What is the Spacing Between (1,1,1) Planes in a Tetragonal Lattice?

[vrinda mukund]

Homework Statement

In a tetragonal lattice a=b=0.25 nm and c= 0.18nm, deduce the spacing between (1,1,1) planes.

Homework Equations

the basic equation in this case is

$$d=\frac{a}{\sqrt{h^2+k^2+l^2}}$$

The Attempt at a Solution

here in the question we are provided with the h,k,l value. my doubt is how to find lattice constant a. for a tetragonal crystal we are having diffrent values for c and a,b. so the lattice constant will not be the same through out the crystal, rite? how to solve this?

 

[nickjer]

Use:
$$d = \frac{2\pi}{\left|\vec{G}\right|}$$
Where $\vec{G}$ is just the shortest reciprocal lattice vector orthogonal to that plane.

I suggest first finding the three reciprocal primitive vectors. And then construct the shortest reciprocal lattice vector orthogonal to the (1,1,1) planes from those.