Hi Tadej, I agree with the general drift of Anatoly's comment--this is what Shelly meant by saying it sounds like a tough problem! But I think it came off sounding a little more harsh than I suspect Anatoly meant it to be, particularly considering some of the systems he himself has examined! Anatoly's description is fair IF only a nearest-neighbor fit is performed. But it's possible that inequivalent sites have very different environments at greater Reff, particularly since niobium is so much heavier than oxygen! For example, there's been a lot of work done that shows that there is a screamingly large difference in the EXAFS spectra of A and B sites in the spinel structure (Vince Harris did a lot of this, for example). In such a case, Artemis is able to find the site occupancy without too much trouble, using a strategy such as Shelly explained. Of course, =seven= freely-floating sites sounds likely to yield nonsense fits. It would help if you could use some physical intuition to try to simplify the problem, at least at first. Consider also using the "restraint" feature in Artemis/Ifeffit liberally in your early fits to keep the fit from wandering off into nonsensical territory. --Scott Calvin Sarah Lawrence College At 12:14 PM 12/15/2005, Anatoly wrote:
boundary="----_=_NextPart_001_01C6019A.F6711239"
You cannot resolve these sites from EXAFS analysis. Even if you had only 2 inequivalent sites of the same central atom with occupancies N1 and N2, you would not be able to resolve N1 and N2 in the fit because different Nb atoms would have similar environments (e.g., 4 and 6 oxygens), and they will have similar Nb-O distances around each site. The best you can do is to try to fit the first nearest neighbor peak as an average Nb-O contribution (if it is a well isolated peak) and try to make use of sigma2 that may turn out to be larger than in some well known Nb oxide reference that you should analyze first.
Anatoly
Dear collegues,
my name is Tadej Rojac and I'm writing from the Institute Jozef Stefan in Ljubljana, Slovenia. I work in the Department of electronic ceramics. Actually, I'm working on a EXAFS spectra with Artemis. What I am trying to do is mainly to describe an EXAFS spectrum with a model concerning the structure of Nb2O5. I'm working togheter with prof. Iztok Arcon, who is a specialist in the field. My main problem is that I have to do some suppositions. In fact Nb2O5 structure is quite complicated. It is composed of seven different Nb positions which I took into account using 7 feffs in Artemis. I don't know the exact occupancies of the seven positions. In order to make the search easier I did at first a supposition that all the occupancies must be positive, which is realistic. I set this with the command "abs" in each feff file. Secondly, I need to supose that the sum of all occupancies is 1. In that way the search for the result is much easier, otherwise I get the sum greater than one, which, for sure, is not the case. My question is how can I do that? For example, if the occupancies are O1, O2, O3, O4, O5, O6 and O7 and I define them with a starting value (let use say the same, so 1/7) than I can do O = O1+O2+O3+O4+O5+O6+O7. Finally I need to do O =1, but here Artemis doesn't want to define the same parameter (O in this case) twice. So, how can I insert the conditions, that the sum of all the occupancies is 1, into Artemis? I hope you can help me.
