Diffraction Flashcards

1
Q

What is the main feature of a crystal?

A

Array of atoms/molecules which have periodic translational symmetry

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What is a lattice?

A

Array of points in space which describe translational symm
Mathematical

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is the basis of a crystal?

A

Atoms or molecules which are attached to each lattice point to give structure

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

How can points in a lattice relate to eachother?

A

r’ = r + n1a + n2b = n3c

Where these a,b,c are along x,y,z axis respectively

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What is a primitive lattice?

A

One lattice point per unit cell

All pairs of lattice points r and r’ related by integer values of cell units

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

How are lattices defined in 3D?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is a cubic cell?

A

4x 3-fold rotation axis
Seen as a cube with a point on each vertex

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What are the 7 possible primitive lattices?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is a body-centered cell?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What is a face-centered lattice?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is a face-centered lattice?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

How many lattice points are in a body-centered cell?

A

2 points

so 2 basis units

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

How many lattice points are in a face-centered-cell?

A

4 lattice points

So 4 basis units

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

How many lattice points and atoms are in the unit cell of hcp?

A

2 atoms but 1 lattice point

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is the range of lattice spacing in a crystal?

A

1-20 angstrom

where 1 angstrom = 10-10 m

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

How do X-rays interact with a 3D lattice?

A

Reflected by planes of the crystal lattice

Difference in phase of waves reflected gives separation of planes of the lattice

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What is Bragg’s Law and how is it used?

A

nλ = 2dsinθ

2 waves in phase must be a whole wavenumber difference

d is distance between planes of lattice

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is the method for understanding sets of lattice planes?

A

Miller Indicies

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

How are the miller indicies done in 2d?

A

Number of times intercept x and y axis

(n1, n2)

Where n1 is number of times planes intercept x axis per cell
And n2 is number of times planes intercept y axis per cell

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Describe these using Miller Indicies

A

LHS: (1,2) plane

RHS: (2,-1) plane

21
Q

What does a negative in miller indicies indicate?

A

Different orientation of the plane
Runs in opposite direction

22
Q

How are miller indicies in 3d worked out?

A

Planes cut x,y,z axes at (1/h, 1/k, 1/l)

These are then reffered to as a (h,k,l) plane

23
Q

Describe these 3d planes using Millers indicies

A

LHS: parallel to z-axis and cuts through others once so is a (1,1,0) plane

RHS: (2,2,3) plane

24
Q

What is the relation of distance between lattice planes and h,k,l for a cubic cell?

A

d = a/Sqrt[h2 + k2 + l2]
where a is the cubic lattice constant

(1/d2) = [h2 + k2 + l2]/a2

25
What is the relation between d and h,k,l for a tetragonal cell?
(1/d2) = [h2 + k2]/a2 + l2/a2
26
What is the relation between d and h,k,l for a orthorombic cell?
(1/d2) = h2/a2 + k2/b2 + l2/c2
27
How many diffraction peaks are seen for a primitive lattice?
Peak for each hkl lattice plane No systematic absences
28
What is the equation relating a to h,k,l?
a2 = (λ2/4sin2θ) (h2+k2+l2)
29
How are crystals measured in a powder?
Measure powder with large number of crystals and assume some are correctly orientated Those at bragg angle will diffract and many so is likely
30
How are crystals measured in a powder?
Measure powder with large number of crystals and assume some are correctly orientated Those at bragg angle will diffract and many so is likely
31
What kind of beam is required for x-ray diffraction?
Monochromatic Use a metal filter
32
What is the format of a diffraction pattern?
2θ is on x-axis (where θ is from detection), this gives d-spacing Intensity is on y-axis
33
How can you find h,k,l from d in diffraction pattern?
1/d2 = [h2+k2+l2]/a2 find 1/d2 for each signal Find h2+k2+l2 from this Then can derive (h,k,l)
34
How can x-ray diffraction pattern show the average particle size?
The broader the diffraction peak then the smaller the particle size Due to destructive interference
35
What is the formula for intensity of h,k,l of a reflection?
I = K x Lp x J x F2 x exp[-2W] x A where I is i not L K = scaling constant, depends on instrument L = lorentz polarisation factor J = multiplicity of {hkl} plane W = debyte temp correction factor A = absorption factor F = structure factor
36
What is the Lorentz polarization factor?
Tabluated correction factor Diffraction polarises incoming X-ray Not all polarisation orientations reflected equally so scattered beam is partially polarised Means intensity of reflected radiation depends on Bragg angle and diffractometer
37
What is J for intensity of a reflected wave?
Multiplicity of {hkl} - equivalent lattice planes are present Squares mean (1,1,1), (-1,1,1), (1,-1,-1), etc all have the same d-spacing (8 with the same 2θ value)
38
What is W, the debye temperature correction factor?
Correction for debye temp Vib motion in solid means diffraction grating not static and decreases intensity This is noticeable at small lattice spacings
39
What is A, the absorption factor?
Generally a standard value for intensity Ignored unless samples have strongly absorbing elements Most affects signals at low 2θ
40
How can you avoid problems with absorption?
Changing wavelength of radiation used
41
What is F, the structure factor of the intensity?
Structural factor relating to structure of crystal to rel intensity F = Σ fq cos2π(hx + ky + lz) + isin2π(hx + ky + lz) where fq is the scattering power of each atom q sin term 0 for cells with inversion symmetry - generally ignored
42
What does fq, the scattering factor, depend on?
Depends on # of electrons of an atom/ion Allows for e- density in a crystal to be calculated But hard to tell isoelectronic apart, e.g. Na+, F-, O2-
43
What is the angular dependence of scattering factor, fq?
X-rays scattered by e- as radiation siimilar size to atom Scattered waves leads to partial destructive interference More e- atoms have larger scattering form factor
44
What diffraction peaks are present for face-centered sturctures?
Diffraction peaks where h,k, and l are either all even or all odd (0 counts as even) Due to structure factor, F
45
What diffraction peaks are present for a body-centered cubic stuctures?
Diffraction peaks when h+k+l = 2n
46
Why are there systematic absences in diffraction patterns?
Arise from additional translational symmetry of centred lattices
47
What are the diffraction peaks present in a primitive lattice?
All present, no absences 100,110,111,200,210, etc.
48
How do you find he lattice parameters from d-spacing?
1/d2 then divide each from initial 1/d2, and then can multiply to get full numbers Then find h2+k2+l2 and plot on x-axis against 1/d2 on y-axis Slope = 1/a2
49
What happens if h2+k2+l2 = 7 ?
Must multiply by a factor as impossible to sum three square integers If first value is 1 then must multiply all by 2 (body-centered)