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Year 2 - Chem > Diffraction > Flashcards

Diffraction Flashcards

1
Q

What is the main feature of a crystal?

A

Array of atoms/molecules which have periodic translational symmetry

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2
Q

What is a lattice?

A

Array of points in space which describe translational symm
Mathematical

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3
Q

What is the basis of a crystal?

A

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

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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

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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

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6
Q

How are lattices defined in 3D?

A
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7
Q

What is a cubic cell?

A

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

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8
Q

What are the 7 possible primitive lattices?

A
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9
Q

What is a body-centered cell?

A
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10
Q

What is a face-centered lattice?

A
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11
Q

What is a face-centered lattice?

A
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12
Q

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

A

2 points

so 2 basis units

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13
Q

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

A

4 lattice points

So 4 basis units

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14
Q

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

A

2 atoms but 1 lattice point

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15
Q

What is the range of lattice spacing in a crystal?

A

1-20 angstrom

where 1 angstrom = 10-10 m

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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

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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

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18
Q

What is the method for understanding sets of lattice planes?

A

Miller Indicies

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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

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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
Q

What is the relation between d and h,k,l for a tetragonal cell?

A

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

26
Q

What is the relation between d and h,k,l for a orthorombic cell?

A

(1/d2) = h2/a2 + k2/b2 + l2/c2

27
Q

How many diffraction peaks are seen for a primitive lattice?

A

Peak for each hkl lattice plane
No systematic absences

28
Q

What is the equation relating a to h,k,l?

A

a2 = (λ2/4sin2θ) (h2+k2+l2)

29
Q

How are crystals measured in a powder?

A

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
Q

How are crystals measured in a powder?

A

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
Q

What kind of beam is required for x-ray diffraction?

A

Monochromatic

Use a metal filter

32
Q

What is the format of a diffraction pattern?

A

2θ is on x-axis (where θ is from detection), this gives d-spacing

Intensity is on y-axis

33
Q

How can you find h,k,l from d in diffraction pattern?

A

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
Q

How can x-ray diffraction pattern show the average particle size?

A

The broader the diffraction peak then the smaller the particle size

Due to destructive interference

35
Q

What is the formula for intensity of h,k,l of a reflection?

A

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
Q

What is the Lorentz polarization factor?

A

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
Q

What is J for intensity of a reflected wave?

A

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
Q

What is W, the debye temperature correction factor?

A

Correction for debye temp

Vib motion in solid means diffraction grating not static and decreases intensity

This is noticeable at small lattice spacings

39
Q

What is A, the absorption factor?

A

Generally a standard value for intensity

Ignored unless samples have strongly absorbing elements

Most affects signals at low 2θ

40
Q

How can you avoid problems with absorption?

A

Changing wavelength of radiation used

41
Q

What is F, the structure factor of the intensity?

A

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
Q

What does fq, the scattering factor, depend on?

A

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
Q

What is the angular dependence of scattering factor, fq?

A

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
Q

What diffraction peaks are present for face-centered sturctures?

A

Diffraction peaks where h,k, and l are either all even or all odd
(0 counts as even)

Due to structure factor, F

45
Q

What diffraction peaks are present for a body-centered cubic stuctures?

A

Diffraction peaks when h+k+l = 2n

46
Q

Why are there systematic absences in diffraction patterns?

A

Arise from additional translational symmetry of centred lattices

47
Q

What are the diffraction peaks present in a primitive lattice?

A

All present, no absences

100,110,111,200,210, etc.

48
Q

How do you find he lattice parameters from d-spacing?

A

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
Q

What happens if h2+k2+l2 = 7 ?

A

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)

Year 2 - Chem (23 decks)

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