Hi Jacob,
The birefringence of a crystal is determined by a three dimensional
shape (the indicatrix) describing how refractive index varies with
direction within the crystal. You can think of this as a 3d ellipse and
the birefringence is given by the difference in length of the two axes
of the ellipse 'seen' by light as it passes through the crystal.
The orientation and shape of the indicatrix are constrained by the point
group symmetry of the crystal. In the case of cubic crystals, the
indicatrix is characterised by four 3-fold axes. The indicatrix for all
cubic crystals is thus a sphere and cubic crystals are non-birefringent.
Hexagonal, trigonal and tetragonal crystals are uniaxial and the
indicatrix is an ellipsoid of revolution
- there is one direction in which the crystal appears non-birefringent.
Orthorhombic, monoclinic and triclinic systems are biaxial -two axes in
which the crystal appears non-birefringent.
A good reference is
Nye (1984). Physical Properties of crystals. Their representation by
tensors and matrices. Clarendon Press, Oxford.
There is a more detailed list of space groups and their tensor optical
properties in there I think.
Cheers,
Robin
Jacob Keller wrote:
> Dear Crystallographers,
>
> is there a list somewhere of spacegroups which can and cannot be
> birefringent? Upon what feature of the spacegroup does this depend?
>
> Jacob Keller
>
> *******************************************
> Jacob Pearson Keller
> Northwestern University
> Medical Scientist Training Program
> Dallos Laboratory
> F. Searle 1-240
> 2240 Campus Drive
> Evanston IL 60208
> lab: 847.491.2438
> cel: 773.608.9185
> email: [log in to unmask]
> *******************************************
|