Re: GSAS informations
Dear Bob and Jon, one reply from the public is: come to share your and to get other ideas to the meeting Size-Strain IV (http://www.xray.cz/s-s4/), a satelite workshop of the EPDIC-9 (http://www.xray.cz/epdic/), end of this summer in Prague. The thinks can be even more complex: The supperposition of narrow and broad peaks can come not only from the size-strain symmetry lower than Laue symmetry (Andreas's example for the polycrystal), but also from a non-homogeneous distribution of lattice defects (for example dislocations), even in the monocrystal. See you in Prague Radovan Von Dreele, Robert B. a écrit: Jon, I risk a public reply here. One possibility everyone should be open to is that a real phase change has occured during some experimental manipulation of your sample. Some phase changes are quite subtle and involve only slight (and at first sight) quite odd line broadening. Higher resolution study sometimes reveals a splitting of these peaks which is then taken as a sign of a phase change. However, without this the linebroadening is sometimes well described by various anisotropic models (and sometimes not!). Historically, one only need reflect on the work done over many years on various high Tc superconductors and their relatives to know what I mean. Andreas does have the right idea about random powders but solid polycrystalline materials (e.g. metal bars) are a different matter especially if they have been "worked" because the various crystallites are no longer in "equal" environments. Fortunately, the kind of stuff that happens in metals is generally much less of a problem i! n the other kinds of materials one studies by powder diffraction so models used in Rietveld refinements can be rather simplified. Bob Von Dreele From: Jon Wright [mailto:[EMAIL PROTECTED] Sent: Mon 4/26/2004 3:45 AM To: [EMAIL PROTECTED] >... to answer to your (too) long questions. May be later, OK? Going back to this quartics versus ellipsoids peak broadening stuff, maybe I can summarise: Why should the distribution of lattice parameters (=strain) in a sample match the crystallographic symmetry? If the sample has random, isolated defects then I see it, but if the strains are induced (eg: by grinding) then I'd expect the symmetry to be broken. Suggests to me the symmetry constraints should be optional, and that the peak shape function needs to know about the crystallographic space group and subgroups. Either the program or the user would need to recognise equivalent solutions when the symmetry is broken (like the "star of k" for magnetic structures). Why would anyone have anything against using an ellipsoid? That same function can be described by the quartic approach, it just has less degrees of freedom. In short, I don't understand why there is such a strong recommendation to use the quartics instead of ellipsoids or why the symmetry is not optional. I'm still persuing this because I have looked at something with a very small anisotropic broadening which seems to fit better with an ellipsoid which breaks the symmetry compared to a quartic which doesn't! Thanks for any advice, Jon -- Radovan Cerny Laboratoire de Cristallographie 24, quai Ernest-Ansermet CH-1211 Geneva 4, Switzerland Phone : [+[41] 22] 37 964 50, FAX : [+[41] 22] 37 961 08 mailto : [EMAIL PROTECTED] URL: http://www.unige.ch/sciences/crystal/cerny/rcerny.htm
Re: GSAS informations
Jon, I risk a public reply here. One possibility everyone should be open to is that a real phase change has occured during some experimental manipulation of your sample. Some phase changes are quite subtle and involve only slight (and at first sight) quite odd line broadening. Higher resolution study sometimes reveals a splitting of these peaks which is then taken as a sign of a phase change. However, without this the linebroadening is sometimes well described by various anisotropic models (and sometimes not!). Historically, one only need reflect on the work done over many years on various high Tc superconductors and their relatives to know what I mean. Andreas does have the right idea about random powders but solid polycrystalline materials (e.g. metal bars) are a different matter especially if they have been "worked" because the various crystallites are no longer in "equal" environments. Fortunately, the kind of stuff that happens in metals is generally much less of a problem i! n the other kinds of materials one studies by powder diffraction so models used in Rietveld refinements can be rather simplified. Bob Von Dreele From: Jon Wright [mailto:[EMAIL PROTECTED] Sent: Mon 4/26/2004 3:45 AM To: [EMAIL PROTECTED] >... to answer to your (too) long questions. May be later, OK? Going back to this quartics versus ellipsoids peak broadening stuff, maybe I can summarise: Why should the distribution of lattice parameters (=strain) in a sample match the crystallographic symmetry? If the sample has random, isolated defects then I see it, but if the strains are induced (eg: by grinding) then I'd expect the symmetry to be broken. Suggests to me the symmetry constraints should be optional, and that the peak shape function needs to know about the crystallographic space group and subgroups. Either the program or the user would need to recognise equivalent solutions when the symmetry is broken (like the "star of k" for magnetic structures). Why would anyone have anything against using an ellipsoid? That same function can be described by the quartic approach, it just has less degrees of freedom. In short, I don't understand why there is such a strong recommendation to use the quartics instead of ellipsoids or why the symmetry is not optional. I'm still persuing this because I have looked at something with a very small anisotropic broadening which seems to fit better with an ellipsoid which breaks the symmetry compared to a quartic which doesn't! Thanks for any advice, Jon
