Materials Theory最新文献

The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of effective (or downfolded) Hamiltonians in small-dimensionality sub-space, usually identified with the so-called active space, of the entire Hilbert space. The resulting downfolded Hamiltonians integrate out the external (out-of-active-space) Fermionic degrees of freedom from the internal (in-the-active-space) parameters of the wave function, which can be determined as components of the eigenvectors of the downfolded Hamiltonians in the active space. This paper will discuss the extension of non-Hermitian (associated with standard CC formulations) and Hermitian (associated with the unitary CC approaches) downfolding formulations to composite quantum systems commonly encountered in materials science and chemistry. The non-Hermitian formulation can provide a platform for developing local CC approaches, while the Hermitian one can serve as an ideal foundation for developing various quantum computing applications based on the limited quantum resources. We also discuss the algorithm for extracting the semi-analytical form of the inter-electron interactions in the active spaces.

In the Portevin–Le Chatelier (PLC) effect sample plastic deformation takes place via localized bands. We present a model to account for band dynamics and the variability the bands exhibit. The approach is tuned to account for strain hardening and the strain-rate dependence for the case of so-called type A (propagating) bands. The main experimental features of the fluctuations are a reduction with strain and increase with the strain rate which is reproduced by a model of plastic deformation with Dynamic Strain Aging, including disorder as a key parameter. Extensions are discussed as are the short-comings in reproducing detailed avalanche statistics.

Dynamic simulation of materials is a promising application for near-term quantum computers. Current algorithms for Hamiltonian simulation, however, produce circuits that grow in depth with increasing simulation time, limiting feasible simulations to short-time dynamics. Here, we present a method for generating circuits that are constant in depth with increasing simulation time for a specific subset of one-dimensional (1D) materials Hamiltonians, thereby enabling simulations out to arbitrarily long times. Furthermore, by removing the effective limit on the number of feasibly simulatable time-steps, the constant-depth circuits enable Trotter error to be made negligibly small by allowing simulations to be broken into arbitrarily many time-steps. For an N-spin system, the constant-depth circuit contains only (mathcal {O}(N^{2})) CNOT gates. Such compact circuits enable us to successfully execute long-time dynamic simulation of ubiquitous models, such as the transverse field Ising and XY models, on current quantum hardware for systems of up to 5 qubits without the need for complex error mitigation techniques. Aside from enabling long-time dynamic simulations with minimal Trotter error for a specific subset of 1D Hamiltonians, our constant-depth circuits can advance materials simulations on quantum computers more broadly in a number of indirect ways.

Ultra pure metals have various applications, e. g. as electrical conductors. Crystallization from the melt, e. g. via zone melting, using the segregation of impurities at the solidification front is the basic mechanism behind different technical processes for the refining of metals and semi-metals. In this paper, we focus on a crystallization methodology with a gas cooled tube (“cooled finger”) dipped into a metallic melt in a rotating crucible. The necessary requirement for purification in a solidification process is a morphologically stable solidification front. This is the only way to enable macroscopic separation of the impurities, e. g. by convection. For cellular or dendritic solidification morphologies, the segregated impurities are trapped into the interdendritic melt and remain as microsegregations in the solidified metal. Morphological stability depends on the temperature gradient G at the solidification front, the solidification front velocity V _front and thermodynamic alloy properties like the segregation coefficients of the impurity elements. To quantify the impact of these parameters on the morphological evolution, especially on the planar/cellular transition and thus on microsegregation profiles, phase field simulations coupled to a thermodynamic database are performed for an aluminium melt with three impurities, Si, Mn and Fe. In particular, we have investigated the morphology evolution from the start of solidification at the cooled finger towards a stationary growth regime, because in the technical process a significant fraction of the melt solidifies along the initial transient. To solve the transient long range temperature evolution on an experimental length scale, the temperature field has been calculated using the homoenthalpic approach together with a 1D temperature field approximation. The simulations provide the process window for an energy efficient purification process, i. e. low thermal gradients, and elucidate the benefit of melt convection.

