[Ifeffit] Cumulant expansion fittings

Frenkel, Anatoly frenkel at bnl.gov
Wed Jan 21 21:39:41 CST 2009

Hi Scott, 
It could be an interesting direction, to use these type of lattice calculations to predict, as you suggested, what type of structures (or host compounds, for dopands), will, if not make it zero, which is probably impossible, but minimize third cumulant. Thus, it may be a rational way to design materials, at least hypothetically, with controlled thermal expansion, or even the lack of thereof. 
I do not care that someone may jump in and patent it, but I will appreciate a Porsche, if possible, when it is licensed.


From: ifeffit-bounces at millenia.cars.aps.anl.gov on behalf of Scott Calvin
Sent: Wed 1/21/2009 10:30 PM
To: XAFS Analysis using Ifeffit
Subject: Re: [Ifeffit] Cumulant expansion fittings


You're right--3 dimensions ruins my symmetry argument. My mistake.

On the other hand, I still suspect that there exists a realistic case 
where forcing the third cumulant to zero cause a much smaller increase 
in chi-square than forcing the fourth cumulant to zero; e.g., a broad, 
flat radial distribution function.

For those of you out there who are relative novices, this is an 
entertaining and informative discussion, but I don't want to lose 
track of the practical point:

It is very rare to find a system where the fourth cumulant is both 
necessary and sufficient. Either the potentials are close enough to 
harmonic that the fourth cumulant makes little difference, or they are 
so far from harmonic that the fourth cumulant alone is not enough.

--Scott Calvin
Sarah Lawrence College

On Jan 21, 2009, at 10:11 PM, Frenkel, Anatoly wrote:

> Thus, I am pretty much convinced, unless there is some mistake in my 
> reasoning, that no case exists in 3D with a zero third cumulant.

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