Re: GSAS informations
Dear Jon, Jon Wright wrote: >... to answer to your (too) long questions. May be later, OK? Going back to this quartics versus ellipsoids peak broadening stuff, maybe I can summarise: Why should the distribution of lattice parameters (=strain) in a sample match the crystallographic symmetry? If the sample has random, isolated defects then I see it, but if the strains are induced (eg: by grinding) then I'd expect the symmetry to be broken. Suggests to me the symmetry constraints should be optional, and that the peak shape function needs to know about the crystallographic space group and subgroups. Either the program or the user would need to recognise equivalent solutions when the symmetry is broken (like the "star of k" for magnetic structures). I would like to present my thoughts here, although some points overlap with points mentined previously by others: One has to think what one looks at: If you look at a single crystal grain, which may show, for whatever reason microstrain broadening (i.e. local distortions, e.g. due to dislocations) which is incompatible with the Laue group/crystal system symmetry. In powder diffraction, however, you look at an ensemble of crystallites, and the line broadening information is averaged. Even if you have a powder of identical crystals, each showing identical line broadening incompatible with Laue symmetry reflections of different width overlap because they have the same d-spacing. By that the line broadening of the crystals incompatible with Laue symmetry cannot be obtained directly from the powder pattern, e.g . by analysing the powder peaks' widths as a function of hkl, as you could do it for a single crystal. You can only analyse averaged widths. Thus you loose the decisive information. However, you may detect hkl dependent changes of the shapes of the reflections, e.g. superlorentzian peaks where, e.g. one broad and two narrow overlap (h00 reflection of a cubic crystals which show strong microstrain along [001] but low microstrain along [100] and [010]). It will be difficult to recognise such effects, unless they are really strong, and it may be even more difficult to interpret that, if you have not specific information about possible sources of the microstrain. The same problem of overlapping reflections of different widths is predicted for certain cases of quartic line broadening when the Laue group symmetry is lower than the crystal system symmetry (E.g. for the Laue class 4/m), as remarked by Stephens (1999). As much as I know, no such case has been reported yet. To summarise: I think refinement of anisotropic line broadening will be much more stable if constrained by symmetry, such that reflections equivalent by symmetry have the same width. One example related with that problem was presented at (I think it was a size broadening case, but similar conclusions may be valid for microstrain) Young, R. A., Sakthivel, A., Bimodal Distributions of Profile-Broadening Effects in Rietveld Refinement, J. Appl. Cryst. 21 (1988) 416 Why would anyone have anything against using an ellipsoid? That same function can be described by the quartic approach, it just has less degrees of freedom. Here I fully agree, and there ARE cases where theory predicts an ellipsoid (e.g. microstrain-like broadening due to composition variations) which should, however, obey the symmetry restrictions. If such a case is present an ellipsoid model should be used obeying the rule to use a minimum of refined parameters. On the other hand, one might imagine other cases, where you have ellipsoid broadening for the single crystals incompatible with symmetry and being then powder-averaged. However, this will be difficult to be recognised and interpreted (see above). In short, I don't understand why there is such a strong recommendation to use the quartics instead of ellipsoids or why the symmetry is not optional. I'm still persuing this because I have looked at something with a very small anisotropic broadening which seems to fit better with an ellipsoid which breaks the symmetry compared to a quartic which doesn't! Thanks for any advice, Jon I think it should be recommended first to use a minimum number of parameters to describe the line broadening, and if possible, secondly to use models which are mathematically compatible with the physics of the origin of the line broadening. Thus in some cases an ellipsoid model should be preferred prior the quartic model, because it needs less parameters. However, I think that are good reasons to keep symmetry restrictions for both the quartic and elipsoid models (see above). But there may be reasons in certain, and probably few cases, where the symmetry restrictions can be lifted, e.g. when you have direction dependent line shapes of the broadening contribution to the peak shapes. But maybe that could also be better modelled by direction dependent shape factors compatible with the crystal symmetry. A
