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?
Re: TOPOLOGICAL CLASSIFICATION OF DEFECTS
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
In reply to Re: TOPOLOGICAL CLASSIFICATION OF DEFECTS by arash_yavari
Disclinations : Step and dislocation dual character
Aryan
You should look at hirth and lothe's work on topological characterization of matensitic interface using disclinations and terraces.
Best Regards
Sreekanth Akarapu
In reply to Disclinations : Step and dislocation dual character by sakarapu
Aryan Its
Aryan
Its disconnections not disclinations; A correction to my previous response
Sreekanth Akarapu