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