Crystal symmetry

[vani_lj]

Hi all,
Can anyone help explaining how during a phase transition, crystal will be more symmetric at high temperature

 

[DrDu]

Think e.g. of the Ising model. You may think of the "spins" as describing a distortion of the unit cell, which may distort in either of two directions. The energy gained by a collective distortion = parallel alignment of N spins is of the order U=-N J where J is the spin spin interaction energy. On the other hand a completely disordered state has an entropy of S= k ln N while an ordered state has S=0.
The relevant quantity is the free energy F=U-TS. At T=0 the ordered state will be more stable however at some critical temperature, the S term will outweigh the U term and the symmetric state with <S_z>=0 will be favoured.

 

[K.rajput]

Can this b xplained on d basis of crystal structure?

 

[M Quack]

There are crystals that undergo changes of lattice symmetry when cooled, e.g. due to the Jahn-Teller effect.

TbVO4 is one of the textbook examples, it is tetragonal (high symmetry) at high temperature and orthorhombic (lower symmetry) at low temperature.

 

[K.rajput]

@ M Quack : Thank You