On Wednesday 11 June 2008 23:55, Robin Owen wrote:
> 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.
I have wondered about this in the past.
That argument only appears to hold if "birefringent" is taken to mean
"different optical index at two angles 90 degrees apart". I think
even in a cubic crystal you can find non-equivalent directions if you
are not limited to a right angle between the two vectors. Does this
not count as birefringence? Or am I misunderstanding the definition?
Ethan
and then there's the issue of anomalous dispersion...
> 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: [EMAIL PROTECTED]
> > *******************************************
>
--
Ethan A Merritt
Biomolecular Structure Center
University of Washington, Seattle 98195-7742
