Re: [ccp4bb] birefringent spacegroups
Thank you Ian for the comment ! Apparently, I was a bit too quick in my answer. By the way, my mentioning of Fresnel's theory was of pure historical interest and not at all to say that the whole story was written at that time. I went back to my Born Wolf (some kind of a bible in the optics field) and I am somewhat surprised of not seeing any comment on that topics. May be the comments exist, but implicitly in the cited litterature... Now, I am still wondering whether external stresses on biological crystals could indeed induce such unexpected birefringence. Philippe Dumas IBMC-CNRS, UPR9002 15, rue René Descartes 67084 Strasbourg cedex tel: +33 (0)3 88 41 70 02 [EMAIL PROTECTED] -Message d'origine- De : CCP4 bulletin board [mailto:[EMAIL PROTECTED] la part de Ian Tickle Envoyé : Thursday, June 12, 2008 9:20 PM À : CCP4BB@JISCMAIL.AC.UK Objet : Re: [ccp4bb] birefringent spacegroups But it seems that Hendrik Lorentz was the first to realise that symmetry breaking of the isotropy of the refractive index other optical properties could occur in cubic crystals at sufficiently short wavelength even in the absence of a distorting force - the spatial-dispersion-induced birefringence effect referred to in the paper. Note that this is an intrinsic effect, it has nothing to do with external stress, electric field etc., and if you read the paper you'll see that such external effects were specifically eliminated as the cause of the observed effect. -- Ian -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Philippe DUMAS Sent: 12 June 2008 19:20 To: Ian Tickle; CCP4BB@JISCMAIL.AC.UK Subject: RE: [ccp4bb] birefringent spacegroups 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. An so, no birefringence should exist (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 [EMAIL PROTECTED] -Message d'origine- De : CCP4 bulletin board [mailto:[EMAIL PROTECTED] la part de Ian Tickle Envoyé : Thursday, June 12, 2008 7:19 PM À : CCP4BB@JISCMAIL.AC.UK 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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ian Tickle Sent: 12 June 2008 17:50 To: Ethan A Merritt; Jacob Keller Cc: CCP4BB@jiscmail.ac.uk Subject: RE: [ccp4bb] birefringent spacegroups Hi Ethan You could be right, see this paper: http://physics.nist.gov/Divisions/Div842/Gp2/DUVMatChar/PDF/In tBiref.pdf Cheers -- Ian -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ethan A Merritt Sent: 12 June 2008 15:46 To: Multiple recipients Cc: CCP4BB@jiscmail.ac.uk 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
Re: [ccp4bb] birefringent spacegroups
-Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ethan Merritt Sent: 12 June 2008 19:41 To: Multiple recipients Cc: CCP4BB@jiscmail.ac.uk Subject: Re: [ccp4bb] birefringent spacegroups 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. 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 No I think you're quite right, birefringence clearly refers to any case where the refractive index is anisotropic for any general pair of directions, not just in specific orthogonal directions. In any case the birefringent direction [110] in cubic is orthogonal to the non-birefringent direction [001] so the old definition is still applicable anyway. BTW here's a patent issued for a method to get around the problems in lithographic fabrication of semiconductors caused by optical elements made from birefringent cubic crystals, so it's a very real problem, not just one of theoretical interest! http://www.patentstorm.us/patents/6844972/fulltext.html Cheers -- Ian Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing [EMAIL PROTECTED] and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674
Re: [ccp4bb] birefringent spacegroups
PS I found a nice presentation from the NIST group explaining the theory behind the cubic birefringence effect: http://math.nist.gov/mcsd/Seminars/2004/2004-06-10-shirley-presentation. pdf . Slide 33 has some nice graphics summarising the birefringence effect in all crystal systems. -- Ian -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ian Tickle Sent: 13 June 2008 11:20 To: Ethan Merritt Cc: CCP4BB@jiscmail.ac.uk Subject: RE: [ccp4bb] birefringent spacegroups -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ethan Merritt Sent: 12 June 2008 19:41 To: Multiple recipients Cc: CCP4BB@jiscmail.ac.uk Subject: Re: [ccp4bb] birefringent spacegroups 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. 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 No I think you're quite right, birefringence clearly refers to any case where the refractive index is anisotropic for any general pair of directions, not just in specific orthogonal directions. In any case the birefringent direction [110] in cubic is orthogonal to the non-birefringent direction [001] so the old definition is still applicable anyway. BTW here's a patent issued for a method to get around the problems in lithographic fabrication of semiconductors caused by optical elements made from birefringent cubic crystals, so it's a very real problem, not just one of theoretical interest! http://www.patentstorm.us/patents/6844972/fulltext.html Cheers -- Ian Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing [EMAIL PROTECTED] and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674 Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing [EMAIL PROTECTED] and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send
Re: [ccp4bb] birefringent spacegroups
