SOLID STATE PHYSICS - allowed reflections

In summary, the conversation discusses determining the first 10 allowed reflections, in order of increasing scattering vector, for an FCC aluminium metal crystal illuminated by a beam of neutrons. The scattering vector, kappa, scattering angle (2theta), miller indices, and the quantity h^2+k^2+l^2 are also to be tabulated. The structure factor is found to be dependent on the values of h, k, and l, with all odd or all even values resulting in a factor of 4f and all other combinations resulting in a factor of 0. The minimal allowed values for h, k, and l are (111), (200), etc., with (110) being forbidden.
  • #1
Anabelle37
39
0

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 [tex]\lambda[/tex]= 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



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 haven't found those values yet??

really stuck...PLEASE HELP!
 
Physics news on Phys.org
  • #2
Anabelle37 said:

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 [tex]\lambda[/tex]= 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



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 haven't found those values yet??

really stuck...PLEASE HELP!

You are going in right direction. The scattering vector is [tex] q = 4\pi\sin(\theta)/\lambda= 2\pi/d[/tex], 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...
 

FAQ: SOLID STATE PHYSICS - allowed reflections

1. What is solid state physics?

Solid state physics is a branch of physics that studies the properties of solid materials, including their structure, behavior, and interactions at the atomic and subatomic levels.

2. What are allowed reflections in solid state physics?

Allowed reflections refer to the specific orientations and angles at which light or other electromagnetic radiation can be reflected off a crystal lattice and still maintain its intensity. These reflections are determined by the symmetry and structure of the crystal lattice.

3. How do allowed reflections affect the diffraction pattern of a crystal?

The allowed reflections of a crystal lattice can greatly impact the diffraction pattern produced by the crystal. The diffraction pattern is a result of constructive and destructive interference of waves, and the allowed reflections determine which waves can interfere and in what direction, ultimately shaping the pattern.

4. What is the importance of allowed reflections in solid state physics?

The allowed reflections in solid state physics play a crucial role in understanding the structure and properties of crystals. By studying the diffraction patterns produced by different allowed reflections, scientists can gather information about the arrangement of atoms in a crystal and make predictions about its behavior and characteristics.

5. How are allowed reflections experimentally determined?

Allowed reflections are determined experimentally through techniques such as X-ray diffraction or electron diffraction. These methods involve shining a beam of particles or waves onto a crystal and analyzing the resulting diffraction pattern to identify the allowed reflections and their corresponding intensities.

Back
Top