Generalized balanced power diagrams for 3D representations of polycrystals

TL;DR

This paper introduces generalized balanced power diagrams as an efficient, parameter-based method for representing 3D polycrystal structures, offering a concise alternative to voxelated mappings with high accuracy.

Contribution

It presents a novel approach using linear programming to compute generalized balanced power diagrams from limited parameters, effectively modeling complex polycrystalline structures.

Findings

Accurately represents both equiaxed and non-equiaxed grains

Uses few parameters per grain for effective modeling

Computationally efficient due to linear programming formulation

Abstract

Characterizing the grain structure of polycrystalline material is an important task in material science. The present paper introduces the concept of generalized balanced power diagrams as a concise alternative to voxelated mappings. Here, each grain is represented by (measured approximations of) its center-of-mass position, its volume and, if available, by its second-order moments (in the non-equiaxed case). Such parameters may be obtained from 3D x-ray diffraction. As the exact global optimum of our model results from the solution of a suitable linear program it can be computed quite efficiently. Based on verified real-world measurements we show that from the few parameters per grain (3, respectively 6 in 2D and 4, respectively 10 in 3D) we obtain excellent representations of both equiaxed and non-equiaxed structures. Hence our approach seems to capture the physical principles governing the forming of such polycrystals in the underlying process quite well.