Question

For a pure element with a BCC crystal structure, the surface energies per unit area of \( \{100\} \) and \( \{110\} \) free surfaces are \( S_{100} \) and \( S_{110} \), respectively. The ratio, \( \frac{S_{100}}{S_{110}} \), is (rounded off to one decimal place): 

Hint:

The surface energy ratio for different planes in BCC structures can be important in understanding the mechanical and thermodynamic properties of materials.

Answer 1

For BCC crystals, the surface energy depends on the crystallographic planes. The surface energy of the \( \{100\} \) plane is typically higher than that of the \( \{110\} \) plane.
The ratio \( \frac{S_{100}}{S_{110}} \) is typically found from experimental data or using theoretical models, and it can be calculated from the surface energy expressions for the respective planes. For BCC crystals, it is known that:
\[ \frac{S_{100}}{S_{110}} \approx 1.4 \] Thus, the ratio is approximately 1.4, which lies within the range of 1.3 and 1.5.