# How can I find the area of an overlayer structure?

What sources would you recommend (or if you could instead explain it to me that would be great). I have never studied crystallography but must do a module on it and in some of the questions we were given to practice the following is asked:

Give the area of a $$(\sqrt{3} \times \sqrt{3})$$R$$30^°$$ surface unit mesh on the surface of an (0001) hcp crystal with lattice parameters a = 4.2 Å and c = 5.5 Å?

• Is this homework?
– Camps
Commented Nov 28, 2020 at 18:10
• This is a common task for overlayer structures, I have changed your title to make it more generally useful. This does look like homework, but this isn't something that is straightforward to look up. Commented Nov 28, 2020 at 18:27
• It is not homework, but examples we were given and not contextualise in, and learning this during a pandemic where I haven't met the lecturer once, made this the only platform where I could try ask for help. Can someone indicate a book for me to learn this stuff? Commented Nov 29, 2020 at 13:59

The 0001 facet area will be only dependent on the $$a$$ lattice constant. To solve for the area of that surface, you will just need to find the area of a rhombus with a $$60^{\circ}$$ angle.
To read the intended cell, start from the unit cell of the 0001 surface. Then multiply the surface vectors by the two values given, $$\sqrt{3}$$ and $$\sqrt{3}$$. Then you rotate the surface vectors around the z axis by the value given, $$30^{\circ}$$.
$$A = S^2\sin(A^{\circ})$$
$$A = (\sqrt{3}*4.2)^2\sin(60^{\circ})$$
$$A = 45.83$$