Quantum annealing for microstructure equilibration with long-range elastic interactions

Abstract

We demonstrate the use and benefits of quantum annealing approaches for the determination of equilibrated microstructures in shape memory alloys and other materials with long-range elastic interaction between coherent grains and their different martensite variants and phases. After a one dimensional illustration of the general approach, which requires to formulate the energy of the system in terms of an Ising Hamiltonian, we use distant dependent elastic interactions between grains to predict the variant selection for different transformation eigenstrains. The results and performance of the computations are compared to classical algorithms, demonstrating that the new approach can lead to a significant acceleration of the simulations. Beyond a discretization using simple cuboidal elements, also a direct representation of arbitrary microstructures is possible, allowing fast simulations with currently up to several thousand grains.

Efficient low temperature Monte Carlo sampling using quantum annealing

“…We point out that due to the random couplings, the energy landscape of the spin glass contains many states with nearby energy values without degeneracy, which avoids the issue of potentially unfair sampling of isoenergetic states. An example from materials science for such a spin glass are misfitting coherent grains in a polycrystalline solid, where the coupling constants result from elastic long-range interactions and external forces 9 . We repeat the quantum annealing read out process 10,000 times to get an estimate of the distribution of identified states, as due to the above mentioned reasons also higher energy states are found in practise.…”

“…Also, overriding the automatic coupling constant renormalization is not possible, as the focus of the approach is to find most efficiently the true ground state. Nevertheless, the use of hybrid methods allows to study significantly larger system sizes than with pure QA 9 .…”

“…Nevertheless, the methodology is applicable also to other problems where thermal excitations can play a role, e.g. for (weak) coherency strains in microstructures with long range elastic interactions 9 . In general, the Ising or QUBO limitation can actually be less severe as it may appear.…”

“…There are many problem types to which QA has been applied, like the demonstration of scaling or algorithmic advantages for QA in specific problem classes 6 – 8 . So far, applications of QA in the field of materials science are still rare, and among them are the determination of equilibrium microstructures with long-range elastic interactions 9 , phase transitions in the transverse field Ising model 10 , the investigation of energy states of frustrated magnetic systems via the Shastry-Sutherland model 11 and the designing of metamaterials 12 . Another example is the combined use of quantum annealers and Boltzmann machines to sample spin glasses and to predict molecular dynamics data of a layer 13 .…”

Phase Field Study of Cr-Oxide Growth Kinetics in the Crofer 22 APU Alloy Supported by Wagner’s Theory

“…The phase field methods also play a major role in the modeling of the phase transformation kinetics in solid state transformations [31], where in particular elastic effects can play an important role and affect both the equilibrium thermodynamics as well as the dynamics of the transformations. More recently, quantum annealing techniques have been developed, which may help to lead to even more efficient descriptions of the solid state transformation equilibration with long range elastic coherency stresses [32]. Other applications for phase field models are related to fracture in brittle and ductile materials [33], grain boundary premelting [34], battery modeling [35] and phase change memory material simulations [36].…”