x-rd/sankar

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QUALITATIVE INTERPRETATION OF POWDER XRD
DATABY Sankar Sasmal (Research Chemist,
Trainee)
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Introduction

• 1895 W.C. Röntgen discovers X-rays (Nobel Prize
  1901)
• 1910 Max von Laue Diffraction Theory (Nobel
  Prize 1912)
• 1915 W.L. Bragg W.H. Bragg NaCl, KCl (Nobel
  Prize Physics)
• 1934 D. Bernal D. Crowfoot examine first
  Proteins
• 1950 DNA double helix structure Watson, Crick,
  Wilkins (Nobel Prize 1963)
• 1958 Myoglobin Structure (Nobel Prize 1962
  Kendrew, Perutz)
• 1971 Insulin (Blundell)
• 1978 First Virus Structure (S.C Harrison)
• 1988 Nobel Prize Photosynthetic reaction center
  (Huber, Michel, Deisenhofer)
• 1997 Nobel Prize ATP-synthase structure (Walker)
• 1997 Nucleosome core particle (T. Richmond)
• 1999 Ribosome Structures (Steitz, )
• 2000 Reovirus core structure (S.C. Harrison)
• 2000 Rhodopsin structure, GPCR (Palczewski et
  al.)
• 2002 ABC-Transporter (D. Rees et al.)
• 2003 R.MacKinnon structures of ion channel
  (Nobel Prize Chemistry 2003

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Why X-ray ?

• Wave length(?)- 0.1 Å lt ? lt 100 Å
• Highly penetrating
• Atomic distances 1.5 Å
• In crystals the typical interatomic spacing 2-3
  Å

hard Soft
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Source

• X-ray tubes Rotating Anode Generators
• 2. Synchrotron Radiation

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Cross section of sealed-off filament X-ray tube
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What is X-ray diffraction ?

• A beam of X-rays directed at a crystal interacts
  with the electrons of the atoms in the
  crystal
• The electrons oscillate under the influence of
  the incoming X-Rays and become secondary
  sources of EM radiation
• The secondary radiation is in all directions.
• The waves emitted by the electrons have the same
  frequency as the incoming X-rays ? coherent
• The emission will undergo constructive or
  destructive interference with waves
  scattered from other atoms
• X-Rays are also reflected, scattered
  incoherently, absorbed, refracted, and
  transmitted when they interact with matter.

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The Laue Equation

• The first kind of scatter process to be
  recognised was discovered by Max von Laue who was
  awarded the Nobel prize for physics in 1914 "for
  his discovery of the diffraction of X-rays by
  crystals".

This is looking at diffraction from atomic arrays
and not planes
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The Braggs Equation
Deviation 2?
dSin?
The path difference between ray 1 and ray 2 2d
Sin? For constructive interference n? 2d Sin?
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Continue..

• The interatomic spacing (a) along the plane does
  not appear
• Only the interplanar spacing (d) appears

shift (systematic) is actually not a problem!
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Continue..

• A physical picture of scattering leading to
  diffraction is embodied in Laues equations
• Braggs method of visualizing diffraction as
  reflection from a set of planes is a
  different way of understanding the phenomenon of
  diffraction from crystals
• The plane picture (Braggs equations) are
  simpler and we usually stick to them

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Terms

• Theta-Theta/Theta-2Theta diffractometer
• Back diffraction
• Small angle (SAXD) / wide angle (WAXD)
  diffraction

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X-RAY DIFFRACTION METHODS
X-Ray Diffraction Method
Laue
Rotating Crystal
Powder
Orientation Single Crystal Polychromatic
Beam Fixed Angle
Lattice constant Single Crystal Monochromatic
Beam Variable Angle
Lattice Parameters Polycrystal (powdered) Monochro
matic Beam Variable Angle
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Diffraction pattern
Amorphous solid
Intensity ?
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Powder diffraction pattern
Particle size and defects
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• Powder diffraction data consists of a record of
  photon intensity versus detector angle 2?
• Diffraction data can be reduced to a list of peak
  positions and intensities
• Each dhkl corresponds to a family of atomic
  planes hkl
• individual planes cannot be resolved- this is a
  limitation of powder diffraction versus
  single crystal diffraction

