Crystal symmetry

  • Thread starter vani_lj
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  • #1
vani_lj
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Hi all,
Can anyone help explaining how during a phase transition, crystal will be more symmetric at high temperature
 

Answers and Replies

  • #2
DrDu
Science Advisor
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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.
 
  • #3
K.rajput
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Can this b xplained on d basis of crystal structure?
 
  • #4
M Quack
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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.
 
  • #5
K.rajput
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@ M Quack : Thank You
 

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