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For the face centered cubic crystal described above, i.e. a = 0.7\: nma=0.7nm, calculate the surface density of atoms (i.e. number of atoms per unit area) on the (111) plane in units of cm^{-2}cm−2. Values within 5% error will be considered correct.

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HW(2 questions) Determine the distance between nearest (110) planes in a simple cubic lattice with a lattice constant of ao = 4.83 Å. (y TE "s The lattice constant of a face-centered-cubicstructure is 4.75 Å. Calculate the surface density of atoms for (a)a (100) plane and (b) a (110) plane. (Ans. (a) 8.86 x 104 cm-2, (b) 6.27 x 1014 cm-2]
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For the simple cubic crystal described above, i.e. a = 0.7\: nma=0.7nm, calculate the surface density of atoms (i.e. number of atoms per unit area) on the (100) plane in unit of cm^{-2}cm−2. Values within 5% error will be considered correct.
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A monoclinic lattice has the following unit cell dimensions: a = 5.00 A° , b =10.0 A° , c =8.00 A° , and β = 110◦. Calculate the unit cell dimensions of the corresponding reciprocal lattice.
If the atomic radius of a metal that has the face-centered cubic crystal structure is 0.2718 nm, calculate the volume of its unit cell in nm³.
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In the Taylor Expansion, it looks like they've made x_0 = x_1, x_2 and made x = x_1 - a, x_2 - a. I don't understand how they can use that substitution for x_0 since it is a constant, and x_1 and x_2 are variables that can change.

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