Raw Data
Position 2q Intensity cts
252000 372.0000
25.2400 460.0000
25.2800 576.0000
25.3200 752.0000
25.3600 1088.0000
25.4000 1488.0000
25.4400 1892.0000
25.4800 2104.0000
25.5200 1720.0000
25.5600 1216.0000
25.6000 732.0000
25.6400 456.0000
25.6800 380.0000
25.7200 328.0000
Reduced data list
hkl dhkl (Å) Relative Intensity ()
012 3.4935 49.8
104 2.5583 85.8
110 2.3852 36.1
006 2.1701 1.9
113 2.0903 100.0
202 1.9680 1.4
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Interpretation

• Determination of interplanar (d) spacings
• Indexing cubic powder patterns
• Determination of unit-cell dimension
• Determination of lattice type
• Phases identification
• Determination of crystallite shape and size
• Determination of percentage of crystallinity
• More.

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Interplanar (d) spacing

• Diffraction patterns are best reported using
  dhkl
• relative intensity rather absolute intensity.

• n? 2dhklSin?hkl
• Three variables ?, ?, and d
• ? is known
• ? is measured in the experiment (2?)
• d is calculated

e.g., for NaCl, 2?220460, ?220230, d2201.9707A0
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Indexing cubic powder patterns

• From Braggs law sin2?1/sin2?2 ?12/?22 for
  constant spacing d

Ref H. P. Klug and L. E. Alexander, X-ray
diffraction procedure, John wiley sons, 2nd
Edition, 440-441
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Unit-cell dimension

• For cubic pattern Braggs equation can be written
  as
• ?

v
h2k2l2
?
a
2
sin?
Ref H. P. Klug and L. E. Alexander, X-ray
diffraction procedure, John wiley sons, 2nd
Edition, 442-443
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Continue.
Ref H. P. Klug and L. E. Alexander, X-ray
diffraction procedure, John wiley sons, 2nd
Edition, 696-697
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Selection / Extinction Rules for determination of
Lattice type
Bravais Lattice Reflections which may be present Reflections necessarily absent
Simple all None
Body centred (h k l) even (h k l) odd
Face centred h, k and l unmixed h, k and l mixed
End centred h and k unmixed C centred h and k mixedC centred
Bravais Lattice Allowed Reflections
SC All
BCC (h k l) even
FCC h, k and l unmixed
DC h, k and l are all oddOrall are even (h k l) divisible by 4
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Continue.
The ratio of (h2 k2 l2) derived from
extinction rules which can be used in the
determination of the lattice type
SC 1 2 3 4 5 6 8
BCC 1 2 3 4 5 6 7
FCC 3 4 8 11 12
DC 3 8 11 16
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Determination of Crystal Structure
n 2? ? Sin? Sin2 ? ratio Index
1 38.52 19.26 0.33 0.11 3 111
2 44.76 22.38 0.38 0.14 4 200
3 65.14 32.57 0.54 0.29 8 220
4 78.26 39.13 0.63 0.40 11 311
5 82.47 41.235 0.66 0.43 12 222
6 99.11 49.555 0.76 0.58 16 400
7 112.03 56.015 0.83 0.69 19 331
8 116.60 58.3 0.85 0.72 20 420
9 137.47 68.735 0.93 0.87 24 422
From the ratios in column 6 we conclude that
FCC
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Phases identification

• The powder diffraction pattern is characteristic
  of the substance
• Each substance in a mixture produces its patterns
  independently
• The pattern indicates the state of chemical
  combination of the element in the material