Re: GSAS informations
>... to answer to your (too) long questions. May be later, OK? Going back to this quartics versus ellipsoids peak broadening stuff, maybe I can summarise: Why should the distribution of lattice parameters (=strain) in a sample match the crystallographic symmetry? If the sample has random, isolated defects then I see it, but if the strains are induced (eg: by grinding) then I'd expect the symmetry to be broken. Suggests to me the symmetry constraints should be optional, and that the peak shape function needs to know about the crystallographic space group and subgroups. Either the program or the user would need to recognise equivalent solutions when the symmetry is broken (like the "star of k" for magnetic structures). Why would anyone have anything against using an ellipsoid? That same function can be described by the quartic approach, it just has less degrees of freedom. In short, I don't understand why there is such a strong recommendation to use the quartics instead of ellipsoids or why the symmetry is not optional. I'm still persuing this because I have looked at something with a very small anisotropic broadening which seems to fit better with an ellipsoid which breaks the symmetry compared to a quartic which doesn't! Thanks for any advice, Jon
Re: GSAS informations
> Dear Prof Popa, > > I had been meaning to implement the quartic form for peak width in a > refinement program for some time, but did not figure out how to generate > the constraints from a general list of symmetry operators. Is there a > simple trick for doing this? I was thinking of just choosing a Dear Jon, Sorry, I had no time and I'll have not at least 5 days to answer to your (too) long questions. May be later, OK? Best wishes Nic. Popa
Re: GSAS informations
> > >(you could be a good boxeur, Armel!), > > Knocked out at round 4 ! Argh ! Some people believe that "fair play" is mainly an Anglo-Saxon apanage (prerogative). Obviously they are wrong. > > Anyway, a sphere was good enough for the previous > size-strain round robin... Hope that the next size-strain > round robin will be more complex, and will succeed > in excluding definitely any ellipsoid from the ring. > > Armel > > Agree with you concerning the complexity of the next SS-RR but, perhaps, we can keep some ellipsoids if they are properly used and in the right place. Best wishes, Nicolae
Re: GSAS informations
(you could be a good boxeur, Armel!), Knocked out at round 4 ! Argh ! Anyway, a sphere was good enough for the previous size-strain round robin... Hope that the next size-strain round robin will be more complex, and will succeed in excluding definitely any ellipsoid from the ring. Armel
Re: GSAS informations
Not violating symmetry restrictions you may either
have the sphere with the terms 11=22=33 and 12=13=23=0
or something else allowing the 12=13=23 terms to be equal
but different from 0. These two possibilities are all you can do
in cubic symmetry with h,k,l permutable. If I am not wrong.
The (111) and (-111) come out with different widths if the {12=13=23} !=
0, but the quartic's have declared this blasphemous as they are symmetry
equivalents... perhaps you should go into hiding before they burn you at
the stake[*]. There would be an equivalent "solution" with (-12=13=23,
etc), so the "something else" is an ellipsoid along the 111 direction,
and you can find the same "solution" if you put the ellipsoid along any
of the 111 directions. Same solutions, but some have the crystal upside
down or on it's side. Sometimes happens if you drop your crystal.
So if (111) and (-111) do not need to be equal in width, someone is
hopefully about explain to me why (100) and (010) do need to be equal in
width in cubic symmetry. I don't understand why they do, and for a
single crystal I have a vague memory of seeing them measured as being
different (it is a very vague memory and I might have been mistaken). In
a powder you don't know which direction is which anymore, but squash
some cubic grains and then shake them up, and each grain will probably
remember which way was up when you squashed it. If you use a subgroup of
your crystal spacegroup for the peak widths then you'll find the same
solution moved by the symmetry operators you threw out to make the
subgroup. Nothing surprising there. I wouldn't generally expect the
crystal defects to have the full crystal symmetry, but some people seem
to be insisting they should have. I am curious as to how that comes
about, especially if the defects interact with each other and eventually
gather themselves up into a full blown symmetry breaking small
distortion. If I were to implement this stuff in PRODD, should I force
the users to apply the symmetry or not? If not it means taking care
internally to sum over the equivalents when computing the peakshape. If
that sum is not carried out, then I can see why problems could arise,
but otherwise it seems unreasonable to insist that everyone use the full
crystal symmetry?
So can someone just tell me why the symmetry is not optional?
Jon
[*] Please excuse my sense of humour.
