1. What’s in your pill?
What about theirs?
Answers from powder x-ray diffraction
Lots of help from Ashfia Huq, Silvina Pagola, Cristian Botez, many other people who don’t care to be mentioned.
Some illustrations here are proxies for real problems.

2.  d Nobel Prize in Physics, 1915,
X-ray  d
( )
( )
Nobel Prize in Physics, 1915,
for Diffraction of X-rays by Crystals.
W.L. Bragg, “X-ray Crystallography,” Scientific American (1968)

3. If the sample is a powder, there will probably be many grains aligned to diffract the incident beam of x-rays.
X-ray beam 2
Q or 2
Intensity
One only measures 2 for a given peak, not its orientation with respect to the lattice. This makes the experiment simpler to perform, but the interpretation harder. Peaks may overlap, and it may not be possible to guess the 3d geometry from only the peak positions.
Diffraction peak positions depend on geometry of the packing of unit cells.
Diffraction peak intensities are related to the positions of the atoms within the unit cell.

4. Real Space - Debye-Scherrer cones
(220)
Incident beam
x-rays or neutrons
(200)
Sample
(111)
Typically 1010 grains of 1 m (109 molecules) each, packed to 50% density

5. Part of a “typical” powder diffraction pattern.

6. Where does a powder diffraction pattern come from?
Instrument –
Strong pitch for use of synchrotron radiation
Not giving an unbiased comparison of available instruments
Properties of sample – emphasize today
Collection of peaks (fingerprint)
Collection of data so that intensities are meaningful
Find a specific lattice, measure one component in tablet
Quantitative analysis of mixtures from structures
Given two patterns, do they come from the same stuff?
Given an x-ray diffraction pattern, can you figure out what it comes from? (If you’ve seen it before? If you haven’t?)
How well can one quantify composition of mixtures?

7. National Synchrotron Light Source ground broken in 1978, started operating (sort of) in 1982.
Currently has the most users, and publishes the most papers (and most papers / $) of any dedicated SR facility.

8. GE (111)
analyzer crystal
Parallel,
Monochromatic
X-ray beam
Scintillation
detector
From
storage
ring
Ion chamber
sample
Si(111) double
monochromator
Powder diffraction station at X3B1 beamline, National Synchrotron Light Source, Brookhaven National Laboratory, U. S. A. (available for general users, rent, or collaboration)

9. What’s in your pill? (fake)
Example 1
What’s in your pill? (fake)
Data taken with very good (~0.007º FWHM) resolution at NSLS – available for scientific collaboration or proprietary access

10. A little work turns up this entry in the Powder Diffraction File

11. What are these weak peaks? The active ingredient?

12. Lattice parameters -> possible peak positions
Space group -> some of those peak positions are not seen
Positions of atoms within the unit cell -> relative intensities of peaks within each phase
X-ray diffractometer optics -> lineshape parameters (fundamental parameters on well-characterized instrument)
Crystallite size, internal strain, lattice defects -> lineshape parameters (not usually very interesting; adjust parameters to give a good fit to lineshape data)
Rietveld method: look at all of your data. Compare the profile with a model, not just the intensities of the diffraction peaks.

13. “Missing” peaks are actually from lactose monohydrate, not in PDF!
Not the best fit in the world, but clear enough

14. We should have read the fine print, and been suspicious.
The only systematic absences in P21 are (0 odd 0).

15. Lesson learned:
Don’t depend on a measurement of a few peaks, when you can utilize all of the structural information that may be available.
Known structures are better than poorly controlled data.

16. Example 2
Can we use intensities from somebody else’s measurement (e.g., in data base) to characterize materials?
Patents are frequently written with claims of powder diffraction data – d spacings and maybe intensities.
U.S. Pharmacopea says that intensities should agree ±20%.
(U.S. Pharmacopea also says that peak positions should be within ±0.1º to ±0.2º of the claimed position. Are you sure your data are that accurate?)
Example, two patterns of Ampicillin (C16H19N3O4S), taken (evidently) on the same sample, by the same (well known) operator. Good data: indexed, collected with internal standard.

