1. Unit V Diffraction and Microscopic techniques ( Basics) 9
Powder X-ray diffraction – principle, instrumentation and application
SEM –EDAX and TEM -principle, instrumentation and application.
X-rays were discovered by Wilhelm Conrad Röntgen in 1895
and X-ray diffraction in 1912

2. X-ray Emission Spectroscopy
X-ray Energy-Dispersive Spectroscopy
X-ray Wavelength-Dispersive Spectroscopy
fiber diffraction, powder diffraction and small-angle X-ray scattering (SAXS).
electron crystallography

3. Bragg's law: Here d is the spacing between diffracting planes, is the incident angle, n is any integer, and λ is the wavelength of the beam. These specific directions appear as spots on the diffraction pattern called reflections. Thus, X-ray diffraction results from an electromagnetic wave (the X-ray) impinging on a regular array of scatterers (the repeating arrangement of atoms within the crystal).

4. gas-filled detectors,
scintillation detectors, and semiconductor detectors.

7. Hence, X-rays can be used for the study of crystal structures
For electromagnetic radiation to be diffracted the spacing in the grating should be of the same order as the wavelength
In crystals the typical interatomic spacing ~ 2-3 Å so the suitable radiation is X-rays
Hence, X-rays can be used for the study of crystal structures
Target
X-rays
Beam of electrons
A accelerating charge radiates electromagnetic radiation

8. K K Mo Target impacted by electrons accelerated by a 35 kV potential
Characteristic radiation → due to energy transitions in the atom K
White radiation
Intensity
0.2
0.6
1.0
1.4
Wavelength ()

9. The fact that diffraction occurs indicates that the atoms are arranged in an ordered pattern, with the spacing between the planes of atoms on the order of short wavelength electromagnetic radiation in the X-ray region. The diffraction pattern could be used to measure the atomic spacing in crystals, allowing the determination of the exact arrangement in the crystal, the crystal structure. The Braggs used von Laue’s discovery to determine the arrangement of atoms in several crystals and to develop a simple 2D model to explain XRD.

10. About 95% of all solid materials can be described as crystalline
About 95% of all solid materials can be described as crystalline. When X-rays interact with a crystalline substance (Phase), one gets a diffraction pattern.
Every crystalline substance gives a pattern; the same substance always gives the same pattern; and in a mixture of substances each produces its pattern independently of the others.
The X-ray diffraction pattern of a pure substance is, therefore, like a fingerprint of the substance. The powder diffraction method is thus ideally suited for characterization and identification of polycrystalline phases.
Amorphous : The atoms are arranged in a random way similar to the disorder we find in a liquid. Glasses are amorphous materials.
Crystalline : The atoms are arranged in a regular pattern, and there is as smallest volume element that by repetition in three dimensions describes the crystal. E.g. we can describe a brick wall by the shape and orientation of a single brick. This smallest volume element is called a unit cell. The dimensions of the unit cell is described by three axes :
a, b, c and the angles between them alpha, beta, gamma.
Hence, a diffracted beam may be described as a beam composed of a large number of scattered rays mutually reinforcing one another.
we use the terms X-ray reflection and X-ray diffraction as synonyms.

11. X-rays can also be refracted (refractive index slightly less than 1) and reflected (at very small angles)

14. Focal spot: 10 mm long/1 mm wide, 2000 watt power capability (~ load 200 watt/mm2),
Focus tube:12 mm long/0.4 mm wide and for Cu X-ray tube (max: 463 watt/mm2)
Soller slit: which contains a set of closely spaced thin metal plates

16. Workflow for solving the structure of a molecule by X-ray crystallography

17. XRD used basically to determine
Position of the atoms inside the crystal
Size of the atoms
Atomic scale difference between materials (alloys & minerals)
Nature of chemical bonds
Atomic structure of new materials
Nature of disorder
Types of crystals
Electronic and elastic properties of materials

18. POWDER X-RAY DIFFRACTOMETRY
A crystalline powder sample will
diffract X-rays but since the
orientations of the individual
crystals are random the data set
produced is a plot of intensity v.s.
diffraction angle or Bragg angle .
Here the sample is sitting on a
flat plate and the plate is turned
about the centre of the
diffractometer at half the rate
through which the counter
moves. This is the /2 or Bragg
scan method.
Notice the plot contains 2 on
the X-axis and X-ray intensity
on the y-axis.

