Question

Calculate the number of broken bonds per square centimeter for Ge (which has a diamond cubic structure except all the atoms are are identical) for the (100) and (111) surfaces. Which surface do you think has the lower surface energy? Why? The lattice constant of Ge is 0.565 nm, and its density is 5.32 g/cm^3.

Answer 1

Given lattice Constant of Ge = 0.565 nm and density = 5.32 g/cm³as Ge has a diamond cubic structure .i.e FCC (Face Cubic Crystal) with two atom basis

Surface Energy (ϒ) = N_s E_Bond where N_s is the number of bond broken per unit area of crystal surface and

E_Bond is the Energy per bond

In the given question N_s is the number of bond broken per unit area of crystal surface is calculate

For (100) N_s = 1.25*10¹⁵ bonds/cm²

For (111) N_s = 0.72*10¹⁵ bonds/cm²

Therefore ,surface (111) has lower surface energy then the(100) surface as surface energy is directly proportional to the N_s which is the number of bond broken per unit area of crystal surface .