Zener ratio

The Zener ratio is a dimensionless number that is used to quantify the anisotropy for cubic crystals. It is sometimes referred as anisotropy ratio and is named after Clarence Zener.^[1] Conceptually, it quantifies how far a material is from being isotropic (where the value of 1 means an isotropic material).

Its mathematical definition is^[1]^[2]

$a_{r}={\frac {2C_{44}}{C_{11}-C_{12}}},$

where $C_{ij}$ refers to Elastic constants in Voigt notation.

^ ^a ^b Z. Li and C. Bradt (July 1987). "The single-crystal elastic constants of cubic (3C) SiC to 1000°C". Journal of Materials Science. 22 (7): 2557–2559. Bibcode:1987JMatS..22.2557L. doi:10.1007/BF01082145. S2CID 135637447.
^ L. B. Freund; S. Suresh (2004). Thin Film Materials Stress, Defect Formation and Surface Evolution. Cambridge University Press.{{cite book}}: CS1 maint: multiple names: authors list (link)

[li-bradt-1] Z. Li and C. Bradt (July 1987). "The single-crystal elastic constants of cubic (3C) SiC to 1000°C". Journal of Materials Science. 22 (7): 2557–2559. Bibcode:1987JMatS..22.2557L. doi:10.1007/BF01082145. S2CID 135637447.

[2] L. B. Freund; S. Suresh (2004). Thin Film Materials Stress, Defect Formation and Surface Evolution. Cambridge University Press.{{cite book}}: CS1 maint: multiple names: authors list (link)

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