X-raydiffraction has a very significant role in crystal determination.. specially in the field of Pharmaceutical analysis. It contains the requirement for M.pharm 1st year according to RGUHS syllabus.

1. X – RAY DIFFRACTION
PRESENTED BY
Iswar Hazarika
Ist yr. M. PHARM.
DEPT. OF PHARMACOLOGY
The Oxford College of Pharmacy,

2. CONTENTS
1. Introduction
2. Production of X-Ray
3. Elementary Crystallography
4. Miller indices
5. Bragg’s law
6. Instrumentation
7. X-Ray diffraction method
8. Application of X-ray diffraction

3. 1. Introduction:
 X-Ray Definition:X-Rays are short wavelength
electromagnetic radiation between UV & gamma ray,
which consist of wavelength in the region about 0.1Å to
100Å
 For analytical purpose, the range of 0.7-2.0 Ao is the
most useful region.
 A German professor Rontgen in 1895 discovered X-ray
while working with a discharge tube
 Barium platinocyanide screen placed near discharge
tube began to glow. The glow continued even when a
wooden screen was placed between them
 These x-rays could pass through bodies, which are opaque
to ordinary light

5. 2. X-Ray generation
For analytical purposes, X-rays are obtained in three
ways:
1. by bombardment of a metal with a beam of high-
energy electrons,
2. by exposure of a substance to a primary beam of X-
rays in order to generate a secondary beam of X-ray
fluorescence,
3. by use of a radioactive source whose decay process
results in X-ray emission,

6. How does X-ray generate:?
 Process of producing X-Rays may be
visualised in terms of Bhor’s theory of
atomic Structure
 When a fast moving electron impinges on
an atom, it may knock out an electron
completely from one of the inner shell of
the atom
 Following that, one of the electron from
outer layer will fall into the vacated orbital
with simultaneous emission of X-Ray
proton

8.  The X-rays are named according to the
shell from which the electron is knocked
out, eg. K X-ray, L X-ray etc.
 K X-ray is again divided into Kα & kβ
depending on whether electron falls from
the closest shell or the next nearest shell
 Kα is again named Kα1 & Kα2 according
to the energy levels of the different
electrons in L-shell & kβ1, kβ2 for kβ rays.
 The energy of these waves is given by the
equation
hν = E(outer shell)- E(inner shell)

9. 3. Elementary Crystallography
Crystallography: Science of study of crystal
forms.
Crystal: A homogenous solid formed by repeating
3dimensional pattern of atoms, ions or molecules
& having smooth external surface
 The aspects of crystallography most important to
the effective interpretation of XRD data are:
I. conventions of lattice description,
II. unit cells,
III. lattice planes,
IV. d-spacing and Miller indices,
V. crystal structure and symmetry elements

10. Unit cell
The smallest group of particles within a
crystal that retains the geometric shape of
the crystal is known as a unit cell
A crystal lattice is a repeating array of any
one of fourteen kinds of unit cells.
There are four types of unit cells that can
be associated with each crystal system.

11. b
a
c
α
β
γ
A UNIT CELL

12. Examine the 14 Bravais Lattices in Detail

13. CRYSTAL SYSTEMS
ORTHORHOMBIC
RHOMBOHEDRAL
TETRAGONAL
CUBIC
HEXAGONAL
MONOCLINIC
TRICLINIC

14. The Bravais lattices
 When the crystal systems are combined with the
various possible lattice centerings, we arrive at the
Bravais lattices.
 They describe the geometric arrangement of the
lattice points, and thereby the translational
symmetry of the crystal.
 In three dimensions, there are 14 unique Bravais
lattices which are distinct from one another in the
translational symmetry they contain. All crystalline
materials recognized until now (not including
quasicrystals) fit in one of these arrangements.
 The Bravais lattices are sometimes referred to as
space lattices.

16. Lattice
◦ Lattice: A lattice is a repeating array of any one
of fourteen kinds of unit cells
◦ If in an actual crystal, we replace all the atoms
or group of atoms or ions which are called
structural units, by points we get a three
dimensional network or arrangement of points
designated as the lattice.
Lattice Notation:
 Lattice points are specified without brackets –100,
101, 102, etc.
 Lattice planes: are defined in terms of the Miller
indices

18. 4. MILLER INDICES:
 Miller Indices are the reciprocals of the fractional
intercepts (with fractions cleared) which the plane makes
with the crystallographic x,y,z axes of the three
nonparallel edges of the cubic unit cell.
 Spacing between planes in a cubic crystal
where dhkl = interplanar spacing between planes with
Miller indices h,k,and l.
a = lattice constant (edge of the cube)
h, k, and l = Miller indices of cubic planes being
considered.
l+k+h
a
=d 222
hkl

19. Example:
The plane shown intercepts a at100, b at
010 and c at 002.
The Miller index of the plane is thus
calculated as 1/1(a), 1/1(b), 1/2(c), and
reduced to integers as 2a,2b,1c.
Miller indices are by convention given in
parentheses, i.e., (221).

