Diffraction and reciprocals Flashcards
What is the path length for in-phase waves?
nY = dsinθ = Delta
Y is used as lambda
What is the path length for out of phase waves?
Y/2
Describe the conditions for in-phase waves
Other name for it?
the difference in distance must be a full multiple of the wavelength = constructive interference = Delta must be a whole number
Describe the conditions for out of phase waves
Other name for it?
occurs at all other angles to in phase
destructive interference
what is Delta?
path difference
What are the conditions for Y for diffraction to be seen?
Y > d
What are the requirements for surface XRD and why?
only grazing incidence can be used to prevent the bulk x-ray diffraction pattern dominating
a synchroton is required for a good signal on the surface
what is a synchroton?
uses the light given off by high energy e- which are forced around a ring by powerful magnets
x-rays are emitted at right angles to the ring
What is a LEED?
low energy electron diffraction - DOESN’T require a synchroton
what is the mean free path?
the average distance an electron travels in a crystal before scattering and losing energy
what is the desired mean free path for LEED?
a minimum value - around 10-100s of eV
How do you calculate the number of diffraction spots?
combining the path difference eq and the de broglie wavelength
to get the formula
nmax= (¬2meE /h) d
bc θ = 90, sin90 = 1
(nmax + nmax)^2 = no. of diffraction spots
Why does θ = 90 for an electron being diffracted?
bc if the movement of the electron is parallel to the surface then it can’t get off the surface
how can you increase the no. of diffraction spots?
by increasing the KE of the electrons
what is the difference between real space and reciprocal lattice vectors?
real = a1, a2
reciprocal = A1, A2
how is the combined matrix arranged for the clean surface LEED?
x along the top row,
y along the bottom row
a1 down the left, a2 down the right
how do you calculate the determinant for LEED?
cross multiply the matrix along the diagonals, then minus the top left product, from the top right products
What is the process of working out a LEED?
1) convert a1/a2/b1/b2 into vectors
2) put into a matrix
3) calculate the determinant
4) swap the original matrix along the diagonals
5) swap the signs of the bottom left and top right values
6) multiply the resulting matrix by 1/det
7) split into A1 and A2 from the final matrix
what do angles in a triangle add upto?
180
what is the angle of hexagonal symmetry?
120
why are low energy e- good for diffraction from surfaces?
they have the correct wavelength and have energy at the minimum mean free path so they don’t go too deep into the surface and so are surface specific
what are considered low energy e-?
50-200 eV
For an LEED how does the length of the lattice vectors change from real space to reciprocal lattice?
if a1 is shorter than a2, A1 will be longer than A2
similarly, if a1 is longer than a2, A1 will be shorter than A2 in the reciprocal
what did we decide for when a1 is negative if pointing down?
on a clean surface the a1 pointing down will be negative
on an overlayer surface the a1 pointing down is positive, however if the b1 is pointing up while the a1 is pointing down, then the b1 will be negative a1
