PS in case you missed it, here's the bottom line from the paper:
"Interestingly, a cubic crystal has seven nonbirefringent axes, four in
the <111>
directions and three in the <100> directions, with birefringence maxima
in the twelve <110> directions."
So it would appear that the optical properties of cubic crystals are
*more* complicated than those of lower symmetry systems, not less! - and
previous conclusions about isotropy of cubic crystals probably arose
because the measurements were simply not precise enough (or not carried
out at short enough wavelength) to detect the effect. However the
relevant theory goes back to Lorentz (1878) so it's not exactly new!
Cheers
-- Ian
> -----Original Message-----
> From: [log in to unmask]
> [mailto:[log in to unmask]] On Behalf Of Ian Tickle
> Sent: 12 June 2008 17:50
> To: Ethan A Merritt; Jacob Keller
> Cc: [log in to unmask]
> Subject: RE: [ccp4bb] birefringent spacegroups
>
> Hi Ethan
>
> You could be right, see this paper:
>
>
http://physics.nist.gov/Divisions/Div842/Gp2/DUVMatChar/PDF/IntBiref.pdf
>
> Cheers
>
> -- Ian
>
>
> > -----Original Message-----
> > From: [log in to unmask]
> > [mailto:[log in to unmask]] On Behalf Of Ethan A Merritt
> > Sent: 12 June 2008 15:46
> > To: Multiple recipients
> > Cc: [log in to unmask]
> > Subject: Re: [ccp4bb] birefringent spacegroups
> >
> > 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: [log in to unmask]
> > > > *******************************************
> > >
> >
> > --
> > Ethan A Merritt
> > Biomolecular Structure Center
> > University of Washington, Seattle 98195-7742
> >
> >
>
>
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