I'm studying the phase transition of crystal induced by tensile stress. There are two crystalline phases, with high and low symmetries respectively. Is it easier for the transition from phase with low symmetry to that with high symmetry? Is there some theories about the symmetry on the phase transition of crystal? Thank you very much!
Yes. Landau theory is the standard theoretical framework for explaining the relationship between symmetry breaking and phase transitions. It is too complicated to explain here, but there are plenty of good introductions to the topic. Please see texts by Martin Dove, Ulrich Müller, Dresselhaus and Cowley.
The role of symmetry for phase transition is commonly relevant since often not that much happened except of a slightly change of (some) atomic positions, i.e. the atomic arrangement becomes a bit less or more symmetric. Coming from a higher symmetry it mainly means that symmetry elements disappear but other remain so that you can derive symmetry relationships (subgroup relationships). It does not always describe the nature of phase transition, e.g. ferrite - austenite, or magnetite - hematite, but for other phases lake the numerous modifications of perovskite-like structures it works perfect and also explains why diffraction patterns of these phases do not change remarkably although their lattice parameters, symmetry and atomic positions do. However, this is only the result of the well-accepted convention defined in International Tables for Crystallography. If you carefully compare these structures you will realize that their atomic positions are extremely similar (despite the different positions within the unit cell).
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