Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder
Is the following being neglected? In a crystal with these putative mosaic microdomains, there will be interference between microdomains at their edges/borders (at least), but since most microdomains are probably way smaller than the coherence length of 3-10 microns, presumably all unit cells in domain A interfere with all unit cells in domains B, C, etc, which are in the same coherence volume. In fact, as I said too unclearly in a previous post, as the putative microdomains become smaller and smaller to the limit of one unit cell, they become indistinguishable from unit cell parameter variation. So I am becoming increasingly suspicious about the existence of microdomains, and wonder what hard evidence there is for their existence? As a thought experiment, one can consider the microdomain theory taken to its limit: a powder diffraction image. In powder diffraction, there are so many crystals (read: microdomains) that each spot is manifested at its Bragg angle at every possible radial position on the detector. Mosaicity would be, what, 360 degrees? So, now imagine decreasing the mosaicity to lower values, and one gets progressively shorter arcs which at lower values become spots. Doesn’t this mean that the contribution from microdomain mosaicity should be to make the spots more like arcs, as we sometimes see in terrible diffraction patterns, and not just general broadening of spots? Put another way: mosaicity should broaden spots in the radial direction (arcs), and unit cell parameter variation should produce straight broadening in the direction of the unit cell variation of magnitude proportional to the degree of variation in that direction. JPK From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Ian Tickle Sent: Thursday, April 24, 2014 7:01 PM To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder Dear Herman On 24 April 2014 22:32, herman.schreu...@sanofi.commailto:herman.schreu...@sanofi.com wrote: The X-ray coherent length is depending on the crystal, not the synchrotron and my gut feeling is that it is at least several hundred unit cells, but here other experts may correct me. I assume you meant that the coherence length is a property of the beam (e.g. for a Cu target source it's related to the lifetime of the excited Cu K-alpha state), not the crystal, e,g, see http://www.aps.anl.gov/Users/Meeting/2010/Presentations/WK2talk_Vartaniants.pdf (slides 8-11). The relevant property of the crystal is the size of the microdomains. You don't get interference because coherence length domain size, i.e. the beam is not coherent over more than 1 domain. This is true for in-house sources synchrotrons, I guess for FELs it's different, i.e. much greater coherence length? This relates to a question I asked on the BB some time ago: if the coherence length is long enough would you start to see the effects of interference in twinned crystals, i.e. would the summation of intensities break down? I defer to the experts on synchrotrons FELs! Cheers -- Ian
Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder
-BEGIN PGP SIGNED MESSAGE- Hash: SHA1 Dear Jakob, your Gedankenexperiment on powder diffraction is not correct. You would record a powder diffraction pattern if you rotated a single crystal around the beam axis and record the result on a single image. This rotation does not affect the mosaicity and the mosaicity of a powder sample related only to the mosaicity of the micro crystals present in the powder. You also do not get arcs when reducing the powderness but you start seeing single spots. This can often be observed in the presence of ice rings. Best, Tim On 04/25/2014 09:32 AM, Keller, Jacob wrote: Is the following being neglected? In a crystal with these putative mosaic microdomains, there will be interference between microdomains at their edges/borders (at least), but since most microdomains are probably way smaller than the coherence length of 3-10 microns, presumably all unit cells in domain A interfere with all unit cells in domains B, C, etc, which are in the same coherence volume. In fact, as I said too unclearly in a previous post, as the putative microdomains become smaller and smaller to the limit of one unit cell, they become indistinguishable from unit cell parameter variation. So I am becoming increasingly suspicious about the existence of microdomains, and wonder what hard evidence there is for their existence? As a thought experiment, one can consider the microdomain theory taken to its limit: a powder diffraction image. In powder diffraction, there are so many crystals (read: microdomains) that