Can we consider strained crystals as periodic crystals in theory and practice?

[PRB147]

Are a strained crystal still crystal?
How to prove it?
Are the unit cells of the strained crystal still the periodic elementary building blocks of the transformed crystal?
Does the transformed crystal own the same volume as that of the perfect crystal?
Can we treat the strained crystal as the periodic crystal in the theoretical aspect?

 

[Useful nucleus]

A strained crystal, is a still a crystal but with reduced symmetry. Take a cubic crystal, apply tensile strain along [001] crystallographic direction, then you end up with a tetragonal crystal with elongated [001] and contracted [010] and [100].

 

[M Quack]

In the real world there are no crystals in the strict sense: No crystal is perfectly periodic because they all have finite size. So a "periodic crystal" is always an approximation - in many many cases a very good approximation.

In theory you can have a strained crystal with perfectly uniform strain. The result is then again perfectly periodic as Useful nucleus points out. In practice strain is usually not uniform, and there are strain gradients in all kinds of directions.

What matters, however, is that the strain usually varies over length scales that are much larger than the unit cell. Therefore the crystal can still be approximated as periodic over that length scale. But there are also exceptions to this rule of thumb.

The same goes for doped crystals such as semiconductors, for alloys, solid solutions, etc. Strictly speaking none of these are perfectly periodic. But to good approximation they can be treated as periodic crystals with some kind of perturbation.