21. Interference
 A source of light gives out energy which is
uniformly distributed in the surrounding
medium.
 If two or more light waves superimpose ,then the
distribution of energy is not uniform.
 If crest of one wave falls on the crest of the other
and trough of one wave falls on the trough of
other, the amplitude of the resultant wave
increases.
 On the other hand ,if the crest of one wave falls
on the trough of the other the resultant
amplitude decreases
 Therefore the light intensity decreases.
 The modification in the distribution of light
energy due to superposition of two or more
waves is called interference

22. 5. BRAGG’s EQUATION
dhkl
 The path difference between ray 1 and ray 2 = 2dhkl Sin
 For constructive interference: n = 2dhkl Sin
Ray 1
Ray 2
Deviation = 2

23. Condition for Bragg’s law
 Two beams with identical wavelength and phase
approach a crystalline solid and are scattered off
two different atoms within it.
 The lower beam traverses an extra length of
2dsinθ
 Constructive interference occurs when this length
is equal to an integer multiple of the wavelength
of the radiation
 A diffraction pattern is obtained by measuring
the intensity of scattered waves as a function of
scattering angle
 Very strong intensities known as Bragg peaks are
obtained in the diffraction pattern when
scattered waves satisfy the Bragg condition

27. 6. INSTRUMENTATION
I. Production of x-rays
II. Collimator
III. Monochromators
IV. Detectors

28. I) Production of x rays
 X-rays are generated when high velocity
electron impinge on a metal target
 Filament of tungsten is a cathode which is
heated by a battery to emit electron
(cathode rays)
 The electron on striking the target (which
is a +ve voltage in the form of anode) will
transfer their energy to its metallic
surface and it gives of X-ray radiation
 Choice of target metal depends upon the
sample to be examined

30. 2) Collimator
 X-rays produced by the target are
randomly directed
 They form a hemisphere with a target at
the center
 In order to get a narrow beam of x-rays,
collimator are used
 It consist of two sets of closely packed
metal plates separated by a small gap
 It absorbs all the X-ray except the narrow
beam that passes between the gap

31. 2) Collimator

32. 3) Monochromator
a) Filter
b) Crystal monochromator
i) Flat crystal monochromator
ii) Curved crystal monochromator

33. a) Filter
 Filter is a window of material that absorbs
undesirable radiation but allows the radiation
of required wavelength to pass
 This method makes use of large difference in
the mass absorption coefficient
Example:
 When Zirconium filter is used for
molybdenum radiation
 Zirconium absorbs strongly the radiation of
molybdenum at short wavelength but weakly
absorb the Kα lines of molybdenum
 Thus it allow Kβ lines to pass
 hence zirconium is a β-filter

35. b) Crystal Monochromator
 It is made up of suitable crystalline
material positioned in the X-ray beam so
that the angle of reflecting planes satisfy
Braggs equation for required wavelength
 It splits the beam into the component
wavelength in the same way as the prism
 Such a crystalline substance is called an
analysing crystal
Its of two type:
◦ Flat crystal monochromator
◦ Curved crystal monochromator

37. Detectors
a) Photographic Methods
b) Counter Methods
i) Geiger-muller tube counter
ii) Proportional counter
iii) Scintillation detector
iv) Solid-state-semi-conductor detector
v) Semi-conductor detector

38. Photographic Methods
 A plane or cylindrical film is
used to record the position
& intensity of the x-ray
beam
 Film after exposing to x-ray
is developed
 The blackening of developed
film is expressed in terms of
density units D given by
I0 & I refer to incident &
transmitted intensities of x-rays
D is related to total x-ray
energy that causes the
blackening of photographic film
Value of D is measured by
densitometer

39. Counter Methods
a) Geiger-muller tube counter:-
 Geiger tube is filled with inert gas like argon
 The central wire anode is maintained at a
positive potential of 800-2500V
 When x-ray enters the Geiger tube, it
undergoes collision with the filling gas resulting
in the production of ion pairs
 The electron produced moves towards the
central anode and the +ve ion moves towards
the outer electrode
 The electron is accelerated by the potential
gradient and causes the ionisation of large
number of argon atoms resulting in production
of avalanche of electrons that are travelling
towards the central anode