each spot is manifested at its Bragg angle at every possible radial position on the detector. Mosaicity would be, what, 360 degrees? So, now imagine decreasing the mosaicity to lower values, and one gets progressively shorter arcs which at lower values become spots. Doesn’t this mean that the contribution from microdomain mosaicity should be to make the spots more like arcs, as we sometimes see in terrible diffraction patterns, and not just general broadening of spots? Put another way: mosaicity should broaden spots in the radial direction (arcs), and unit cell parameter variation should produce straight broadening in the direction of the unit cell variation of magnitude proportional to the degree of variation in that direction. JPK From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Ian Tickle Sent: Thursday, April 24, 2014 7:01 PM To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder Dear Herman On 24 April 2014 22:32, herman.schreu...@sanofi.commailto:herman.schreu...@sanofi.com wrote: The X-ray coherent length is depending on the crystal, not the synchrotron and my gut feeling is that it is at least several hundred unit cells, but here other experts may correct me. I assume you meant that the coherence length is a property of the beam (e.g. for a Cu target source it's related to the lifetime of the excited Cu K-alpha state), not the crystal, e,g, see http://www.aps.anl.gov/Users/Meeting/2010/Presentations/WK2talk_Vartaniants.pdf (slides 8-11). The relevant property of the crystal is the size of the microdomains. You don't get interference because coherence length domain size, i.e. the beam is not coherent over more than 1 domain. This is true for in-house sources synchrotrons, I guess for FELs it's different, i.e. much greater coherence length? This relates to a question I asked on the BB some time ago: if the coherence length is long enough would you start to see the effects of interference in twinned crystals, i.e. would the summation of intensities break down? I defer to the experts on synchrotrons FELs! Cheers -- Ian - -- - -- Dr Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A -BEGIN PGP SIGNATURE- Version: GnuPG v1.4.12 (GNU/Linux) Comment: Using GnuPG with Icedove - http://www.enigmail.net/ iD8DBQFTWiJpUxlJ7aRr7hoRAvhpAKCWt3PwAQsPnUgMlHjYoGS/7lVlGACglWpz K+rZPikLZBwe+CrK29WhBnc= =4a9F -END PGP SIGNATURE-
Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder
your Gedankenexperiment on powder diffraction is not correct. You would record a powder diffraction pattern if you rotated a single crystal around the beam axis and record the result on a single image. If you wanted to do it with a single crystal, you would have to rotate the crystal through all possible rotations in 3d, not just around the axis of the beam, because you would then miss all the reflections which were not in the diffraction condition at that phi angle. I agree that it could be done this way (not sure why this is important though.) This rotation does not affect the mosaicity and the mosaicity of a powder sample related only to the mosaicity of the micro crystals present in the powder. You also do not get arcs when reducing the powderness but you start seeing single spots. This can often be observed in the presence of ice rings. You are talking about powderness, which I would guess is a measure of the completeness of the sampling of all possible orientations of the constituent crystals, and I agree with what you say would happen. I said, however, mosaicity, which is a measure of the breadth of the distribution of the orientation angles of the microdomains/microcrystals. By decreasing powderness, one would do nothing to mosaicity. If one could arrange the microdomains into some range of orientation angles, one would reduce the mosaicity, and get arcs. I wish I had a picture of an arc-containing diffraction pattern--I've seen them from time to time, and they're always of course bad news. Anyone on the list have such a diffraction pattern handy? JPK On 04/25/2014 09:32 AM, Keller, Jacob wrote: Is the following being neglected? In a crystal with these putative mosaic microdomains, there will be interference between microdomains at their edges/borders (at least), but since most microdomains are probably way smaller than the coherence length of 3-10 microns, presumably all unit cells in domain A interfere with all unit cells in domains B, C, etc, which are in the same coherence volume. In fact, as I said too unclearly in a previous post, as the putative microdomains become smaller and smaller to the limit of one unit cell, they become indistinguishable from unit