# Relationship interatomic spacing or interplanar spacing and grain size

## Main Question or Discussion Point

is interplanar spacing or interatomic spacing directly proportional to grain size?

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Mapes
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What are your thoughts? Although this may not be homework, for homework-type questions we need to see your attempt at figuring things out yourself before giving comments.

for e.g., what material, i mean polycrystalline or single crystal, etc.
So people here would clarify your doubts.
To me, there is no direct relation between particle size, gran size and spacing.

is polycrystalline that i am interested. from debye-scherrer formula where D = k(lamda)/(FWHM)(costheta). i wan to connect spacing and grain size. is it possible? i thought spacing is directly proportional to grain size.

Hi i am sure about the result but it will be helpful.
we know the following three formula:
$${\rm 1.~}2d\sin\theta=n\lambda, \hspace{3mm} {\rm 2.~}d=\frac{a}{\sqrt{h^2+k^2+l^2}}, \hspace{3mm} {\rm 3.~}D=\frac{K\lambda}{\beta\cos\theta}.$$
From these three formulae you arrive at the following two formulae:
$$D=\frac{K\lambda}{\beta\cos\left[\sin^{-1}\left(\frac{n\lambda}{2d}\right)\right]} =\frac{K\lambda}{\beta\cos\left[\sin^{-1}\left(\frac{n\lambda\sqrt{h^2+k^2+l^2}}{2a}\right)\right]}$$
$$\theta$$ and $$\beta$$ are in degrees and radians, respectively.
This is how i related particle size and 'd' spacing.
good luck

Last edited:
thanks a lot.