Hi Scott, Thank you for pointing out at Vince's work on ferrites. It is a nice demonstration of the effect of site occupancy by dopants on EXAFS. In Vince's APL 68, 2082 (1996), they found the distribution of Zn between A and B sites (octahedral and tetrahedral) by including MS, as you described. However, he varied only one parameter in the fit to the MS range - site occupancy, keeping all other fixed (p. 2083). As such, it is not a non-linear least square fit, but a linear least square fit of a (linear) combination of fixed functions, and thus the chi-squared of such fit must have a single minimum - either within the range of x, or at the boundary (x=0 or 1, as they obtained in most cases). What Tadej is describing seems more like a general, non-linear least squares fit problem, that has N minima in chi squared of which N-1 are false. It is counter-intuitive to assume that the contributions of EXAFS from each inequivalent Nb can be fixed in the fit except for its fractional occupancy. What about sigma2 of different MS paths? They can be equal in certain cases of collinear focusing paths, or you can use other constraints, e.g., correlated debye model to calculate them ab initio and constrain in the fit, but the former case is very rare for a multi-site system, and the latter approach (correlated debye model) is very difficult to test for such a complex system before you make sure that you can use these calculations in such fits. Thus, you obviously reduce the number of variables but you may exclude the true, physical, minimum of chi squared from your parameter space. Anatoly -----Original Message----- From: ifeffit-bounces@millenia.cars.aps.anl.gov [mailto:ifeffit-bounces@millenia.cars.aps.anl.gov]On Behalf Of Scott Calvin Sent: Saturday, December 17, 2005 5:29 PM To: XAFS Analysis using Ifeffit Subject: RE: [Ifeffit] my problem Hi Tadej, I agree with the general drift of Anatoly's comment--this is what Shelly meant by saying it sounds like a tough problem! But I think it came off sounding a little more harsh than I suspect Anatoly meant it to be, particularly considering some of the systems he himself has examined! Anatoly's description is fair IF only a nearest-neighbor fit is performed. But it's possible that inequivalent sites have very different environments at greater Reff, particularly since niobium is so much heavier than oxygen! For example, there's been a lot of work done that shows that there is a screamingly large difference in the EXAFS spectra of A and B sites in the spinel structure (Vince Harris did a lot of this, for example). In such a case, Artemis is able to find the site occupancy without too much trouble, using a strategy such as Shelly explained. Of course, =seven= freely-floating sites sounds likely to yield nonsense fits. It would help if you could use some physical intuition to try to simplify the problem, at least at first. Consider also using the "restraint" feature in Artemis/Ifeffit liberally in your early fits to keep the fit from wandering off into nonsensical territory. --Scott Calvin Sarah Lawrence College At 12:14 PM 12/15/2005, Anatoly wrote:
boundary="----_=_NextPart_001_01C6019A.F6711239"
You cannot resolve these sites from EXAFS analysis. Even if you had only 2 inequivalent sites of the same central atom with occupancies N1 and N2, you would not be able to resolve N1 and N2 in the fit because different Nb atoms would have similar environments (e.g., 4 and 6 oxygens), and they will have similar Nb-O distances around each site. The best you can do is to try to fit the first nearest neighbor peak as an average Nb-O contribution (if it is a well isolated peak) and try to make use of sigma2 that may turn out to be larger than in some well known Nb oxide reference that you should analyze first.
Anatoly
Dear collegues,
my name is Tadej Rojac and I'm writing from the Institute Jozef Stefan in Ljubljana, Slovenia. I work in the Department of electronic ceramics. Actually, I'm working on a EXAFS spectra with Artemis. What I am trying to do is mainly to describe an EXAFS spectrum with a model concerning the structure of Nb2O5. I'm working togheter with prof. Iztok Arcon, who is a specialist in the field. My main problem is that I have to do some suppositions. In fact Nb2O5 structure is quite complicated. It is composed of seven different Nb positions which I took into account using 7 feffs in Artemis. I don't know the exact occupancies of the seven positions. In order to make the search easier I did at first a supposition that all the occupancies must be positive, which is realistic. I set this with the command "abs" in each feff file. Secondly, I need to supose that the sum of all occupancies is 1. In that way the search for the result is much easier, otherwise I get the sum greater than one, which, for sure, is not the case. My question is how can I do that? For example, if the occupancies are O1, O2, O3, O4, O5, O6 and O7 and I define them with a starting value (let use say the same, so 1/7) than I can do O = O1+O2+O3+O4+O5+O6+O7. Finally I need to do O =1, but here Artemis doesn't want to define the same parameter (O in this case) twice. So, how can I insert the conditions, that the sum of all the occupancies is 1, into Artemis? I hope you can help me.
