# [Ifeffit] Inconsistency of the amplitude reduction factor

Scott Calvin scalvin at sarahlawrence.edu
Thu Sep 18 09:09:48 CDT 2014

```This is an excellent point, and I'd like to elaborate yet further. :)

How does one tell whether transferability is justified or not, based on the experimental data?

Perform fits with the S02 constrained to some reasonable value (perhaps the average of your results). Compare the reduced chi square reported by the fit for the case where S02 was guessed to the one where it was constrained. If the reduced chi square is significantly higher for the constrained case, then transferability is not justified; i.e., the data is fit better, in a statistical sense, when S02's are fit separately for each spectrum. If it's lower or about the same, then transferability is justified. (But keep in mind that an apparent lack of transferability might be due to inconsistent determinations of the edge jumps.)

How much higher is "significantly" higher? There's a statistical test called the Hamilton test that can help you decide that, if you really want to be careful about things. But looking at the reduced chi square is a good first step.

Note that what I'm saying is closely related to Bruce's other comment about including error bars on the reported values. If the reported ranges including error bars all overlap, it's also likely that you'll find that constraining all the fits to have the same value of S02 will not increase the reduced chi squares significantly.

So what if transferability is justified by the data (i.e. compatible with it)? Does that mean you should do it?

At that point the decision which to present as the "primary" fit becomes to some extent aesthetic. The statistics are then telling you that the data is consistent with transferability, but of course there may be some "actual" variations due, perhaps, to the cause Bruce suggested. Would you prefer to explain in a paper why you are constraining the S02's to be the same, or why you have different values for them? In either case, if you had performed fits both ways, you could look at the values generated by both sets of fits and see if they were consistent; that is, if the ranges specified by their error bars overlap. If that were the case, you could say so in your paper, and then whether or not you constrained the S02s to be the same becomes mostly a non-issue for readers. And if the ranges didn't overlap, then you should report that too, suggesting that there is some additional uncertainty based on your results based on the question of S02.

--Scott Calvin
Sarah Lawrence College

On Sep 18, 2014, at 9:04 AM, Bruce Ravel <bravel at bnl.gov> wrote:

> On 09/18/2014 07:23 AM, Scott Calvin wrote:
>> Hi Hoon,
>>
>> Using a reference value is not always a good idea, because experimental
>> effects can play a role.
>
> I want to elaborate a bit on this point in Scott's post, particularly
> given the nature of your sample.
>
> The materials in a battery, as they charge or discharge, can undergo
> changes in morphology.  Morphology can have an impact on the measured
> amplitude.  More specifically, inhomogeneity in the sample -- pinholes,
> for instance -- have a known effect on the amplitude.  See, for example:
>
>   http://dx.doi.org/10.1103/PhysRevB.23.3781
>   http://dx.doi.org/10.1016/0167-5087(83)90730-5
>   http://gbxafs.iit.edu/training/thickness_effects.pdf
>
> My point is that you may need to question the assumption that S02 even
> should be transferable in your measurement.
>
> B
>
>
>> BUT, S02 should not change during charge-discharge on a single sample,
>> or a series of samples prepared and measured similarly. Instead, it's
>> likely something correlated with S02 in the fit is changing, and so the
>> fitting routine is getting a bit confused and attributing part of the
>> change to S02. (That's not a knock on the fitting routine; it doesn't
>> know any better unless you tell it!)
>>
>> I think the best recommendation is to do a simultaneous fit on multiple
>> spectra, constraining the S02 to be the same for each. So you're still
>> fitting S02, but forcing all the spectra to use the same value.
>>
>> Second best is to fit one spectrum and allow S02 to vary, and then
>> constrain all the other fits to use that value.
>>
>> --Scott Calvin
>> Sarah Lawrence College
>>
>> On Sep 18, 2014, at 7:06 AM, HOON Kim <science at live.co.kr
>> <mailto:science at live.co.kr>> wrote:
>>
>>> Hello,
>>>
>>> I am a bit confused about the amplitude reduction factor (S0^2), in a
>>> sense that whether this factor must be determined by fitting or
>>> constrained by a reference value for a specific element. I'm dealing
>>> with a cathode composite (for lithium-ion battery) comprised of two
>>> crystal phases. During charge-discharge, the amplitude reduction
>>> factor changes and at a certain state of charge (SOC) it changes a lot
>>> such as from 0.77 to 0.67. My understanding is that it may reflect
>>> the phase transition of the material into the amplitude reduction
>>> factor. But, I'm not sure ... I need advice on this.
>>>
>>> Thank you !
>>>
>>> Kind Regards,
>>> HOON
>>> _______
>>
>>
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>
>
> --
>  Bruce Ravel  ------------------------------------ bravel at bnl.gov
>
>  National Institute of Standards and Technology
>  Synchrotron Science Group at NSLS --- Beamlines U7A, X24A, X23A2
>  Building 535A
>  Upton NY, 11973
>
>  Homepage:    http://bruceravel.github.io/home/
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