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TOPOLOGICAL CLASSIFICATION OF DEFECTS

When we topologically classify the defects in ordered media, we consider the character of the fundamental group of the associated order parameter space. To construct those groups, we circumscribe the line defects by circles and the point defects by spheres.
My question is what is done for a surface (possibly infinite) defect, say domain walls. My query primary concerns crystal lattices. I want to characterize the essential defects in solid crystals--for dislocation and interstitial/vacancy, it is straightforward. But what to be done in case of grain/phase boundary?

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Arash_Yavari's picture

Dear Ayan:

For surface defects Volovik (1978) suggested the use of relative homotopy groups. Look at the following paper:
Trebin, H.A., The topology of non-uniform media in condensed matter physics, Advances in Physics, 1982 vol. 31, Issue 3, p.195-254

Regards,
Arash

Aryan

 

You should look at hirth and lothe's work on topological characterization of matensitic interface using disclinations and terraces.

 

Best Regards

Sreekanth Akarapu

Aryan

 

Its disconnections not disclinations; A correction to my previous response

 

 

Sreekanth Akarapu

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