Theory of XRDwebsite.ppt - Prolab Systems Jeddah... · Theory of XRD The principles behind X-ray...

$: Theory of XRDwebsite.ppt - Prolab Systems Jeddah... · Theory of XRD The principles behind X-ray diffraction 16 April 2012 Ing. Bas ter Mull Area Business Manager$
Theory of XRD

The principles behind X-ray diffraction 16 April 2012Ing. Bas ter MullArea Business Manager

Overview

• Introduction• XRD versus XRF• What is diffraction ?• XRD analysis • Focusing optics• Detectors

4/14/2012 2Workshop XRF & XRD, Abu Dhabi

States of matter

SOLID LIQUID GAS

Note: XRD can only measure the solid ! ! !


Matter in solid stateCrystalline Amorphous

Single crystal Polycrystalline


Overview

• Introduction• XRD versus XRF• What is diffraction ?• XRD analysis • Focusing optics• Detectors• Products


The difference of XRD to XRF

• Let us have a look to the analysis of a Limestone– …from an XRF point of view

– … and from an XRD point of view



The real questions on these results from XRD perspective are:

Is all Ca really represented with Calcite (CaCO3) ?Is the calculated oxide for Si the right number?Is SiO2 Quartz or is it Cristoballite or is it perhaps amorphous SiliconOxide? Is the Magnesite present? (MgCO3)Is this MgCO3 calculation right?

Analyte Compound Concentrationformula (%)

Mg MgCO3 2.91Al Al2O3 0.39Si S iO2 1.16P P2O5 0.01S SO3 0.01K K2O 0.06Ca CaCO3 95.16Ti TiO2 0.02Mn MnO 0.01Fe FeCO3 0.20Sr SrO 0.06Zr ZrO2 0.01Cl Cl 0.00

Results obtained by XRF analysis



• The results on the limestone obtained by XRD - Rietveld analysis

– CaCO3 Calcite: 86.3 %

– CaMg(CO3)2 Dolomite: 12.6 %

– SiO2 Quartz: 1.1 %

– No Magnesite (MgCO3)!

Analyte Compound Concentrationformula (%)

Mg MgCO3 2.91Al Al2O3 0.39Si S iO2 1.16P P2O5 0.01S SO3 0.01K K2O 0.06Ca CaCO3 95.16Ti TiO2 0.02Mn MnO 0.01Fe FeCO3 0.20Sr SrO 0.06Zr ZrO2 0.01Cl Cl 0.00

Results obtained by XRF analysis


Overview



XRD

Scattering is the interaction of waves with matter

– Electromagnetic radiation is scattered at atoms, molecules and ions

– Scattering of visible light in gases (Raleigh-scattering in the atmosphere)

• …. and in crystals ?


XRD

• A single particle scatters in all directions

• In crystals an incident single wavelength is scattered into distinct directions. This is caused by interference of the scattered beams.

• The directions and intensity of the beams depend on the distances and on the type of the building blocks (atoms, ions, molecules) the crystal lattice is made of; and on the wavelength.

• An ideal powder sample represents all possible orientations of a crystal in space.


XRDX-ray diffraction is used for:

• Fingerprinting - (qualitative) characterization of crystalline solids

• Quantitative determination of phases in mixtures

• --------------------------------------------------------------• High resolution diffraction of epitaxial thin films (semiconductors...)

• Reflectometry (Δ density, thickness, roughness)

• Determination of the structure of (single) crystals

• Texture, orientation distribution function

• Stress, determination of the lattice strain

• High-throughput screening, crystallization experiments (solvates, solvents)

• -------------------------------------------------------------

X-ray diffraction is the most important characterization tool used in mineralogy, solid state chemistry and material science !!!


X-rays: electromagnetic radiation with a wavelength from 0.1 Å to 100 Å (0.01 nm to about 10 nm).

What are X-rays?


Generation of X-rays

• Electrons are emitted by a hot filament

• High voltage accelerates electrons

• Electrons bombard anode material at high speed

• Kinetic energy of electrons largely transferred into heat and X-ray radiation

Current (mA)

Voltage (kV)



Continuous radiation: caused by deceleration of electrons when passing the positively charged nuclei in the anode or when colliding with electrons of the anode atoms.

KL

M

Radiation (Bremsstrahlung)

Decelerated electron


KL

M

Knocked-out electron

Decelerated electron


Characteristic radiation: When an atom is bombarded with sufficiently high energy electrons (E > Ec ) electrons can be knocked out from their shell.


