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
Transcript
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.
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
• 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.
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
