Phonons radiated by moving dislocations in disordered alloys (original) (raw)
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Physical Review B, 2006
Using atomistic simulations of dislocation motion in Ni and Ni-Au alloys we report a detailed study of the mobility function as a function of stress, temperature, and alloy composition. We analyze the results in terms of analytic models of phonon radiation and their selection rules for phonon excitation. We find a remarkable agreement between the location of the cusps in the -v relation and the velocity of waves propagating in the direction of dislocation motion. We identify and characterize three regimes of dissipation whose boundaries are essentially determined by the direction of motion of the dislocation, rather than by its screw or edge character.
Nanomaterials, 2020
A canonical quantization procedure is applied to the interaction of elastic waves—phonons—with infinitely long dislocations that can oscillate about an equilibrium, straight line, configuration. The interaction is implemented through the well-known Peach–Koehler force. For small dislocation excursions away from the equilibrium position, the quantum theory can be solved to all orders in the coupling constant. We study in detail the quantum excitations of the dislocation line and its interactions with phonons. The consequences for the drag on a dislocation caused by the phonon wind are pointed out. We compute the cross-section for phonons incident on the dislocation lines for an arbitrary angle of incidence. The consequences for thermal transport are explored, and we compare our results, involving a dynamic dislocation, with those of Klemens and Carruthers, involving a static dislocation. In our case, the relaxation time is inversely proportional to frequency, rather than directly pro...
Dislocation drag from phonon wind in an isotropic crystal at large velocities
Philosophical Magazine, 2019
The anharmonic interaction and scattering of phonons by a moving dislocation, the photon wind, imparts a drag force v B(v, T, ρ) on the dislocation. In early studies the drag coefficient B was computed and experimentally determined only for dislocation velocities v much less than transverse sound speed, c T. In this paper we derive analytic expressions for the velocity dependence of B up to c T in terms of the third-order continuum elastic constants of an isotropic crystal, in the continuum Debye approximation, valid for dislocation velocities approaching the sound speed. In so doing we point out that the most general form of the third order elastic potential for such a crystal and the dislocation-phonon interaction requires two additional elastic constants involving asymmetric local rotational strains, which have been neglected previously. We compute the velocity dependence of the transverse phonon wind contribution to B in the range 1%-90% c T for Al, Cu, Fe, and Nb in the isotropic Debye approximation. The drag coefficient for transverse phonons scattering from screw dislocations is finite as v → c T , whereas B is divergent for transverse phonons scattering from edge dislocations in the same limit. This divergence indicates the breakdown of the Debye approximation and sensitivity of the drag coefficient at very high velocities to the microscopic crystalline lattice cutoff. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory of dislocation drag at high velocities with realistic phonon dispersion relations, inclusion of lattice cutoff effects, MD simulation data, and more accurate experimental measurements.
Theory of electron–phonon–dislon interacting system—toward a quantized theory of dislocations
New Journal of Physics, 2018
We provide a comprehensive theoretical framework to study how crystal dislocations influence the functional properties of materials, based on the idea of a quantized dislocation, namely a 'dislon'. In contrast to previous work on dislons which focused on exotic phenomenology, here we focus on their theoretical structure and computational power. We first provide a pedagogical introduction that explains the necessity and benefits of taking the dislon approach and why the dislon Hamiltonian takes its current form. Then, we study the electron-dislocation and phonon-dislocation scattering problems using the dislon formalism. Both the effective electron and phonon theories are derived, from which the role of dislocations on electronic and phononic transport properties is computed. Compared with traditional dislocation scattering studies, which are intrinsically single-particle, loworder perturbation and classical quenched defect in nature, the dislon theory not only allows easy incorporation of quantum many-body effects such as electron correlation, electron-phonon interaction, and higher-order scattering events, but also allows proper consideration of the dislocation's long-range strain field and dynamic aspects on equal footing for arbitrary types of straight-line dislocations. This means that instead of developing individual models for specific dislocation scattering problems, the dislon theory allows for the calculation of electronic structure and electrical transport, thermal transport, optical and superconducting properties, etc, under one unified theory. Furthermore, the dislon theory has another advantage over empirical models in that it requires no fitting parameters. The dislon theory could serve as a major computational tool to understand the role of dislocations on multiple materials' functional properties at an unprecedented level of clarity, and may have wide applications in dislocated energy materials.
