Heyup Richochet.
If you have not already found the answer, I have a bit more information regarding this (from Duderstadt and Hamilton), however the explanation is based very much around first principles and doesn't go into particular reactor types. However I shall summarise:
With regards to resonance absorption, an increase in fuel temperature will lead to Doppler broadening of resonances with a corresponding decrease in self shielding, hence an increase in resonance absorption.
The Doppler coefficient will tend to be more positive in a core with a hard spectrum such as a metal fueled core (magnox for example). To soften the spectrum, you can use oxide fuels (AGR). The oxygen will degrade the spectrum to yield a negative Doppler coefficient.
AGR's are graphite moderated and so are solid moderators. The primary reactivity effect is due to a hardening of the thermal neutron spectrum with increasing temperature, which causes a change in "thermal group constants".
I've tried to put this ino useful terms, but the last sentence of the section states this:
"The magnitude and sign of the associated moderator temperature coefficient depends on a number of complicated interactions, which leads to a rather complicated dependance on temperature".....
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From my own knowledge though, why would such a question be of any real importance? Here is why I say that: (you may already know this! so sorry if you do!)
Short term reactivity feedback is the effect of the core temperature on the neutron multiplication factor of the core, which is expressed as the temperature coefficient of reactivity, hence the change in reactivity due to change in core temperature.
I can only really explain it a little from the view of the core as a whole, so temperature feedback affects reactor stability. If it possessed a positive coefficient, then an increase in temps would lead to an increase in reactivity, hence the power would increase, causing a further increase in temps and so on, and the reactor would be unstable. A more desirable situation would be for a negative coefficient hence a decrease in power with temperature.
But here's the thing: the coefficient depends on many processes within the core (I was just thinking of the core as a whole for simplicity). Which in turn, depend on the type of reactor. But a typical reactor has a very non-uniform temperature distribution. i.e. the temperature is very different in the fuel where the fission process takes place and cooler in the clad and even cooler in the moderator/coolant. So here we introduce the different concepts of fuel coefficent, moderator and clad etc.
Fuel temperature changes respond rapidily to an power level changes (changes in neutron flux) and the amount of time it takes for this temperature change to affect the clad and in turn moderator and coolant is slow.
These can then be subdivided in into prompt and delayed components - fuel = promt, everything else = delayed.
Prompt reactor feedback mechanisms are of most importance to reactor control/safety, as they tend to limit any transients. Hence, temperature coefficients are not a useful quantity, as a more useful quantity would be the change in reactivity due to power (neutron flux).
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From my little bit of research, I could only find ONE case where it would be useful, but even then it is pushing it a bit:
If a reactor is at zero power (no neutron flux, shut down), and the coolant was heated up, then this would change the reactivity of the coolant/moderator and clad and eventually fuel, so depending on many things such as the moderator:fuel ratio and so on, this would change the multiplication factor slightly, depending on whether the reactor has a positive of negative temp coeff.
That's about as much as I could really find out, and I feel, it was probably of little use with regards to your original question!
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