17. Indeed, the two patterns agree within 20%, except for four of the strongest peaks!

18. Preferred orientation.
Lesson learned:
The sample geometry can have a profound influence on the measured intensity.
Preferred orientation.
There are various means to minimize issues of preferred orientation. It is usually best to load samples in a thin glass tube.
(Not a perfect guarantee.)
Broad beam
Bragg-Brentano

19. Example 3 The x-ray data gives almost no information.
Patent no. 0,000,000, “ process.”
“Disclosed is a new method of producing  which involves reacting the magnesium halide salt of … Also disclosed are two polymorphic crystalline Forms I and II of , and methods of their production.
“The x-ray powder diffraction pattern [of Form I] is characterized by d-spacings of 6.44, 5.69, 5.36, 4.89, 4.55, 4.31, 3.85, 3.59, and 3.14.
“The x-ray powder diffraction pattern [of Form II] is characterized by d-spacings of 14.09, 10.36, 7.92, 7.18, 6.40, 5.93, 5.66, 5.31, 4.68, 3.90, 3.60, and 3.25.”
The x-ray data gives almost no information.
“If you make  with those diffraction peaks, we’ll sue.”
How accurately do peaks have to match? All of them?

20. Real problem. Somebody is interested in knowing if their material would infringe that patent
Data on client’s raw material, collected with very good angular resolution using synchrotron radiation
Patent claims 2 1

21. What can we learn about this material?
Any crystalline material is characterized by its lattice.
The lattice dimensions (lattice parameters) govern the position of all possible diffraction peaks. c a    b
The math is a bit tedious, but the problem is to find A,B,…,F such that every peak can be assigned (h,k,l) so that its position is given by this equation.

22. Indexing: First step is to get accurate peak positions.
(locally developed software, model lineshapes, we’re not GUI programmers)
Raw Data
zoom
Lineshape
fit
5.0767, , , ,
, , , ,
, , , ,
, , , ,
, , , ,
CHOICE=3, IDIV=0,
D1=.0001,D2=.0001,
VOL=8000, CEM=40,
MONO=140, MERIT=20,
END
xmxmxxmx
Data for
computer
search

23. A = xxxxxxxxx .000847 A ALFA = 90.000000 .000000 DEG Output from TREOR
B = xxxxxxxxx A BETA = DEG
C = xxxxxxxxx A GAMMA = DEG
UNIT CELL VOLUME = xxxxxxx A**3
H K L SST-OBS SST-CALC DELTA 2TH-OBS 2TH-CALC D-OBS FREE PARAM.
NUMBER OF OBS. LINES = 20
NUMBER OF CALC. LINES = 23
M( 20)= 192 AV.EPS.=
F 20 = 620.( , 32)
M CF. J.APPL.CRYST. 1(1968)108
F CF. J.APPL.CRYST. 12(1979)60
0 LINES ARE UNINDEXED
M-TEST= 192 UNINDEXED IN THE TEST= 0
Output from
TREOR
5.0767
5.7644

24. Armed with a probable lattice, we can check how it fits the data.
Use a profile fit (Pawley or Le Bail).
Peak positions are controlled by the lattice
Adjust parameters which control the diffraction peak widths, etc.

25. API is only a few percent of the tablet weight
API is only a few percent of the tablet weight. Shows up very clearly in the intact tablet. No sample grinding, etc.
x32
x20

26. Indexing the pattern allows us to account for EVERY observed diffraction peak.
Strong statement about sample purity (of crystalline phases).

27. Example 4 Quantitative Analysis of Mixtures
The International Union of Crystallography sponsored a Round-Robin to assess accuracy of methods in use by participants.
Pharmaceutical mixtures of crystalline Mannitol, Sucrose, Valine, Nizatidine, starch (amorphous).
From the IUCr’s standpoint, this was a disappointment. Only two participants submitted solutions from their own data, and one from IUCr’s data. (I wasn’t any of these. Cast no stones.)
Why? I can only guess:
IUCr’s data on one component was a little bit wrong
(P21/n vs. P21/c), coordinates on another were wrong(?), etc.
The patterns are complicated – call for good resolution.

28. The IUCr furnished lab data for people who wanted to analyze it.

30. Blow up part of the pattern

31. Results of IUCr Quantitative Phase Analysis Round Robin
Pharmaceutical sample #1

34. Pharm sample 2 – only show crystalline components – there was also 30 wt% amorphous starch

35. Lesson learned, QPA round robin:
Maybe quantitative analysis from x-ray diffraction is not as mature a technique as everybody imagines.
All of our performance in this task is below what we could be proud of.
The example given was a hard problem! Really demanded high resolution, and had serious problems with preferred orientation.

36. Conclusions:
High quality data is very important. Resolution and sample preparation.
Think about x-ray diffraction as giving information about the fundamental structure of your material, not just a list of peaks.
I have not discussed structure solutions from powder data. Covered in talk by A. Huq, and posters by C. Botez and S. Cuffini.
I do not want to leave the impression that synchrotron radiation is prerequisite to good data. It certainly helps.