# What does $d$-spacing between planes in a crystal lattice mean?

I have trouble understanding the meaning of $d$-spacing. $d$-spacing is supposed to give the interplanar distance. For a cubic lattice

$$d_{hk \ell}= \frac {a} { \sqrt{h^2 + k^2 + \ell ^2} }$$

What i know is 100 plane and 200 plane are parallel, when i calculate the $d$-spacing for 100 plane and 200 plane i get two different answers; as the formula itself involves $hkl$. What is $d$-spacing then? Distance between parallel set of planes?

## 2 Answers

It's the distance between members of families of parallel planes. These planes are the semi-reflective surfaces which are responsible for Bragg reflection, and this is the d of Bragg's law.

There are many good write-ups on the web; find the tutorial that meets your needs: https://en.wikipedia.org/wiki/X-ray_crystallography#Tutorials

It is the distance between adjacent planes in a family of parallel planes labelled by Miller Indices.

Miller Indices $[hlk]$ are used to design families of planes. Here, for example, you can find the explanation of how to compute them. Since you have to reduce the numbers to the lowest term (i.e. divide by the least common multiple), you can see that in the case a cubic crystal you will only have $[hlk]=[100],[010]$ and $[001]$, therefore $d$ will always be equal to $a$.

If you want to compute the distance between the planes $(200)$ and $(400)$ of the family $[100]$, that would just be $2d=2a$, and so on.