Re: GSAS informations
> Not violating symmetry restrictions you may either > have the sphere with the terms 11=22=33 and 12=13=23=0 > or something else allowing the 12=13=23 terms to be equal > but different from 0. These two possibilities are all you can do > in cubic symmetry with h,k,l permutable. If I am not wrong. You are. The cross terms have disappear even at orthorhombic (monoclinic has only one). Cubic is an orthorhombic to which a 3-fold axis is added on the big diagonal resulting in 11=22=33. Nicolae
Re: GSAS informations
I just wanted to add my 2 cents to this argument... I think one big point in all the discussion on size and strain concerns the difference between what IS in the specimen, what we see with our probe (X-rays or neutrons, presumably) and what we reconstruct using A model. In most cases the model do not answer the easy question: "what is in the specimen?" I want to stress the "A" because in any case what we get is just a guess... subtle philosophers could speculate on this.. but I bet we're all scientists and not mere philosophers.. Anyway, people start their analysis with simple models and try to improve them.. easy but effective! As far as I know (well microelectronics is reality I think!) there is NO connection between grain shape (and therefore crystallite shape) and symmetry (or any descriptor for it). In this case the ellipsoid model could work, but is completely missing reality! The good scientist, however knows the limits of validity and the hypotheses on which the model is based (most modern scientists tend to forget this concept...) and knows that he obtained some "effective fit". Ok, specimens we analyse are simpler but... we are not dealing with specimens containing a set of perfect, equal, ordered, aligned crytallites.. More likely we have a distribution of shapes, sizes and orientation that can screw things up! In this case we can just hope that some simple model will accommodate all the mess! And using ANY anisotropic model is in most cases better than using none if you just care of "good fit". As for symmetry restrictions.. well.. they are welcome if they are consistent with the nature of diffraction (peak overlapping is always a painful problem in line profile analysis), but they are just related to our probe (X-rays, neutrones) and NOT with the original crystallites! Of course music changes if we talk about strain broadening. That's why Stephens models is good as an effective way of treating anisotropic broadening because "it fits better", but I'd not attach any physical meaning to the numbers you get out of it... I have written a bit too much I bet... so better if I go back to my size/strain modelling! OOps I was forgetting... Armel's replies to Nicolae emails are really great (you could be a good boxeur, Armel!), but I do not agree on one point: >Yes, anisotropic line broadening is rarely observed >with cubic compounds unless in very special cases >of faulting. this is true if you restrict the scope to size broadening only. Otherwise, line defects can be a source of anisotropic brodening in cubic materials (but you need a "good amount" to appreciate the effect)... Mat PS. There is no unique and simple solution to the problem... there are just scientists with their ability to attach the proper meaning to their results! -- w g( o 0 )g --oOO--(_)---OOo---oOO-w-OOo--- Department of Materials Engineering and Industrial Technologies University of Trento 38050 Mesiano (TN) Matteo Leoni, PhD ITALY .ooo0 0ooo. Tel +39 0461 882416e-mail: [EMAIL PROTECTED] ( ) ( ) Fax +39 0461 881977 \ (---) /-- \_) (_/ | | | | .ooo0 0ooo. ( ) ( ) \ ( ) / \_) (_/
Re: GSAS informations
He could ask the master how is the nature so perfect. Or could conclude by himself that powders are not single crystals, so that symmetry may lead to systematic overlap and irrecoverable loss of information. Yes, anisotropic line broadening is rarely observed with cubic compounds unless in very special cases of faulting. Yes most crystals, when seen through the powder diffraction method, seem to grow along symmetry axis, due to that averaging produced by exact overlapping according to the symmetry. how then you searched for size anisotropy in CeO2 with ARIT? Or the symmetry restrictions are optional? Not violating symmetry restrictions you may either have the sphere with the terms 11=22=33 and 12=13=23=0 or something else allowing the 12=13=23 terms to be equal but different from 0. These two possibilities are all you can do in cubic symmetry with h,k,l permutable. If I am not wrong. Armel
Re: GSAS informations
> > >Presume one of your students makes a fit on a sample having only size > >anisotropy and he is able to determine the six parameters of the ellipsoid. > >But after that he has a funny idea to repeat the fit changing (hkl) into > >equivalents (h'k'l'). He has a chance to obtain once again a good fit, with > >other ellipsoid parameters but with (approximately) the same average size, > >this > >time in other direction > >[lamda/cos(theta)/M(hkl)=lamda/cos(theta)/M(h'k'l')]. Am I wrong? > > But why to presume so soon that people are dumb ? > > You may also presume that the student is not stupid enough > for trying to determine the 6 parameters of the ellipsoid in any case > and that he applies restrictions related to the symmetry, as > recommended in the software manual (the software name was > ARIT)... That manual says that the 6 parameters are obtainable > only in triclinic symmetry, etc. > > I prefer to presume first that people are smart, and may be change > my opinion later. > > I guess that the Lij in GSAS are explained to be symmetry- > restricted as well. > > Armel > By contrary, I presumed a smart student observing immediately that by applying to the ellipsoid the symmetry restrictions he obtains some strange ellipsoids: for orthorhombic the principal axes are always along the crystal axis, for trigonal, tetragonal & hexagonal they are always rotation ellipsoids with 3,4,6 - fold axis as rotation axes. He could ask the master how is the nature so perfect. How know the crystal to grows always along the symmetry axis? But the most wondered will be the student seeing that for cubic crystals the ellipsoid is in fact a sphere. To not risk the next examination probably he will not put this question: how then you searched for size anisotropy in CeO2 with ARIT? Or the symmetry restrictions are optional? Nicolae Popa
Re: GSAS informations
