Crystallography and X ray Diffraction - Quick Overview

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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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