19. UNIT CELL TYPES and THE SEVEN CRYSTAL SYSTEMS
Cubic a = b = c.  =  =  = 90º.
Tetragonal a = b  c.  =  =  = 90º.
Orthorhombic a  b  c.  =  =  = 90 º.
Monoclinic a  b  c.  = = 90º,   90º.
Triclinic a  b  c..       90º.
Rhombohedral a = b = c.  =  =   90 º.
(or Trigonal)
Hexagonal a = b  c.  =  = 90º,  = 120º.
Orthorhombic a c b
In general, six parameters are required to define the shape and size of a unit cell,
these being three cell edge lengths (conventionally, defined as a, b, and c),
and three angles (conventionally, defined as , , and ). In the strict mathematical
sense, a, b, and c are vectors since they specify both length and direction.
is the angle between b and c,  is the angle between a and c,  is the angle
between a and b. The unit cell should be right handed. Check the cell above with your right hand
When these unit cells are combined with possible “centering” there are
14 different Bravais lattices.

20. Cubic
Tetragonal
Orthorhombic
Monoclinic
Triclinic
Primitive Cell
Body
Centred
Cell
Face
End Face Centred P I F C
Trigonal
Hexagonal

21. CRYSTAL PLANES AND MILLER INDICES
The use of crystal planes to describe the
structure of crystals goes back to the
start of crystallography and crystal
planes were used by Bragg to explain
diffraction as will be seen later.
Crystal planes are defined by the
intercepts they make on the
crystal axes of the unit cell.
The inverse of these fractions are
the Miller Indices of the planes.
In (a) the intercepts are ½, ½, 1 and
the Miller Indices are (2 2 1).
In (c) the intercepts on b and c are at
infinity the inverse of which is 0 and
the plane is the (2 0 0).
In (d) the plane cuts the negative c
axis at -1 and thus is (1 1 -1). In
crystallography -1 is often written ī
and pronounced “Bar 1”.

22. DIFFRACTION AND THE BRAGG EQUATION
Max von Laue was the first to
suggest that crystals might
diffract X-rays and he also
provided the first explanation
for the diffraction observed.
However, it is the explanation
provided by Bragg that is simpler
and more popular.
In the Bragg view crystal
planes act a mirrors.
Constructive interference
is observed when the path
difference between the two
reflected beams in (a) = nl.
The path difference in (a) is
2my. Since my/d = sin
2my = 2dsin = nl
where d is the interplanar spacing.

23. SOLVING A CRYSTAL STRUCTURE BY
SINGLE CRYSTAL DIFFRACTION TECHNIQUES
N.B. The crystal must be a single crystal.
Bragg's equation specifies that, if a crystal is rotated
within a monochromatic X-ray beam, such that every
conceivable orientation of the crystal relative to the beam
is achieved, each set of planes will have had the
opportunity to satisfy the Bragg equation and will have
given rise to reflection.
In order to solve a crystal structure it is necessary
to record a large number of reflections.
This implies accurately measuring their intensities and
recording their directions with respect to crystal orientation
and initial X-ray beam direction.
Many experimental techniques have been devised
to achieve this. The steps involved in a crystal structure
determination are summarised in the flow chart.

