbidden from the field theoretical point of view. We show that the elastic divergences at the dislocation core are removed. We also discuss the Mach cones produced by supersonic screw dislocat…
The aim of this paper is to provide new results and insights for a screw dislocation in functionally graded media within the gauge theory of dislocations. We present the equations of motion for dislocations in inhomogeneous media. We specify the equations of motion for a screw dislocation in a functionally graded material. The material properties are assumed to vary exponentially along the x and y-directions. In the present work we give the analytical gauge field theoretic solution to the problem of a screw dislocation in inhomogeneous media. Using the dislocation gauge approach, rigorous anal…
The dislocation core field, which comes in addition to the Volterra elastic field, is studied for the <111> screw dislocation in alpha-iron. This core field, evidenced and characterized using ab initio calculations, corresponds to a biaxial dilatation, which we modeled within the anisotropic linear elasticity. We show that this core field needs to be considered when extracting quantitative information from atomistic simulations, such as dislocation core energies. Finally, we look at how dislocation properties are modified by this core field, by studying the interaction between two dislocations…
The interplay of screw dislocations with carbon atoms is investigated in tungsten at high temperature using in situ straining experiments in a transmission electron microscope (TEM) and through ab initio calculations. When the temperature is high enough to activate carbon diffusion, above 1373 K, carbon segregates in the core of screw dislocations and modifies their mobility, even for a carbon concentration as low as 1 appm. TEM observations reveal the reappearance of a Peierls mechanism at these high temperatures, with screw dislocations gliding viscously through nucleation and propagation of…
The interaction of screw dislocations with an applied stress is studied using atomistic simulations in conjunction with a continuum treatment of the role played by the far field boundary condition. A finite cell of atoms is used to consider the response of dislocations to an applied stress and this introduces an additional force on the dislocation due to the presence of the boundary. Continuum mechanics is used to calculate the boundary force which is subsequently accounted for in the equilibrium condition for the dislocation. Using this formulation, the lattice resistance curve and the associ…
In body-centred-cubic (bcc) metals migrating 1/2<111> screw dislocations experience a periodic energy landscape with a triangular symmetry. Atomistic simulations, such as those performed using the nudged-elastic-band (NEB) method, generally predict a transition-pathway energy-barrier with a double-hump; contradicting Ab Initio findings. Examining the trajectories predicted by NEB for a particle in a Peierls energy landscape representative of that obtained for a screw dislocation, reveals an unphysical anomaly caused by the occurrence of monkey saddles in the landscape. The implications for mot…
Plasticity in zirconium is controlled by 1/3<1-210> screw dislocations gliding in the prism planes of the hexagonal close-packed structure. This prismatic and not basal glide is observed for a given set of transition metals like zirconium and is known to be related to the number of valence electrons in the d band. We use ab initio calculations based on the density functional theory to study the core structure of screw dislocations in zirconium. Dislocations are found to dissociate in the prism plane in two partial dislocations, each with a pure screw character. Ab initio calculations also show…
We investigate the effect of hydrogen on the mobility of a screw dislocation in body-centered cubic (bcc) iron using first-principles calculations, and show that an increase of screw dislocation velocity is expected for a limited temperature range. The interaction energy between a screw dislocation and hydrogen atoms is calculated for various hydrogen positions and dislocation configurations with careful estimations of the finite size effects, and the strongest binding energy of a hydrogen atom to the stable screw dislocation configuration is estimated to be $256\pm32$ meV. These results are i…
The modest aim of this short article is to provide some new results for a screw dislocation in a functionally graded material within the theory of gradient elasticity. These results, based on a displacement formulation and the Fourier transform technique, extends earlier findings (Lazar, M., 2007. On a screw dislocation in a functionally graded material, Mech. Res. Comm. 34, 305-311) obtained by the stress function method, to the case of the second gradient elasticity. Rigorous and easy-to-use analytical expressions for the displacements, the strains and the stresses are obtained which are fre…
We use a real-space formulation of orbital-free DFT to study the core energetics and core structure of an isolated screw dislocation in Aluminum. Using a direct energetics based approach, we estimate the core size of a perfect screw dislocation to be $\approx$ 7 $|{\bf b}|$, which is considerably larger than previous estimates of $1-3~|{\bf b}|$ based on displacement fields. The perfect screw upon structural relaxation dissociates into two Shockley partials with partial separation distances of 8.2 Å~and 6.6 Å~ measured from the screw and edge component differential displacement plots, respecti…
We report the first ab initio density-functional study of <111> screw dislocations cores in the bcc transition metals Mo and Ta. Our results suggest a new picture of bcc plasticity with symmetric and compact dislocation cores, contrary to the presently accepted picture based on continuum and interatomic potentials. Core energy scales in this new picture are in much better agreement with the Peierls energy barriers to dislocation motion suggested by experiments.
