the expressions for the surface energies of the ideal (100), (110), and (111) surfaces of a material with a simple cubic crystal structure in terms of the lattice parameter "a" and the change in enthalpy per unit area (ΔH_sub) are as follows:
1. γ_100 = ΔH_sub / (a^2)
2. γ_110 = ΔH_sub / (a^2 * sqrt(2))
3. γ_111 = ΔH_sub / (a^2 * sqrt(3))
The surface energy (γ) of a crystal surface can be expressed in terms of the surface area (A) and the change in enthalpy (ΔH_sub) per unit area associated with the formation of the surface. For a simple cubic crystal structure, we can consider the three most common crystallographic planes: (100), (110), and (111).
1. For the (100) surface:
The surface area A_100 of a (100) plane is given by the formula:
A_100 = a^2,
where "a" is the lattice parameter (the length of one side of the cubic unit cell).
The surface energy γ_100 for the (100) surface is then given by:
γ_100 = ΔH_sub / A_100
γ_100 = ΔH_sub / (a^2)
2. For the (110) surface:
The surface area A_110 of a (110) plane is given by the formula:
A_110 = a^2 * sqrt(2),
where "a" is the lattice parameter.
The surface energy γ_110 for the (110) surface is then given by:
γ_110 = ΔH_sub / A_110
γ_110 = ΔH_sub / (a^2 * sqrt(2))
3. For the (111) surface:
The surface area A_111 of a (111) plane is given by the formula:
A_111 = a^2 * sqrt(3),
where "a" is the lattice parameter.
The surface energy γ_111 for the (111) surface is then given by:
γ_111 = ΔH_sub / A_111
γ_111 = ΔH_sub / (a^2 * sqrt(3))
So, the expressions for the surface energies of the ideal (100), (110), and (111) surfaces of a material with a simple cubic crystal structure in terms of the lattice parameter "a" and the change in enthalpy per unit area (ΔH_sub) are as follows:
1. γ_100 = ΔH_sub / (a^2)
2. γ_110 = ΔH_sub / (a^2 * sqrt(2))
3. γ_111 = ΔH_sub / (a^2 * sqrt(3))