Characteristic radiation: An electron from a higher shell takes the place of the knocked-out electron. The energy difference between both shells is released in the form of X-ray radiation of a specific wavelength.

KL

M

Characteristic radiation

KαKβ




L-shell

III

III

Kα2 Kα1

K-shell


Kα1 and Kα2 radiation:

Kα radiation comprises two wavelengths: Kα1 and Kα2.

The wavelengths correspond to the transitions from the L-shell to the K-shell. The L-shell has three energy levels from which level I is empty.


NaCl - Sodium Chloride

A Simple Crystal Structure


A crystal is constructed by the ‘infinite’ repetition in space of identical ‘building blocks’.

Grid system

Building block

Crystal+

b

a

The Crystalline State


Building block describes arrangement of groups of atoms

Grid system describes how building block repeat in space

The lattice parameters describe the ‘infinite repetition’ unit. A volume element whose edges are successive grid lines.

The Crystalline State


The (111) planes

Lattice Planes


d100

c

b

ad200

Lattice Planes

(100) (200) (110)

(110) (111) (102)


X-ray diffraction

λ 2λ 3λ

First order Second order Third order

d

θ θC

D

B

B’

A

A’

λλ

d

A C

B

B'

B"

C'

C"

A'

A"

θ

Bragg’s law:

nλ=2dsinθConstructive interference is

detected when the path-length difference is equal to an

integer number of wavelengths


Technique 2d sin θ

XRF Unknown Fixed Variable

XRD Fixed Unknown Variable

n λ

XRD versus XRF


X-ray diffraction experiment

2d

Incident beam

Lattice plane 1



2d

Incident beam

Lattice plane 2



2d

Incident beam

Lattice plane 3


This is later the result: A diffraction pattern ! ! !


Structure

• The d-spacings of lattice planes depend on the size of the unit cell and determine the position of the peaks.

• The intensity of each peak is caused by the crystallographic structure, i.e. the position of the atoms within the unit cell and their thermal vibration.

• The line width and shape of the peaks may be derived from conditions of measuring and properties - like particle size - of the sample material.


XRD is a 3D phenomina


3D picture of powdser and poly crystalline samples


Overview

• Introduction• XRD versus XRF• What is diffraction ?• XRD analysis • Focusing optics• Detectors• Products


XRD… How does it work and what information can it deliver

• In principle the XRD diagram contains all information about:

– Mineralogical phasecomposition of the sample

– Structural information about the present phases

– Quantitative phase composition in the sample

– Information needed to perform full pattern (Rietveld) analysis



What sort of information ispresent in this picture?



Measured XRD Diagramwith identified Phases



Identified Phases



List of possible candidatesderived from ICDD database



Mineralogical (database) and semi – quantitative info

about the identified Phases


XRD

- RIR- Calibration- Rietveld

Structure and Microstructure Analysis

Qualitative Quantitative

Phase Analysis

X-Ray Powder DiffractionApplications


Overview



X-ray tube

Soller slit Soller slit

Anti-scatter slit

Receiving slit

Monochr.

Divergence slit

Sample stage

Mask

Detector

Goniometer

Classical Powder Diffractometer


Element Symbol Kαλ [nm] Application Chromium Cr 0.2291 large unit cells (clays, organic

materials, zeolites), steel (residual stress)

Iron Fe 0.1937 matrix effects of Fe and Cr Cobalt Co 0.1791 ferro materials Copper Cu 0.1542 standard tube Molybdenum Mo 0.0710 single crystal, small unit cells (metals) Silver Ag 0.0561 high absorbing materials Tungsten W 0.0211 Laue camera (continuum needed)

X-ray Operation Conditions

Anode material = choice of wavelength


line focus

pointfocus

Point•micro-diffraction•texture•psi-stress

Line•general•phase analysis•omega-stress

X-ray Operation Conditions

Focus orientation: line focus and point focus


divergence slit anti-scatter slit

Divergence Slit & Anti-scatter Slit

Divergence slit & anti-scatter slit: determining illuminated and observed length


Influence of divergence slit

opening

Divergence Slit & Anti-Scatter Slit


tube focus receiving slit

Tube Focus and Receiving Slit

Tube focus and receiving slit: determining instrument resolution


Receiving slit settings (6º take-off angle)

Tube Focus and Receiving Slit


Soller slit Soller slit

Soller Slits

Soller slits: limiting axial divergence


Soller Slits

• Soller slits consist of large numbers of parallel plates in the plane of diffraction.

