- #1

ChrisJ

- 70

- 3

## Homework Statement

Calculate the reciprocal lattice vectors for LiF.

Given the lattice parameter ##a = 0.402 nm## calculate the magnitude of the ##\textbf{G_{220}}##

reciprocal lattice vector for LiF and thus deduce the Bragg angle for the (2,2,0)

Bragg peak for incoming wavelength of ##0.9 nm.##

## Homework Equations

##d=\frac{2 \pi}{|\textbf{G}_{220}|} ##

##|\textbf{G}_{220}| = \frac{2 \pi}{a}\sqrt{h^2+k^2+l^2}##

##2d \sin{\theta} = n \lambda ##

## The Attempt at a Solution

This is not coursework, it is a question from a past exam paper I'm trying to do in preparation for my exam.

In a previous bit of the question we are given the positions of the Lithium and Flourine atoms and I deduced it was a FCC with 2 basis atoms, I have never calculated the reciprocal lattice vectors for FCC with basis of 2 atoms before, so just went ahead as I have always done hoping it was the same, but I assume that is not correct and is why I am getting it wrong.

But I don't know why they asked us to calculate them anyway, as in the notes we were given are included the equations in the relevant equations section above, so I just did.

[tex]

|\textbf{G}_{220}| = |\textbf{G}_{220}| = \frac{2 \pi}{a}\sqrt{2^2+2^2}= \frac{4\sqrt{2}\pi}{4.02 \times 10^{-10}}=4.42\times 10^{10} \textrm{m}^{-1} \\

\sin{\theta}=\frac{\lambda |\textbf{G}_{220}| }{4 \pi} = \frac{9 \cdot 4.42}{4 \pi}

[/tex]

Which I obviously can't take the inverse sin of since its not between 0-1 .