Shear deformation of diamond cubic lattice

[handsomecat]

I'm doing MD calculations and I am having trouble providing a satisfactory explanation for the following to my profs.

I am trying to calculate c44 for a diamond cubic crystal (Si), and to do that I have to calculate energy vs shear strain. For each value of the shear strain, I have to do relaxation (eg. conjugate gradient) because forces appear on the atoms. What I am asked to do is to explain why there are forces on the atoms.

"A shear strain reduces the symmetry of the crystal" is deemed to be an insufficient reason for this. (Background: my profs have little background in solid state physics ).

Right now I am thinking that I will prove it by calculations i.e. i consider the coordination polyhedron for any Si atom (which is a tetrahedron), and show that shearing this will result in a net force on the atom.

Is there any other way that I can convince them? eg. analogous examples using bathroom tiles?

 

[BigJDubs]

Yes, you can use analogous examples to explain why forces appear on atoms. For example, when you put a shear strain on a block of tiles, the tiles will be forced to move in order to accommodate the strain. The same is true for atoms in a crystal structure; they will be forced to move in order to accommodate the strain. This results in a net force on each atom.

 

[charng]

There are a few different ways to explain the forces on atoms in a shear deformation of a diamond cubic lattice. One way is to consider the atomic arrangement in a diamond cubic lattice. In this lattice, each atom is bonded to four neighboring atoms in a tetrahedral arrangement. When a shear strain is applied, the lattice is distorted and the tetrahedral arrangement of atoms is no longer symmetrical. This can result in some atoms being closer together or farther apart than others, causing repulsive or attractive forces between the atoms. Additionally, the distortion of the lattice can also cause changes in bond angles and lengths, leading to changes in the strength of the bonds and resulting in forces on the atoms.

Another way to explain the forces on atoms in a shear deformation is to consider the concept of strain energy. When a material is deformed, energy is stored in the material as strain energy. This energy is released when the material returns to its original shape. In the case of a shear deformation, the distortion of the lattice causes a change in the strain energy, resulting in forces on the atoms as they try to return to their original positions.

Analogous examples using everyday objects, such as bathroom tiles, can also be helpful in explaining the concept of forces in a shear deformation. For example, if you imagine a floor covered in square tiles and you push one corner of the floor up, the tiles will shift and the corners of the tiles will no longer be aligned. This will result in forces between the tiles as they try to realign themselves. Similarly, in a diamond cubic lattice, the shear strain causes a distortion of the lattice, resulting in forces between the atoms as they try to realign themselves to their original positions.

Ultimately, the forces on atoms in a shear deformation can be explained by considering the atomic arrangement, changes in bond lengths and angles, and the concept of strain energy. By showing the effects of shear strain on the atomic structure and energy of the material, you can provide a convincing explanation for the forces on atoms in a diamond cubic lattice.