X-ray Diffraction Analysis Principle Ins 674d18

X-ray Diffraction Analysis Principle, Instrument and Method

M.S.Pandian Dept of Earth Sciences Pondicherry University

X-ray Diffraction Analysis Principle, Instrument and Method

M.S.Pandian Dept of Earth Sciences Pondicherry University

Lecture Topics • X-ray Diffraction • Powder X-ray Diffractometer • Applications of Powder XRD (continued in next part…)

• X-ray Diffraction • Powder X-ray Diffractometer

Electromagnetic Spectrum

Interaction of X-ray with Matter

• Fluorescence • Ionisation • Diffraction

Fluorescence

Ionisation

Ionisation Ionizing radiations carry enough energy to break chemical bonds and separate electrons from the parent atoms and molecules, thereby creating ions in the irradiated material.

Diffraction Coherent scattering of X-ray by crystalline substance

Matter • Chemical composition • Physical property • Crystal structure Crystalline Amorphous

Diamond and Graphite

Crystalline Substances (inorganic)

Crystalline Substances • Ordered arrangement of atoms • Atom positions are regularly repeated in space following a pattern defined by crystal lattice • Distribution of atoms in crystal structure follows one of 14 Bravais Lattices derived from 6 Crystal System.

•

e

The 14 Bravais Lattices

Bravais Lattices

Molecules, Unit Cell & Crystal

Every crystal structure has a unit cell Smallest unit into which a crystal structure can be broken down that sill retains the properties of the whole structure

Crystal System Each crystal system has a different axis length and angles that separate the atoms – lengths of the axes are a, b, and c – angles between the atom planes are ,  and  Crystal Cubic

Axis Length a=b=c

Angles  =  =  = 90

Rhombohedral

a=b=c

 =  =   90

Tetragonal

a=bc

 =  =  = 90

Orthorhombic

a=bc

 =  =  = 90

Hexagonal

a=bc

 =  = 90,  = 120

Monoclinic

abc

 =  = 90,   90

Triclinic

abc

      90

z





c b y

a 

x

Crystal System

Lattice Planes

Miller Index (William Hallowes Miller 1839) • Defining particular plane of the atom with Miller Index • 3 steps to determine the Miller Index – Find the intercepts x = 2, y = 3, and z = 2 from figure – Take the reciprocal of the axis length, 1/2, 1/3, and 1/2 – Find LCM and then multiply the reciprocal z – Then, the Miler Index is (3, 2, 3)…… 6*1/2, 6*1/3, 6*1/2.. • Example, c=2 a=2 b=3 y

x

X-ray Diffraction • The spacing of atoms in crystal lattices is of the same order as the wavelength of X-radiation (0.1 to 100 Angström ). Von Laue discovered (1912) that a crystal could be used as a diffraction grating for X-rays.

• William Lawrence Bragg discovered (1912) law relating the spacing between atoms in a crystal to the angle at which X-rays are scattered when they strike the crystal. nλ = 2d Sin θ

•In-phase scattering of 2 rays depends on the distance d and the wavelength (λ) of the incident radiation. •The distance l is equal to d sinθ. For the 2 rays to scatter in phase, λ= 2d sinθ. This is Bragg’s lawin its simplest form.

X-Ray Diffraction • Bragg equation relates the spacing between adjacent crystal planes and the  angle of diffraction.

 = 2d sin  d spacing between crystal planes  angle of scattering  wavelength of x-ray beam 2 diffraction angle.

Diffraction of X-ray by Lattice Planes

X-ray Diffraction in Crystalline Materials •Every crystalline substance produces a unique diffraction pattern, which is a fingerprint of the material •In polycrystalline materials each phase produces its pattern independently of the others. •X-ray diffraction analysis is thus ideally suited for characterization and identification of phases.

• X-ray Diffraction

• X-ray Diffractometer Powder Single Crystal

X-ray Powder Diffractometer –X-ray tube –Goniometer and optical path –Sample holder –Detector

X-ray Powder Diffractometer –X-ray tube –Goniometer and optical path –Sample holder –Detector

Generation of X-rays

When an atom is bombarded with sufficiently high energy electrons, electrons of the atom are knocked out from their shell (excited state, unstable). Leads to transition of electrons to fill up the vacancy (ground state, stable). Each electron transition generates X-rays of a specific energy (with wave length in the range from 0.1Å to 100Å) equivalent to that shell.

CuKα1 CuKα2 Kα1/Kα2 CuKβ

= = = =

1.540598 1.544426 2 1.392250

X-ray Tube

X-ray Tube

Goniometer: 2 Theta - Theta

Goniometer: Theta - Theta

Goniometer in Theta-Theta Geometry

Optical Path – Soller slits – Divergence slit – Beam Mask – Sample – Anti-Scatter slit – Receiving slit – Monochromator or Beta filter

Basic Geometry of a diffractometer without monochromator

Geometry of a diffractometer with monochromator Detector Soller slits Receiving slit

X-ray tube (line focus)

Soller slits

Beam mask Divergence slit

Curved crystal monochromator (Graphite)

Anti scatter slit

Polycrystalline sample

Sample Preparation

Powder Sample Preparation on a Aluminium Holder

Detector: Scintillation Counter

Scintillation detectors work by transferring the X-ray photon into light by Tl activated NaI crystal. This in turn will release electrons which fall sequentially on 10 dynodes which multiplies the electrons 2 exp10 causing a negative pulse

Detector: Proportional Counter

Gas filled (Ar-Methane) counter. X-rays cause ionization of the gas. Ions are drawn to wire at high tension. At the wire they cause a dip in the high voltage which is counted as a pulse.

General Scan Condition Generator Settings: Step Size [°2Th.]: Scan Step Time [s]: Scan range [°2Th.]:

25 mA, 40 kV 0.0200 1.0000 15-75

Amorphous Patterns

Counts

150

Metal Tape 5991

100

50

0 20

30

40

50 Position [°2Theta]

60

70

80

XRD Pattern of a Mineral

Peak Parameters: 2θ, d spacing, I/Io, FWHM (λ = 2d Sin θ)

Peak Broadening due to • Instrument: optics, convolution of beam • Sample: Particle size, Crystal defects (lattice strain, vacancy, substitution, interstitial)

Instrumental broadening in silicon standard

Peak Broadening due to Crystallite Size

Peak Broadening due to Lattice Strain

• X-ray Diffraction • Powder X-ray Diffractometer

• Applications of Powder XRD…continued in next part