cell parameter variation. So I am becoming increasingly suspicious about the existence of microdomains, and wonder what hard evidence there is for their existence? As a thought experiment, one can consider the microdomain theory taken to its limit: a powder diffraction image. In powder diffraction, there are so many crystals (read: microdomains) that each spot is manifested at its Bragg angle at every possible radial position on the detector. Mosaicity would be, what, 360 degrees? So, now imagine decreasing the mosaicity to lower values, and one gets progressively shorter arcs which at lower values become spots. Doesn’t this mean that the contribution from microdomain mosaicity should be to make the spots more like arcs, as we sometimes see in terrible diffraction patterns, and not just general broadening of spots? Put another way: mosaicity should broaden spots in the radial direction (arcs), and unit cell parameter variation should produce straight broadening in the direction of the unit cell variation of magnitude proportional to the degree of variation in that direction. JPK From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Ian Tickle Sent: Thursday, April 24, 2014 7:01 PM To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder Dear Herman On 24 April 2014 22:32, herman.schreu...@sanofi.commailto:herman.schreu...@sanofi.com wrote: The X-ray coherent length is depending on the crystal, not the synchrotron and my gut feeling is that it is at least several hundred unit cells, but here other experts may correct me. I assume you meant that the coherence length is a property of the beam (e.g. for a Cu target source it's related to the lifetime of the excited Cu K-alpha state), not the crystal, e,g, see http://www.aps.anl.gov/Users/Meeting/2010/Presentations/WK2talk_Vartan iants.pdf (slides 8-11). The relevant property of the crystal is the size of the microdomains. You don't get interference because coherence length domain size, i.e. the beam is not coherent over more than 1 domain. This is true for in-house sources synchrotrons, I guess for FELs it's different, i.e. much greater coherence length? This relates to a question I asked on the BB some time ago: if the coherence length is long enough would you start to see the effects of interference in twinned crystals, i.e. would the summation of intensities break down? I defer to the experts on synchrotrons FELs! Cheers -- Ian - -- - -- Dr Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A -BEGIN PGP SIGNATURE- Version: GnuPG v1.4.12 (GNU/Linux
Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder
Thanks to all—I’ve got the paper now JPK From: Keller, Jacob Sent: Friday, April 25, 2014 1:58 PM To: 'Oliver Zeldin' Cc: CCP4BB@jiscmail.ac.uk Subject: RE: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder Does anyone know of a place where one can obtain this reference for free? I would contact Darwin himself, but I suspect he wouldn’t write back. I think this is the original paper proposing the mosaic block model, and I’d really like to see his reasoning. Darwin, C. G. (1922). Philos. Mag. 43, 800±829. The reflexion of X-rays from imperfect crystals JPK From: oliver.zel...@gmail.commailto:oliver.zel...@gmail.com [mailto:oliver.zel...@gmail.com] On Behalf Of Oliver Zeldin Sent: Friday, April 25, 2014 1:03 PM To: Keller, Jacob Cc: CCP4BB@jiscmail.ac.ukmailto:CCP4BB@jiscmail.ac.uk Subject: Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder Dear Jacob, In terms of the effect of crystal (lattice) defects on diffraction spot profiles, there are two great papers by Colin Nave that discuss this: http://journals.iucr.org/d/issues/1998/05/00/issconts.html and http://journals.iucr.org/d/issues/1998/05/00/issconts.html . There is also this paper on the nature of mosaic micro-domains: http://journals.iucr.org/d/issues/2000/08/00/en0024/en0024.pdf. I am sure there must be other references for the 'nature' of lattice disorder, and it anyone can point to them, I would be grateful. Cheers, Oliver On Fri, Apr 25, 2014 at 6:20 AM, Keller, Jacob kell...@janelia.hhmi.orgmailto:kell...