Presume one of your students makes a fit on a sample having only size anisotropy and he is able to determine the six parameters of the ellipsoid. But after that he has a funny idea to repeat the fit changing (hkl) into equivalents (h'k'l'). He has a chance to obtain once again a good fit, with other ellipsoid parameters but with (approximately) the same average size, this time in other direction [lamda/cos(theta)/M(hkl)=lamda/cos(theta)/M(h'k'l')]. Am I wrong? But why to presume so soon that people are dumb ? You may also presume that the student is not stupid enough for trying to determine the 6 parameters of the ellipsoid in any case and that he applies restrictions related to the symmetry, as recommended in the software manual (the software name was ARIT)... That manual says that the 6 parameters are obtainable only in triclinic symmetry, etc. I prefer to presume first that people are smart, and may be change my opinion later. I guess that the Lij in GSAS are explained to be symmetry- restricted as well. Armel
Re: GSAS informations
Hi, > It seems that we disagree on the meaning of some > english words. English is not my mother language, so I may be > wrong. Nor mine, so I can be equally wrong (or worse). > I was able to put one word on that definition (thanks for it) in my > previous email : distribution (a size distribution). > > In these earlier works (maybe you define any earlier work as > being "naive" ?) it is not at all the crystallite shape which is > approximated by an ellipsoid. The ellipsoid is there for > modelling the variation of the average size M(hkl) (which is > the mean of the size distribution). If ellipsoid models the crystallite shape is an approximation, good or not good, if models the average size "seen" in powder diffraction as function of direction is a mistake (see next comment). > > So, thanks, I used ellipsoids in 1983-87 for describing some > simple size and strain anisotropy effects in the Rietveld method. > I think that no elementary principle was violated, though Presume one of your students makes a fit on a sample having only size anisotropy and he is able to determine the six parameters of the ellipsoid. But after that he has a funny idea to repeat the fit changing (hkl) into equivalents (h'k'l'). He has a chance to obtain once again a good fit, with other ellipsoid parameters but with (approximately) the same average size, this time in other direction [lamda/cos(theta)/M(hkl)=lamda/cos(theta)/M(h'k'l')]. Am I wrong? If not, how you explain him that averages of the size distribution are the same in different directions once were approximated by an ellipsoid? And what set of ellipsoid parameters you advice to consider, the first or the second one? > particularly stupid. The ellipsoid method was applied to the > recent Size-Strain Round Robin CeO2 sample, giving > results not completely fool (in the sense that not a > lot of anisotropy was found for that cubic sample > showing almost size-effect only, and quasi-isotropy). Not surprisingly. Take a sphere and put two cones at the ends of one diameter. Certainly the finite high of cone means anisotropy. Refine the same CeO2 pattern. Very probably you will find zero for the cone high. Is this funny model equally good? > cubic case showing strong stacking fault effects for HNbO3 > (cubic symmetry). A neutron pattern is available. I would be interested > in a better estimation of the size and strain effects on that sample > (not only a phenomenological fit). Can you provide that better > estimation ? > > Best wishes with HNbO3, > > Armel Le Bail Strong staking faults effect? I would accept your challenge, but I'm not sure that with a knife in place of scissors is possible to do easy tailoring. That doesn't mean the knife is good for nothing. Best wishes and ... il faut pas s'enerver Nicolae Popa
Re: GSAS informations
Nicolae Popa wrote:
the condition to not violate some elementary principles, in particular,
here, the invariance to symmetry.
Dear Prof Popa,
I had been meaning to implement the quartic form for peak width in a
refinement program for some time, but did not figure out how to generate
the constraints from a general list of symmetry operators. Is there a
simple trick for doing this? I was thinking of just choosing a
particular peak like hkl=(1,2,3) where all the fifteen quartic terms
look to be different, and then just comparing the terms generated by
symmetry equivalent peaks. Then if the code for getting equivalent
reflections is OK, the constraints can be determined, messily, that way.
Is this on the right track?
I was also wondering if the user should be allowed to choose a different
symmetry for the peak widths compared to the crystal structure. I
thought it was possible to measure quite different peak shapes for
equivalent hkl's in heavily deformed single crystals...? Something like
a powdered iron sample which has strains introduced by being squashed
between two magnets might have a lower symmetry for the peak broadening
compared to the cubic crystal symmetry. Does the powder averaging
somehow wash this kind of effect away? What about small distortions
which only show up in the peak widths and where the space group change
does not generate superstructure peaks (eg P4/m to P2/m)? At some point
in a series of datasets going through a second order transition you'd
want to go from tetragonal to monoclinic in a smooth way. What about
samples containing a mixture of strained and unstrained crystallites? I
guess that ought to modelled as two phases?
Thanks in advance for any advice. Sadly I don't know if I will ever find
to the time to get this peakshape stuff going until I have a sample that
really needs it...
Jon
PS: With the debate raging over which is the "right" approach, I got
very confused, is one an extension of the other...? Assuming you
normalise the L11 etc by the reciprocal cell metric tensor elements (who
wouldn't ?-), then making them all equal gives isotropic strain.
Allowing those Lij to be different from each other gives an ellipsoid
with six degrees of freedom, which would seem to be related to the S_hkl
parameters as below. Going to the quartic form just allows the elements
in that matrix to be inconsistent with the Lij parameters (eg the
entries for L11*L11, L22*L22 and L11*L22 do not agree on the L11 and L22
values). In implementing this stuff it would seem more sane to define
Lij as being normalised by the cell parameters (RM11 etc in GSAS) and to
subtract off the isotropic contribution (LY). Then define the S_hkl in
terms of the Lij and "LY" - with the diagonal elements as Lij^2 and the
off diagonal elements as being the difference between the values needed
to fit the peaks, and the values predicted by the Lij's. This means that
the anisotropic broadening model with just one direction (stec? in GSAS)
can also be implemented by making two of the eigenvectors of an Lij
based matrix be equal (you could refine a direction).