_______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
Hi Anatoly, Yes, Vince's 1996 APL is linear, but check out the paper I co-authored with him: APL 81, 3828 (2002). Actually, the better reference for this discussion is the longer companion paper, in PRB 66, 224405 (2002). I agree with you that the "arbitrary" things I did in that paper (and similar ones) do not have airtight justification, and I have no doubt whatsoever that the fits I found are not the "true, physical minimum." In fact, I say so in my paper. The question is not whether such a fit is as true as possible, but whether it is providing useful information in which we can have a good degree of confidence. In the case of spinels, the effect of A or B sites on the spectrum out at the cation-cation distance is HUGE. Sure, I didn't know what is the right way to constrain the sigma2's, and that leads to some additional quantitative uncertainty in the site occupancy found. But do I believe that I can tell the difference between 30% and 50% occupancy by this method? Absolutely. I could (and did) play with different constraint schemes, and the results were consistent enough to give me confidence. Of course, having some confirmation from probes such as XRD and magnetic measurements helps too. So I guess I'm saying that such fits must be viewed with caution, but they still provide useful information...particularly if we take our time and "stress" them a bit to make sure they aren't too sensitive to "arbitrary" constraint decisions that we have made. --Scott Calvin Sarah Lawrence College At 07:09 PM 12/17/2005, you wrote:
Hi Scott,
Thank you for pointing out at Vince's work on ferrites. It is a nice demonstration of the effect of site occupancy by dopants on EXAFS. In Vince's APL 68, 2082 (1996), they found the distribution of Zn between A and B sites (octahedral and tetrahedral) by including MS, as you described. However, he varied only one parameter in the fit to the MS range - site occupancy, keeping all other fixed (p. 2083). As such, it is not a non-linear least square fit, but a linear least square fit of a (linear) combination of fixed functions, and thus the chi-squared of such fit must have a single minimum - either within the range of x, or at the boundary (x=0 or 1, as they obtained in most cases).
What Tadej is describing seems more like a general, non-linear least squares fit problem, that has N minima in chi squared of which N-1 are false. It is counter-intuitive to assume that the contributions of EXAFS from each inequivalent Nb can be fixed in the fit except for its fractional occupancy. What about sigma2 of different MS paths? They can be equal in certain cases of collinear focusing paths, or you can use other constraints, e.g., correlated debye model to calculate them ab initio and constrain in the fit, but the former case is very rare for a multi-site system, and the latter approach (correlated debye model) is very difficult to test for such a complex system before you make sure that you can use these calculations in such fits.
Thus, you obviously reduce the number of variables but you may exclude the true, physical, minimum of chi squared from your parameter space.
Anatoly
Anatoly --
I think I'm siding with Scott on this, but maybe I'm no understanding
all your points. As far as I can tell, Tadij did not say that only N
would be varied in an anlysis -- The question was how to constrain the
total coordination number from a set of scattering paths: Shelly and
Scott answered that, pretty well I think.
Now, I agree that if 7 oxygen paths make up a "first shell" with a
narrow range of distances (though this was not actually clear from the
original question, it does seem likely), there's no way you'll be able
to measure 6 independent coordination numbers. But if there were 2
paths / atom types that made up a first shell, than relative occupancy
can certainly be determined. As a concrete example, determining the
number of Rb-Br and Rb-Cl neighbors in a salt solution is almost
certainly possible. ;). If the two atoms are the same species, they
just need to be sufficiently separated in distance.
On 12/17/05, Anatoly Frenkel
Hi Scott,
Thank you for pointing out at Vince's work on ferrites. It is a nice demonstration of the effect of site occupancy by dopants on EXAFS. In Vince's APL 68, 2082 (1996), they found the distribution of Zn between A and B sites (octahedral and tetrahedral) by including MS, as you described. However, he varied only one parameter in the fit to the MS range - site occupancy, keeping all other fixed (p. 2083). As such, it is not a non-linear least square fit, but a linear least square fit of a (linear) combination of fixed functions, and thus the chi-squared of such fit must have a single minimum - either within the range of x, or at the boundary (x=0 or 1, as they obtained in most cases).
I don't think it's important whether a linear or non-linear algorithm is used for the analysis, especially when compared to what was varied in the analysis (well, for some problems a linear approach is not possible, but even when a linear approach is possible it's not obvious that it's better than a non-linear approach). Whether or not there is a single minimum or not (and, related, what would make different minima distinguishable) is also more a matter of the problem, and not the algorithm used to find a solution. For a simple problem with 1 variable for relative intensities of two basis functions, it is very likely to have one minimum, no matter whether a linear or non-linear approach is used (as an aside, 1 variable does not always mean one minimum, but we're usually dealing with well-behaved problems). In any event, claiming that linear v. non-linear algorithm makes a difference is a dangerous and/or silly position to take for someone analyzing XAFS data. We have to use non-linear methods -- do you find this troubling?
What Tadej is describing seems more like a general, non-linear least squares fit problem, that has N minima in chi squared of which N-1 are false.
