condensed-mattercrystalsdiffractionsolid-state-physics
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?
The reciprocal vector [hkl] is perpendicular to the planes described by the Miller indices (hkl). This is a general relationship, not specific to cubic systems. So yes, it works for hexagonal too. Same is true for the relationship that gives the spacing of the planes as the inverse of the magnitude of the corresponding reciprocal vector (up to a factor of $ 2 \pi $). If you look up the proofs of these relationships you will see that no assumption about the crystal symmetry is made.
I could only find this poor-quality picture. It should give you an idea, anyway. For example, consider the first picture in the first row: $(l,m,n)=(1,0,0)$ in that case, and it is easy to verify that the distance between the grey planes is
$$d=a$$
In the second case, $(l,m,n)=(1,1,0)$, and you can see that
$$d=\frac a {\sqrt 2}$$
etc.
Best Answer
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