Elastic properties of cubic crystals: Every's versus Blackman's diagram

TL;DR

This paper compares Every's and Blackman's diagrams for classifying elastic properties of cubic crystals, finding that Every's diagram generally shows stronger correlations and reveals linear relationships among different material groups.

Contribution

The study provides a comparative analysis of two dimensionless diagrams, demonstrating the superior correlation properties of Every's diagram for cubic crystal elastic classification.

Findings

Every's diagram exhibits higher correlation coefficients than Blackman's diagram.

Linear relationships between variables are more evident in Every's diagram.

Alignment along lines of constant Poisson's ratio is observed across materials.

Abstract

Blackman's diagram of two dimensionless ratios of elastic constants is frequently used to correlate elastic properties of cubic crystals with interatomic bondings. Every's diagram of a different set of two dimensionless variables was used by us for classification of various properties of such crystals. We compare these two ways of characterization of elastic properties of cubic materials and consider the description of various groups of materials, e.g. simple metals, oxides, and alkali halides. With exception of intermediate valent compounds, the correlation coefficients for Every's diagrams of various groups of materials are greater than for Blackaman's diagrams, revealing the existence of a linear relationship between two dimensionless Every's variables. Alignment of elements and compounds along lines of constant Poisson's ratio $\nu(<100>,\textbf{m})$, ($\textbf{m}$ arbitrary perpendicular to <100>) is observed. Division of the stability region in Blackman's diagram into region of complete auxetics, auxetics and non-auxetics is introduced. Correlations of a scaling and an acoustic anisotropy parameter are considered.