X-ray diffraction Content• Brief history and introduction• Applications of x-ray (general)• X-ray diffraction and basic principle• Instrumentation/components • Bragg’s Equation• Basic of crystallography/Miller indices• XRD pattern and FWHM• Phase identification• Sample preparation• Application of PXRD• Advantages/disadvantages• PXRD Characterisation for Nanomaterials: nanoparticles, carbon

nanostructures, 2D nanolayered structure, 3D AC, the collapse of 2D layered structure

• Summary

Anna Bertha Röntgen Wilhelm Conrad Röntgen

In 1895 Röntgen discovers X-rays 1901: The First Nobel Prize in Physics

History of X-rays

The discovery of the diffraction of X-rays by crystals “Diffraction pattern”

Max von Laue1914: The Nobel prize for physics

W. H. Bragg and his son W. L. Bragg and the diffraction of x-rays by crystals.

1915: The Nobel prize for physics

The analysis of crystal structure by means of X-rays

Electromagnetic waves (EM)E = hc ll = wavelength

(nm)

1/l = wavenumbers (cm-1)

What is X-ray DiffractionProperties and generation of

X-rayBragg’s LawBasics of CrystallographyXRD PatternPowder DiffractionApplications of XRD

1. Powder x-ray diffraction (PXRD)2. Small angle x-ray 3. Single crystal X-ray 4. Protein x-ray5. X-ray imaging –

X-ray and X-ray Diffraction

POWDER X-RAY DIFFRACTION (PXRD)• Primarily used for phase identification of a crystalline material • Provide information on unit cell dimensions

Basic Principles • Crystalline substances act as three-dimensional diffraction

gratings for X-ray wavelengths similar to the spacing of planes in a crystal lattice (Max von Laue, 1912).

• Based on constructive interference of monochromatic X-rays and a crystalline sample.

• The interaction of the incident rays with the sample produces constructive interference (and a diffracted ray) when conditions satisfy 

Bragg’s law: nλ=2d sin θ

X-ray Tube

Sample stage

Detector

An X-ray Diffractometer

Production of X-raysCross section of sealed-off filament X-ray tube

X-rays are produced whenever high-speed electrons collide with a metal target.A source of electrons – hot W filament, a high accelerating voltage (30-50kV) between the cathode (W) and the anode, which is a water-cooled block of Cu or Mo containing desired target metal.

Characteristic X-ray Lines

Spectrum of Mo at 35kV

K and K2 will causeExtra peaks in XRD pattern, but can be eliminated by adding filters.

is the mass absorption coefficient of Zr.

-----

l=2dsin

Characteristic X-ray Lines

Spectrum of Mo at 35kV

K and K2 will causeExtra peaks in XRD pattern, but can be eliminated by adding filters.

is the mass absorption coefficient of Zr.

-----

l=2dsin

What Is Diffraction?A wave interacts with

A single particle

A crystalline material

The part ic le scatters the incident beam uniformly in all directions.

The scattered beam may add together in a few directions and reinforce each other to give diffracted beams.

Constructive and Destructive Interference of Waves

Constructive Interference Destructive InterferenceIn Phase Out Phase

Constructive interference occurs only when the path difference of the scattered wave from consecutive layers of atoms is a multiple of the wavelength of the x-ray.

Bragg’s Law and X-ray DiffractionHow waves reveal the atomic structure of crystals

nl = 2dsin() n-integer Diffraction occurs only when Bragg’s Law is satisfiedCondition for constructive interference (X-rays 1 & 2) from planes with spacing d

Deriving Bragg’s Law: nl = 2dsin

Constructive interferenceoccurs only when

nl = AB + BC

AB=BC

nl = 2AB

Sin=AB/d

AB=dsin

nl =2dsin

l=2dhklsinhkl

n – integer, called the order of diffraction

Basics of Crystallography

A crystal consists of a periodic arrangement of the unit cell into a lattice. The unit cell can contain a single atom or atoms in a fixed arrangement.

