What class should I take to learn about topological defects?

Question

I am currently presuing my doctorate. My subject area is solid state physics/ crystal structure.

I am looking to learn more about defects in crystals. I was wondering if it would be more prudent to take math class in topology to learn more about these defects than to take another class in solid state.

OR are there any other classes that any one can recoment. (or maybe just a book that I can study on my own)

(mind you I was also a math major, so a rigorous math class should be no problem for me)

Answer 1

I guess it depends on your specific interests. If you are looking for the effects of crystalline defects on the structural properties of materials you should be able to find a good resource in Dieter (mechanical metallurgy) or Hertzberg (mechanical behavior of materials). This would cover all of the relevant classes from 1-D to 3-D; point defects such as vacancies, 2-D defects such as dislocations, etc.; it will also discuss how these defects control the macroscopic properties of the given class of materials.

If you are interested in the electronic properties of defects I can look up some references for you. For my PhD I took a class on "Defects in Semiconductors" from Pierre Petroff at UC Santa Barbara - it was a very interesting class - although small, only 3 students! We discussed the effects of defects on the electronic and optical properties of elemental and compound semiconductors; also, the characterization of defects was introduced. We primarily worked off of Prof. Petroff's notes, but there were a few texts that I had checked out from the library, if you are interested send me a reply and I will pull out my old notes. A lot of the info. was from journal articles.

Hope this was helpful.

Answer 2

Hi farrell

Topology math classes will teach you formalisms - dimensionality, natural deformations, connections, transports, etc. It will help you largely from a definitional perspective, and to understand implications. I come at topology from the GR perspective, so its useful to me to understand about theoretical spaces, deformations, connections, etc, but I'm not sure how much that will help you. I think you're going to want a lot of context for your topology. OTOH, if you're a maths major you'll probably find it fun and diverting (if you did ok at geometry and vector calculus it's not too hard).


Hope this helps!
The Chicken

Answer 3

Mathematical Modelling of Crystalline Bodies

Answer 4

you need to learn the most essence part of that course, actually every math course shall be taken seriously, i personally think