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

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 ν( 100 , m), (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.

Lattice instabilities in metallic elements

“…The Born stability criteria are fulfilled for all points inside a prism in the (s 1 , s 2 , and s 3 ) space with s 1 > 0 and a triangular base, as shown in Fig. 5 (Paszkiewicz, Pruchnik, and Zieliński, 2001;Paszkiewicz and Wolski, 2008). That base is called the stability triangle.…”

“…4 for tungsten that the transverse phonons at the Brillouin zone boundary in the [100] and [110] directions are stable, but the transverse zone boundary mode in the [111] direction is unstable. Paszkiewicz and Wolski (2007) used the concept of the stability triangle to discuss Young's modulus E, the shear modulus G, and Poisson's number for cubic lattices.…”

Mechanical and electronic properties of diborides of transition 3d–5d metals from first principles: Toward search of novel ultra-incompressible and superhard materials

“…Sometimes [149][150][151] for such analysis (for cubic crystals) the Blackman's diagram is used, which is a plot of two dimensionless ratios of elastic constants F 12 = C 12 /C 11 versus F 44 = C 44 /C 11 , Fig. 12.…”

First-principles investigation of elastic anomalies in niobium at high pressure and temperature

“…It shows that the linear compressibility is strictly isotropic, whereas the Young's modulus displays a strong anisotropy, which is in agreement with the well-known behavior of other cubic crystals system. 49,50 To intuitively understand the elastic anisotropy, the anisotropic characters of shear modulus, Young's modulus and linear compressibility of BCC Nb at 60 GPa are also calculated (see Figs. S8 and S9 in Supplementary Material).…”