Crystal Symmetry: Explaining High Temp Effects

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    Crystal Symmetry
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Discussion Overview

The discussion centers on the relationship between temperature and crystal symmetry during phase transitions, exploring how crystals exhibit higher symmetry at elevated temperatures. Participants examine theoretical models and specific examples to understand this phenomenon.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant introduces the Ising model to illustrate how spins can represent distortions in a crystal's unit cell, suggesting that at high temperatures, the entropy term in the free energy equation becomes significant enough to favor a symmetric state.
  • Another participant questions whether the explanation can be framed in terms of crystal structure, indicating a desire for a more structural perspective on the topic.
  • A participant provides an example of TbVO4, noting that it exhibits changes in lattice symmetry due to the Jahn-Teller effect, being tetragonal at high temperatures and orthorhombic at low temperatures.

Areas of Agreement / Disagreement

Participants have not reached a consensus, as there are multiple viewpoints regarding the mechanisms behind crystal symmetry changes with temperature, and the discussion remains open-ended.

Contextual Notes

The discussion does not resolve the assumptions underlying the Ising model or the specific conditions under which the Jahn-Teller effect influences symmetry changes.

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
 
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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.
 
Can this b xplained on d basis of crystal structure?
 
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.
 
@ M Quack : Thank You
 

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