crystallography and x ray diffraction - quick overview
DESCRIPTION
TRANSCRIPT
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Crystal Structure
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Crystal structure of a material is way in which atoms, ions, molecules are periodically arranged in 3-D space. Crystal structure = lattice + motifA lattice is a 3-D array of points in space.Every lattice point must have identical surroundings.Basic unit of Lattice structure is called Unit Cell
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Unit Cell
The length of the unit cell along the x, y, and z direction are defined as a, b, and c.
The angles between the crystallographic axes are defined by:α = the angle between b and cβ = the angle between a and cγ = the angle between a and b
Unit Cell - Basic structural unit or building block of Lattice
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Crystal System and Bravais Lattice
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Crystal Structure - Periodic Table
Now we got the basis of Crystal structure in 3D. Lets move toward Planes (2D) or Surface.
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Crystal Plane and Notation
Consider the plane in pink, which is one of an infinite number of parallel plane each a consistent distance (“a”) away from the origin
The plane intersects the x-axis at point a. It runs parallel along y and z axes.
Thus, this plane can be designated as (1,∞,∞)
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Miller Indices are the Miller Indices are the reciprocals of the parameters reciprocals of the parameters of each crystal faceof each crystal face
Procedure :•Identify the coordinate intercepts•Take reciprocals•Clear fractions•Cite specific planes in parentheses
Miller Indices
X Y Z
Intercept 1 ∞ ∞
Reciprocal
1/1 1/∞ 1/∞
Clear 1 0 0
INDICES 1 0 0
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Miller Indices
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Advantage of Miller Indices
For cubic crystals, the angle, f between two planes, (h1 k1 l1) and (h2 k2 l2) is given by
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Stereographic Projection of Crystal Plane
Representing a plane normal
010
100
001
(north)
(south)
Projection of Planes on to a plane
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Stereographic Projection
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Stereographic Projection
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Stereographic Projection
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Stereographic Projection
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Stereographic Projection
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Stereographic Projection
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Reciprocal Lattice
In the reciprocal lattice, sets of parallel (hkl) atomic planes are represented by a single point located a distance 1/dhkl from the lattice origin and is normal to the planes separating the original vector.
γ + γ* = 180° hkl
hkl dd
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Reciprocal Lattice in 3D
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Reciprocal Lattice in Plane Projection
(100)
(110)
(111)
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Electromagnetic Spectrum
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Interference
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Interference and Geometry
Slits
Interference Pattern
Square Rectangular Square Oblique
Now If one imagine crystal Lattice instead of slit geometry, its interference pattern is reciprocal lattice
Basically , Interference pattern is reciprocal of slit geometry
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X ray Interaction with Matter
PHOTON SCATTERING: COHERENTCOMPTON
PHOTON DISAPPEARANCE PHOTOELECTRIC EFFECT PAIR PRODUCTIONPHOTODISINTEGRATION
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Diffraction and Bragg’s Law
set of latticeplanes
d
X-rays
d sin
To find dhkl , one can fix λ and vary θ (PXRD) or vise versa (Laue Method)
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Ewald’s Sphere
Explanation of Ewald’s Sphere using – Animation http://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/ewald.php
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Ewald’s Sphere
Explanation of Ewald’s Sphere using – Animation http://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/ewald.php
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Ewald’s Sphere
Explanation of Ewald’s Sphere using – Animation http://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/ewald.php
• http://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/ewald.php
• animation
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Ewald’s Sphere - Animation
Ewald’s Sphere + Reciprocal Lattice + Projection = X – ray Diffraction
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Ewald’s Sphere + Reciprocal Lattice + Projection
Live Demonstration (simulated )
http://phillips-lab.biochem.wisc.edu/software.html
XRayView : A Virtual X-Ray Crystallography Laboratory
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X – Ray Production
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X – Ray TypesWhen the target material of the X-ray tube is bombarded with electrons accelerated from the cathode filament, two types of X-ray spectra are produced.
Bremsstrahlung X-Rays
The continuous spectra consists of a range of wavelengths of X-rays with minimum wavelength and intensity
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X – Ray TypesWhen the target material of the X-ray tube is bombarded with electrons accelerated from the cathode filament, two types of X-ray spectra are produced.
Characteristic X-ray Spectra
Characteristic spectra is produced at high voltage as a result of specific electronic transitions that take place within individual atoms of the target material.
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X – Ray TypesWhen the target material of the X-ray tube is bombarded with electrons accelerated from the cathode filament, two types of X-ray spectra are produced.
Characteristic X-ray Spectra
Characteristic spectra is produced at high voltage as a result of specific electronic transitions that take place within individual atoms of the target material.
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X – Ray TypesWhen the target material of the X-ray tube is bombarded with electrons accelerated from the cathode filament, two types of X-ray spectra are produced.
Bremsstrahlung X-Rays
Characteristic spectra is produced at high voltage as a result of specific electronic transitions that take place within individual atoms of the target material.
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X – Ray Tubes
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Some Diffraction Technique demands monochromatic X-ray (not Laue method). Kβ line in the X-ray spectrum needs to be removed.
Mass absorption coefficientof the β-filter.
Anode
Cu
Co Fe Cr Mo
Filter Ni Fe Mn V Zr
Filter
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X ray Detection
Three Principle Types of X ray detection:
Photographic FilmsCountersFlorescent Screens and CCDS
Photographic Films • Film has excellent resolution.• Inexpensive.• Very long exposures
Counters:Counters produce electrical signal from an incident X
ray radiation. Counters are for rigorous studies of intensities with X –rays.
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X ray Detectors
PhosphorsA thin phosphor screen converts the incident x-rays into optical photons, which the CCD detects..
1Performance Parameter :Phosphor - Camera Optics - CCD Efficiency and ResolutionControl Electronics - Software
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Types of X-ray Diffraction
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Acklowdegement
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