1. X-ray powder diffraction
Characterization Techniques
X-ray powder diffraction
Bartłomiej Gaweł,
Norwegian University of Science and Technology (NTNU)

2. Introduction X-Rays were discovered by Wilhelm Röntgen in 1895
X-Rays : Short wavelength form of electromagnetic radiation
First Nobel Price in Physics in 1901
Wilhelm Röntgen
An X-ray picture (radiograph) of Röntgens wife’s hand
Wikipedia

3. X-ray sources: X-ray tube
X-Ray photons are produced following the ejection of an inner orbital electron from an irradiated atom and subsequent transition of atomic orbital electrons from states of high to low energy.
Bremsstrahlung X-Rays

4. X-ray sources: synchrotron radiation
It’s far more intense (>106) than lab sources
Tunable energy
Light comes in rapid pulses - useful for time resolution

5. Diffraction theory: translation symmetry
Escher painting 2b
A translation is simply moving an object in some direction without a rotation
Lattice is a configurations of points
used to describe the orderly
arrangement of atoms in a crystal b
Crystalline materials have structures with translational symmetry a 2a
The unit cell contains the smallest
atomic group that is needed to define
the structure under repetition.

6. Diffraction theory: plane lattieces
There are five different ways to translate a point in two-dimensions.
oblique
rectangular
square
hexagonal
rectangular (centered)

7. Diffraction theory: 3D crystal systems
triclinic, a ≠ b ≠ c;  ≠  ≠  ≠ 90˚
monoclinic, a ≠ b ≠ c;  =  = 90˚;  ≠ 90˚
orthorhombic , a ≠ b ≠ c;  =  =  = 90˚
tetragonal a = b ≠ c;  =  =  = 90˚
hexagonal a = b ≠ c;  =  = 90˚;  = 120˚
trigonal a = b = c;  =  =  ≠ 90˚
cubic a = b = c;  =  =  = 90˚
The unit cell constants define
the length of the
translation vectors and the
angles between them

8. Diffraction theory: 14 Bravais Lattices
NaCl, cubic lattice
F lattice

9. Diffraction theory: symmetry oparations
Only some symmetry operations are consistent with translational symmetry and these are the only symmetry operations that occur in crystals (i.e there is no 5-fold axis of symmetry) m _ 1

10. Diffraction theory: Point and space groups
Crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a point fixed while moving each atom of the crystal to the position of an atom of the same kind. That is, an infinite crystal would look exactly the same before and after any of the operations in its point group. There is 32 crystallographic point groups
Point group determines morphology, optical, electric, magnetic
and mechanic properties of crystal
The space group of a crystal is a description of the symmetry of the crystal (point group symmetry with Bravais lattice), and can have one of 230 types.

11. Diffraction theory: Bragg’s Law
nl = 2dsinq
n is an integer determined by the order given,
λ is the wavelength of the X-rays,
d is the spacing between the planes in the atomic lattice,
θ is the angle between the incident ray and the scattering planes.
William Henry Bragg

12. Diffraction theory: Fourier Transform
Crystal
Diffraction Pattern

13. X-ray sources and Diffraction theory: Summary
X-rays are produced using X-ray tubes and synchrotrons
Synchrotrons radiation is far more intense than lab sources
The unit cell defines the crystal structure
There is 7 3D crystal systems and 14 Bravais Lattices
Crystals can be described using different symetry oparation like translations and rotations
Using Fourier Transformation is it possible to calculate atomic positions from Diffraction pattern.

14. Diffraction in practice: Diffraction Pattern

15. Diffraction in practice: Diffraction Pattern

16. Diffraction in practice: X-ray powder diffractometer
Bragg-Brentano
Reflection
Debye-Scherrer
Capillary

17. Uses of X-Ray Powder Diffraction
• Identification of single-phase materials – minerals, chemical
compounds, ceramics or other engineered materials.
• Identification of multiple phases in microcrystalline mixtures
(e.g. rocks)
• Quantitative determination of amounts of different phases in
multi-phase mixtures
• Determination of crystallite size from analysis of peak broadening
• Crystallographic structural analysis and unit-cell calculations
for crystalline materials
Determination of pores ordering in porous materials.

18. Identification of crystalline materials
The Miller indices h k l describe diffraction planes.
It is possible to calculate unit cell parameters (indexing) or interplanar spacing d
orthorhombic lattice a b c,
• d = 1 /[(h/a)2+(k/b)2+(l/c)2]1/2
cubic:
• d = a/[h2+k2+l2]1/2
To match, we need a
database of powder diffraction patterns
(peaks positions)

19. Crystalography Open Databese: http://www.crystallography.net/
Databases
ICDD (International Centre for Diffraction Data) Powder Diffraction File (PDF2 or PDF4) contains (2007) 199,574 entries (172,360 inorganic & 30,728 organic)
Previous it was called JCPDS…(Joint Committee for Powder Diffraction Standards) and before that ASTM
Crystalography Open Databese:
Inorganic Crystal Structure Database

20. Identification of crystalline materials

21. Quantitative Phase Analysis (QPA)
Reference Intensity Ratio (RIR) method – structure model not necessary
If concentration
of standard and analyte
Ia - intensity of reflection
K - contains structure factor, multiplicity,
Lorentz-polarization factor, temperature factor + scale factor for reflection
- density
 - Linear attenuation coefficient
S – standard compound (i. e. corundum or silicon powder)

22. Polymorphism and allotropism – crystal structure makes a difference
Polymorphism in materials science is the ability of a solid material to exist
in more than one form or crystal structure
Allotropism is a behavior exhibited by certain chemical elements:
these elements can exist in two or more different forms, known
as allotropes of that element

23. Crystallites size analysis
- Before grinding
After grinding
Grinding cause peaks broadening

24. Crystallites size analysis
Peak fitting, calculation internal width
Pseudo-voigt peak function

25. Crystallites size analysis - Scherrer equation
K – Scherrer constant,
– the wavelength of the X-rays,
D – average crystallite size
b – peak width,
q – the scattering angle

26. Mesoporous materials
Hexagonal 2D pores ordering (space group p6m) _
Cubic 3D pores ordering (space group Im3m)
Some amorphous mesoporous materials (i.e. Silica SBA15, SBA16)
show diffraction peaks at low 2q angle region due to mesopores ordering

27. Crystal structure determination
ZnSe(mxda)1/2 , mxda - m-xylylenediamine
a = (8) Å, b = (2) Å, c = (6) Å
Space group Ccm21 (No. 36).

28. • Identification of crystalline phases in materials.
Conclusions:
XRPD is useful in:
• Identification of crystalline phases in materials.
• Quantitative determination of amounts of different phases in multi-phase mixtures
• Determination of crystallite size from analysis of peak broadening
• Crystallographic structural analysis
Determination of pores ordering and pore size in porous materials.

29. Literature: http://mcescher.com/
CountSymmetryElements/PointGroupSymmetry/PointGroupSymmetry.html
Dehong Chen et al. J. Mater. Chem., 2006, 16, 1511–1519
Wikipedia
Bruker materials

30. Thank you for your attention
This project is funded by the Norwegian Financial Mechanism. Registration number: NF-CZ07-ICP Name of the project: „Formation of research surrounding for young researchers in the field of advanced materials for catalysis and bioapplications“