Temperature dependence of the mechanical properties of equiatomic solid solution alloys with face-centered cubic crystal structures

Dynamic fracture mechanics

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Dislocations in solids

The origin of the Peierls model and its relation to that of Frenkel and Kontorova are described. Within this model there are three essentially different formulae for the stress required to move a dislocation rigidly through a perfect lattice, associated with the names of Peierls, Nabarro and Huntington. There are also three distinct approaches to experimental estimates of the Peierls stress, depending on the Bordoni internal friction peak, the flow stress at low temperatures and Harper-Dorn creep. The results in the case of close-packed metals can be reconciled with the aid of ideas due to Benoit et al. and to Schoeck. The analytical elegance of Peierls's solution depends on the assumption of a sinusoidal law of force across the glide plane. This is physically unrealistic. Foreman et al. and others have obtained interesting results using other laws of force, while still operating in the framework of the Peierls model. The locking-unlocking model extends the ideas to the case in which the dislocation core has two mechanically stable configurations.

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Fifty-year study of the Peierls-Nabarro stress

The low-temperature plastic yield of $\ensuremath{\alpha}$-Fe single crystals is known to display a strong temperature dependence and to be controlled by the thermally activated motion of screw dislocations. In this paper, we present molecular dynamics simulations of $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$${112}$ screw dislocation motion as a function of temperature and stress in order to extract mobility relations that describe the general dynamic behavior of screw dislocations in pure $\ensuremath{\alpha}$-Fe. We find two dynamic regimes in the stress-velocity space governed by different mechanisms of motion. Consistent with experimental evidence, at low stresses and temperatures, the dislocations move by thermally activated nucleation and propagation of kink pairs. Then, at a critical stress, a temperature-dependent transition to a viscous linear regime is observed. Critical output from the simulations, such as threshold stresses and the stress dependence of the kink activation energy, are compared to experimental data and other atomistic works with generally very good agreement. Contrary to some experimental interpretations, we find that glide on ${112}$ planes is only apparent, as slip always occurs by elementary kink-pair nucleation/propagation events on ${110}$ planes. Additionally, a dislocation core transformation from compact to dissociated has been identified above room temperature, although its impact on the general mobility is seen to be limited. This and other observations expose the limitations of inferring or presuming dynamic behavior on the basis of only static calculations. We discuss the relevance and applicability of our results and provide a closed-form functional mobility law suitable for mesoscale computational techniques.

https://digital.library.unt.edu/ark:/67531/metadc870872/m2/1/high_res_d/1117937.pdf

Stress and temperature dependence of screw dislocation mobility in α -Fe by molecular dynamics

The activation energy ΔH ∗ for forming a rectangular kink pair in a dislocation on a Peierls potential is calculated. If the potential is smooth and has only one minimum, the energy ΔH ∗ (τ) decreases monotonously with the applied stress τ. If the potential has the shape of a camel-hump, with an intermediate minimum, discontinuities appear in ΔH ∗ (τ) . When the top of the potential is nearly flat or has a shallow minimum, the ΔH ∗ (τ) curve has a hump, causing a hump in the temperature dependence of the critical shear stress.

Kink pair nucleation and critical shear stress

A dislocation moving in a lattice accelerates and decelerates due to the lattice periodicity and emits lattice waves. Simulations of this process in square and triangular lattices have been presented. Under a small stress, less than 70--80 % of the Peierls stress, a dislocation moving from an unstable position cannot overcome the next Peierls hill because it loses energy by emitting lattice waves. With a larger stress a long-distance motion of a dislocation is possible. When a dislocation moves slowly, lattice waves of dipolar type are emitted in the direction perpendicular to the motion of the dislocation. When the dislocation velocity is about half of the shear wave velocity, a V-shaped pattern of strong lattice vibration forms behind the moving dislocation because of the restricted propagation directions of the excited lattice waves. When the dislocation velocity exceeds 70% of the shear wave velocity, pair creation of dislocations occurs, which leads to dislocation cascading. A dislocation can move faster than the shear wave velocity in the square lattice, and there is no discontinuous change between subsonic and supersonic motions. The dislocation velocity is not proportional to the applied stress. The energy loss of the moving dislocation is about one order of magnitude larger than the theoretical value estimated by phonon-scattering mechanisms, even at room temperature.

Lattice wave emission from a moving dislocation

The Peierls stress is calculated for a discrete Peierls—Nabarro model of a dislocation. Unlike the original continuum model where a continuous distribution of infinitesimal dislocations was considered, the discreteness of the slip plane is maintained throughout the calculation, and the Peierls stress τp is determined as the critical applied stress beyond which the stability of the system breaks. Results for three types of interatomic shear potential are well approximated by the relation τp G∞ exp(−Ah/b), as predicted by the continuum model, G being the shear modulus, b the spacing between slip planes, b the length of the Burgers vector and A a constant depending on the potentials. The magnitude of τp of the discrete model is larger than that of the continuum model for the same sinusoidal potential. Long-range potentials give low τp although they are still larger than experimental values.

The critical stress in a discrete Peierls–Nabarro model

We study the finite-temperature transition to the $m=1/2$ magnetization plateau in a model of interacting $S=1/2$ spins with longer-range interactions and strong exchange anisotropy on the geometrically frustrated Shastry-Sutherland lattice. This model was shown to capture the qualitative features of the field-induced magnetization plateaus in the rare-earth tetraboride, ${\text{TmB}}_{4}$. Our results show that the transition to the plateau state occurs via two successive transitions with the two-dimensional Ising universality class, when the quantum exchange interactions are finite, whereas a single phase transition takes place in the purely Ising limit. To better understand these behaviors, we perform Monte Carlo simulations of the classical generalized four-state chiral clock model and compare the phase diagrams of the two models. Finally, we estimate a parameter set that can explain the magnetization curves observed in ${\text{TmB}}_{4}$. The magnetic properties and critical behavior of the finite-temperature transition to the $m=1/2$ plateau state are also discussed.

Finite-temperature phase transition to the m=(1)/(2) plateau phase in the spin- (1)/(2) XXZ model on the Shastry-Sutherland lattices

We study photon-assisted transport in a single-level quantum dot system under a periodically oscillating field. Photon-assisted current noise in the presence of the Coulomb interaction is calculated based on a gauge-invariant formulation of time-dependent transport. We derive the vertex corrections within the self-consistent Hartree-Fock approximation in terms the Floquet-Green's functions (Floquet-GFs) and examine the effects of the Coulomb interaction on the photon-assisted current noise. Moreover, we utilize an effective temperature to characterize nonequilibrium properties under the influence of the ac field. The vertex corrections are suppressed by the rise of the effective temperature, whereas characteristic peak structures appear in the frequency spectra of the vertex corrections. The present result provides a useful viewpoint for understanding photon-assisted transport in interacting electron systems.

T. Suzuki

Papers

Kink pair nucleation and critical shear stress

Lattice wave emission from a moving dislocation

The critical stress in a discrete Peierls–Nabarro model

Finite-temperature phase transition to the m=(1)/(2) plateau phase in the spin- (1)/(2) XXZ model on the Shastry-Sutherland lattices

Effects of Coulomb interaction on photon-assisted current noise through a quantum dot