24. d dSin The path difference between ray 1 and ray 2 = 2d Sin
BRAGG’s EQUATION
Deviation = 2
Ray 1
Ray 2     d 
dSin
The path difference between ray 1 and ray 2 = 2d Sin
For constructive interference: n = 2d Sin

25. But this is still reinforced scattering and NOT reflection
Extra path traveled by incoming waves  AY
These can be in phase if and only if
 incident = scattered
Extra path traveled by scattered waves  XB
But this is still reinforced scattering and NOT reflection

26. Diffraction = Reinforced Coherent Scattering
Bragg’s equation is a negative law  If Bragg’s eq. is NOT satisfied  NO reflection can occur  If Bragg’s eq. is satisfied  reflection MAY occur
Diffraction = Reinforced Coherent Scattering
Reflection versus Scattering
Reflection
Diffraction
Occurs from surface
Occurs throughout the bulk
Takes place at any angle
Takes place only at Bragg angles
~100 % of the intensity may be reflected
Small fraction of intensity is diffracted
X-rays can be reflected at very small angles of incidence

27. n is an integer and is the order of the reflection
n = 2d Sin
n is an integer and is the order of the reflection
For Cu K radiation ( = 1.54 Å) and d110= 2.22 Å n
Sin  1
0.34
20.7º
First order reflection from (110) 2
0.69
43.92º
Second order reflection from (110)
Also written as (220)

28. In XRD nth order reflection from (h k l) is considered as 1st order reflection from (nh nk nl)

31. Crystal Intensity → Diffraction angle (2) → Intensity →90
180
Crystal
Schematic of difference between the diffraction patterns of various phases 90
180
Diffraction angle (2) →
Intensity →
Monoatomic gas 90
180
Diffraction angle (2) →
Intensity →
Liquid / Amorphous solid
300
310

35. Joint Committee on Powder Diffraction Standards (JCPDS)

40. SAED Patterns of Single Crystal, Polycrystalline and Amorphous Samplesb c
020
110
200 r1 r2
Single crystal Fe (BCC) thin film-[001]
Polycrystalline thin film of Pd2Si
Amorphous thin film of Pd2Si. The diffuse
halo is indicative of scattering from an
amorphous material.

41. Indexing Diffraction Pattern-ratio technique
Any 2-D section of a reciprocal lattice can be defined by two vectors so only need to index 2 spots.
1.Choose one spot to be the origin and
measure r1
2.measure the spacing of a second spot r2
3.measure the angle, 
4.prepare a table giving the ratios of the
spacings of permitted diffraction planes
in the known structure
5.take measured ratio r1/r2 and locate a value close to this in
the table
6.assign more widely-spaced plane (lower indices) to the
shorter r value
7.calculate angle between pair of planes of the type you have
indexed
8.if measured  agrees with one of possible value, accept
indexing. if not, revisit the table and select another possible
pair of planes
9.finish indexing the pattern by vector addition.

42. Indexing Electron Diffraction Patterns
If we know the index for two diffraction spots
It is possible to index the rest of the spots by
Using vector addition as shown. Every spots
Can be reached by a combination of these two
Vectors.

43. Uses of X-ray Powder Diffraction
In general, powder diffraction data are unsuitable for solving crystal structures.
Some advances have recently been made using the Rietveld method. However
this is far from trivial and it works best in relatively simple cases. It is very difficult
to be sure that the unit cell is correct as the reflections overlap and are difficult to
resolve from one another.
Important advantages and uses of powder diffraction:
1. The need to grow crystals is eliminated.
2. A powder diffraction pattern can be recorded very rapidly and the technique
is non-destructive.
3. With special equipment very small samples may be used (1-2mg.)
4. A powder diffraction pattern may be used as a fingerprint. It is often superior to
an infrared spectrum in this respect.
5. It can be used for the qualitative, and often the quantitative, determination of
the crystalline components of a powder mixture.
6. Powder diffractometry provides an easy and fast method for the detection of
crystal polymorphs. Powder patterns are provided when a drug is being
registered with the FDA. (Polymorphs are different crystal forms of the same
substance.)