Determine the lattice parameter

[Helpless guy]

Homework Statement

Given this image http://postimg.org/image/m9dyiqwy3/ find the lattice parametre of the reciprocal lattice and the coordinates of the point x.

Homework Equations

a*[/B]=2π(b×c)/(a⋅b×c)
b*=2π(c×a)/(b⋅c×a)
c*=2π(a×b)/(c⋅a×b)
Which are the vectors of the reciprocal lattice
a is the lattice parametre
3. The Attempt at a Solution
Since I am studyng a fcc structure, my vectors a,b,c are a=(a/2)(j+k), b=(a/2)(i+k), c=(a/2)(i+j)
and the reciprocal's are a*=(-i+ j+ k), b*=(i -j + k), c*=(i+ j -k).
This is as far as I can get by myself: My teacher showed that the volume of te reciprocal space is the same as the original, but multiplied by a factor of (4π/a). I know there has to be something which will give me the key to find a*; but I can`t find it myself.

Any help is appreciated.
Thanks.

 

[mark726]

Thank you for your post. It seems that you are on the right track in your attempt at finding the lattice parameter and coordinates of the point x in the reciprocal lattice. As you mentioned, the volume of the reciprocal space is equal to the original space multiplied by a factor of (4π/a). This means that the lattice parameter a* can be found by dividing 4π by the lattice parameter a. Therefore, the lattice parameter a* = 4π/a.

To find the coordinates of the point x, you can use the formula for the vectors of the reciprocal lattice that you have mentioned in your post. You will need to substitute the values of a*, b*, and c* that you have calculated using the formula for the reciprocal lattice vectors. This will give you the coordinates of the point x in terms of the lattice parameter a.

I hope this helps. If you have any further questions, please do not hesitate to ask.
Scientist