Molecular science is governed by the dynamics of electrons and atomic nuclei, and by their interactions with electromagnetic fields. A faithful physicochemical understanding of these processes is crucial for the design and synthesis of chemicals and materials of value for our society and economy. Although some problems in this field can be adequately addressed by classical mechanics, many demand an explicit quantum mechanical description. Such quantum problems require a representation of wave functions that grows exponentially with system size and therefore should naturally benefit from quantum computation on a number of logical qubits that scales only linearly with system size. In this perspective, we elaborate on the potential benefits of quantum computing in the molecular sciences, i.e., in molecular physics, chemistry, biochemistry, and materials science.

Microstructure simulations for quaternary alloys are still a challenge, although it is of high importance for alloy development. This work presents a Phase field (PF) approach capable of resolving phase transformation in a multicomponent system with a simple and effective way to include the thermodynamic and kinetic information for such a complex system. The microstructure evolution during diffusional transformation between FCC and BCC phase at 700 °C for AlCrFeNi alloys was simulated, accounting for composition dependence and off-diagonal terms in the diffusion tensor. The reliability of the presented PF method is validated by comparing the 1-D simulation results with simulations by Diffusion Module (DICTRA) of Thermo-Calc Software. Additionally, 2-D PF simulations of precipitate growth and Ostwald ripening are performed for different alloy systems, and the coarsening behavior is compared. Results showed that thermodynamic and kinetic information is accurately described in the applied PF method. The simulation results show that the diffusion behavior is influenced evidently by variations in the amounts of the different elements in the system. These findings demonstrate the necessity of applying accurate thermodynamic and kinetic models to fully understand the complex interdiffusion behavior in high and medium entropy alloys.

Using a previously developed phase field modeling method, where interface energies are described by spherical gaussians that allow the modeling of complex anisotropies, a new phase field model was developed to model 5-D anisotropy in polycrystalline grain growth. We present the use of quaternions, assigned to individual grains as orientations and misorientations for grain boundaries, as a means of simulating the ongoing mesoscale changes during anisotropic polycrystalline grain growth. The full 5-D landscape is scanned in MATLAB, and the grain boundary (GB) energy of each grain boundary is calculated from the continuous function developed by Bulatov et al. MATLAB is then used to find all local minima in the GB energy which are stored for use in the phase field model. The methodology of including these minima in the phase field model involves using 2-D gaussian switches, which match the misorientation between grains with misorientations for the GB energy minima. Within a threshold range of the minima misorientation, the switch activates a spherical Gaussian to set the GB energy to the desired value creating in combination a full 5D GB energy space. This creates a GB energy that morphs in real time and space as the GB plane or grain orientations change. Implementation methods of the model are outlined for the Multiphysics Object Oriented Simulation Environment (MOOSE), where reduced order parameters still retain individual grain identification useful for individually assigned quaternions.

Since crystal plasticity is the result of moving and interacting dislocations, it seems self-evident that continuum plasticity should in principle be derivable as a statistical continuum theory of dislocations, though in practice we are still far from doing so. One key to any statistical continuum theory of interacting particles is the consideration of spatial correlations. However, because dislocations are extended one-dimensional defects, the classical definition of correlations for point particles is not readily applicable to dislocation systems: the line-like nature of dislocations entails that a scalar pair correlation function does not suffice for characterizing spatial correlations and a hierarchy of two-point tensors is required in general. The extended nature of dislocations as closed curves leads to strong self-correlations along the dislocation line. In the current contribution, we thoroughly introduce the concept of pair correlations for general averaged dislocation systems and illustrate self-correlations as well as the content of low order correlation tensors using a simple model system. We furthermore detail how pair correlation information may be obtained from three-dimensional discrete dislocation simulations and provide a first analysis of correlations from such simulations. We briefly discuss how the pair correlation information may be employed to improve existing continuum dislocation theories and why we think it is important for analyzing discrete dislocation data.