Atomistic simulations, based either on an empirical interatomic potential or on ab initio calculations, are used to study the pyramidal glide of a 1/3 <1-210> screw dislocation in hexagonal close-packed zirconium. Generalized stacking fault calculations reveal a metastable stacking fault in the first order pyramidal {10-11} plane, which corresponds to an elementary pyramidal twin. This fault is at the origin of a metastable configuration of the screw dislocation in zirconium, which spontaneously appears when the dislocation glides in the pyramidal plane.
By direct application of stress in molecular statics calculations we identify the stress components that affect the glide of 1/2<111> screw dislocations in bcc tungsten. These results prove that the hydrostatic stress and the normal stress parallel to the dislocation line do not play any role in the dislocation glide. Therefore, the Peierls stress of the dislocation cannot depend directly on the remaining two normal stresses that are perpendicular to the dislocation, as proposed by Koester A, Ma A, Hartmaier A. Acta Mater 2012;60:3894 but, instead, on their combination that causes an equibiaxi…
We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations bilinear in the elastic distortion tensor and dislocation density tensor for the force and pseudomoment stresses of an isotropic solid. The constitutive relations contain six material parameters. In this theory both the force and pseudomoment stresses are asymmetric. The theory possesses four characteristic lengths l1, l2, l3 and l4 which are given explicitely. We first derive the three-dimensional Green tensor of the master equation for the force stresses in …
The properties of perfect screw dislocations have been investigated for several zinc-blende materials such as diamond, Si, $β$-SiC, Ge and GaAs, by performing first principles calculations. For almost all elements, a core configuration belonging to shuffle set planes is favored, in agreement with low temperature experiments. Only for diamond, a glide configuration has the lowest defect energy, thanks to an sp$^2$ hybridization in the core.
On the basis of the classical dislocation theory, the Solid Solution Hardening (SSH) is commonly ascribed to the pinning of the edge dislocations. At the atomic level, the theoretical study of the dislocation cores contrasts with such a prediction. Using the static molecular simulations with some interatomic effective potentials, we demonstrate numerically that the critical resolved shear stress associated to a screw dislocation in a random Ni(Al) single crystal has same order as the edge one. Such a result is imposed by the details of the dislocation stacking fault and the core dissociation i…
The stability of the perfect screw dislocation in silicon has been investigated using both classical potentials and first-principles calculations. Although a recent study by Koizumi et al . stated that the stable screw dislocation was located in both the 'shuffle' and the 'glide' sets of {111} planes, it is shown that this result depends on the classical potential used, and that the most stable configuration belongs to the 'shuffle' set only, in the centre of one hexagon. We also investigated the stability of an sp 2 hybridization in the core of the dislocation, obtained for one metastable con…
Basal slip of a screw dislocations in hexagonal closed-packed titanium is investigated with ab initio calculations. We show that a basal dissociation is highly unstable and reconfigures to other structures dissociated in a first order pyramidal plane. The obtained mechanism for basal slip corresponds to the migration of the partial dislocations and of the associated stacking fault ribbon in a direction perpendicular to the dissocia-tion plane. Presented results indicate that both basal and pyramidal slip will operate through the Peierls mechanism of double-kink nucleation and will be equally a…
The interaction between carbon and screw dislocations in tungsten is investigated using ab initio calculations. The presence of carbon atoms in the vicinity of the dislocation induces a reconstruction, with the dislocation relaxing to a configuration, the hard core structure, which is unstable in pure tungsten. The reconstruction corresponds to a strong binding of carbon in the prismatic sites created by the dislocation which is perfect for high concentrations of carbon segregated on the dislocation line. However, the reconstruction is only partial for lower atomic fractions, with the dislocat…
The influence of magnetism on the properties of screw dislocations in body-centered cubic chromium is investigated by means of ab initio calculations. Screw dislocations having Burgers vectors 1/2 111 and 100 are considered, following experimental observations showing activity for both slip systems. At low temperature, chromium has a magnetic order close to antiferromagnetism along 100 directions, for which 1/2 111 is not a periodicity vector. Hence, dislocations with Burgers vectors 1/2 111 generate magnetic faults when shearing the crystal, which constrain them to coexist and move pairwise, …
