Elastic Anisotropy vs Crystal packing

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SUMMARY

The discussion focuses on the relationship between elastic anisotropy and crystal packing in inorganic crystals, specifically analyzing the dependence of single-crystal Young's modulus (1/s11) on crystallographic direction. It highlights that certain peaks in Young's modulus correspond to closely-packed planes, yet concludes that close-packing does not universally dictate stiffness. Citing Hertzberg's "Deformation and Fracture Mechanics of Engineering Materials," it notes that while some directions exhibit stiffness, such as <111> in fcc Al and Au and <100> in bcc Mo, there is no consistent pattern across all materials.

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  • Understanding of single-crystal Young's modulus
  • Familiarity with crystallographic directions and their notation
  • Knowledge of close-packed structures in crystallography
  • Basic concepts from materials science, particularly deformation and fracture mechanics
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handsomecat
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I have calculated the dependence of (1/s11) ie. single-crystal young's modulus on crystallographic direction for an inorganic crystal.

I've noticed that certain peaks correspond to closely-packed planes eg. a psedo-hexagonal arrangement is seen in directions where the peaks (ie. local maxima) for (1/s11) occur.

I wonder if one can immediately conclude that the strength of the bonding and/or peak in the young's modulus is due to the way the atoms are packed. Any comments?
 
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According to Hertzberg's Deformation and Fracture Mechanics of Engineering Materials, it is not typically the case that close-packed directions are stiffest. In fcc Al and Au and in bcc Fe, the <111> direction is stiffest. In bcc Mo, the <100> direction is stiffest. There doesn't seem to be a pattern.
 
ok, great, thank you so much, that settles a lot of things.

I should then say that (1) some directions are stiffer than others (2) these directions happen to have close-packing.
 

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