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7. Formulate an expression for the surface energies of ideal (100),(110), and (111) surfaces of a material that adopts a simple cubic crystal structure. Leave your expression for γ in terms of a and ΔHsub. ​.

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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))

User Keith Otto
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