Crystals consist of planes of atoms that are spaced a distance d apart, but can be resolved into many atomic planes, each with a different d-spacing.

a, b and c (length) and , and (angles between a, b and c) are lattice constants or parameters which can be determined by XRD.

smallest building block

Unit cell (Å)

Lattice

CsCl

d1

d2

d3

a b

c

z [001]

y [010]

x [100] crystallographic axes

Single crystal

System Axial lengths Unit cell and angles

Cubic a=b=c===90o

a

a

cTetragonal

a=bc===90o

ba

cOrthorhombic

abc===90o

a

Rhombohedrala=b=c==90o

Hexagonala=bc==90o =120o

c

ab

Monoclinicabc==90o

b a

cTriclinic

abc90o

c

Seven crystal Systems

a

Miller Indices - hkl

(010)

Miller indices-the reciprocals of thefractional intercepts which the planemakes with crystallographic axes

Axial length 4Å 8Å 3ÅIntercept lengths 1Å 4Å 3ÅFractional intercepts ¼ ½ 1Miller indices 4 2 1

h k l

4Å 8Å 3Å 8Å /4 1 /3 0 1 0 h k l

a b ca b c

Miller indices form a notation system in crystallography for planes in crystal lattices.

X-ray Diffraction Pattern

2

I Simple Cubic

l=2dhklsinhklBragg’s Law: l(Cu K)=1.5418Å

BaTiO3 at T>130oC

dhkl

20o 40o 60o

(hkl)

X-ray Diffraction Pattern

l(Cu K)=1.5418Å A multiphase sample. This sample was run more slowly than the others to get higher intensity, which makes it easier to effectively identify many of the peaks. Major phases include quartz, halite, clinochlore and either illite or muscovite.

XRD PatternSignificance of Peak Shape in XRD

1.Peak position

2.Peak width

3.Peak intensity

http://www.youtube.com/watch?v=MU2jpHg2vX8 XRD peak analysis

I

2

Peak Width - Full Width at Half Maximum(FWHM)

1. Particle orgrain size

2. Residualstrain

Determine

XRD patterns from other states of matter

Constructive interferenceStructural periodicity

DiffractionSharp maxima

Crystal

Liquid or amorphous solidLack of periodicity One or twoShort range order broad maxima

Monatomic gas

Atoms are arranged Scattering Iperfectly at random decreases with

2

Powder X-Ray Diffraction (most widely used for polycrystals)

A powder sample is in fact an assemblage of small crystallites, oriented at random in space.

2 2

Polycrystallinesample

Powdersample

crystallite

d1

d3

d2

d1d2 d3

Detection of Diffracted X-ray by A Diffractometer

§ x-ray detectors (e.g. Geiger counters) is used instead of the film to record both the position and intensity of the x-ray peaks

§ The sample holder and the x-ray detector are mechanically linked

§ If the sample holder turns , the detector turns 2, so that the detector is always ready to detect the Bragg diffracted x-ray

X-raytube

X-raydetector

Sampleholder

2

Phase Identification(One of the most important uses of XRD)

• Obtain XRD pattern• Measure d-spacings• Obtain integrated intensities• Compare data with known standards in

the JCPDS file, which are for random orientations (there are more than 50,000 JCPDS cards of inorganic materials).

JCPDS Card

1.File number 2.Three strongest lines3.Lowest-angle line 4.Chemical formula and name 5.Data on dif-fraction method used 6.Crystallographic data 7.Optical and otherdata 8.Data on specimen 9.Data on diffraction pattern.

Quality of data

Sample Preparation

Powders: 0.1m < particle size <40 m Peak broadening less diffraction occurring

http://www.youtube.com/watch?v=lwV5WCBh9a0 at~2:00-5:10

Peak broadening less diffraction occurring

Sample Preparation

Powders: 0.1m < particle size <40 m

http://www.youtube.com/watch?v=lwV5WCBh9a0 at~2:00-5:10

Sample Preparation

http://www.youtube.com/watch?v=lwV5WCBh9a0 at~2:00-5:10

Bulks: smooth surface after polishing, specimens should be thermal annealed to eliminate any surface deformation induced during polishing.

X-ray Tube

Sample stage

Detector

An X-ray Diffractometer

Advantages Powerful and rapid (< 20 min) technique for identification of an unknown inorganic

materials

In most cases, it provides an unambiguous mineral determination

Minimal sample preparation is required

XRD units are widely available

Data interpretation is relatively straight forwardDisadvantages Homogeneous and single phase material is the best for identification of an unknown

Must have access to a standard reference file of inorganic compounds (d-spacings, hkls)

Requires tenths of a gram of material which must be ground into a powder

For mixed materials, detection limit is ~ 3% of sample

For unit cell determinations, indexing of patterns for non-isometric crystal systems is complicated

Peak overlay may occur and worsens for high angle 'reflections'

PXRD Characterisation for Nanomaterials1. Pure phase determination

2. Confirmation of the present of host-guest phases

3. Host-guest interactions; intercalation, exfoliations, etc.4. Nanostructures formation: eg. 2D-layered structure,

nanoparticles, etc.

