# Elastic Anisotropy vs Crystal packing

• handsomecat
In summary, the conversation discussed the dependence of (1/s11) on crystallographic direction for an inorganic crystal. It was noted that certain peaks correspond to closely-packed planes, possibly indicating a strong bond or high young's modulus. However, according to Hertzberg's Deformation and Fracture Mechanics of Engineering Materials, this is not always the case as different materials have different stiffest directions. This information helped to clarify the relationship between close-packing and stiffness.
handsomecat
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?

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.

## 1. What is elastic anisotropy?

Elastic anisotropy refers to the directional dependence of elastic properties, such as stiffness and strength, in a material. This means that the material's response to stress and strain can vary depending on the direction in which it is applied.

## 2. What is crystal packing?

Crystal packing refers to the arrangement of atoms, ions, or molecules in a crystal lattice. It is an important factor in determining the physical and chemical properties of a material, including its elastic anisotropy.

## 3. How does crystal packing affect elastic anisotropy?

The arrangement of atoms in a crystal lattice can influence the direction-dependent behavior of a material's elastic properties. For example, if the atoms are arranged in a highly ordered, symmetric pattern, the material may exhibit higher levels of elastic anisotropy.

## 4. Are all materials elastically anisotropic?

No, not all materials exhibit elastic anisotropy. Some materials, such as isotropic metals, have the same elastic properties in all directions and are considered to be elastically isotropic.

## 5. How is elastic anisotropy measured?

Elastic anisotropy can be measured through various techniques, such as ultrasonic measurements, X-ray diffraction, and mechanical testing. These methods allow scientists to determine the material's elastic constants and how they vary with direction.

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