It might be more work for the programmer, but numerically things should
be more stable if the functions refined are more orthogonal to each
other. Fitting the anisotropy as the difference between the peak widths,
rather than their absolute values should make life easier, at least for
getting the fit started. Also I much prefer to have refined values where
I can ask if something is within esd of being zero! (Is the anisotropic
broadening "significant"? Am I in a false minimum?)
width = sqrt{( L11 h*h ) ( L11 h*h )^T }
( L22 k*k ) ( L22 k*k )
( L33 l*l ) ( L33 l*l )
( L12 h*k ) ( L12 h*k )
( L13 h*l ) ( L13 h*l )
( L23 k*l ) ( L23 k*l )
giving: (work out the h,k,l powers from the 11, 12 etc)
( L11*L11, L22*L11, L33*L11, L12*L11, L13*L11, L23*L11 )
( L11*L22, L22*L22, L33*L22, L12*L22, L13*L22, L23*L22 )
( L11*L33, L22*L33, L33*L33, L12*L33, L13*L33, L23*L33 )
( L11*L12, L22*L12, L33*L12, L12*L12, L13*L12, L23*L12 )
( L11*L13, L22*L13, L33*L13, L12*L13, L13*L13, L23*L13 )
( L11*L23, L22*L23, L33*L23, L12*L23, L13*L23, L23*L23 )
The fifteen S_hkl parameters are then:
1 L11*L114 L11*L127 L22*L23
2 L22*L225 L11*L138 L33*L13
3 L33*L336 L22*L129 L33*L23
10 L11*L22 + L12*L12
11 L11*L33 + L13*L13
12 L22*L33 + L23*L23
13 L12*L23 + L22*L13
14 L13*L23 + L33*L12
15 L12*L13 + L11*L23
So one could make a peakshape with the 6 by 6 matrix above and implement
all of the different models (single direction, ellipsoid and quartic
form) in terms of the constraints on the matrix elements.
Can someone tell me if all that is "right" or "wrong"? I was kind of
hoping that if I ever do get around to it, I could have a single peak
shape function which works for everything and never needs to be messed
about with again...!
Would there be any rea
Re: GSAS informations
To a happy Easter, It seems that we disagree on the meaning of some english words. English is not my mother language, so I may be wrong. The naive character doesn't come from the approximation of the crystallite shape by an ellipsoid, but from the approximation of the size effect in powder diffraction by ellipsoid. In powder diffraction it is seen not one, but a (big) number of crystallites more or less randomly oriented. The crystallites in reflection "show" different diameters, not only one. I was able to put one word on that definition (thanks for it) in my previous email : distribution (a size distribution). In these earlier works (maybe you define any earlier work as being "naive" ?) it is not at all the crystallite shape which is approximated by an ellipsoid. The ellipsoid is there for modelling the variation of the average size M(hkl) (which is the mean of the size distribution). Certainly, always one can use ellipsoids as a first approximation for any kind of anisotropy, with the condition to not violate some elementary principles, in particular, here, the invariance to symmetry. So, thanks, I used ellipsoids in 1983-87 for describing some simple size and strain anisotropy effects in the Rietveld method. I think that no elementary principle was violated, though certainly the word "violation" can be used as a definition for an "extreme approximation". But calling it "first approach twenty years ago" is less violent, even if you think that it is particularly stupid. The ellipsoid method was applied to the recent Size-Strain Round Robin CeO2 sample, giving results not completely fool (in the sense that not a lot of anisotropy was found for that cubic sample showing almost size-effect only, and quasi-isotropy). Not surprisingly, people are mainly interested to obtain a good structure refinement and ignore by-products like strain an size. Doesn't mean that strain and size can not be estimated better. I have gathered some interesting examples of anisotropic effects (at large) in a database of powder patterns. There is a famous cubic case showing strong stacking fault effects for HNbO3 (cubic symmetry). A neutron pattern is available. I would be interested in a better estimation of the size and strain effects on that sample (not only a phenomenological fit). Can you provide that better estimation ? It was a D1A (ILL) pattern and you could use the CeO2 well-crystallized sample powder pattern made on the D1A instrument for the Size-Strain Round Robin. Type the keyword HNbO3 in the search system of PowBase and you will have a hyperlink toward a .zip file containing the data : http://sdpd.univ-lemans.fr/powbase/ See a part of the neutron powder pattern at : http://sdpd.univ-lemans.fr/powbase/31.gif The ellipsoid approach is of course unable to provide anything correct with that case... Can your approach tell something ? This would interest a lot of people. The thermodynamics is phenomenological science, have we to consider it a naive or a less naive science? You use the word "naive", not me, I only cited it under quotes. I would never use it concerning any science. I just tried to show that even the application of ellipsoids in order to model size and strain anisotropy was not "naive". It was old Science (in the sense "accepted for publication twenty years ago" ;-). Best wishes with HNbO3, Armel Le Bail
Re: GSAS informations
