Hafnia / Zirconia polymorphs as a function of T

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SUMMARY

The discussion centers on the polymorphic transformations of hafnia and zirconia as a function of temperature. At room temperature, both materials exhibit a monoclinic structure, which transitions to a tetragonal structure upon heating, and ultimately to a cubic fluorite structure before melting. The conversation highlights the counterintuitive nature of increasing symmetry with temperature, raising questions about the relationship between entropy, degeneracy, and symmetry in these phases.

PREREQUISITES
  • Understanding of phase transitions in materials science
  • Knowledge of crystallography, specifically monoclinic, tetragonal, and cubic structures
  • Familiarity with thermodynamics concepts, particularly entropy and degeneracy
  • Basic principles of solid-state physics
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  • Research the thermodynamic principles governing phase transitions in materials
  • Study the relationship between entropy and symmetry in crystalline structures
  • Explore the specific properties of hafnia and zirconia at varying temperatures
  • Investigate the implications of symmetry changes on material properties and applications
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Materials scientists, physicists, and engineers interested in the thermal behavior of hafnia and zirconia, as well as those studying phase transitions and crystallography.

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The room temperature polymorph of hafnia and zirconia is the less symetric monoclinic, by heating both of them trasform to the more ordered tetragonal structure, by further heating they transform to the cubic flourite structure and eventually they melt.

To me it looks counter intuitive that they get more and more symmetric by heating up to the melting point! Any explanations or thoughts?
 
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Let me explain more,
My undesrtanding is that the entorpy is proprtional to the degenracy or the number of accesible states. Also heating adds more entropy to the system.
However, the symmetry tends to reduce the degenracy which (to me) seems to contradict that the entropy of the cubic phase should be larger than the entropy of the monoclinic one.

Am I wrong in my argument?
 

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