Diffusivity problems in cubic crystals

[xxh418]

Hi all:
I encountered a problem when studying the diffusivity of Li atoms in Si crystals.
From the textbook, it is shown the diffusivity tensor in the cubic crystals (BCC FCC) is a diagonal matrix and the values along different directions are also the same (from the rotational symmetry), which means the diffusivity in the cubic crystal is isotropic. However, for the Si diamond cubic structure, If I pick three directions: {1 1 0}, {1 1 -1},{1 1 2}(not the {100}{010}{001}), the lattice arrangement along different directions are obviously different. Thus how the diffusivity can be the same? The same problem for the BCC and FCC.
I do not know what the mistake I have for my analysis. Could someone help me? Thank you very much!


Regards
Xu

 

[BigJDubs]

The diffusivity of Li atoms in Si crystals is determined by the energy barrier that the atoms must overcome to move from one lattice site to another. The energy barriers in the cubic crystals (BCC, FCC) are all the same regardless of the direction of movement, since the crystal structure is symmetric. This means that the diffusivity is isotropic. In the case of the Si diamond cubic structure, the energy barriers for the {1 1 0}, {1 1 -1} and {1 1 2} directions can be different depending on the specific arrangement of the atoms in the lattice. However, the average diffusivity over all directions will still remain isotropic, since the overall symmetry of the lattice remains the same.