> Our whole science is a so bad approximation to the Universe... > > For the representation of an isotropic size effect , you may imagine > the mean size being the same in all directions, obtaining a > sphere. The same for a mean strain value. > > Introducing some anisotropy in mean size and mean strain in the > Rietveld method was done in the years 1983-87 by the "naive" view that > the mean size M(hkl) in any direction could be approximated by > an ellipsoid rather than a sphere, and the same for the mean > strain (hkl). See for instance J. Less-Common Metals > 129 (1987) 65-76. Hello Messieur Le Bail, (and thanks for explaining how to pass from sphere - isotropy to ellipsoid - anisotropy). The naive character doesn't come from the approximation of the crystallite shape by an ellipsoid, but from the approximation of the size effect in powder diffraction by ellipsoid. In powder diffraction it is seen not one, but a (big) number of crystallites more or less randomly oriented. The crystallites in reflection "show" different diameters, not only one. Concerning the mean strain, another confusion. In fact the mean strain gives the peak shift, sometimes reasonably described by an ellipsoid in (hkl) (for example not-textured samples under hydrostatic pressure). But the strain broadening is related on the strain dispersion (you wrote not ) that in first approximation is a symmetrized quartic form and its square root (giving breadth) is never an ellipsoid. Certainly, always one can use ellipsoids as a first approximation for any kind of anisotropy, with the condition to not violate some elementary principles, in particular, here, the invariance to symmetry. It has no relevance to use the thermal ellipsoids as argument. The thermal ellipsoids are a natural consequence of the harmonic vibration of the atoms and no principle is violated, even if, some times, this is a rough approximation because of a high contribution of anharmonicity. > > Less "naive" representations were applied in the years 1997-98 > (so, ten years later). But these less naive representations were not > providing any size and strain estimations, Not surprisingly, people are mainly interested to obtain a good structure refinement and ignore by-products like strain an size. Doesn't mean that strain and size can not be estimated better. >the fit was quite better > (especially in cases showing stacking faults, with directional effects > hardly approximated by ellipsoids) but remained "phenomenological". The thermodynamics is phenomenological science, have we to consider it a naive or a less naive science? Best wishes a happy Easter, Nicolae Popa > You can find experts in thermal vibration explaining that the ellipsoid > representation used by crystallographers is an extremely naive view > of the reality, and they are right. But crystallographers continue to > calculate these Uij (and there is a table giving Uij restrictions) > which in most cases provide a minimal and sufficient representation > of thermal vibrations... > Armel > >
Re: GSAS informations
Hi, >The coefficients Lij in the formula you wrote have no significance. Our whole science is a so bad approximation to the Universe... For the representation of an isotropic size effect , you may imagine the mean size being the same in all directions, obtaining a sphere. The same for a mean strain value. Introducing some anisotropy in mean size and mean strain in the Rietveld method was done in the years 1983-87 by the "naive" view that the mean size M(hkl) in any direction could be approximated by an ellipsoid rather than a sphere, and the same for the mean strain (hkl). See for instance J. Less-Common Metals 129 (1987) 65-76. Less "naive" representations were applied in the years 1997-98 (so, ten years later). But these less naive representations were not providing any size and strain estimations, the fit was quite better (especially in cases showing stacking faults, with directional effects hardly approximated by ellipsoids) but remained "phenomenological". The old naive view provided at least (bad) estimations of the directional values of the mean size and strain parameters. Behind that ellipsoidal approximation of the mean size and strain are even more important "details": one has also to define what could be the size distribution and the strain distribution. Simplifying naively, the mean size and strain play on the profile width, and the size and strain distributions play on the profile shape. In the earlier approachs, the size and strain distributions were also naively represented (frequently Cauchy-like for the size distribution, and Gaussian for the strain distribution - but do not confuse the shapes of the size and strain distributions with profile shapes). Nowadays, people are using flexible profile shapes and seem to be not concerned at all with the exact relation between the profile shape and the size and strain distributions (some profile shapes could correspond to unrealistic size and strain distributions (for instance a negative proportion of crystallites for some given sizes, etc). This looks quite naive to me as well... Probably in ten or twenty years, more essential improvements will make the current view looking very naive; this is to be expected ;-). You can find experts in thermal vibration explaining that the ellipsoid representation used by crystallographers is an extremely naive view of the reality, and they are right. But crystallographers continue to calculate these Uij (and there is a table giving Uij restrictions) which in most cases provide a minimal and sufficient representation of thermal vibrations... With some experience, looking at a powder diffraction pattern, you may visually approximate the mean coherent domain size : small, medium or large. Do you really need the exact size distribution and exact mean size in all crystallographic directions ? Rarely ;-). Armel