We employ density-functional-theory calculations to analyze the interactions between oxygen interstitial atoms and <a>-type screw dislocations (<a> = a<11-20>/3 ) in alpha-titanium, based on investigations of generalized stacking fault (GSF) energies, dislocation core structures and the strain field of an oxygen interstitial. Compared with the substitutional atoms such as Al, there is a large repulsive interaction between oxygen interstitials at the octahedral site and an <a>-type screw dislocation core, since the volume for the interstitial atom between Ti lattice sites is largely reduced in …
The Peierls stress of the a/2<110> screw dislocation belonging to the shuffle set is calculated for silicon using density functional theory. We have checked the effect of boundary conditions by using two models, the supercell method where one considers a periodic array of dislocations, and the cluster method where a single dislocation is embedded in a small cluster. The Peierls stress is underestimated with the supercell and overestimated with the cluster. These contributions have been calculated and the Peierls stress is determined in the range between 2.4 x 10-2 and 2.8 x 10-2 eV Å-3. When m…
The ability of a body-centered cubic metal to deform plastically is limited by the thermally activated glide motion of screw dislocations, which are line defects with a mobility exhibiting complex dependence on temperature, stress, and dislocation segment length. We derive an analytical expression for the velocity of dislocation glide, based on a statistical mechanics argument, and identify an apparent phase transition marked by a critical temperature above which the activation energy for glide effectively halves, changing from the formation energy of a double kink to that of a single kink. Th…
Enhanced Elevated-Temperature Strength in Refractory Complex Concentrated Alloys via Temperature-Induced Transition from Screw-to-Edge Dislocation Control
University of California, Davis（加州大学戴维斯分校）；Oak Ridge National Laboratory（橡树岭国家实验室）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
Recent experiments suggest that Mg condensation at threading dislocations induce current leakage, leading to degradation of GaN-based power devices. To study this issue, we perform first-principles total-energy electronic-structure calculations for various Mg and dislocation complexes. We find that threading screw dislocations (TSDs) indeed attract Mg impurities, and that the electronic levels in the energy gap induced by the dislocations are elevated towards the conduction band as the Mg impurity approaches the dislocation line, indicating that the Mg-TSD complex is a donor. The formation of …
Thermally-activated $\small{\nicefrac{1}{2}}<111>$ screw dislocation motion is the controlling plastic mechanism at low temperatures in body-centered cubic (bcc) crystals. Motion proceeds by the nucleation and propagation of atomic-sized kink pairs susceptible of being studied using molecular dynamics (MD). However, MD's natural inability to properly sample thermally-activated processes as well as to capture $\{110\}$ screw dislocation glide calls for the development of other methods capable of overcoming these limitations. Here we develop a kinetic Monte Carlo (kMC) approach to study single s…
A number of recent Molecular Dynamics (MD) simulations have demonstrated that screw dislocations in face centered cubic (fcc) metals can achieve stable steady state motion above the lowest shear wave speed ($v_\text{shear}$) which is parallel to their direction of motion (often referred to as transonic motion). This is in direct contrast to classical continuum analyses which predict a divergence in the elastic energy of the host material at a crystal geometry dependent `critical' velocity $v_\text{crit}$. Within this work, we first demonstrate through analytic analyses that the elastic energy …
Theoretical calculations of the structure, formation and migration of kinks on a non-dissociated screw dislocation in silicon have been carried out using density functional theory calculations as well as calculations based on interatomic potential functions. The results show that the structure of a single kink is characterized by a narrow core and highly stretched bonds between some of the atoms. The formation energy of a single kink ranges from 0.9 to 1.36 eV, and is of the same order as that for kinks on partial dislocations. However, the kinks migrate almost freely along the line of an undi…
The cross-slip process of a screw $<$a$>$ dislocation from the basal to the prismatic plane in magnesium was studied using the density functional theory and the molecular dynamics calculations. An atomistic method for calculating the total Peierls energy map has been devised to track the transition path of a dissociated and/or constricted screw $<$a$>$ dislocation in the cross-slip process. The barrier of a screw $<$a$>$ dislocation from the basal to the prismatic plane is estimated by the density functional theory for the first time to be $61.4\pm 2.0$ meV per Burgers vector length. The activ…
Spatial dependence of the magnetic field and the superconducting current in a flux line pinned by a screw dislocation are computed. Interaction of a superconducting vortex with the chiral-symmetry breaking elastic strain of a screw dislocation results in a helical current along the axis of the dislocation. It is argued that screw dislocations make impossible a force-free arrangement of flux lines in the presence of a transport current.
