Materials Theory最新文献

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.

The growth and interconnection of fission gas bubbles in the hotter central regions of U-(Pu)-Zr nuclear fuel has been simulated with a phase-field model. The Cahn-Hilliard equation was used to represent the two-phase microstructure, with a single defect species. The volume fraction of the bubble phase and surface area of the bubble-matrix interface were determined during growth and interconnection. Surface area increased rapidly during the initial stages of growth, then slowed and finally decreased as bubble interconnection began and coarsening acted to reduce surface area. The fraction of the bubbles vented to a simulation domain boundary, f_V, was quantified as a measure of the microstructure’s interconnectivity and plotted as a function of porosity p. The defect species diffusivity was varied; although changes in diffusivity significantly affected the microstructure, the plots of f_V vs. p did not change significantly. The percolation threshold p_c was calculated to be approximately 0.26, depending on the assumed diffusivity and using an initial bubble number density based on experimental observations. This is slightly smaller than the percolation threshold for continuum percolation of overlapping 3D spheres. The simulation results were used to parameterize two different engineering-scale swelling models for U-(Pu)-Zr in the nuclear fuel performance code BISON.

Fission gas release within uranium dioxide nuclear fuel occurs as gas atoms diffuse through grains and arrive at grain boundary (GB) bubbles; these GB bubbles grow and interconnect with grain edge bubbles; and grain edge tunnels grow and connect to free surfaces. In this study, a hybrid multi-scale/multi-physics simulation approach is presented to investigate these mechanisms of fission gas release at the mesoscale. In this approach, fission gas production, diffusion, clustering to form intragranular bubbles, and re-solution within grains are included using spatially resolved cluster dynamics in the Xolotl code. GB migration and intergranular bubble growth and coalescence are included using the phase field method in the MARMOT code. This hybrid model couples Xolotl to MARMOT using the MultiApp and Transfer systems in the MOOSE framework, with Xolotl passing the arrival rate of gas atoms at GBs and intergranular bubble surfaces to MARMOT and MARMOT passing evolved GBs and bubble surface positions to Xolotl. The coupled approach performs well on the two-dimensional simulations performed in this work, producing similar results to the standard phase field model when Xolotl does not include fission gas clustering or re-solution. The hybrid model performs well computationally, with a negligible cost of coupling Xolotl and MARMOT and good parallel scalability. The hybrid model predicts that intragranular fission gas clustering and bubble formation results in up to 70% of the fission gas being trapped within grains, causing the increase in the intergranular bubble fraction to slow by a factor of six. Re-solution has a small impact on the fission gas behavior at 1800 K but it has a much larger impact at 1000 K, resulting in a twenty-times increase in the concentration of single gas atoms within grains. Due to the low diffusion rate, this increase in mobile gas atoms only results in a small acceleration in the growth of the intergranular bubble fraction. Finally, the hybrid model accounts for migrating GBs sweeping up gas atoms. This results in faster intergranular bubble growth with smaller initial grain sizes, since the additional GB migration results in more immobile gas clusters reaching GBs.

Strain energy decomposition methods in phase field fracture models separate strain energy that contributes to fracture from that which does not. However, various decomposition methods have been proposed in the literature, and it can be difficult to determine an appropriate method for a given problem. The goal of this work is to facilitate the choice of strain decomposition method by assessing the performance of three existing methods (spectral decomposition of the stress or the strain and deviatoric decomposition of the strain) and one new method (deviatoric decomposition of the stress) with several benchmark problems. In each benchmark problem, we compare the performance of the four methods using both qualitative and quantitative metrics. In the first benchmark, we compare the predicted mechanical behavior of cracked material. We then use four quasi-static benchmark cases: a single edge notched tension test, a single edge notched shear test, a three-point bending test, and a L-shaped panel test. Finally, we use two dynamic benchmark cases: a dynamic tensile fracture test and a dynamic shear fracture test. All four methods perform well in tension, the two spectral methods perform better in compression and with mixed mode (though the stress spectral method performs the best), and all the methods show minor issues in at least one of the shear cases. In general, whether the strain or the stress is decomposed does not have a significant impact on the predicted behavior.

Direct Molecular Dynamics (MD) simulations are being increasingly employed to model dislocation-mediated crystal plasticity with atomic resolution. Thanks to the dislocation extraction algorithm (DXA), dislocation lines can be now accurately detected and positioned in space and their Burgers vector unambiguously identified in silico, while the simulation is being performed. However, DXA extracts static snapshots of dislocation configurations that by themselves present no information on dislocation motion. Referred to as a sweep-tracing algorithm (STA), here we introduce a practical computational method to observe dislocation motion and to accurately quantify its important characteristics such as preferential slip planes (slip crystallography). STA reconnects pairs of successive snapshots extracted by DXA and computes elementary slip facets thus precisely tracing the motion of dislocation segments from one snapshot to the next. As a testbed for our new method, we apply STA to the analysis of dislocation motion in large-scale MD simulations of single crystal plasticity in BCC metals. We observe that, when the crystal is subjected to uniaxial deformation along its [001] axis, dislocation slip predominantly occurs on the {112} maximum resolved shear stress plane under tension, while in compression slip is non-crystallographic (pencil) resulting in asymmetric mechanical response. The marked contrast in the observed slip crystallography is attributed to the twinning/anti-twinning asymmetry of shears in the {112} planes relatively favoring dislocation motion in the twinning sense while hindering dislocations from moving in the anti-twinning directions.