@janelia.hhmi.org wrote: your Gedankenexperiment on powder diffraction is not correct. You would record a powder diffraction pattern if you rotated a single crystal around the beam axis and record the result on a single image. If you wanted to do it with a single crystal, you would have to rotate the crystal through all possible rotations in 3d, not just around the axis of the beam, because you would then miss all the reflections which were not in the diffraction condition at that phi angle. I agree that it could be done this way (not sure why this is important though.) This rotation does not affect the mosaicity and the mosaicity of a powder sample related only to the mosaicity of the micro crystals present in the powder. You also do not get arcs when reducing the powderness but you start seeing single spots. This can often be observed in the presence of ice rings. You are talking about powderness, which I would guess is a measure of the completeness of the sampling of all possible orientations of the constituent crystals, and I agree with what you say would happen. I said, however, mosaicity, which is a measure of the breadth of the distribution of the orientation angles of the microdomains/microcrystals. By decreasing powderness, one would do nothing to mosaicity. If one could arrange the microdomains into some range of orientation angles, one would reduce the mosaicity, and get arcs. I wish I had a picture of an arc-containing diffraction pattern--I've seen them from time to time, and they're always of course bad news. Anyone on the list have such a diffraction pattern handy? JPK On 04/25/2014 09:32 AM, Keller, Jacob wrote: Is the following being neglected? In a crystal with these putative mosaic microdomains, there will be interference between microdomains at their edges/borders (at least), but since most microdomains are probably way smaller than the coherence length of 3-10 microns, presumably all unit cells in domain A interfere with all unit cells in domains B, C, etc, which are in the same coherence volume. In fact, as I said too unclearly in a previous post, as the putative microdomains become smaller and smaller to the limit of one unit cell, they become indistinguishable from unit cell parameter variation. So I am becoming increasingly suspicious about the existence of microdomains, and wonder what hard evidence there is for their existence? As a thought experiment, one can consider the microdomain theory taken to its limit: a powder diffraction image. In powder diffraction, there are so many crystals (read: microdomains) that each spot is manifested at its Bragg angle at every possible radial position on the detector. Mosaicity would be, what, 360 degrees? So, now imagine decreasing the mosaicity to lower values, and one gets progressively shorter arcs which at lower values become spots. Doesn’t this mean that the contribution from microdomain mosaicity should be to make the spots more like arcs, as we sometimes see in terrible diffraction patterns, and not just general broadening of spots? Put another way: mosaicity should broaden spots in the radial direction (arcs), and unit cell parameter variation should produce straight broadening in the direction of the unit cell variation of magnitude proportional to the degree of variation in that direction. JPK From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UKmailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Ian
Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder
Thank you all for your comments/references and now I have a better understanding of what could be actually happening. But I have a feeling that disorder, where the twin domains can interfere with each other, is not actually so unusual. And in some cases MR might be possible to reveal a partial structure. (I ran into papers like this before but I couldn't think of one at the top of my head.) Why there is not a package out there to allow refinement against such data? I feel that if you have phase information it is possible to model the translation between different micro-domains... Sincerely, Chen On Apr 25, 2014, at 3:21 PM, Keller, Jacob kell...@janelia.hhmi.org wrote: Thanks to all—I’ve got the paper now JPK From: Keller, Jacob Sent: Friday, April 25, 2014 1:58 PM To: 'Oliver Zeldin' Cc: CCP4BB@jiscmail.ac.uk Subject: RE: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder Does anyone know of a place where one can obtain this reference for free? I would contact Darwin himself, but I suspect he wouldn’t write back. I think this is the original paper proposing the mosaic block model, and I’d really like to see his reasoning. Darwin, C. G. (1922). Philos. Mag. 43, 800±829. The reflexion of X-rays from imperfect crystals JPK From: oliver.zel...@gmail.com [mailto:oliver.zel...