On Thursday 12 June 2008 11:19, Philippe DUMAS wrote:
> Hello,
>
> A short comment of historical interest: the first theory about "double
> refraction in crystals" (with explicit calculation of the index ellipsoid)
> goes back to 3 memoirs by A. Fresnel in 1821 and 1822. So, we are even in
> "older regions".
>
> This being said, in cubic crystals the index ellipsoid can only be a sphere.
But the ellipsoid is only a convenient approximation based on properties
evaluated at 3 orthogonal axes. It is not a complete description, it is
simple model. More complex models may describe more complex properties,
as is the case in the paper that Ian refers to.
> And so, no birefringence should exist
If "birefringence" is formally defined in terms of the approximating
ellipsoid, this is correct. I do not know if this is the case or not.
But if birefringence is generalized to mean "optical index varies with
incident illumination vector" then I believe all protein crystals
are birefringent.
I may be talking nonsense here. If so, I welcome the opportunity to
learn better.
Ethan
> (unless there is some external cause of
> anisotropy: mecanical stress, electric field,...). See Born & Wolff
> (principles of optics) p. 703. May be, our "biological crystals" might quite
> easily develop such "stress birefringence"...
> Philippe Dumas
> IBMC-CNRS, UPR9002
> 15, rue René Descartes 67084 Strasbourg cedex
> tel: +33 (0)3 88 41 70 02
> [log in to unmask]
>
>
>
> -----Message d'origine-----
> De : CCP4 bulletin board [mailto:[log in to unmask]]De la part de Ian
> Tickle
> Envoyé : Thursday, June 12, 2008 7:19 PM
> À : [log in to unmask]
> Objet : Re: [ccp4bb] birefringent spacegroups
>
>
> 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
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> > > >
> > >
> > > --
> > > Ethan A Merritt
> > > Biomolecular Structure Center
> > > University of Washington, Seattle 98195-7742
> > >
> > >
> >
> >
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