Incommensurate phases- what is that?

1. Jan 18, 2007

arabesque

Hello!
I need Your help. If anybody knows, tell me please what incommensurate phases mean. If anybody knows, give me please corresponding links.
Thanks.

2. Jan 18, 2007

ZapperZ

Staff Emeritus
Your question makes no sense if you do not put in some effort to explain the context of the question.

Zz.

3. Jan 19, 2007

arabesque

I'm sorry. I have the task to write about incommensurate phases in our subject "quantum theory of solids". I've found the article Bak. "Commensurate phases, incommensurate phases and the
devil’s staircase". Rep. Prog. Phys., Vol. 45, 1982. Printed in Great Britain. But it isn't so clear,in my opinion, what incommensurate phases mean.

4. Jan 19, 2007

ZapperZ

Staff Emeritus
I don't quite have the time to read that paper (review papers such as those in Rep. Prog. Phys are notoriously long!). However, I'll explain in general what "incommensurate" means in condensed matter physics.

Take a sheet of paper that has square grids on it. Now, let's say that at all the intersection of the lines (i.e. the corners of the squares), we have a lattice point where you have lattice ions. Now, let's also say that you measure the magnetic moment across this grid and you see that there is a periodicity of the variation of the magnetic moment (for simplicity, let's say is is a sine wave from some arbitrary origin). Now, it is possible that this periodicity doesn't quite match the period of the lattice ions. You could have the period of the magnetic moment variation corresponding to, say, 2 1/3 lattice constant. So here, you can say that the period of the magnetic moment of this system is incommensurate with the lattice. One can also say that the phase of the magnetic moment is incommensurate with the phase of the charge variation, since the charges due to the location of the ions repeats every lattice constant.

Zz.

5. Jan 19, 2007

Gokul43201

Staff Emeritus
This is slightly different from what I learnt about things that are commensurate or incommensurate with each other. If I recall my classical mechanics, two quantities with periods p and q are commensurate if p/q is rational and incommensurate when p/q is irrational.

6. Jan 19, 2007

ZapperZ

Staff Emeritus
That is a more stringent criteria for commensuration, whereby it states that you simply cannot get one from the other via a simple multiple. What I described is a more simplistic and naive approach to incommensuration, which I think is used in areas such as inelastic neutron scattering on YBCO, for example, where the "resonance peak" is incommensurate with the lattice periodicity in k-space.

Zz.

7. Jan 19, 2007

arabesque

Thank you, ZapperZ and Gokul43201!!!