On the velocity dependence of the dislocation drag coefficient from phonon wind
2018
The phonon wind mechanism, that is, the anharmonic interaction and scattering of phonons by a moving dislocation, imparts a drag force B(v, T, ρ) v on the dislocation. The drag coefficient B has been previously computed and experimentally determined only for dislocation velocities v much less than transverse sound speed, c T. In this paper we derive an expression for the velocity dependence of B up to c T in terms of the third-order elastic constants of the crystal. We compute the velocity dependence of the phonon wind contribution to B in the range 1%-90% c T for Al, Cu, Fe, and Nb in the isotropic Debye approximation, and to better accuracy than in earlier studies. It is proved that the drag coefficient for screw dislocations scattering transverse phonons is finite as v → c T , whereas B is divergent for edge dislocations scattering transverse phonons in the same limit. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory with more realistic phonon dispersion relations, MD simulations, and more accurate measurements.
Ab initio calculation of phonon dispersions in size-mismatched disordered alloys
Physical Review B, 2010
Size mismatch and the resulting local lattice relaxations play a very crucial role in determining the latticedynamical properties of substitutionally disordered alloys. In this paper we focus on the influence of size mismatch between the components of a disordered alloy on the phonon dispersions, by considering the illustrative examples of Cu 0.715 Pd 0.285 and Cu 0.75 Au 0.25 systems. A combination of ab initio electronic-structure method and the transferable force-constant model has been used as a first-principles tool to compute the interatomic force constants between various pairs of chemical specie in a disordered alloy. The Green'sfunction based itinerant coherent-potential approximation is then used to compute the phonon-dispersion relations by performing the configuration averaging over the fluctuations in the mass and the force constants due to the size mismatch. A systematic investigation on the influence of the size mismatch of end-point components of an alloy on the phonon spectra is carried out in detail. We show that the consideration of the local lattice relaxation as a manifestation of size mismatch is important in addressing the correct behavior of the phonon dispersions in these alloys. Our results are in good agreement with the experimental results in case of Cu 0.715 Pd 0.285 . In case of Cu 0.75 Au 0.25 , our results predict a resonance behavior which is not observed experimentally. Based upon an analysis of the interatomic force constants between various pairs of chemical specie, we explain the reason of this discrepancy.
Journal of Physics: Condensed Matter, 2011
In an attempt to obtain reliable first-principles phonon dispersions of random alloys, we have developed a method to calculate the dynamical matrix, with respect to the wavevector space of the ideal lattice, by averaging over the force constants of a special quasi-random structure. Without additional approximations beyond standard density functional theory, the present scheme takes into account the local atomic position relaxations, the composition disorder, and the force constant disorder in a random alloy. Numerical results are presented for disordered Cu 3 Au, FePd, and NiPd and good agreement between the calculations and the inelastic neutron scattering data is observed.
Physical Review B, 2011
There has been increasing evidence about the effects of short-range order (or local chemical environment effects) on the lattice dynamics of alloys, which eventually affect the vibrational entropy difference among various phases of a compound, and hence their relative stability. In this article, we present an ab initio calculation of the lattice dynamics and the vibrational entropy of disordered systems with short-range order. The features in the phonon density of states were found to change systematically with chemical short-range order in the alloy. Plausible explanations for our smaller value of vibrational entropy of mixing compared to experiment are given in some detail. A general trend of the magnitude of vibrational entropy of mixing is explained by making a connection to the phonon lifetime broadening, an intrinsic property of any multiple scattering phenomenon. We illustrate the method by applying it to a body-centered cubic Fe 1−x Cr x alloy.
Science China Physics, Mechanics & Astronomy, 2017
The dependence of dislocation mobility on stress is the fundamental ingredient for the deformation in crystalline materials. Strength and ductility, the two most important properties characterizing mechanical behavior of crystalline metals, are in general governed by dislocation motion. Recording the position of a moving dislocation in a short time window is still challenging, and direct observations which enable us to deduce the speed-stress relationship of dislocations are still missing. Using large-scale molecular dynamics simulations, we obtain the motion of an obstacle-free twinning partial dislocation in face centred cubic crystals with spatial resolution at the angstrom scale and picosecond temporal information. The dislocation exhibits two limiting speeds: the first is subsonic and occurs when the resolved shear stress is on the order of hundreds of megapascal. While the stress is raised to gigapascal level, an abrupt jump of dislocation velocity occurs, from subsonic to supersonic regime. The two speed limits are governed respectively by the local transverse and longitudinal phonons associated with the stressed dislocation, as the two types of phonons facilitate dislocation gliding at different stress levels.