MicroStructural Hierarchy Descriptor (μSHD)–property correlations of silicon carbide ceramics

A uniform rule between hardness and structure hierarchy of ceramics in both direct and inverse Hall–Petch regimes

“…It is such characteristics that make wavelets the best analysis tools for microstructures of materials from the perspectives of both physics and mathematics. In Huang's work, 10,12 8 scales, each with 8 orientations, thus a total of 64 wavelets were used for microstructural analyses to obtain a hierarchical feature consisting of 64 μSHDs or 36 μSHDs if 6 scales and each with 6 orientations were used. A plot with the μSHD as the ordinate and the serial number of the hierarchical features as the abscissa is called a μSHD curve.…”

“…In Huang's work, 10,12 8 scales, each with 8 orientations, thus a total of 64 wavelets were used for microstructural analyses to obtain a hierarchical feature consisting of 64 $$\umu$$SHDs or 36 $$\umu$$SHDs if 6 scales and each with 6 orientations were used. A plot with the $$\umu$$SHD as the ordinate and the serial number of the hierarchical features as the abscissa is called a $$\umu$$SHD curve.…”

“…As mentioned above, the principles behind the $$\umu$$SHD has been introduced in Huang's original work 10,12 . For completeness, the essence of the theory is recapped in this section along with the core ideas and steps on how the $$Asc$$ is proposed and constructed on the basis of the $$\umu$$SHD.…”

“…The MST is based on multi‐resolution wavelet analyses (MRWA) on digital images, which is a technique not yet available in Smith's era, and becomes even more complicated to construct a series of invariants as characteristic features. In previous work, 12 correlations between the $$\umu$$SHD curves and the mechanical, electrical and thermal properties of SiC ceramics have been identified. However, the relationship between hardness and the proposed $$\umu$$SHD has not been dealt with in Huang's original work.…”