40. Geiger-muller tube counter:-
800-2500V , OUTPUT PULSE- 1-10V

41. b) Proportional Counter
Its construction is same as that of Geiger tube counter.
Gas used - Xenon & Krypton
(heavy gas is used) ?
Because it is easily ionised
The voltage applied is less than that of Geiger plateau
Dead time – (~0.2 µs)
Sensitivity & efficiency – is comparable with Geiger
tube counter

42. c) Scintillation Detector
 In Scintillation detector, there is a large NaI
crystal activated with a small amount of thallium
 When X-ray is incident upon the crystal, the
pulses of visible light are emitted
 Visible light so obtained can be detected by a
photomultiplier tube
 Crystals used – sodium iodide, anthracene,
naphthalene, & p-terphenol in
xylene.
 Dead time - very short and this allows for
counting of high rates

44. d) Solid state semi-conductor detector
 In this type of detector, the electrons produced by X-ray
beam are promoted to conduction band
 The current which flows is directly proportional to the
incident x-ray energy.
 Main disadvantage – we have to use this detector at low
temperature to minimise the noise & prevent deterioration
in characteristics

45. e) Semi-conductor Detectors
 Si(Li) and Ge(Li)
 Principle of Semi-conductor detector is
same as proportional counter, except the
materials used are in a solid state
 When x-ray falls on a semiconductor or a
silicon lithium-drifted detector, it
generates an electron (-e) and a hole
(+e).

46. Semi-conductor Detectors

47. X-Ray Diffraction Methods
Used for investigating internal structures.
The following methods are used:-
1. Laue Photographic method
a) Transmission Method
b) Back-Reflection method
2. Bragg X-ray spectrometer
3. Rotating crystal Method
4. Powder Diffraction Method

48. Laue Photographic Method
The Laue method is mainly used to
determine the orientation of large single
crystals
 White radiation is reflected from, or
transmitted through, a fixed crystal
Two Types:-
a. Transmission Method: In the transmission Laue
method, the film is placed behind the crystal to
record beams which are transmitted through the
crystal.
b. Back Reflection Method: In the back-reflection
method, the film is placed between the x-ray
source and the crystal. The beams which are
diffracted in a backward direction are recorded.

49. Transmission method
Main features
i) A is source of x-ray (White
radiation) which is obtained from
a tungsten target at about
60,000V
ii) B is a pinhole collimator. When
X-ray pass through this pinhole
collimator, a fine pencil of x-rays
is obtained. The small is the
diameter the sharper is the
interference
iii) C is a crystal whose internal
structure is to investigated. The
crystal is set on a holder to adjust
its orientation
iv) D is a film arranged on a rigid
base. This film is provided with
beam stop to prevent direct beam
from causing excessive fogging of
the film

50.  The position of crystal
is held stationary in a
beam of X-ray
 The X-ray after passing
through the crystal are
diffracted and are
recorded on a
photographic plate
 Crystal orientation is
determined from the
position of the spots
 Each spot can be
indexed, i.e. attributed
to a particular plane,
using special charts
 The Leonhardt chart is
used for transmission
patterns.

51. b. Back Reflection Method
 Crystal orientation is
determined from the
position of the spots
 Each spot can be
indexed, i.e.
attributed to a
particular plane,
using special charts
 The Greninger chart
is used for back-
reflection patterns

52. Bragg’s X-Ray Spectrometer Method
 X-ray from the anticathode Q
are allowed to pass through
adjustable slit A & allowed to
fall on Crystal C
 The position of the crystal can
be adjusted by the vernier
along the circular scale
 The reflected rays passes
through slit D and enters the
ionization chamber through
narrow aluminum window
 The ionization chamber is
mounted on an arm & its
position is determined by a
second vernier
 Each plate of two is connected
to +ve and –ve of battery to
measure the strength of
ionization current

53. Working:
 The crystal is mounted in such a position that
θ=0o & ionization chamber adjusted to
receive the X-rays
 The crystal and ionization chamber are made
to move in small steps so that the angle
through which the chamber is moved is twice
the angle through which the crystal is rotated
 The ionization at first falls but for certain
value of θ it rises sharply & this corresponds
to the direction of x-ray spectrum

54. Measurement of λ
 The wavelength of X-ray can be
determined by employing the following
equation
2dsinθ = nλ
 The value of θ for various spectra
produced by reflection from a crystal is
measured & the mean value of λ/d is
determined
 The value of λ/d is known as lattice
constant
Lattice constant = λ/d
 Knowing d, the wavelength λ can be
calculated

