[Wien] alakali anisotropy

[Dominik Legut]

Dear colleagues,

recently, I came across the elastic anisotropy
ratio in cubic metals defined as a ratio of the
trigonal shear modulus C_44 and the tetragonal shear
modulus C'=(1/2)(C_11-C_12), i.e. A = C_44/C'.
There is one striking fact I would like to understand:

For tungsten, a 5d metal, A = 1, i.e. tungsten is
elastically isotropic! On the other hand, the alkali
metals, the most free-electron metals, exhibit the
highest elastic anisotropy factor among the elements:

Element  A
----------
Li   9.391
Na   8.286
Rb   7.435
K    7.250
Cs   7.220
----------

One would expect that alkali metals, as nearly free-electron
metals, would be also nearly elastically isotropic. On the
other hand, a high elastic anisotropy could be expected in
d-metals, such as tungsten, exhibiting directional bonds. As I show
above, just the opposite is true. Does anybody of you know what
is the origin of such a high elastic anisotropy in alkali
metals? And why is tungsten elastically isotropic? I will be
grateful for any hint or reference!

With Best Regards,

Sincerely,

Dominik Legut

P.S. I know that these questions are not related to the Wien code, but
still this is a physical community...