Abstract
Multicomponent alloys show intricate microstructure evolution, providing materials engineers with a nearly inexhaustible variety of solutions to enhance material properties. Multicomponent microstructure evolution simulations are indispensable to exploit these opportunities. These simulations, however, require the handling of high-dimensional and prohibitively large data sets of thermodynamic quantities, of which the size grows exponentially with the number of elements in the alloy, making it virtually impossible to handle the effects of four or more elements. In this paper, we introduce the use of tensor completion for high-dimensional data sets in materials science as a general and elegant solution to this problem. We show that we can obtain an accurate representation of the composition dependence of high-dimensional thermodynamic quantities, and that the decomposed tensor representation can be evaluated very efficiently in microstructure simulations. This realization enables true multicomponent thermodynamic and microstructure modeling for alloy design.
Highlights
A number of recent discoveries has largely increased the interest in multicomponent alloy design
Tensor completion of thermodynamic data In material science, we are familiar with the tensorial character of becomes impossible to generate, store, or handle the huge data sets
The computational difficulties caused by this exponential dependence are known as the curse of dimensionality.[28]
Summary
A number of recent discoveries has largely increased the interest in multicomponent alloy design. The reason is that the proposed methods were either for a specific case and cannot be generalised towards systems containing other types of phases, or become prohibitively complex or computation and data-intensive when the number of elements in the alloy is increased. We used a canonical polyadic decomposition (CPD) with the factor vectors constrained to polynomial expressions[31] to include highdimensional thermodynamic data sets obtained from a CALPHAD model in phase-field simulations. The addition of more elements does not lead to a substantial increase of the complexity, and the number of coefficients and the computational cost to evaluate a CPD depend only linearly on the number of components in the system, in contrast to an exponential increase of the amount of thermodynamic data represented.
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