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### Topic: X-ray Diffraction Question  (Read 2436 times)

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#### G O D I V A

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##### X-ray Diffraction Question
« on: October 06, 2009, 05:33:17 AM »
I cant seem to understand what this is implying.

With the equation nλ = 2dsinθ, it is standard procedure for analyzing the diffraction patterns of powder samples using n = 1.  This use is justified in that the nth order diffraction of any hkl plane occurs at an angle identical to the first order diffraction of the nh nk nl planes (which is parallel to hkl).

what does that mean?

#### cth

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##### Re: X-ray Diffraction Question
« Reply #1 on: October 06, 2009, 09:32:37 AM »
The h,k,l numbers form a vector perpendicular to the h,k,l planes (which are parallel to one another as well). The length of that vector h,k,l is inversely proportional to the space between planes.
So, for h,k,l=1,0,0 : the planes are perpendicular to the x axis and the distance between them is 1.
For h,k,l=2,0,0 : the planes are also perpendicular to x but with an inter-plane distance of 1/2.
For h,k,l=3,0,0 : the inter-plane distance is 1/3.
And so on...

If dhkl is the distance between planes, then d2h,2k,2l = dhkl/2
d3h,3k,3l = dhkl/3
and so on....

Now, let's go back to Bragg's law: nλ = 2dsinθ.
First case: n=1       then    λ = 2dhklsinθ
Second case: n=2   then    2λ = 2dhkl sinθ      λ = 2(dhkl/2)sinθ       λ = 2d2h,2k,2lsinθ       Bragg's law for n=1 and 2h,2k,2l

So, more generally:  Bragg's law for n and h,k,l  Bragg's law for n=1 and nh,nk,nl

When you write Bragg's law λ = 2dsinθ, it doesn't mean that the n number is gone. It is just "incorporated" into the d

See http://en.wikipedia.org/wiki/Miller_index for more explanation

#### G O D I V A

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##### Re: X-ray Diffraction Question
« Reply #2 on: October 06, 2009, 10:20:03 AM »
epic explanation, you should rewrite my book