Applications of XRD(a nondestructive technique)

• To identify crystalline phases• To determine structural properties: Lattice parameters (10-4Å), strain, grain size, phase composition, preferred orientation, order-disorder

transformation, thermal expansion, etc.• To measure thickness of thin films and multilayers• To determine atomic arrangement• To image and characterize defects

Detection limits: ~3% in a two phase mixture ~0.1% with synchrotron radiation.

https://www.youtube.com/watch?v=CpJZfeJ4poE phased contrast x-ray imaging

1) 0D nanomaterialChitosan nanoparticles

CHITOSAN HEXACONAZOLEDAZOMET

chitosan-hexaconazole NP chitosan-dazomet NP chitosan-hexazonazole/dazomet NP

F a r h a t u n e t a l . , P I 2018703220

STRUCTURAL CHARACTERIZATION (FTIR & XRD)

Powder XRD patterns of CEN, free hexaconazole, free dazomet in CHEN (A), CDEN (B) and CHDEN (C)

What is X-ray Diffraction

Properties and generation of X-ray

Bragg’s Law

Basics of Crystallography

XRD Pattern

Powder Diffraction

Applications of XRD

2) XRD pattern of graphite (3D), GO (2D), rGO (2D) and MWCNTs (1D)

Types of materials a) Amorphous b) Crystalline

Nanolayered materials

Bragg’s law nl = 2d sin

3. 2D NANOLAYERED STRUCTURE

Characterisation of 2D nanolayered materials using PXRD technique (clay-polymer nanocomposite)

Characterisation of 2D nanolayered materials using PXRD technique (clay-polymer nanocomposite)

Mater. Res. Bull.

SPATIAL ORIENTATION OF THE DRUG MOLECULES IN THE LAYERED INORGANIC INTERLAMELLAE

Depends on a) The size of the guest (ChemOffice)b) Spatial orientation of the guest (XRD

data and (a))

1) Project 1: LDH-based (2D nanomaterials)

Agronanofungicides: LDH-fungicide nanocomposites

FUNGICIDE(Guest)

LDH(host)

hexaconazole

Zn/Al-LDH-hexaconazole nanocomposites (XRD)

hexaconazole

LDH

Bragg’s lawnl = 2d sin

2D LAYERED STRUCTURE

n d nxd/Å1 29.45 29.452 14.83 29.663 9.65 28.954 7.30 29.205 5.84 29.206 4.96 29.767 4.25 29.758 3.67 29.36

Avg 29.42

12 3 4 5 6 7 8

Spatial orientation of hexaconazole and sodium dodecylbenzenesulfonate in the intergallery of Zn/Al-LDH

hexaconazole

sodium dodecylbenzenesulfonate

HZALDH nanocomposite

Palm Kernel Shell Activated Carbon as an Inorganic Framework for Shape-Stabilized Phase Change Material, Nanomaterials 2018, 8, 689; doi:10.3390/nano8090689

4. 3D NANOMATERIAL - AMOURPHOUS

5. 3D Physicochemical properties of hydroxyapatite/montmorillonite nanocomposite prepared by powder sintering, Results in Physics, Volume 15, December 2019, 102540

What is X-ray DiffractionProperties and generation of X-ray

Bragg’s LawBasics of Crystallography

Application of XRD Pattern(a) Zn–Al–LDH before thermal treatment and Zn–Al–LDH at calcined temperature range of 50, 100 and 150 ℃, with (*) ZnO phase. (b) Zn–Al–LDH at calcined temperatures of 200, 250 and 300 ℃. The small black square represents the LDH

phase after calcination above 150 ℃.

Take home keywords• XRD, PXRD, diffraction, constructive interference • Bragg’s Equation (nl=2dsin )• Amorphous/Crystalline/Miller indices/polycrystals• XRD pattern and FWHM• Phase identification, JCPDS, ICDD• X-ray diffractometer/goniometer • Sample preparation• Application of PXRD• Advantages/disadvantages• Examples of PXRD characterisation for nanomaterials