A solvable model for excitonic complexes in one dimension

It is known experimentally that stable few-body clusters containing negatively-charged electrons (e) and positively-charged holes (h) can exist in low-dimensional semiconductor nanostructures. In addition to the familiar exciton (e+h), three-body 'charged excitons' (2e+h and 2h+e) have also been observed. Much less is known about the properties of such charged excitons since three-body problems are generally very difficult to solve, even numerically. Here we introduce a simple model, which can be considered as an extended Calogero model, to calculate analytically the energy spectra for both a charged exciton and a neutral exciton in a one-dimensional nanostructure, such as a finite-length quantum wire. Apart from its physical motivation, the model is of mathematical interest in that it can be related to the Heun (or Heine) equation and, as shown explicitly, highly accurate, closed form solutions can be obtained.Comment: 14 pages, 3 figures, To appear in J. Math. Phy

NiTi shape-memory transformations: minimum-energy pathways between austenite, martensites, and kinetically-limited intermediate states

NiTi is the most used shape-memory alloy, nonetheless, a lack of understanding remains regarding the associated structures and transitions, including their barriers. Using a generalized solid-state nudge elastic band (GSSNEB) method implemented via density-functional theory, we detail the structural transformations in NiTi relevant to shape memory: those between body-centered orthorhombic (BCO) groundstate and a newly identified stable austenite ("glassy" B2-like) structure, including energy barriers (hysteresis) and intermediate structures (observed as a kinetically limited R-phase), and between martensite variants (BCO orientations). All results are in good agreement with available experiment. We contrast the austenite results to those from the often-assumed, but unstable B2. These high- and low-temperature structures and structural transformations provide much needed atomic-scale detail for transitions responsible for NiTi shape-memory effects.Comment: 4 pages, 4 figure

Auslander Systems

The authors generalize the dynamical system constructed by J. Auslander in 1959, resulting in perhaps the simplest family of examples of minimal but not strictly ergodic systems. A characterization of unique ergodicity and mean-L-stability is given. The new systems are also shown to have zero topological entropy and fail to be weakly rigid. Some results on the set of idempotents in the enveloping semigroup are also achieved

Free-energy landscape of nucleation with an intermediate metastable phase studied using capillarity approximation

Capillarity approximation is used to study the free-energy landscape of nucleation when an intermediate metastable phase exists. The critical nucleus that corresponds to the saddle point of the free-energy landscape as well as the whole free-energy landscape can be studied using this capillarity approximation, and various scenarios of nucleation and growth can be elucidated. In this study we consider a model in which a stable solid phase nucleates within a metastable vapor phase when an intermediate metastable liquid phase exists. We predict that a composite critical nucleus that consists of a solid core and a liquid wetting layer as well as pure liquid and pure solid critical nuclei can exist depending not only on the supersaturation of the liquid phase relative to that of the vapor phase but also on the wetting behavior of the liquid surrounding the solid. The existence of liquid critical nucleus indicates that the phase transformation from metastable vapor to stable solid occurs via the intermediate metastable liquid phase, which is quite similar to the scenario of nucleation observed in proteins and colloidal systems. By studying the minimum-free-energy path on the free-energy landscape, we can study the evolution of the composition of solid and liquid within nuclei not limited to the critical nucleus.Comment: 9 pages, 8 figures, Journal of chemical physics to be publishe

Anomalous magneto-structural behavior of MnBi explained: a path towards an improved permanent magnet

Low-temperature MnBi (hexagonal NiAs phase) exhibits anomalies in the lattice constants (a, c) and bulk elastic modulus (B) below 100 K, spin reorientation and magnetic susceptibility maximum near 90 K, and, importantly for high-temperature magnetic applications, an increasing coercivity (unique to MnBi) above 180 K. We calculate the total energy and magneto-anisotropy energy (MAE) versus (a, c) using DFT+U methods. We reproduce and explain all the above anomalies. We predict that coercivity and MAE increase due to increasing a, suggesting means to improve MnBi permanent magnets.Comment: 4 pages, 5 figure

Numerical model of solid phase transformations governed by nucleation and growth. Microstructure development during isothermal crystallization

A simple numerical model which calculates the kinetics of crystallization involving randomly distributed nucleation and isotropic growth is presented. The model can be applied to different thermal histories and no restrictions are imposed on the time and the temperature dependencies of the nucleation and growth rates. We also develop an algorithm which evaluates the corresponding emerging grain size distribution. The algorithm is easy to implement and particularly flexible making it possible to simulate several experimental conditions. Its simplicity and minimal computer requirements allow high accuracy for two- and three-dimensional growth simulations. The algorithm is applied to explore the grain morphology development during isothermal treatments for several nucleation regimes. In particular, thermal nucleation, pre-existing nuclei and the combination of both nucleation mechanisms are analyzed. For the first two cases, the universal grain size distribution is obtained. The high accuracy of the model is stated from its comparison to analytical predictions. Finally, the validity of the Kolmogorov-Johnson-Mehl-Avrami model is verified for all the cases studied

Beyond the constraints underlying Kolmogorov-Johnson-Mehl-Avrami theory related to the growth laws

The theory of Kolmogorov-Johnson-Mehl-Avrami (KJMA) for phase transition kinetics is subjected to severe limitations concerning the functional form of the growth law. This paper is devoted to side step this drawback through the use of correlation function approach. Moreover, we put forward an easy-to-handle formula, written in terms of the experimentally accessible actual extended volume fraction, which is found to match several types of growths. Computer simulations have been done for corroborating the theoretical approach.Comment: 18 pages ;11 figure