This document discusses X-ray diffraction (XRD) spectroscopy and provides examples of applying XRD principles to characterize different materials. It describes the basic principles of how XRD works using Bragg's law and Miller indices to identify crystal planes. Examples are given for characterizing silver nanoparticles, graphite, graphene oxide, and zinc oxide nanoparticles using XRD, including estimating particle sizes from XRD peak widths and identifying functional groups from infrared spectroscopy. References are also provided for further reading.

1. Spectroscopy
XRD
(X-Ray Diffraction on powders)
Dr. Chris
UP, Feb. 2016

2. Energy regions of electromagnetic
waves

3. Different principles
(1) Energy absorption
E1 and E2 are different states of a molecule:
 Vibrational states -> IR spectroscopy
 Nuclear spin states -> NMR spectroscopy
 electronic states -> UV/VIS spectroscopy

4. (2) Energy emission
Raman (infrared)
Fluorescence (uv)

5. (3) XRD “spectroscopy”
Different principle: reflection of X-Rays on a sample

6. Generation of X-Rays
The target metal
defines the energy of
the x-rays

7. Excitation of INNER electrons, falling back emits X-Rays
Typical metals are Mo (λ = 0.07 nm) and Cu (λ = 0.154 nm)

8. XRD Principle
Different planes in a crystal give different signals =
positive interference of waves

9. Why 2 ϴ ?
The Bragg diffraction condition contains only one
factor of θ: 2dsinθ=nλ
It should be noted that θ refers to the incidence angle
of the x-ray beam, and the beam is actually deflected
by an angle of 2θ, as illustrated in the image below:

10. Bragg’s Law

12. PLANES IN CRYSTALS
MILLER INDICES

13. Crystal lattices – 3 cubic structures
NaCl type

14. Movie clip:
youtube.com/watch?v=pMTA_wiY784

15. Indices h k l
http://slideplayer.org/slide/792387/#

17. Identify crystal layers
Miller indices h k l
http://www.iue.tuwien.ac.at/phd/dhar/node17.html

18. Practice Miller layers
½  2

19. Negative indices

21. Examples

22. Miller Indices Example
http://www.wolframalpha.com/widget/widgetPopup.jsp?p
=v&id=cc011df99e5873930ccb659743a221b&title=Calculat
e%20Miller%20Indices%20for%20Planes&theme=purple&i
0=1&i1=2&i2=0&podSelect=&showAssumptions=1&show
Warnings=1

23. Cubic structure – interplanar distances

24. Calculate plane distances

25. Examples

26. Examples
http://www.slideshare.net/meonly21Icandependonh
imallmylifeAA/xrd-lecture-1

27. What is the unit cell dimension a of NaCl ?
Use plane 111 with 2x theta = 27 deg
and λ = 1.54 nm (Cu-Kα)

28. Which plane will give a signal at
2x theta = 46 deg when the cubic constant
a = 0.5 nm and λ = 1.54 nm ?

29. X-rays with wavelength 1.54 Å are “reflected” from the
(1 1 0) planes of a cubic crystal with unit cell a = 6 Å.
Calculate the Bragg angle, ϴ, for orders of reflection, n =
1-5.

30. Use Braggs Law to calculate possible values for ϴ :
Solution:

31. Indexing Example

32. constant
Find out which hkl combinations using in this
formula will give a constant value.

34. ESTIMATED PARTICLE SIZES

35. http://mahendrakoppolu.blogspot.com/2013/07
/online-crystallite-size-calculator.html

36. AG NANOPARTICLES

37. From jcpds database
http://comptech.compres.us/tools/jcpds/
In Angstrom =
10 x nm
VERSION: 4
COMMENT: Silver (04-0783, shock wave)
K0: 120.800
K0P: 4.84000
SYMMETRY: CUBIC
A: 4.08620
ALPHAT: 0.000000
DIHKL: 2.3590 100. 1.00 1.00 1.00
DIHKL: 2.0440 52. 2.00 0.00 0.00
DIHKL: 1.4450 32. 2.00 2.00 0.00
DIHKL: 1.2310 36. 3.00 1.00 1.00
DIHKL: 1.1760 12. 2.00 2.00 2.00
DIHKL: 1.0215 6. 4.00 0.00 0.00
DIHKL: 0.9375 23. 3.00 3.00 1.00
DIHKL: 0.9137 22. 4.00 2.00 0.00
DIHKL: 0.8341 23. 4.00 2.00 2.00

