X-ray diffraction and Bragg's law

[Martin89]

Homework Statement

The Attempt at a Solution

Hi All,

I have two issues with this question. First of all when I put the given values into the Bragg condition for diffraction I get two different wavelengths when the question implies there is only one. Secondly, I don't know how I can calculate the lattice plane spacing, d, from the given information. Any help would be appreciated, thanks!

 

[Lord Jestocost]

The correct formula is:
λ = 2 d_hkl sinθ_hkl
In case of a cubic lattice with lattice parameter a one has :
d_hkl = a / sqr(h² + k² + l²)
You have now to find out what (h k l ) planes give rise to the second and what (h k l ) planes give rise to the third scattering peak in the X-ray diffractogramm of CsI.

 

[Martin89]

The correct formula is:
λ = 2 d_hkl sinθ_hkl
In case of a cubic lattice with lattice parameter a one has :
d_hkl = a / sqr(h² + k² + l²)
You have now to find out what (h k l ) planes give rise to the second and what (h k l ) planes give rise to the third scattering peak in the X-ray diffractogramm of CsI.

I have no idea how to work that out from the given information...in lectures we were shown how to calculate d when the lattice plane was known

 

[Lord Jestocost]

You can try various (h k l ) combinations till you get a matching λ or have a look at, for example, page 8 & 9 of [PDF]What We Will See in Xrd of Simple Cubic, Bcc, Fcc? - UC Berkeley

 

[Martin89]

You can try various (h k l ) combinations till you get a matching λ or have a look at, for example, page 8 & 9 of [PDF]What We Will See in Xrd of Simple Cubic, Bcc, Fcc? - UC Berkeley

I still can't get it to work out. The ratio of sqr(h² + k² + l²) from when m=2, to when m=3 is 8.18...

 

[Lord Jestocost]

There is no "m" in the equation λ = 2 d_hkl sinθ_hkl. Do you understand that the scattering peaks which are observed at 10.8° and 13.3° are due to scattering from different planes with different Miller indices. This has nothing to do with mth-order reflections.