SOLID STATE PHYSICS - allowed reflections

[Anabelle37]

Homework Statement

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.

Homework Equations

2d_hklsin(theta)=lambda

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

d_hkl= 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 S_basis = 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 S_basis=4f otherwise S_basis = 0

how do i find the first 10 allowed reflections??
and how do i do it in order of increasing scattering vector if i haven't found those values yet??

really stuck...PLEASE HELP!

 

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Homework Statement

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.

Homework Equations

2d_hklsin(theta)=lambda

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

d_hkl= 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 S_basis = 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 S_basis=4f otherwise S_basis = 0

how do i find the first 10 allowed reflections??
and how do i do it in order of increasing scattering vector if i haven't found those values yet??

really stuck...PLEASE HELP!

You are going in right 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...