55. Measurement of d
 The lattice spacing d is connected to cell
edge by the following relation
d = a(√2)/2 for simple lattice
d = a/2 for fcc crystal lattice
d = a(√3)/2 for bcc crystal lattice
 Where a can be calculated as
a=[(M*n)/(N*ρ)]1/3
◦ M= Molecular Weight
◦ n= No. of atoms in unit cell
◦ N= Avogadro’s number
◦ Ρ= Density

56. Determination of crystal structure by bragg’s
law:
 The X-rays are allowed to fall on the crystal
surface
 Then crystal is rotated to reflect from various
lattice planes
 Then various ratio of lattice spacing for various
group of spacing is obtained
 This ratio has been found to be different for
different crystals
 The experimentally observed ratios are compared
with the calculated ratios
(i) d100:d110:d111 = 1:1/√2:1/√3 for simple cubic
lattice
(ii) d100:d110:d111 = 1:1/√2:1/√3 for fcc crystal
(iii) d100:d110:d111 = 1:1/√2:1/√3 for bcc crystal

57. Rotating Crystal Method

58.  X-rays are generated in the x-ray tube
 The beams are made monochromatic by
filter
 Monochromatic rays then passes through
collimating system
 Xrays then falls on crystal mounted on a
shaft which can be rotated at a uniform
uniform angular ratee by a small motor
 When the shaft rotates it satisfies bragg’s
relation which produces spot on
photographic plate

59. Powder crystal Method
 Main features
i) A is source of x-ray.
ii) X-ray beam falls on the
powder P through slits S1 & S2
function of this slits is to get
narrow pencil of x-ray.
iii) Fine powder P struck on a hair
by means of gum is suspended
vertically in the axis of
cylindrical camera. This
enables sharp lines to be
obtained on the photographic
film which is surrounded by
powder crystal in form of
circular arc.
iv) The x-rays after falling on the
powder passes out of the
camera through a cut in the
film so as to minimise the
fogging produced by beam.
v) On the flat photographic plate
the observed pattern consist of
traces.

60. Powder crystal Method
 THEORY
When a monochromatic beam of x-ray is allowed to
fall on the powder of a crystal, then the following possibilities
may happen…
i) There will be some particles out of the random orientation of
small crystals in fine powder, which lie within a given set of
lattice planes for reflection to occur
ii) While another fraction of a grains will have another set of
planes in the correct position for the reflections to occur and
so on.
iii) Reflections are also possible in the different order of each set.

61.  All the like orientations of the grains due
to the reflection for each set of planes &
for each order will constitute a diffraction
cone
 Crystal structure can be obtained from the
arrangement of the traces & their relative
traces
 If angle of incidence is θ, the angle of
reflection will be 2θ
 If the film radius is r, the circumference
2πr corresponds to a scattering angle of
360o

62.  Then we can write
 l/2πr = 2θ/360
 θ = 360l/πr
 The value of θ can be calculated from the
equation
 substituting this value in Bragg’s equation
the value of d can be calculated
Application:
 The method is useful for cubic crystals
 Methods is used for determining the complex
structure of metals
 This method is useful to make distinction
between the allotropic modification of the
same substance

63. Applications of X-Rays
 Structure of crystals
 Polymer characterization
 Soil classification based on crystallinity
 Analysis of industrial dusts
 Corrosion products can be studied
 Tooth enamel and dentine have been
examined
 Degree of crystallinity of a polymer and
sludge
 Elucidating the structure of RNA and DNA
 Determination of cis and trans isomers
 Particle size determination
 Crystalline compounds (gall stones) in the
body can be detected

64. REFERENCES
1. Chatwal GR, Anand SK. Instrumental Methods
of Chemical analysis. 5th edition. Himalaya
Publishing house. 2.303-2.339
2. Connolly JR. introduction to X-Ray Powder
Diffrection. Elementary Crystallography for X-
ray, Spring 2012
3. http://en.wikipedia.org/wiki/X-
ray_crystallography
4. http://en.wikipedia.org/wiki/Bragg%27s_law
5. http://www.matter.org.uk/diffraction/x-
ray/laue_method.htm
6. http://www.xtal.iqfr.csic.es/Cristalografia/parte
_06-en.html
7. Gauglitz G, Vo-dinh T. Handbook of
spectroscopy. Wiley-Vch GmbH & Co. publisher
page.360