Composition of two-point correlation functions of subcomposites in heterogeneous materials

Abstract

Microstructural two-point correlation functions (TPCFs) are a well-known class of statistical descriptors that can be used for the characterization and reconstruction of microstructurally heterogeneous media. The core of this study is the presentation and verification of a new estimation for the TPCF of an arbitrary phase in a multiphase heterogeneous medium based on the composition of the TPCFs for the other phases or alternatively other subcomposites. The necessary conditions for the new estimation to be a phase-TPCF consisting of the limit conditions, slope condition at the origin, triangular inequality and the positivity of its spectral density are successfully verified. To demonstrate the validity of our proposed estimation, the TPCFs of two phases of a three-phase heterogeneous material are evaluated separately using their SEM images. Then the proposed composition approach is utilized to estimate the TPCF of the third phase, which compares well with its TPCF evaluated directly using its SEM image. As a separate verification attempt, we applied the proposed estimation to the TPCF of a low concentration sample of ZrO2 nanocomposite to estimate the TPCF of another ZrO2 nanocomposite of higher concentration. The estimated TPCF compares again well with the one evaluated directly from SAXS data. Finally, we calculate the effective thermal properties of the same high concentration ZrO2 nanocomposite by employing the newly estimated TPCF in the strong-contrast relations. The observed agreements make the proposed composition technique quite reliable to be applied to similar problems.