38. Ag Nanoparticles XRD
http://www.azonano.com/article.aspx?ArticleID=2318#5

39. Particle size estimation
Debye-Scherrer Formula:
λ = 0.154 nm , W = width at half maximum = 0.011 rad,
Theta = 45 deg

40. Plane distance
http://pubs.rsc.org/en/content/articlehtml/2013/ce/c3ce40497h

41. a = b = c = 0.4081 nm
 Distance between 111 planes
 between 100 planes

42. GRAPHITE AND GRAPHENE OXIDE
(GO)

43. JCPDS DatabaseVERSION: 4
COMMENT: Graphite
K0: 100.000
K0P: 4.00000
SYMMETRY: HEXAGONAL
A: 2.456
C: 6.696
VOLUME: 34.9786
ALPHAT: 00.00E0
DIHKL: 3.3480 100. 0 0 2
DIHKL: 2.1270 3. 1 0 0
DIHKL: 2.0271 17. 1 0 1
DIHKL: 1.7953 3. 1 0 2
DIHKL: 1.6740 7. 0 0 4
DIHKL: 1.5398 5. 1 0 3
DIHKL: 1.2280 2. 1 1 0
DIHKL: 1.1529 3. 1 1 2
DIHKL: 1.1333 2. 1 0 5
DIHKL: 1.1160 2. 0 0 6
It needs 4 indices to
describe the planes in
hexagonal structure

44. Indices for HCP structures
http://www.materials.ac.uk/elearning/matter
/crystallography/indexingdirectionsandplanes
/indexing-of-hexagonal-systems.html

45. https://www.youtube.com/watch?v=vK913oWl_XI

46. Graphite and Graphene Oxide
http://www.rsc.org/suppdata/cc/c
0/c0cc01259a/c0cc01259a.pdf

47. Graphite structure

49. http://bgcryst.com/symp14/papers/291_Shalaby_
BCC_47-1_2015.pdf

50. Reduced GO: 2θ = 26.29 degree
With λ = 0.154 nm the distance between the planes:
The close d-spacing of RGO to pristine graphite and
disappearance of peak at 2θ = 12.43 degree indicate
that the oxygen containing group of graphite oxide
have been efficiently removed

51. From: Nanomaterials 2015, 5, 826-834
Graphene Oxide Synthesis from Agro Waste
The peak at 2θ = 11.6° indicates an interlayer distance
of 0.79 nm  fully oxidized graphite sheets

52. FT-IR spectrum of GO

53. In the IR spectrum typical peaks of functional groups
can be identified:
Around 3500 cm-1: O-H stretching
1700 cm-1: typical for C=O stretching
1600 cm-1: C-C vibrations of graphite
1210 cm-1: C-OH stretching

54. From: Chem. Commun., 2011,47, 12370-12372
One-pot reduction of graphene oxide at subzero
temperatures

55. From: J. Chil. Chem. Soc. vol.58 no.4 Concepción dic. 2013
http://dx.doi.org/10.4067/S0717-97072013000400067
GREEN SYNTHESIS AND CHARACTERIZATION OF
GRAPHITE OXIDE BY ORTHOGONAL EXPERIMENT
Different
oxidation
parameters for
graphite

57. From: SENSORS AND ACTUATORS B CHEMICAL
199:190–200 · AUGUST 2014

58. ZINC OXIDE NANOPARTICLES

59. Hexagonal Closest Packing

60. Zinc oxide XRD – Wurzite Structure
http://www.hindawi.com/journals/isrn/2012/372505/

61. Estimate particle sizes

62. Nanoscience and Nanotechnology 2015, 5(1): 1-6
Synthesis of Zinc Oxide Nanoparticles via Sol – Gel
Route and Their Characterization

64. Hope this was helpful !
Please follow Ajarn Chris on Facebook