• Soller slits limit the spread of the incident and diffracted X-ray beam out of the plane of diffraction: 0.02, 0.04 and 0.08 rad.

– large effect on intensities

– moderate effect on resolution (low/high 2θ)

• It is good practice to place similar Soller slits in the incident and diffracted beam.


Effect of Soller Slits

Soller Slits


β-filter & Monochromator

diffracted beam

monochromator

Possible places β-filter


β-filter or monochromator: removing

unwanted radiation



• The β-filter and the diffracted beam monochromator remove unwanted wavelengths like the Kβ-line and continuous radiation.

• The β-filter selectively absorbs radiation.

• Monochromators select radiation by means of diffraction.


Sup

pre

ssio

n

Wavelength

Cu

Kα

W L

αC

u K

β

Ni filter


Use filter material with absorption edgein between Kα and Kβline.

For example:Cu-radiation

Ni filter• Intensity Cu Kα : 50 %• Intensity Cu Kβ : 1%


Element Symbol

β-filter

Thickness [μm]

Kβ reductio

n

Kα reductio

n Chromium Cr V 13 98 45 Cobalt Co Fe 16 99 51 Copper Cu Ni 20 99 58 Molybdenum Mo Zr 75 97 54


Anode materials and corresponding β-filters


receiving slit

Curved graphite diffractedbeam monochromator

detector entrance slit

λ > λCu

λ < λCu


Only X-ray waves with correct wavelength pass the entrance slit of the detector.

Others do not focus in the entrance slit of the detector.


Diffracted Beam Monochromator

Anti scatter slit

Detector

Curved crystalmonochromator(Graphite)

Receiving slit

Polycrystalline sample

Soller slits

X-ray tube(line focus)

Divergence slit

Soller slits

Beam mask


Overview



Detection of X-rays

• Gas filled proportional detectors

• Linear Detectors– X’Celerator

– PIXcel


Detection of X-rays

• Gas Filled Proportional Detectors– For wavelengths longer than Cu Kα or lower energy

than 8 keV

– Filled with a mixture of gasses: argon-methane, xenon-methane or neon-methane

– X-rays ionize the gas in the detector


X-rays ionize the gas, the ions are drawn to the wire by the high tension. At the wire they cause a dip in the high voltage which is counted as a pulse.

Detection of X-rays

Gas Filled Detector +HT

C

A

X-rays in

Time

V


Linear detectors: X’Celerator and PIXcel Detectors


X’Celerator and PIXcel Detector

• Fast collection of diffraction data through many individual detectors in a row

• No compromise in resolution for powders and other polycrystalline materials

• Easy to use - no re-calibration, gas flow or cooling water


Point detectors in Bragg – Brentano mode

Receiving slit + detector


Line focus

Divergence slit

Scan directionScan direction

Classical geometry (Bragg-Brentano)



active length

Scanning Mode

Each strip acts as an individual detector


What is RTMS Technology ?


X’Celerator

Line focus

Divergence slit





X’Celerator

Line focus

Divergence slit



PIXcel

• the PIXcel detector: the One


What is the PIXcel Detector?

• The PIXcel is a solid state detector that comprises more than 65,000 pixels, each 55 x 55 microns in size.

• Each pixel has its own circuitry, giving rapid readout time and high dynamic range: more than 13 million counts per second per pixel row.


PIXcel: Count Rate Linearity per Pixel Row

PIXcel count rate linearity

0.0E+00

1.0E+07

2.0E+07

3.0E+07

0.0E+00 1.0E+07 2.0E+07 3.0E+07

Incident intensity (cps)

Mea

sure

d in

tens

ity (c

ps)

PIXcel detectorIdeal line


PIXcel Detector Versus X’Celerator Detector

• For scanning applications only, a PIXcel collects similar data as an X’Celerator

• It is up to 150 % faster

• It has the smallest channel width

• Possibilities for static measurements

• Possibilities for high dynamic range point detector measurements

• Maintenance-free detector (even no cooling fan needed)


PIXcel Applications: Static Measurements

• PIXcel offers static measurements– Possible to take snapshots with a time resolution of

only few seconds

• Useful for several applications– Non-ambient measurements (phase transitions)– Also for nano-materials

• Use of special interface that allows to put the detector closer to the sample


2D X-ray diffractionIn a 2D 2theta scan the 2Ddetector intercepts a number of diffraction cones resulting in Debye rings at different 2thetapositions


Theory of XRDwebsite.ppt - Prolab Systems Jeddah... · Theory of XRD The principles behind X-ray...

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