Relationship interatomic spacing or interplanar spacing and grain size

  • Thread starter kimmylsm
  • Start date
  • #1
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Main Question or Discussion Point

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

Answers and Replies

  • #2
Mapes
Science Advisor
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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.
 
  • #3
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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
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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
611
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Hi i am sure about the result but it will be helpful.
we know the following three formula:
[tex]
{\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}.
[/tex]
From these three formulae you arrive at the following two formulae:
[tex]
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]}
[/tex]
[tex]\theta[/tex] and [tex]\beta[/tex] are in degrees and radians, respectively.
This is how i related particle size and 'd' spacing.
good luck
 
Last edited:
  • #6
19
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thanks a lot.
 

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