1. { What is usually going to cause you trouble? Texture effects
- affects peak intensity
Sample displacement
- affects peak 2q position {
Identification processes depend on position, intensity pairs

2. Optics of a Diffractometer
Incident Beam Slits b a O
Specimen S
Diffractometer
Axis
Line
Source F
Receiving Slit
to counter

3. Diffractometer Geometry
goniometer circle
focusing
circle R q O F rf
2 q S
specimen
Specimen needs to be:
centered on the goniometer circle and
Tangent to the focusing circle

4. Specimens and Sampling
Types of Specimens
Thick samples
Good intensity…but problems defining depth (position)
Thin specimens
No penetration depth effect (good position)… but low intensity

5. Texture and Specimen Displacement
Particle size
Particle orientation
Particle shape
Particle statistics
X-ray absorption
Particle Size
Particle Distribution

6. Example: Is there real gold in Goldschlager?

7. Preferred Orientation Results in Exaggerated Au (200) Peak

8. Preferred Orientation Results in Exaggerated Alpha Lactose Hydrate (040,080) Peak
Heavy
Orientation
on 040,080
Raw Data
Effexor
Ventafaxine HCl
PDF
Lactose Hydrate
PDF

9. Tip – Examine Peak Widths
Peak width (FWHM) narrower
than instrumental broadening

10. ZAP !
Childrens Vitamin
Note: 400 lightning strikes/hr during data collection

11. Specimens and Sampling
Crystallite Statistics
How many crystallites are enough?
Are the crystallites randomly oriented?
Particle Size Effects
Particle size distributions
Amorphous surface layers

12. Specimen Preparation Properties of a Good Specimen
Representative of the sample
Grain size less than 200 mesh (74 microns)
Finer sizes may be required
Preferably as loose grains

13. Specimen Preparation Instrument Geometry and Absorption
Beam must see specimen unimpeded
Working thickness of specimen defined by beam penetration (t0.5 = 1/
Ideal position has t0.5 on axis of rotation
Thin or tiny specimens may yield sharpest diffraction peaks or lines

14. Tip: Narrow or spotty peaks may be a sign of orientation or poor
sampling statistics (small samples)
Film
Courtesy Forensic
Science Service
Counter
- Courtesy ORNL
2D Detector
- Courtesy Bruker-AXS

15. Geometry of a Diffractometer3
Angle is too high?
Sample is high.
Angle is too low?
Sample is low. 1 2
Rotation Axis
1. Ideal diffracted beam position
2. Diffracted beam from low specimen
3. Diffracted beam from high specimen
- Rule of displaced specimens
0.001 inch = 25m = 0.01o 2

16. Diffractometer Specimens
Specimen Requirements
Flat specimen surface
Smooth specimen surface
Area greater than that irradiated by beam
Specimen support gives zero diffraction or zero contribution
Thickness greater than 10t0.5
Random grain orientation
Sufficient grains for crystallite statistics

17. Properties of a Sample Size of sieved particles
200 mesh m
325 mesh m
400 mesh m
600 mesh m
1000 mesh m
Minimum diameter passes sieve

19. Properties of a Sample Particle Shapes
Equant equal dimensional
Tabular short dimension
Bladed long, intermediate, short
Acicular short dimensions
Long dimensions align parallel to the specimen surface

20. Before shaking
After shaking
Before shaking
Before shaking
After shaking
After shaking
[Tim] – demo with trail mix

21. Particle Size vs. Crystallite Size
Particles may be aggregates of crystals
Particle size greater than crystallite size

22. Particle Size vs. Crystallite Size
Particles may be single crystals
Particle size equal to crystallite size

23. Particle Size vs. Crystallite Size
Particles may be imperfect single crystals
Particle size larger than crystallite size

24. Particle Size vs. Crystallite Size
Crystal domains
Individual domains are perfect
Boundaries
Dislocations
Twin walls
Anti-phase walls
Stacking faults

25. Particle Statistics
The limiting factor in modern QXRPD is the specimen
Preferred orientation
Is the sample random?
Particle statistics
Are there enough particles?

