# Relationship interatomic spacing or interplanar spacing and grain size

1. Apr 7, 2010

### kimmylsm

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

2. Apr 7, 2010

### Mapes

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.

3. Apr 7, 2010

### Rajini

Before posting your question please supply more information..
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.

4. Apr 7, 2010

### kimmylsm

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.

5. Apr 7, 2010

### Rajini

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: Apr 7, 2010
6. Apr 7, 2010

### kimmylsm

thanks a lot.

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