Understanding the 12% Lattice Mismatch and Twin Defect Formation in Cu/Au Deposition

The lattice mismatch between two materials is defined as the percentage difference between their lattice constants, which are the distances between the atoms in their crystal structures. In this case, the lattice constant of gold (Au) is 0.4078 nm, while that of copper (Cu) is 0.3615 nm. Therefore, the lattice mismatch between Au and Cu is calculated as follows:

(0.3615 - 0.4078) / 0.4078 x 100% = -11.4%

However, this calculation assumes that the lattice constants of the two materials are equal in all three dimensions. In reality, the crystal structures of Au and Cu are different, and the lattice mismatch is anisotropic, meaning it varies in different directions. The value of 12% reported in the paper likely reflects the maximum lattice mismatch between Au and Cu in the direction that promotes the formation of twin defects.