Crystal Symmetry: Explaining High Temp Effects

In summary, the conversation discusses how the symmetry of a crystal changes during a phase transition at high temperatures. The Ising model is used as an example to explain how the energy and entropy of the system affect the stability of the ordered state. The concept of free energy is also introduced. The conversation also brings up the example of crystals, such as TbVO4, that undergo changes in lattice symmetry when cooled. The Jahn-Teller effect is mentioned as a possible explanation for this phenomenon.
  • #1
vani_lj
5
0
Hi all,
Can anyone help explaining how during a phase transition, crystal will be more symmetric at high temperature
 
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  • #2
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
Can this b xplained on d basis of crystal structure?
 
  • #4
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
@ M Quack : Thank You
 

What is crystal symmetry?

Crystal symmetry refers to the organized and repetitive arrangement of atoms or molecules in a crystal lattice. This arrangement is characterized by specific patterns and orientations, which determine the physical and chemical properties of the crystal.

Why is crystal symmetry important?

Crystal symmetry is important because it helps us understand and predict the behavior of crystals under different conditions. It also allows us to identify and classify different types of crystals based on their symmetry elements and symmetry operations.

How does high temperature affect crystal symmetry?

High temperature can cause changes in crystal symmetry by disrupting the orderly arrangement of atoms or molecules in the crystal lattice. This can result in changes in the physical properties of the crystal, such as expansion or contraction, as well as changes in its chemical reactivity.

What are some examples of high temperature effects on crystal symmetry?

One example is the thermal expansion of crystals, where an increase in temperature causes the crystal lattice to expand, leading to changes in its symmetry. Another example is phase transitions, where a crystal undergoes a change in its structure and symmetry as the temperature increases.

How do scientists explain high temperature effects on crystal symmetry?

Scientists use various techniques such as X-ray diffraction, microscopy, and thermal analysis to study and explain high temperature effects on crystal symmetry. These techniques allow them to observe the changes in crystal structure and symmetry as the temperature changes, and to understand the underlying physical and chemical processes involved.

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