Abstract and subjects
We propose an elastic-anisotropy measure. Zener's familiar anisotropy index
A
=
2
C
44
∕
(
C
11
−
C
12
)
applies only to cubic symmetry [
Elasticity and Anelasticity of Metals
(
University of Chicago Press
, Chicago,
1948
), p.
16
]. Its extension to hexagonal symmetry creates ambiguities. Extension to orthorhombic (or lower) symmetries becomes meaningless because
C
11
−
C
12
loses physical meaning. We define elastic anisotropy as the squared ratio of the maximum/minimum shear-wave velocity. We compute the extrema velocities from the Christoffel equations [
M. Musgrave
,
Crystal Acoustics
(
Holden-Day
, San Francisco,
1970
), p.
84
]. The measure is unambiguous, applies to all crystal symmetries (cubic-triclinic), and reduces to Zener's definition in the cubic-symmetry limit. The measure permits comparisons between and among different crystal symmetries, say, in allotropic transformations or in a homologous series. It gives meaning to previously unanswerable questions such as the following: is zinc (hexagonal) more or less anisotropic than copper (cubic)? is alpha-uranium (orthorhombic) more or less anisotropic than delta-plutonium (cubic)? The most interesting finding is that close-packed-hexagonal elements show an anisotropy near 1.3, about half that of their close-packed-cubic counterparts. A central-force near-neighbor model supports this finding.