Re: GSAS informations
Dear Christophe, The coefficients Lij in the formula you wrote have no significance. This formula is a naive representation of strain anisotropy that falls at the first analysis. It is enough to change the indices hkl into equivalent indices and you obtain other Gamma. As a consequence, in cubic classes for example, the microstrain anisotropy doesn't exist, which is a nonsense. The correct formulae are indeed in Peter Stephens paper (at least for a part of Laue classes) but also in a paper by Popa, J. Appl. Cryst. (1998) 31, 176-180, where the physical significance of coefficients is explicitly stated. Hence, if denote by Eij the components of the microstrain tensor in an orthogonal coordinate system related to crystallite, then the coefficients are some linear combinations (specific to every Laue class) of the averages . Best wishes, Nicolae Popa - Original Message - From: Christophe Chabanier To: [EMAIL PROTECTED] Sent: Wednesday, April 07, 2004 6:45 PM Subject: GSAS informations Hello everybody,i have a question about the GSAS software. Indeed, i would like to know what are exactly the L11, L22, L33L23 parameters. I saw that these parameters represent the anisotropic microstrain in material. Moreover, there is an empirical _expression_ which uses these parameters as following : Gamma(L) = L11*h^2 + L22*k^2 + L33*l^2 + 2*L12*hk + 2*L13*hl + 2*L23*kl I would like to know and understand the physical representation of these parameters and this _expression_.Thanks in advance Christophe ChabanierINRS-Énergie, Matériaux et Télécommunications 1650 Blvd. Lionel Boulet C. P. 1020, Varennes Qc, Canada J3X 1S2Tél: (450) 929 8220Fax: (450) 929 8102Courriel: [EMAIL PROTECTED]
Re: GSAS informations
>From my experience both functions #3 and #4 work fine when broadening anisotropy is >not significant. I found #4 more works better when anisotropy is large (up to 2 times); in this case improvement is substantial Peter Zavalij -Original Message- From: Maxim V. Lobanov [mailto:[EMAIL PROTECTED] Sent: Wednesday, April 07, 2004 11:05 AM To: [EMAIL PROTECTED] At least, in the classical article by Peter Stephens (J. Appl. Cryst., 32, 281) it is written about this and similar approaches that "these methods have been successful in producing improved line-shape fits, even though no theoretical justification or microscopic model has been given". The description is given in the GSAS manual. I asssume this is a phenomenological treatment, which appears quite reasonable and convenient... By the way, GSAS has Stephens' formulation as well. Sincerely, Maxim. > > i have a question about the GSAS software. Indeed, i would like to know >what are exactly the L11, L22, L33L23 parameters. I saw that these >parameters represent the anisotropic microstrain in material. Moreover, >there is an empirical expression which uses these parameters as following : > > L22*k^2 + L33*l^2 + 2*L12*hk + 2*L13*hl + 2*L23*kl > > I would like to know and understand the physical representation of these >parameters and this expression. > __ Maxim V. Lobanov Department of Chemistry Rutgers University 610 Taylor Rd Piscataway, NJ 08854 Phone: (732) 445-3811
Re: GSAS informations
At least, in the classical article by Peter Stephens (J. Appl. Cryst., 32, 281) it is written about this and similar approaches that "these methods have been successful in producing improved line-shape fits, even though no theoretical justification or microscopic model has been given". The description is given in the GSAS manual. I asssume this is a phenomenological treatment, which appears quite reasonable and convenient... By the way, GSAS has Stephens' formulation as well. Sincerely, Maxim. > > i have a question about the GSAS software. Indeed, i would like to know >what are exactly the L11, L22, L33L23 parameters. I saw that these >parameters represent the anisotropic microstrain in material. Moreover, >there is an empirical expression which uses these parameters as following : > > L22*k^2 + L33*l^2 + 2*L12*hk + 2*L13*hl + 2*L23*kl > > I would like to know and understand the physical representation of these >parameters and this expression. > __ Maxim V. Lobanov Department of Chemistry Rutgers University 610 Taylor Rd Piscataway, NJ 08854 Phone: (732) 445-3811
GSAS informations
Hello everybody, i have a question about the GSAS software. Indeed, i would like to know what are exactly the L11, L22, L33L23 parameters. I saw that these parameters represent the anisotropic microstrain in material. Moreover, there is an empirical _expression_ which uses these parameters as following : Gamma(L) = L11*h^2 + L22*k^2 + L33*l^2 + 2*L12*hk + 2*L13*hl + 2*L23*kl I would like to know and understand the physical representation of these parameters and this _expression_. Thanks in advance Christophe Chabanier INRS-Énergie, Matériaux et Télécommunications 1650 Blvd. Lionel Boulet C. P. 1020, Varennes Qc, Canada J3X 1S2 Tél: (450) 929 8220 Fax: (450) 929 8102 Courriel: [EMAIL PROTECTED]
