Hi Bikash,

to my understanding there is no difference. Both expressions decribe the same. A 'factor' is often also named a 'term'. 

Thank You Dr. Martens. But I am confused as  there are some articles which compares the EXAFS results by calculating Debye-Waller Term (2Ϭ2) from the Debye-Waller factor(Ϭ2) whereas some uses this term interchangeably.  In EXAFS  Debye-Waller factor (Ϭ2)  is also called as Mean Square Relative Displacement (MSRD) and is defined as the square of the standard deviation of the half path length. How does it differ and what is the physical significance while comparing the data with Debye-Waller Factor (Ϭ2) and  with Debye- Waller term (2Ϭ2).

Hi Bikash,

the Debye-Waller factor (Ϭ2) is, as you said, also called as Mean Square Relative Displacement (MSRD) and is defined as the square of the standard deviation of the mean position of the atoms and  not of the (whatever) half path length.

I must admit, that I do not really know wether some time the factor 2 is included by some colleagues and some times not. We have to be always sure that the factor 2 is included in the exponential term of the EXAFS description when we want to compare the EXAFS amplitudes.

I think if dealing with the 'Debye-Waller Term (2Ϭ2)' the total  thermal influence onto the EXAFS amplitude is meant, where the thermal motion of both a) the center atom and b) the scattering atom contibute to. (2Ϭ2)' is indeed the incorporated in the description of the EXAFS formula..

In case of the ' Debye-Waller Factor (Ϭ2)'  only the thermal contibution of one of the atoms is meant.

Thank You Dr. Martens for your valuable explanation. Can we use simply multiply the Debye -Waller factor by 2 to get the influence of the thermal motion of the absorbing atom and the scattering atom as I think the effect of thermal motion of by the absorber and the scattering atom  will not be always same. Also can you please explain the presence of the square of the photoelectron wave number K2 along with the Debye-Waller Factor (Ϭ2) in the EXAFS formula.

Sorry Bikash, I was wrong. The appearence of the factor '2' looks quite plausible in my answer above, but it is wrong.

I have done a closer look at the derivation of the EXAFS  formula (fortunately I have got a copy of the Phd thesis of my former student colleague A. Werner, who sketched the derivation in a simpler form than it is presented in the literature) .

The Ϭ2 is the square of the standard deviation of the relative distance of the center atom and the scattering atom and not of its absolut position. The distribution p(r) of the relative R distance due to thermal motion is assumed to be Gaussian:

                p(r) ~exp(-(r-R)2/(2Ϭ2))

Here the '2' automatically pops up in combination with Ϭ2 due to the introduction of the Gaussian profile and the 2Ϭ2 stay  together during the derivation of the EXAFS formula.

The ' k2 ' coming along with Ϭ2 in the EXAFS formula is a consequence of an infinite (0 < r < infinity) integral over r of  the Gaussian distribution and the outgoing electron wave;  p(r)*1/r²*sin(2rk+phi)*exp(-2r/lamdda).

I personally never have  calculated/performed the integral neither performed the complete derivation of the formula.

You can find derivations of the EXAFS formula by:

E. A. Stern; Phys. Rev. B10, 3027ff (1974) and

 P. A. Lee and J. B. Pendry; Phys Rev. B11, 2795ff (1975). Both papers are tough to read. I have never understood them completely.

I have not access to them yet, sorry

 Thank You Dr Martens for the valuable explanation. I have downloaded these reference articles. Really appreciate your timely help.

Hi Bikash et al.,

I would just add to the above discussion that in EXAFS the mean square relative displacement (MSRD or sigma^2) includes both thermal and static disorder.

This is significant especially in terms of the relative orientation of displacements and this will depend on site symmetry.

While in XRD this displacement is always relative to the mean distance separating the two atomic species, in EXAFS this relative displacement may include displacements in opposite directions, therefore, the MSRD in EXAFS can be double the Debye-Waller factor used in XRD, or, significantly smaller (~half as large) as well.

There is a fantasitc (and accessible to everyone) discussion of sigma^2 in Calvin's book:

Scott Calvin. XAFS for Everyone. CRC Press, Boca Raton, 2013. ISBN 1439878633. URL: https://www.crcpress.com/XAFS-for-Everyone/Calvin/p/book/9781439878637.

I would also read Bruce Ravel's treatment of this issue (although specifically in the context of the Demeter suite, the general principles remain solid): https://bruceravel.github.io/demeter/documents/Artemis/extended/ss.html

or check out the classics:

Extended X-Ray Absorption Fine Structure Debye-Waller Factors. I. Monatomic Crystals. December 1979, Physical Review B 20(12), DOI: 10.1103/PhysRevB.20.4908

Ultimately, the MSRD or sigma^2 are similar but not the same in these techniques.

Cheers