Understanding the Hard Sphere Model of Crystallography

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SUMMARY

The discussion centers on the hard sphere model of crystallography as presented in C Hammond's "Basics of Crystallography and Diffraction" (third ed.). It highlights that no elements exhibit this structure due to the tendency of atoms in the second layer to occupy interstitial spaces in the layer below. The conversation emphasizes that while the hard sphere model suggests a geometric arrangement, electron orbital considerations can influence atomic positioning, particularly in single-element crystals where directional bonds are less significant.

PREREQUISITES
  • Understanding of crystallography principles
  • Familiarity with atomic structure and electron orbitals
  • Knowledge of energy considerations in crystal stability
  • Basic concepts of close-packed structures in materials science
NEXT STEPS
  • Study the implications of electron orbital hybridization in crystal structures
  • Research the differences between close-packed and body-centered cubic structures
  • Explore the role of interstitial sites in crystal lattice stability
  • Learn about the applications of the hard sphere model in materials science
USEFUL FOR

Students and professionals in materials science, crystallographers, and anyone interested in the theoretical foundations of crystal structures and their stability.

Poliona
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I am currently studying C Hammond's "Basics of Crystallography and Diffraction" (third ed.). In the first chapter ,concerning hard sphere model, I have found the following statement:
There are, in fact, no examples of elements with this structure because, as the model building shows,the atoms in the second layer tend to slip into the ‘hollows’ or interstices between the atoms in the layer below. This also accords with energy considerations: unless electron orbital considerations predominate,layers of atoms stacked in this ‘close packed’ way generally have the lowest (free) energy and are therefore most stable.

I cannot make sense of what he meant by "unless electron orbital considerations predominate" and I'd be thankful if someone could provide me with an explanation.
 
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I think it is suggesting that while the geometry of a molecule may be determined by directional bonds, that these are not important within crystals of single elements, so the hard sphere model is applicable.
 

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