26. Particle Statistics How many particles are necessary for randomness?
Describe orientation analytically
Represent all Bragg planes of a given set (hkl) by a perpendicular vector
Toothpick
& candy

27. Particle Statistics
Randomness requires that the “weighted” distribution of these vectors be uniform over space
Number of vectors per crystallite is the multiplicity

28. Particle Statistics
If the specimen is random, vectors (toothpicks) from a given hkl set
trace out a hemisphere “dome” above the sample – kush ball effect
Only small portion of this dome actually sampled in q-2q scan
detector
X-ray source
Specimen

29. XRD2: Definition - Diffraction Pattern in 3D Space
(a) Single crystal pattern
(b) Polycrystalline samples with poor grain sampling statistics (large grain size, thin film, inhomogeneous structure, micro area, small amount of sample)
(c) Ideal powder diffraction pattern

31. Grit from man’s clothing Control grit from gasoline-powered grinder
Small specimen
Limited particles

32. X-ray
source
accepted
range
detector
Specimen

33. Example of a highly oriented polycrystalline material: ZnO
~2000 Å
across
c-axis
a-axis
Typical grain
Microstructure happens to take on
symmetry of molecular structure.
Not always the case!
ZnO unit cell: a = 3.25, c = 5.2 Å
(many orders of mag. smaller!!!)
~½ billion unit cells in typical grain
(0.2 mm across, 1 mm long)

34. Since grains have the appearance of fibers this makes for a
simplistic picture of our grain orientation model.
We can place our vector parallel to the long (c-axis) of the grains and see the ‘kush ball’ effect.
random
oriented

35. Number of Particles Volume of sample in X-ray beam
V= (area of beam) (2x half-depth of penetration)
Assume area = 1cm x 1cm = 100mm2
t1/2 = 1/m,where m = linear absorption coefficient
mSiO2 = 97.6 cm-1 ~ 100 cm-1 = 10 mm-1
V = (100) (2) (10-1) mm3 = 20 mm3
Assume crystallite size = particle size

36. Number of Particles # of particles in irradiated volume
D = mm mm mm
Particles in
20 mm x x x 1010
How many particles are sufficient to allow randomness to be achieved?

37. Analyzing the Particle Distribution
Area of a sphere of unit radius = 4p steradians
Effect of particle size
40 mm mm mm
Area/Pole
AP = 4p = x x x 10-10 #

38. Analyzing the Particle Distribution
Because the particle is small compared to the sample, the divergence is limited by the size of the X-ray target and the particle size.

39. Conditions for Diffraction
X-ray Target
Divergence Slit
Sample
Diffracting Particle
This tends to further limit the accepted toothpicks

40. Summary # of Particles which may diffract
area that represents the window of accepted toothpicks
area of the sphere designated to an individual toothpick
# =
Top view
of unit sphere = AD AP

41. Summary 40mm 10mm 1mm # diffraction particles 12 760 38000
To achieve 1% accuracy
s = n/n
Std. err. = 2.3 s < 1%
n>52900

42. Summary Even 1 mm particles do not achieve goal
Other factors affecting analysis
% of phase in sample
Decreases # of particles per phase
hkl multiplicity
Increases with crystal symmetry
*Maybe crystallite size is smaller than particle size
- will help boost statistics

43. TABLE I
Intensity measurements on fractions of less than 325-mesh quartz powder. Tabulated
values are areas in arbitrary units of the 3.33A maximum as counted with the Geiger-
counter X-ray spectrometer using CuKa radiation. (Klug and Alexander, 1974)
15-50um um um Less than 5um
Specimen No Fraction Fraction Fraction Fraction
, , , ,055
, , , ,040
, , , ,386
, , , ,212
, , , ,460
, , , ,260
, , , ,241
, , , ,428
, , , ,406
, , , ,444
Mean area: 8, , , ,293
Mean deviation: 1,
Mean % deviation:

44. Theoretical % Mean Deviation of Intensities
High absorption magnifies intensity variation
Effective
Particle
Dimension
m)
Volume
m)3
= 5 20
% Mean Deviation of I
100
500
2000
Organics Metal- SiO2 Cu, Ni, Ag, Pb
Organics TiO2
After A,K,K (1948)

45. End Mark