@gmail.com] On Behalf Of Oliver Zeldin Sent: Friday, April 25, 2014 1:03 PM To: Keller, Jacob Cc: CCP4BB@jiscmail.ac.uk Subject: Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder Dear Jacob, In terms of the effect of crystal (lattice) defects on diffraction spot profiles, there are two great papers by Colin Nave that discuss this: http://journals.iucr.org/d/issues/1998/05/00/issconts.html and http://journals.iucr.org/d/issues/1998/05/00/issconts.html . There is also this paper on the nature of mosaic micro-domains: http://journals.iucr.org/d/issues/2000/08/00/en0024/en0024.pdf. I am sure there must be other references for the 'nature' of lattice disorder, and it anyone can point to them, I would be grateful. Cheers, Oliver On Fri, Apr 25, 2014 at 6:20 AM, Keller, Jacob kell...@janelia.hhmi.org wrote: your Gedankenexperiment on powder diffraction is not correct. You would record a powder diffraction pattern if you rotated a single crystal around the beam axis and record the result on a single image. If you wanted to do it with a single crystal, you would have to rotate the crystal through all possible rotations in 3d, not just around the axis of the beam, because you would then miss all the reflections which were not in the diffraction condition at that phi angle. I agree that it could be done this way (not sure why this is important though.) This rotation does not affect the mosaicity and the mosaicity of a powder sample related only to the mosaicity of the micro crystals present in the powder. You also do not get arcs when reducing the powderness but you start seeing single spots. This can often be observed in the presence of ice rings. You are talking about powderness, which I would guess is a measure of the completeness of the sampling of all possible orientations of the constituent crystals, and I agree with what you say would happen. I said, however, mosaicity, which is a measure of the breadth of the distribution of the orientation angles of the microdomains/microcrystals. By decreasing powderness, one would do nothing to mosaicity. If one could arrange the microdomains into some range of orientation angles, one would reduce the mosaicity, and get arcs. I wish I had a picture of an arc-containing diffraction pattern--I've seen them from time to time, and they're always of course bad news. Anyone on the list have such a diffraction pattern handy? JPK On 04/25/2014 09:32 AM, Keller, Jacob wrote: Is the following being neglected? In a crystal with these putative mosaic microdomains, there will be interference between microdomains at their edges/borders (at least), but since most microdomains are probably way smaller than the coherence length of 3-10 microns, presumably all unit cells in domain A interfere with all unit cells in domains B, C, etc, which are in the same coherence volume. In fact, as I said too unclearly in a previous post, as the putative microdomains become smaller and smaller to the limit of one unit cell, they become indistinguishable from unit cell parameter variation. So I am becoming increasingly suspicious about the existence of microdomains, and wonder what hard evidence there is for their existence? As a thought experiment, one can consider the microdomain theory taken to its limit: a powder diffraction image. In powder diffraction, there are so many crystals (read: microdomains) that each spot is manifested at its Bragg angle at every possible radial position on the detector. Mosaicity would be, what, 360 degrees? So, now imagine
Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder
There are two kinds of coherence length: transverse and longitudinal. Longitudinal coherence is often quoted as delta-lambda/lambda, which is easy to calculate but unfortunately completely irrelevant for diffraction from crystals. If it weren't then Laue diffraction wouldn't produce spots. Transverse coherence tends to be around 3-10 microns with 1 A x-rays, depending on the detector distance. Yes, that's right, the detector distance. Longer detector distances give you a bigger coherence length, especially when the source is very far away, like it is at a synchrotron. How this happens is easiest to picture if you consider the simplest possible diffraction situation: a point source of x-rays, two atoms, and a detector. As long as the atoms are very close together relative to the distances from the sample to the source and the detector, then you have the far field diffraction situation. This is where both atoms are within the coherence length, Bragg's diagram for Bragg's Law holds: parallel incoming rays and parallel outgoing rays. But what if the atoms are very far apart? Obviously, the scattering from two atoms on different sides of the room will just add as intensities. And if they are very close together, then Bragg's Law holds and they scatter coherently. What most people think of as the coherence length is the point of transition between these two kinds of scattering. This point is rather conveniently defined as the