P. L. Leath

Phonons in random alloys: The itinerant coherent-potential approximation

We present the itinerant coherent-potential approximation (ICPA), an analytic, translationally invariant, and tractable form of augmented-space-based multiple-scattering theory 1 8 in a single-site approximation for harmonic phonons in realistic random binary alloys with mass and force-constant disorder. We provide expressions for quantities needed for comparison with experimental structure factors such as partial and average spectral functions and derive the sum rules associated with them. Numerical results are presented for Ni 5 5 Pd 4 5 and Ni 5 0 Pt 5 0 alloys which serve as test cases the former for weak force-constant disorder and the latter for strong. We present results on dispersion curves and disorder-induced widths. Direct comparisons with the single-site coherent potential approximation (CPA) and experiment are made which provide insight into the physics of force-constant changes in random alloys. The CPA accounts well for the weak force-constant disorder case but fails for strong force-constant disorder where the ICPA succeeds.

Size effect and statistics of fracture in random materials

Abstract We review the mathematical and microstructural foundations of fracture statistics and the associated size effect in the average tensile fracture strength of random materials. When the flaw population in a material has an algebraic tail, the fracture statistics are of a Weibull form and the size effect is algebraic. When the flaw population is exponential, the fracture statistics are of a new, “modified Gumbel form”, and the size effect is logarithmic. Most microstructural models with uncorrelated disorder are predicted to lie in the “modified Gumbel class”. We argue that the standard Gumbel form is a poor statistic to use in the analysis of tensile fracture.

Thermodynamics of Mesoscopic Vortex Systems in 1+1 Dimensions

The behavior of vortices in dirty type-II superconductors has been a subject of intense studies in the past decade [1]. Aside from the obvious technological significance of vortex pinning, understanding the physics of such interacting many-body systems in the presence of quenched disorder is a central theme of modern condensed matter physics. Similarities between the randomly pinned vortex system and the more familiar mesoscopic electronic systems [2] are highlighted by a recent experimental study of a planar vortex array threaded through a thin crystal of 2H-NbSe2 by Bolle et al. [3]. Interesting behaviors, including the sample-dependent magnetic responses known as “fingerprints,” have been observed for such a mesoscopic vortex system. The disordered planar vortex array is well studied theoretically [4‐ 9]. It is one of the few disorder-dominated systems for which quantitative predictions can be made, including a finite-temperature “vortex glass” phase [5] characterized by anomalous vortex displacements [4], and universal variation of magnetic susceptibility [9]. However, until the work of Bolle et al., there were hardly any experimental studies of this system, with difficulties stemming partly from the weak magnetic signals in such 2D systems. Also, numerical simulations have been limited by the slow glassy dynamics [10], although the availability of special optimization algorithms did lead to the elucidation of the zero-temperature problem in recent years [11]. In this Letter, we describe numerical studies of the thermodynamics of the vortex glass via a mapping to a discrete dimer model with quenched disorder. A new polynomial algorithm for the dimer problem circumvents the glassy dynamics and enables us to study large systems at finite temperatures. Our results obtained in the dilute (singleflux-pinning) regime compare well with the experiment by Bolle et al. [3], while those obtained in the collectivepinning regime strongly support the renormalization-group theory of the vortex glass, including its prediction of universal susceptibility variation [9]. The model.—The dimer model consists of all complete dimer coverings D on a square lattice L as illustrated in

FAILURE PROBABILITIES AND TOUGH-BRITTLE CROSSOVER OF HETEROGENEOUS MATERIALS WITH CONTINUOUS DISORDER

The failure probabilities or the strength distributions of heterogeneous 1D systems with continuous local strength distribution and local load sharing have been studied using a simple, exact, recursive method. The fracture behavior depends on the local bond-strength distribution, the system size, and the applied stress, and crossovers occur as system size or stress changes. In the brittle region, systems with continuous disorders have a failure probability of the modified-Gumbel form, similar to that for systems with percolation disorder. The modified-Gumbel form is of special significance in weak-stress situations. This new recursive method has also been generalized to calculate exactly the failure probabilities under various boundary conditions, thereby illustrating the important effect of surfaces in the fracture process.

Application of polynomial algorithms to a random elastic medium

A randomly pinned elastic medium in two dimensions is modeled by a disordered fully-packed loop model. The energetics of disorder-induced dislocations is studied using exact and polynomial algorithms from combinatorial optimization. Dislocations are found to become unbound at large scale, and the elastic phase is thus unstable giving evidence for the absence of a Bragg glass in two dimensions.

Towards a first principles description of phonons in Ni

Using a combination of density-functional perturbation theory and the itinerant coherent potential approximation, we study the effects of atomic relaxation on the inelastic incoherent neutron scattering cross sections of disordered Ni

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Pt

Pt

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disordered alloys: the role of relaxation

alloys. We build on previous work, where empirical force constants were adjusted {\it ad hoc} to agree with experiment. After first relaxing all structural parameters within the local-density approximation for ordered NiPt compounds, density-functional perturbation theory is then used to compute phonon spectra, densities of states, and the force constants. The resulting nearest-neighbor force constants are first compared to those of other ordered structures of different stoichiometry, and then used to generate the inelastic scattering cross sections within the itinerant coherent potential approximation. We find that structural relaxation substantially affects the computed force constants and resulting inelastic cross sections, and that the effect is much more pronounced in random alloys than in ordered alloys.