False? What does that mean? Sure, there may be multipe minima in chi-square. If so, either these can be distinguished because some have lower chi-squares than others, or that cannot be distinguished because the chi-squares are close. I assume that by using the word False that you somehow don't believe statistics or the model used. In my view, since one is making a model to describe a distribution of atoms, "False" is a useles concept -- all models are false in the sense that they are simplifications of reality, but some models are better than others. In this example, if 6 relative coordination numbers were used, I would expect the error bars to blow up, which means local minima in chi-square would be within the estimated errors, and there would not be N-1 "False minima", but 1 very broad minima. Perhaps you have a counter-example?
It is counter-intuitive to assume that the contributions of EXAFS from each inequivalent Nb can be fixed in the fit except for its fractional occupancy. What about sigma2 of different MS paths?
I don't think Tadij said this. But it does sound like what Harris et al may have done (ie, if they only had one unknown in their model, they must have made some assertions abou the other parameters. Does that not bother you as much??
... Thus, you obviously reduce the number of variables but you may exclude the true, physical, minimum of chi squared from your parameter space.
Again, I think I do not understand. What does "True, physical, minimum of chi squared" mean? You make a model, you do a fit, you understand the statistical parameters and consider making other models. In the end you pick the model that fits your data best and has the most sensible interpretation. I would consider "True, physical" to mean the complete description of the distribution of atoms sampled. A typical measurement samples the local coordination of around 10^9 atoms. If we have good data, we may be able to fit as many as 10 parameters to describe the first shell of the partial pair distribution function of these 10^9 atoms. So "True" and "Physical" are a bit far removed from our ability to see with our data. We must make model for the distribution and compare these models to our data. Generally, one picks the model that best matches the data as the most likely model. It's often called "best fit", but rarely called "True". Are you worried about the situation in which there are minima in chi-square that are clearly distinct (outside the error bars) and for which the model with significantly lower chi-square is a worse physical explanation (or disagrees with other measurements)? This seems to be a common fear, but I find it to be largely unfounded. Can you (or anyone) give an example of this? There seem to be a lot of stories about this, but most of the stories I've heard end up being at least partially due to ignoring (or not even trying to estimate) the error bars (and often partially due to someone wanting to believe something that their data doe not support). Of course, you can certainly pick multiple models and get different results. Is that a problem?? Since I'm not understanding your concerns with the way analysis is done with Ifeffit, perhaps you can clarify these concerns. Thanks, --Matt
Hi Matt,
Rb-Br/Rb-Cl is a different story. There, the neighbors are different (Br,Cl)
and the central atom is the same (Rb). It is a piece of cake. Here (in
Nb2O5) the neighbors are the same (O), and the central atoms are at multiple
sites. Of course, it would be very cute if they very neatly arranged around
each individual Nb out of 7 (seven) inequivalent Nb atoms so that each
Nb(i)-O shell had a distinct (and degenerate) Nb(i)-O distance, and so that
all 7 Nb(i)-O shells were separated by the distance larger than the
resolution in EXAFS experiment to detect such split.
It may be possible for ABO3 perovskites with a single B site to detect the
split in B-O shell (Nb in KNbO3 displaces toward 111 direction and there is
a distinct group of three oxygens closer to it and another group of 3
oxygens, farther away from it, and that spread can be as large as 0.3 A or
so). But: during the analysis you constrain these shells to have 3 oxygens
in each group, and it is not the case here because the site occupancy is not
known.
Your other comments are too open ended and not exactly interpreting what I
wrote in my original message. Forgive me for not replying.
Anatoly
-----Original Message-----
From: matt.newville@gmail.com [mailto:matt.newville@gmail.com] On Behalf Of
Matt Newville
Sent: Monday, December 19, 2005 2:48 PM
To: anatoly.frenkel@yu.edu; XAFS Analysis using Ifeffit
Subject: Re: [Ifeffit] my problem
Anatoly --
I think I'm siding with Scott on this, but maybe I'm no understanding
all your points. As far as I can tell, Tadij did not say that only N
would be varied in an anlysis -- The question was how to constrain the
total coordination number from a set of scattering paths: Shelly and
Scott answered that, pretty well I think.
Now, I agree that if 7 oxygen paths make up a "first shell" with a
narrow range of distances (though this was not actually clear from the
original question, it does seem likely), there's no way you'll be able
to measure 6 independent coordination numbers. But if there were 2
paths / atom types that made up a first shell, than relative occupancy
can certainly be determined. As a concrete example, determining the
number of Rb-Br and Rb-Cl neighbors in a salt solution is almost
certainly possible. ;). If the two atoms are the same species, they
just need to be sufficiently separated in distance.