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: [EMAIL PROTECTED] ***
Re: [ccp4bb] birefringent spacegroups
Hi Jacob, Chek out Section 2 in the following paper: Echalier et al. (2004) Assessing crystallization droplets uding birefringence. Acta Cryst D60, 696-702. It offers a very effective summary of the physical basis of crystal birefringence and reiterates the classification of crystal optics based on isotropic, uniaxial and biaxial systems. My understanding is that a favorable crystal orientation with respect to the direction of view is important for being able to observe appreciable birefringence from uniaxial and biaxial crystals. This can be especially tricky to get from biaxial crystals, i.e. crystals with orthorhombic or monoclinic or triclinic point-group symmetry, projecting their optically anisotropic axis in the plane of the view. Crystals with cubic symmetry are optically isotropic and are therefore not birefringent. Best wishes Savvas -Original Message- From: CCP4 bulletin board [mailto:[EMAIL PROTECTED] On Behalf Of Jacob Keller Sent: Thursday, June 12, 2008 2:33 AM To: CCP4BB@JISCMAIL.AC.UK Subject: [ccp4bb] birefringent spacegroups 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] ***
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: [EMAIL PROTECTED] *** -- Ethan A Merritt Biomolecular Structure Center University of Washington, Seattle 98195-7742
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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ethan A Merritt Sent: 12 June 2008 15:46 To: Multiple recipients Cc: CCP4BB@jiscmail.ac.uk 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: [EMAIL PROTECTED] *** -- Ethan A Merritt Biomolecular Structure Center University of Washington, Seattle 98195-7742 Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing [EMAIL PROTECTED] and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674
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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ian Tickle Sent: 12 June 2008 17:50 To: Ethan A Merritt; Jacob Keller Cc: CCP4BB@jiscmail.ac.uk 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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ethan A Merritt Sent: 12 June 2008 15:46 To: Multiple recipients Cc: CCP4BB@jiscmail.ac.uk 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: [EMAIL PROTECTED] *** -- Ethan A Merritt Biomolecular Structure Center University of Washington, Seattle 98195-7742 Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing [EMAIL PROTECTED] and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused
Re: [ccp4bb] birefringent spacegroups
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 [EMAIL PROTECTED] -Message d'origine- De : CCP4 bulletin board [mailto:[EMAIL PROTECTED] la part de Ian Tickle Envoyé : Thursday, June 12, 2008 7:19 PM À : CCP4BB@JISCMAIL.AC.UK 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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ian Tickle Sent: 12 June 2008 17:50 To: Ethan A Merritt; Jacob Keller Cc: CCP4BB@jiscmail.ac.uk 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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ethan A Merritt Sent: 12 June 2008 15:46 To: Multiple recipients Cc: CCP4BB@jiscmail.ac.uk 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
Re: [ccp4bb] birefringent spacegroups
But it seems that Hendrik Lorentz was the first to realise that symmetry breaking of the isotropy of the refractive index other optical properties could occur in cubic crystals at sufficiently short wavelength even in the absence of a distorting force - the spatial-dispersion-induced birefringence effect referred to in the paper. Note that this is an intrinsic effect, it has nothing to do with external stress, electric field etc., and if you read the paper you'll see that such external effects were specifically eliminated as the cause of the observed effect. -- Ian -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Philippe DUMAS Sent: 12 June 2008 19:20 To: Ian Tickle; CCP4BB@JISCMAIL.AC.UK Subject: RE: [ccp4bb] birefringent spacegroups 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. An so, no birefringence should exist (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 [EMAIL PROTECTED] -Message d'origine- De : CCP4 bulletin board [mailto:[EMAIL PROTECTED] la part de Ian Tickle Envoyé : Thursday, June 12, 2008 7:19 PM À : CCP4BB@JISCMAIL.AC.UK 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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ian Tickle Sent: 12 June 2008 17:50 To: Ethan A Merritt; Jacob Keller Cc: CCP4BB@jiscmail.ac.uk Subject: RE: [ccp4bb] birefringent spacegroups Hi Ethan You could be right, see this paper: http://physics.nist.gov/Divisions/Div842/Gp2/DUVMatChar/PDF/In tBiref.pdf Cheers -- Ian -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Ethan A Merritt Sent: 12 June 2008 15:46 To: Multiple recipients Cc: CCP4BB@jiscmail.ac.uk 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
[ccp4bb] birefringent spacegroups
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] ***
Re: [ccp4bb] birefringent spacegroups
All cubic crystals, as far as I am aware, will not birefringe. All others can (but it may be weak for reasons that don't depend on symmetry). On Wed, Jun 11, 2008 at 5:33 PM, Jacob Keller [EMAIL PROTECTED] 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] *** -- - William G. Scott contact info: http://chemistry.ucsc.edu/~wgscott Please reply to: [EMAIL PROTECTED]