Interactions among dislocations and solute atoms are the basis of several important processes in metals plasticity. In body-centered cubic (bcc) metals and alloys, low-temperature plastic flow is controlled by screw dislocation glide, which is known to take place by the nucleation and sideward relaxation of kink pairs across two consecutive \emph{Peierls} valleys. In alloys, dislocations and solutes affect each other's kinetics via long-range stress field coupling and short-range inelastic interactions. It is known that in certain substitutional bcc alloys a transition from solute softening to…
Plasticity in hexagonal close-packed zirconium is controlled by screw dislocations which easily glide in the prismatic planes where they are dissociated. At high enough temperatures, these dislocations can deviate out of the prism planes to also glide in the first order pyramidal and basal planes. To get a better understanding of these secondary slip systems, we have performed molecular dynamics (MD) simulations of a screw dislocation gliding in a basal plane. The gliding dislocation remains dissociated in the prism plane where it performs a random motion and occasionally cross-slips out of it…
We show here how density functional theory calculations can be used to predict the temperatureand orientation-dependence of the yield stress of body-centered cubic (BCC) metals in the thermallyactivated regime where plasticity is governed by the glide of screw dislocations with a 1/2 <111> Burgers vector. Our numerical model incorporates non-Schmid effects, both the twinning/antitwinning asymmetry and non-glide effects, characterized through ab initio calculations on straight dislocations. The model uses the stress-dependence of the kink-pair nucleation enthalpy predicted by a line tension mod…
A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress field of an infinitely long screw dislocation in a cylinder, a dipole of screw dislocations and a coaxial screw dislocation in a finite cylinder. The stress fields have no singularities in the dislocation core and they are modified in the core due to the presence of localized moment stress. Additionally, we calculated the elastoplastic energies for the screw dis…
Based on the atomistic studies presented in Part I we develop analytical yield criteria for single crystals that capture the effect of shear stresses other than the Schmid stress (non-glide stresses) on the shear stress needed for dislocation glide (Peierls stress). These yield criteria characterize a non-associated plastic flow that originates owing to the complex response of 1/2<111> screw dislocations to an applied stress tensor. Employing these criteria we identify the operative slip systems for tensile/compressive loading along various axes within the standard stereographic triangle and d…
We report on thermal transport properties of wurtzite GaN in the presence of dislocations, by using molecular dynamics simulations. A variety of isolated dislocations in a nanowire configuration were analyzed and found to reduce considerably the thermal conductivity while impacting its temperature dependence in a different manner. We demonstrate that isolated screw dislocations reduce the thermal conductivity by a factor of two, while the influence of edge dislocations is less pronounced. The relative reduction of thermal conductivity is correlated with the strain energy of each of the five st…
Graphite is the thermodynamically stable form of carbon, and yet is remarkably difficult to synthesise. A key step in graphite formation is the removal of defects at high temperature ($>$2300~$^{\circ}$C) that allow graphenic fragments to rearrange into ordered crystallites. We find the critical defect controlling graphitisation is a screw dislocation that winds through the layers like a spiral staircase, inhibiting lateral growth of the graphenic crystallites ($L_a$) and preventing AB stacking of Bernal graphite. High-resolution transmission electron microscopy (HRTEM) identifies screws as in…
We propose a mesoscopic model that explains the factor of two to three discrepancy between experimentally measured yield stresses of BCC metals at low temperatures and typical Peierls stresses determined by atomistic simulations of isolated screw dislocations. The model involves a Frank-Read type source emitting dislocations that become pure screws at a certain distance from the source and, owing to their high Peierls stress, control its operation. However, due to the mutual interaction between emitted dislocations the group consisting of both non-screw and screw dislocations can move at an ap…
Owing to their non-planar cores 1/2<111> screw dislocations govern the plastic deformation of BCC metals. Atomistic studies of the glide of these dislocations at 0 K have been performed using Bond Order Potentials for molybdenum and tungsten that account for the mixed metallic and covalent bonding in transition metals. When applying pure shear stress in the slip direction it displays significant twinning-antitwinning asymmetry for molybdenum but not for tungsten. However, for tensile/compressive loading the Schmid law breaks down in both metals, principally due to the effect of shear stresses …
In traditional body-centered cubic (bcc) metals, the core properties of screw dislocations play a critical role in plastic deformation at low temperatures. Recently, much attention has been focused on refractory high-entropy alloys (RHEAs), which also possess bcc crystal structures. However, unlike face-centered cubic high-entropy alloys (HEAs), there have been far fewer investigations on bcc HEAs, specifically on the possible effects of chemical short-range order (SRO) in these multiple principal element alloys on dislocation mobility. Here, using density functional theory, we investigate the…
