Diffraction and reciprocals

Question 1

What is the path length for in-phase waves?

Answer 1

nY = dsinθ = Delta

Y is used as lambda

Question 2

What is the path length for out of phase waves?

Answer 2

Y/2

Question 3

Describe the conditions for in-phase waves

Other name for it?

Answer 3

the difference in distance must be a full multiple of the wavelength = constructive interference = Delta must be a whole number

Question 4

Describe the conditions for out of phase waves

Other name for it?

Answer 4

occurs at all other angles to in phase

destructive interference

Question 5

what is Delta?

Answer 5

path difference

Question 6

What are the conditions for Y for diffraction to be seen?

Answer 6

Y > d

Question 7

What are the requirements for surface XRD and why?

Answer 7

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

Question 8

what is a synchroton?

Answer 8

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

Question 9

What is a LEED?

Answer 9

low energy electron diffraction - DOESN’T require a synchroton

Question 10

what is the mean free path?

Answer 10

the average distance an electron travels in a crystal before scattering and losing energy

Question 11

what is the desired mean free path for LEED?

Answer 11

a minimum value - around 10-100s of eV

Question 12

How do you calculate the number of diffraction spots?

Answer 12

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

Question 13

Why does θ = 90 for an electron being diffracted?

Answer 13

bc if the movement of the electron is parallel to the surface then it can’t get off the surface

Question 14

how can you increase the no. of diffraction spots?

Answer 14

by increasing the KE of the electrons

Question 15

what is the difference between real space and reciprocal lattice vectors?

Answer 15

real = a1, a2
reciprocal = A1, A2

Question 16

how is the combined matrix arranged for the clean surface LEED?

Answer 16

x along the top row,
y along the bottom row

a1 down the left, a2 down the right

Question 17

how do you calculate the determinant for LEED?

Answer 17

cross multiply the matrix along the diagonals, then minus the top left product, from the top right products

Question 18

What is the process of working out a LEED?

Answer 18

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

Question 19

what do angles in a triangle add upto?

Answer 19

180

Question 20

what is the angle of hexagonal symmetry?

Answer 20

120

Question 21

why are low energy e- good for diffraction from surfaces?

Answer 21

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

Question 22

what are considered low energy e-?

Answer 22

50-200 eV

Question 23

For an LEED how does the length of the lattice vectors change from real space to reciprocal lattice?

Answer 23

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

Question 24

what did we decide for when a1 is negative if pointing down?

Answer 24

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

Question 25

What is M*?

Answer 25

the matrix notation for the reciprocal matrix (once the final matrix has been produced)

Question 26

For an overlayer what do you use in the matrix?

Answer 26

b1 and b2 are in the matrix in terms of their lengths relative to a1 and a2

(a1 a2
a1 a2)

where b1 is the top row, b2 is the bottom row

Question 27

Compare the real space lattice drawing to the reciprocal LEED surface representation in terms of the dark/light dots

Answer 27

in the real space: background colour (often lighter) = clean surface, dark spots on top = the overlayer

in the reciprocal space: overlayer extra spots = lighter in colour, dark spots = clean surface substrate spots