distance between two atoms when the path from the source to one atom to a given detector pixel becomes 0.5 wavelengths longer than the same path through the other atom. As long as both atoms lie in the Bragg plane (that's the plane perpendicular to the s vector, which is the vector difference between the incoming and outgoing beam directions), the far-field approximation tells us they should also be in phase, but if they are far enough apart the 0.5 A change in total path length is enough to change the scattering completely from constructive to destructive interference. In ordinary optics, this is called the edge of the first Fresnel zone. So, if your source is very far away, emitting 1 A x-rays, and your detector is 1 meter away, then moving one atom 10 microns away from the centerline of the beam makes the path from that atom to the detector 1-sqrt(1^2+10e-6^2) = 0.5 A longer. So that implies the coherence length is 10 microns. But if the detector is only 100 mm away, that gives you 0.1-sqrt(0.1^2+3e-6^2) = 0.5 A, so 3 um is the coherence length. Of course, this is for the ideal case of a point source very far away. In reality finite beam divergence will mess up the coherence inasmuch as a divergent source looks like an array of sources all viewing the sample through a pinhole. What you then get on the detector is the sum of the patterns from all those sources, so the coherence is not as clean. That is, you don't see the Fourier transform of the crystal shape in every spot. Mosaic spread also messes up coherence in this way. Some might even define the mosaic domain size as the inverse of the effective coherence length. But, the long and short of all this is that as long as your detector pixels are bigger than the coherence length the coherence doesn't really matter. Hope that makes sense, -James Holton MAD Scientist On Thu, Apr 24, 2014 at 2:32 PM, herman.schreu...@sanofi.com wrote: Dear Chen, Twinning can be thought of as of two or more macro-crystals glued or grown together. The reason that the reflections often overlap is that they share one common plane from which they grow in different directions. Many twinning tests are based on the fact that the two (or more) macro crystals do not interfere, which changes the intensity distributions. Since there is no interference, twinning cannot make spots disappear. Moreover, translational operations between twin domains would be equivalent to move the crystal a little in the beam, as with centering, which will not have any influence on the diffraction pattern (except for weak diffraction because of missing the beam). Disorder can have many causes, but is caused by different orientations of residues/molecules/whatever in different asymmetric units. It is close range, so there will be interference. However, since it is usually randomly distributed over the crystal, it will not cause disappearance of spots. The X-ray coherent length is depending on the crystal, not the synchrotron and my gut feeling is that it is at least several hundred unit cells, but here other experts may correct me. Disappearance of spots can occur due to a wrong space group assignment (e.g. screw axis have been overlooked) or translational non-crystallographic symmetry. In this case, I would first run a modern MR program to see if you get a solution and otherwise you will have to analyze very careful your space group, unit cell etc. to find out what is going on. My 2 cents, Herman *Von:* CCP4
Re: [ccp4bb] AW: [ccp4bb] Twinning VS. Disorder
Dear Herman On 24 April 2014 22:32, herman.schreu...@sanofi.com wrote: The X-ray coherent length is depending on the crystal, not the synchrotron and my gut feeling is that it is at least several hundred unit cells, but here other experts may correct me. I assume you meant that the coherence length is a property of the beam (e.g. for a Cu target source it's related to the lifetime of the excited Cu K-alpha state), not the crystal, e,g, see http://www.aps.anl.gov/Users/Meeting/2010/Presentations/WK2talk_Vartaniants.pdf(slides 8-11). The relevant property of the crystal is the size of the microdomains. You don't get interference because coherence length domain size, i.e. the beam is not coherent over more than 1 domain. This is true for in-house sources synchrotrons, I guess for FELs it's different, i.e. much greater coherence length? This relates to a question I asked on the BB some time ago: if the coherence length is long enough would you start to see the effects of interference in twinned crystals, i.e. would the summation of intensities break down? I defer to the experts on synchrotrons FELs! Cheers -- Ian