Body-centred cubic (BCC) transition metals tend to be brittle at low temperatures, posing significant challenges in processing and major concerns for damage tolerance. The brittleness is largely dictated by the screw dislocation core; the nature and control of which remain a puzzle after nearly a century. Here, we introduce a physics-based material index \{chi}, the energy difference between BCC and face-centred-cubic structures, that guides manipulation of core properties. The lattice friction and nucleation barrier have near-linear scaling with \{chi} and the core transforms from non-degener…
The fully two-dimensional Peierls barrier map of screw dislocations in BCC iron has been calculated using the first principles method to identify the migration path of a dislocation core. An efficient method to correct the effect of the finite size cell used in the first principles method on the energy of a lattice defect was devised to determine the accurate barrier profile. We find that the migration path is close to a straight line which is confined in a $\{110\}$ plane and the Peierls barrier profile is single-humped. This result clarifies a reason that the existing empirical potentials of…
In this paper, the dynamics of a system of a finite number of screw dislocations is studied. Under the assumption of antiplane linear elasticity, the two-dimensional dynamics is determined by the renormalised energy. The interaction of one dislocation with the boundary and of two dislocations of opposite Burgers moduli are analysed in detail and estimates on the collision times are obtained. Some exactly solvable cases and numerical simulations show agreement with the estimates obtained.
Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line defects moving at constant velocity. Troubled by singularities at certain `critical' velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences are usually attributed to neglecting the finite size of the core and to the restriction to constant velocity. In the isotropic limit, accelerating pure screw and edge dislocations were studied s…
By means of linear theory of elastoplasticity, solutions are given for screw and edge dislocations situated in an isotropic solid. The force stresses, strain fields, displacements, distortions, dislocation densities and moment stresses are calculated. The force stresses, strain fields, displacements and distortions are devoid of singularities predicted by the classical elasticity. Using the so-called stress function method we found modified stress functions of screw and edge dislocations.
Compared to cubic metals, whose primary slip mode includes twelve equivalent systems, the lower crystalline symmetry of hexagonal close-packed metals results in a reduced number of equivalent primary slips and anisotropy in plasticity, leading to brittleness at the ambient temperature. At higher temperatures, the ductility of hexagonal close-packed metals improves owing to the activation of secondary c+a pyramidal slip systems. Thus understanding the fundamental properties of corresponding dislocations is essential for the improvement of ductility at the ambient temperature. Here, we present t…
Hydrogen segregation around a straight screw dislocation in bcc iron
Laboratoire des Sciences de l’Ingénieur pour l’Environnement (LaSIE) - UMR CNRS 7356（环境工程科学实验室）；Laboratoire des Sciences des Procédés et des Matériaux (LSPM) - UPR 3407（工艺与材料科学实验室）
We theoretically demonstrate that screw dislocation (SD), a 1D topological defect widely present in semiconductors, exhibits ubiquitously a new form of spin-orbit coupling (SOC) effect. Differing from the widely known conventional 2D Rashba-Dresselhaus (RD) SOC effect that typically exists at surfaces/interfaces, the deep-level nature of SD-SOC states in semiconductors readily makes it an ideal SOC. Remarkably, the spin texture of 1D SD-SOC, pertaining to the inherent symmetry of SD, exhibits a significantly higher degree of spin coherency than the 2D RD-SOC. Moreover, the 1D SD-SOC can be tun…
Carbon nanofibers (NFs) have been envisioned with broad promising applications, such as nanoscale actuators and energy storage medium. This work reports for the first-time super-elastic tensile characteristics of NFs constructed from a screw dislocation of carbon nanocones (NF-S). The NF-S exhibits three distinct elastic deformation stages under tensile, including an initial homogeneous deformation, delamination, and further stretch of covalent bonds. The delamination process endows the NF-S extraordinary tensile deformation capability, which is not accessible from its counterpart with a norma…
Pinning interaction between a screw dislocation and a void in fcc copper is investigated by means of molecular dynamics simulation. A screw dislocation bows out to undergo depinning on the original glide plane at low temperatures, where the behavior of the depinning stress is consistent with that obtained by a continuum model. If the temperature is higher than 300 K, the motion of a screw dislocation is no longer restricted to a single glide plane due to cross slip on the void surface. Several depinning mechanisms that involve multiple glide planes are found. In particular, a depinning mechani…
