# Observing Thermodynamic Phase Transitions Via Neutron Scattering

1. Sep 3, 2011

### .J.

Hi, before I start this is not coursework or any work attached to my degree but part of an internship at a neutron research facility at a level appropriate for Masters students and higer, so I felt it necessary to post it here rather than the homework section (sorry if I'm mistaken). I've been given some neutron scattering (time of flight) data of a powder sample at different temperatures. I am trying to analyse and identify phase transitions, however I'm finding this a bit difficult.

I've been able to obtain Bragg preaks for the 5 different temperatures by extracting the elastic line and plotting the intensity against the wave vector transfer (Q). I've been told that a change in peak position indicates a phase transition as this means there is a change in atomic/molecular spacings. Is this true? Or is this assumption only valid if there is a change in ratio of atomic spacings (say a/b), as changes in thermodynamic expansion should be uniform in all axies, where as a phase transition will result in a change in structure?

The 5 peaks I obtained (seen in PTFEpowder.jpg) all have slightly different positionings, with this I assume that I need the ratio of atomic spacing to identify a phase transtion. But out of all the peaks, the biggest shift seems to be between 300K and 270K. I happen to know that there is a transition at 303K and 297K, does this (hardly) larger shift provide any evidence of a phase transition (possibly the 297K one), or am I just getting desperate?

To analyse this more accuratley I've calculated the atomic spacings using the following reasoning:

Bragg's law n*(lambda) = 2*d*sin(theta)

Q = 4*(pi)*sin(theta)/(lambda)

combine to get : d = 2*(pi)/Q

After plotting d against temperature I got the graph shown in dVsT.jpg. From this you can see that d steadily increases with temperature, but after 270K d evolves with temperature at a more rapid rate. Can this be used as any evidence of a phase transition? if not, is there any other signs I can look out for?

I've also obtained the density of states at the different temperatures, but the program I'm using cannot find the phonon dispersion curves needed to calculate the specific heat of which I could use to find phase transitions.

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Last edited: Sep 3, 2011
2. Sep 6, 2011

### Mike H

I've seen people argue for phase transitions on far more subtle effects than what you've got there. ;)

It's been a while since I last thought about neutron scattering, but generally when you see a deviation from a linear temperature dependence for some quantity you're measuring, you've got yourself a phase or dynamical transition of some sort going on in your system.

You may want to check out the following paper:

http://www.lehigh.edu/imi/docs_relaxation/papers/Frick_Science_1995.pdf [Broken]

Good luck!

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