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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?

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    $\begingroup$ Is this homework? $\endgroup$
    – Camps ♦
    Commented Nov 28, 2020 at 18:10
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    $\begingroup$ 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. $\endgroup$
    – Tristan Maxson
    Commented Nov 28, 2020 at 18:27
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    $\begingroup$ 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? $\endgroup$
    – user7077252
    Commented Nov 29, 2020 at 13:59

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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, $30^{\circ}$.

$A = S^2\sin(A^{\circ})$

$A = (\sqrt{3}*4.2)^2\sin(60^{\circ})$

$A = 45.83$

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  • $\begingroup$ Thank you so much for your help. Could you advise me of any good sources to learn? I currently possess "Modern Techniques of Surface Science 3rd ed."by Woodruff but it seems to be too advanced for my knowledge of the area, I was looking for something more into like. $\endgroup$
    – user7077252
    Commented Nov 28, 2020 at 19:54
  • $\begingroup$ To be completely honest, I am not the person to ask. I only know this from having to do it in the context of matching crystal lattices to each other. Maybe someone else can point you to a good resource. $\endgroup$
    – Tristan Maxson
    Commented Nov 28, 2020 at 21:12

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