On 12/17/05, Anatoly Frenkel
Hi Scott,
Thank you for pointing out at Vince's work on ferrites. It is a nice demonstration of the effect of site occupancy by dopants on EXAFS. In Vince's APL 68, 2082 (1996), they found the distribution of Zn between A and B sites (octahedral and tetrahedral) by including MS, as you described. However, he varied only one parameter in the fit to the MS range - site occupancy, keeping all other fixed (p. 2083). As such, it is not a non-linear least square fit, but a linear least square fit of a (linear) combination of fixed functions, and thus the chi-squared of such fit must have a single minimum - either within the range of x, or at the boundary (x=0 or 1, as they obtained in most cases).
I don't think it's important whether a linear or non-linear algorithm is used for the analysis, especially when compared to what was varied in the analysis (well, for some problems a linear approach is not possible, but even when a linear approach is possible it's not obvious that it's better than a non-linear approach). Whether or not there is a single minimum or not (and, related, what would make different minima distinguishable) is also more a matter of the problem, and not the algorithm used to find a solution. For a simple problem with 1 variable for relative intensities of two basis functions, it is very likely to have one minimum, no matter whether a linear or non-linear approach is used (as an aside, 1 variable does not always mean one minimum, but we're usually dealing with well-behaved problems). In any event, claiming that linear v. non-linear algorithm makes a difference is a dangerous and/or silly position to take for someone analyzing XAFS data. We have to use non-linear methods -- do you find this troubling?
What Tadej is describing seems more like a general, non-linear least squares fit problem, that has N minima in chi squared of which N-1 are false.
False? What does that mean? Sure, there may be multipe minima in chi-square. If so, either these can be distinguished because some have lower chi-squares than others, or that cannot be distinguished because the chi-squares are close. I assume that by using the word False that you somehow don't believe statistics or the model used. In my view, since one is making a model to describe a distribution of atoms, "False" is a useles concept -- all models are false in the sense that they are simplifications of reality, but some models are better than others. In this example, if 6 relative coordination numbers were used, I would expect the error bars to blow up, which means local minima in chi-square would be within the estimated errors, and there would not be N-1 "False minima", but 1 very broad minima. Perhaps you have a counter-example?
It is counter-intuitive to assume that the contributions of EXAFS from each inequivalent Nb can be fixed in the fit except for its fractional occupancy. What about sigma2 of different MS paths?
... Thus, you obviously reduce the number of variables but you may exclude
I don't think Tadij said this. But it does sound like what Harris et al may have done (ie, if they only had one unknown in their model, they must have made some assertions abou the other parameters. Does that not bother you as much?? the
true, physical, minimum of chi squared from your parameter space.
Again, I think I do not understand. What does "True, physical, minimum of chi squared" mean? You make a model, you do a fit, you understand the statistical parameters and consider making other models. In the end you pick the model that fits your data best and has the most sensible interpretation. I would consider "True, physical" to mean the complete description of the distribution of atoms sampled. A typical measurement samples the local coordination of around 10^9 atoms. If we have good data, we may be able to fit as many as 10 parameters to describe the first shell of the partial pair distribution function of these 10^9 atoms. So "True" and "Physical" are a bit far removed from our ability to see with our data. We must make model for the distribution and compare these models to our data. Generally, one picks the model that best matches the data as the most likely model. It's often called "best fit", but rarely called "True". Are you worried about the situation in which there are minima in chi-square that are clearly distinct (outside the error bars) and for which the model with significantly lower chi-square is a worse physical explanation (or disagrees with other measurements)? This seems to be a common fear, but I find it to be largely unfounded. Can you (or anyone) give an example of this? There seem to be a lot of stories about this, but most of the stories I've heard end up being at least partially due to ignoring (or not even trying to estimate) the error bars (and often partially due to someone wanting to believe something that their data doe not support). Of course, you can certainly pick multiple models and get different results. Is that a problem?? Since I'm not understanding your concerns with the way analysis is done with Ifeffit, perhaps you can clarify these concerns. Thanks, --Matt
participants (3)
-
Anatoly Frenkel -
Matt Newville -
Scott Calvin