SOLID STATE PHYSICS - allowed reflections (1 Viewer)

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Anabelle37

1. The problem statement, all variables and given/known data

Aluminium metal is FCC with lattice parameter a=0.405nm. suppose that n Al crystal is illuminated by a beam of neutrons with wavelength $$\lambda$$= 1.078 angstrom
(a) determine the first 10 allowed reflections, in order of increasing scattering vector, counting (101),(110),(1bar01) as one reflection.
(b) tabulate the scattering vector, kappa, the scattering angle (2theta), the miller indices and the quantity h^2+k^2+l^2.

2. Relevant equations

2dhklsin(theta)=lambda

bragg's law: 2dsin(theta)=N*lambda

dhkl= a/sqrt(h^2+k^2+l^2)

kappa = 4*pi*sin(theta)/lambda

3. The attempt at a solution[/b]

i found the structure factor to be Sbasis = f(1+exp(-i*pi(h+k))+exp(-i*pi(l+k))+exp(-i*pi(h+l))

and if h,k,l re all odd or all even then Sbasis=4f otherwise Sbasis = 0

how do i find the first 10 allowed reflections??
and how do i do it in order of increasing scattering vector if i havent found those values yet??

1. The problem statement, all variables and given/known data

Aluminium metal is FCC with lattice parameter a=0.405nm. suppose that n Al crystal is illuminated by a beam of neutrons with wavelength $$\lambda$$= 1.078 angstrom
(a) determine the first 10 allowed reflections, in order of increasing scattering vector, counting (101),(110),(1bar01) as one reflection.
(b) tabulate the scattering vector, kappa, the scattering angle (2theta), the miller indices and the quantity h^2+k^2+l^2.

2. Relevant equations

2dhklsin(theta)=lambda

bragg's law: 2dsin(theta)=N*lambda

dhkl= a/sqrt(h^2+k^2+l^2)

kappa = 4*pi*sin(theta)/lambda

3. The attempt at a solution[/b]

i found the structure factor to be Sbasis = f(1+exp(-i*pi(h+k))+exp(-i*pi(l+k))+exp(-i*pi(h+l))

and if h,k,l re all odd or all even then Sbasis=4f otherwise Sbasis = 0

how do i find the first 10 allowed reflections??
and how do i do it in order of increasing scattering vector if i havent found those values yet??

You are going in right direction. The scattering vector is $$q = 4\pi\sin(\theta)/\lambda= 2\pi/d$$, so to have first 10 reflection you should take minimal allowed h,k,l.

This would be (111), (200),...

By the way (110), mentioned in the beginning is forbidden...

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