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Powder diffraction files
The task of building up a collection of known
patterns was initiated by Hanawalt, Rinn, and
Fevel at the Dow Chemical Company (1930s). They
obtained and classified diffraction data on some
1000 substances. After this point several
societies like ASTM (1941-1969) and the JCPS
began to take part (1969-1978). In 1978 it was
renamed the Int. Center for Diffraction Data
(ICDD) with 300 scientists worldwide. In 1995 the
powder diffraction file (PDF) contained nearly
62,000 different diffraction patterns with 200
new being added each year. Elements, alloys,
inorganic compounds, minerals, organic compounds,
organo-metallic compounds.
Hanawalt Hanawalt decided that since more than
one substance can have the same or nearly the
same d value, each substance should be
characterized by its three strongest lines (d1,
d2, d3). The values of d1-d3 are usually
sufficient to characterize the pattern of an
unknown and enable the corresponding pattern in
the file to be located.
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JCPDS Card
Quality of data
1.file number 2.three strongest lines
3.lowest-angle line 4.chemical formula and name
5.data on diffraction method used
6.crystallographic data 7.optical and other data
8.data on specimen 9.data on diffraction pattern.
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Single component
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Mixture of two components (no superposed of lines)
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Continue.
Cu2O
Ref H. P. Klug and L. E. Alexander, X-ray
diffraction procedure, John wiley sons, 2nd
Edition, 515-516
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Mixture of two components ( superposed lines)


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Continue.
Mn2TiO4
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Peak broadening

• Peak broadening due to crystallite size
• Peak broadening due to the instrumental profile
• Peak broadening due to microstrain
• Peak broadening due to solid solution
  inhomogeneity
• Temperature factors

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Continue.
Due to instrumentation
Due to solid solution inhomogeneity
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Effect of Lattice Strain on Diffraction Peak
Position and Width
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Crystallite Size and The Scherrer Equation
Increasing Grain size (t)
Intensity
Diffraction patterns of nanocrystalline silicon
(331) Peak of cold-rolled and Annealed 70Cu-30Zn
(brass)
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Continue.

• Crystallite size less than 100nm peak
  broadening occur
• As grain size decreases, hardness increases, peak
  become broader
• The crystallite size broadening is most
  pronounced at large angles 2Theta
• L K? / ß COS?
• Peak Width due to crystallite size varies
  inversely with crystallite size

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Continue.

• The constant of proportionality, K (the Scherrer
  constant) depends on
• The how the width is determined
• The shape of the crystal
• The size distribution
• The most common values for K are
• 0.94 for FWHM of spherical crystals with cubic
  symmetry
• 0.89 for integral breadth of spherical crystals
  w/ cubic symmetry
• 1, because 0.94 and 0.89 both round up to 1
• K actually varies from 0.62 to 2.08

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Methods used to Define Peak Width

• Full Width at Half Maximum (FWHM)
• the width of the diffraction peak, in radians, at
  a height half-way between background and the peak
  maximum
• measured always in radian unit
• Integral Breadth
• the total area under the peak divided by the peak
  height
• the width of a rectangle having the same area and
  the same height as the peak

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Continue.
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Crystallite shape
ß(h1k1l1)
K1COS?2

R
ß(h2k2l2)
K2COS?1
ß 200 0.0127 radian ß 200/ ß 220
0.993 ß 220 0.0128 radian ß 222/ ß
200 1.244 ß 222 0.0159 radian ß 222/ ß
220 1.236
Ref H. P. Klug and L. E. Alexander, X-ray
diffraction procedure, John wiley sons, 2nd
Edition, 696-697
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Percentage of crystalinity

• In a X-ray diffraction method, total intensity
  from certain volume of the sample are always
  fixed by their combination of the atoms even they
  are amorphous phase or crystalline phase
• Sharpe profile are detected from the crystal
  phase are and broad peak profile from the
  amorphous phase area
• Rietveld method can provide very accurate
  estimates of the relative and/or absolute
  abundance of the components of multiphase samples
• Ic Area of crystalline phase
• It Total area of the profile

Ic It
Crystalinity()XcK
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Continue.
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What more?

• Texture analysis
• Determination of solvus line in phase diagrams
• Phase transition study
• Dust analysis
• Stress analysis
• Identification of clay mineral

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