Re: [Ifeffit] Lattice parameters: EXAFS vs. XRD
Hi Scott, I believe we had a conversation about this last January. XAFS is not sensitive to the crystallographic lattice constants. It measures the spacing between atoms. Because of thermal vibrations and other disorder terms, the average distance between atoms is larger than the distance between the lattice points. --Matt On Fri, Dec 25, 2009 at 12:04 PM, Scott Calvin scal...@slc.edu wrote: Merry Christmas, everyone! Yes, I'm pondering EXAFS on Christmas... Here's an issue that I bet has been worked out, and I bet someone on this list knows the result and where it's been published. It's well known that the MSRD (sigma squared) for EXAFS differs substantially from the Debye-Waller factor in XRD, because the first is the variance in the interatomic distance, and the second is the variance in the atomic position relative to a lattice point. But what about the lattice parameter implied by the nearest-neighbor distance in EXAFS as compared to the lattice parameter found by XRD? It is certainly true that in most materials, particularly highly symmetric materials, the nearest-neighbor pair distribution function is not Gaussian, and generally has a long tail on the high-r side. (This is largely because the hard-core repulsion keeps the atoms from getting much closer than their equilibrium positions.) So imagine a set of atoms undergoing thermal vibrations around a set of lattice points. For concreteness, let's consider an fcc material like copper metal. The lattice points themselves are further apart than they would be without vibration, sure, but that's not the question. The question is whether the square root of two multiplied by the average nearest-neighbor distance is still equal to the spacing between lattice points. My hunch is that the answer is no, and that the EXAFS implied value will be slightly larger. While the average structure is still closed-packed, the local structure will not be. And in a local structure that is not closed-packed, the atoms will occasionally find positions quite far from each other, but will never be very close. In a limiting case where melting is approached, it's possible to imagine an atom migrating away from its lattice point altogether, leaving a distorted region around the defect. While XRD would suppress the defect, EXAFS would dutifully average in the slightly longer nearest-neighbor distances associated with it. Just to be clear, I am not talking about limitations in some particular EXAFS model used in curve-fitting. For example, constraining the third cumulant to be zero is known to yield fits with nearest-neighbor parameters that are systematically reduced. In fact, limitations like that mean the question can't be answered just by looking at a set of experimental results: I can make my fitted lattice parameter for copper metal go up or down a little bit by changing details of a fitting model or tinkering with parameters that themselves have some uncertainty associated with them, like the photoelectron's mean free path. (Fortunately, this kind of tinkering will affect standards and samples in similar ways, and thus don't affect my confidence in EXAFS analysis as a tool for investigating quantitatively differences between samples, or between samples and a standard.) My question is about the ACTUAL pair distribution function in a real fcc metal. To the degree it's a question about analysis, it's about XRD: In an fcc metal should the expectation value of the nearest-neighbor separation, multiplied by the square root of two, equal the lattice spacing as determined by XRD? --Scott Calvin Sarah Lawrence College ___ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit ___ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
Re: [Ifeffit] Lattice parameters: EXAFS vs. XRD
A correction to Matt's email: In random alloys, smaller size atoms and larger size atoms are at different average distances (measured by EXAFS and other local-structure-sensitive techniques, e.g., XRD/PDF) that are, respectively, smaller and larger than the distance between the average lattice points (measured by XRD). Anatoly From: ifeffit-boun...@millenia.cars.aps.anl.gov on behalf of Matt Newville Sent: Wed 12/30/2009 11:47 AM To: XAFS Analysis using Ifeffit Subject: Re: [Ifeffit] Lattice parameters: EXAFS vs. XRD Hi Scott, I believe we had a conversation about this last January. XAFS is not sensitive to the crystallographic lattice constants. It measures the spacing between atoms. Because of thermal vibrations and other disorder terms, the average distance between atoms is larger than the distance between the lattice points. --Matt On Fri, Dec 25, 2009 at 12:04 PM, Scott Calvin scal...@slc.edu wrote: Merry Christmas, everyone! Yes, I'm pondering EXAFS on Christmas... Here's an issue that I bet has been worked out, and I bet someone on this list knows the result and where it's been published. It's well known that the MSRD (sigma squared) for EXAFS differs substantially from the Debye-Waller factor in XRD, because the first is the variance in the interatomic distance, and the second is the variance in the atomic position relative to a lattice point. But what about the lattice parameter implied by the nearest-neighbor distance in EXAFS as compared to the lattice parameter found by XRD? It is certainly true that in most materials, particularly highly symmetric materials, the nearest-neighbor pair distribution function is not Gaussian, and generally has a long tail on the high-r side. (This is largely because the hard-core repulsion keeps the atoms from getting much closer than their equilibrium positions.) So imagine a set of atoms undergoing thermal vibrations around a set of lattice points. For concreteness, let's consider an fcc material like copper metal. The lattice points themselves are further apart than they would be without vibration, sure, but that's not the question. The question is whether the square root of two multiplied by the average nearest-neighbor distance is still equal to the spacing between lattice points. My hunch is that the answer is no, and that the EXAFS implied value will be slightly larger. While the average structure is still closed-packed, the local structure will not be. And in a local structure that is not closed-packed, the atoms will occasionally find positions quite far from each other, but will never be very close. In a limiting case where melting is approached, it's possible to imagine an atom migrating away from its lattice point altogether, leaving a distorted region around the defect. While XRD would suppress the defect, EXAFS would dutifully average in the slightly longer nearest-neighbor distances associated with it. Just to be clear, I am not talking about limitations in some particular EXAFS model used in curve-fitting. For example, constraining the third cumulant to be zero is known to yield fits with nearest-neighbor parameters that are systematically reduced. In fact, limitations like that mean the question can't be answered just by looking at a set of experimental results: I can make my fitted lattice parameter for copper metal go up or down a little bit by changing details of a fitting model or tinkering with parameters that themselves have some uncertainty associated with them, like the photoelectron's mean free path. (Fortunately, this kind of tinkering will affect standards and samples in similar ways, and thus don't affect my confidence in EXAFS analysis as a tool for investigating quantitatively differences between samples, or between samples and a standard.) My question is about the ACTUAL pair distribution function in a real fcc metal. To the degree it's a question about analysis, it's about XRD: In an fcc metal should the expectation value of the nearest-neighbor separation, multiplied by the square root of two, equal the lattice spacing as determined by XRD? --Scott Calvin Sarah Lawrence College ___ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit ___ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit winmail.dat___ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
Re: [Ifeffit] Lattice parameters: EXAFS vs. XRD
Thanks, Matt--you give a complete and satisfying discussion of this on January 23 on this list. I forgot about that because it came at the tail end of a long discussion as to whether C3 could ever be 0, but I suspect what you said then was rattling around in the back of my head and only settled in last week. --Scott Calvin Sarah Lawrence College On Dec 30, 2009, at 8:47 AM, Matt Newville wrote: Hi Scott, I believe we had a conversation about this last January. XAFS is not sensitive to the crystallographic lattice constants. It measures the spacing between atoms. Because of thermal vibrations and other disorder terms, the average distance between atoms is larger than the distance between the lattice points. --Matt ___ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
