X-ray diffraction. Equipment Bruker D8 Analytical X-ray Systems.

$: X-ray diffraction. Equipment Bruker D8 Analytical X-ray Systems.$
X-ray diffractionX-ray diffraction

EquipmentEquipment

Bruker D8 Analytical X-ray Systems

X-ray beam sourceX-ray beam source Bruker D8 ADVANCE uses an x-ray tube with a Cu anode as the Bruker D8 ADVANCE uses an x-ray tube with a Cu anode as the

primary x-ray beam source. In this component x-rays are generated primary x-ray beam source. In this component x-rays are generated when a focused electron beam accelerated across a high voltage when a focused electron beam accelerated across a high voltage field bombards a stationary solid Cu target. As electrons collide with field bombards a stationary solid Cu target. As electrons collide with atoms in the target and slow down, a continuous spectrum of x-rays atoms in the target and slow down, a continuous spectrum of x-rays is emitted, which is termed Bremsstrahlung radiation. is emitted, which is termed Bremsstrahlung radiation.

The high energy electrons also eject inner shell electrons in atoms The high energy electrons also eject inner shell electrons in atoms through the ionization process. When a free electron fills the shell, through the ionization process. When a free electron fills the shell, an x-ray photon with energy characteristic of the target material is an x-ray photon with energy characteristic of the target material is emitted. emitted.

Common targets used in x-ray tubes include Cu and Mo, that emit 8 Common targets used in x-ray tubes include Cu and Mo, that emit 8 keV and 14 keV x-rays with corresponding wavelengths of 1.54 Å keV and 14 keV x-rays with corresponding wavelengths of 1.54 Å and 0.8 Å, respectively. and 0.8 Å, respectively.

Wavelengths for X-Ray sourceWavelengths for X-Ray sourceCopper

Anodes

Bearden

(1967)

Holzer et al.

(1997)

Cobalt

Anodes

Bearden

(1967)

Holzer et al.

(1997)

Cu K1 1.54056Å 1.540598 Å Co K1 1.788965Å 1.789010 Å

Cu K2 1.54439Å 1.544426 Å Co K2 1.792850Å 1.792900 Å

Cu K 1.39220Å 1.392250 Å Co K 1.62079Å 1.620830 Å

Molybdenum

Anodes

Chromium

Anodes

Mo K1 0.709300Å 0.709319 Å Cr K1 2.28970Å 2.289760 Å

Mo K2 0.713590Å 0.713609 Å Cr K2 2.293606Å 2.293663 Å

Mo K 0.632288Å 0.632305 Å Cr K 2.08487Å 2.084920 Å

Often quoted values from Cullity (1956) and Bearden, Often quoted values from Cullity (1956) and Bearden, Rev. Mod. Rev. Mod. Phys. Phys. 3939 (1967) are incorrect. (1967) are incorrect.

Values from Bearden (1967) are reprinted in Values from Bearden (1967) are reprinted in international Tables for X-international Tables for X-Ray CrystallographyRay Crystallography and most XRD textbooks. and most XRD textbooks.

Most recent values are from HMost recent values are from Höölzer et al. lzer et al. Phys. Rev. APhys. Rev. A 5656 (1997) (1997)

BRAGG’s EQUATION

d

dSin

The path difference between ray 1 and ray 2 = 2d Sin

For constructive interference: n = 2d Sin

Ray 1

Ray 2

Deviation = 2

NanoLab/NSF NUE/BummNanoLab/NSF NUE/Bumm

θθ - 2 - 2θθ Scan ScanThe The θθ - 2 - 2θθ scan maintains these angles with the scan maintains these angles with the sample, detector and X-ray sourcesample, detector and X-ray source

Normal to surface

Only planes of atoms that share this normal will be seen in the θ - 2θ Scan

Powder diffraction data can be collected using either transmission or Powder diffraction data can be collected using either transmission or reflection geometry, as shown below. Because the particles in the reflection geometry, as shown below. Because the particles in the powder sample are randomly oriented, these two methods will yield powder sample are randomly oriented, these two methods will yield the same datathe same data

Reflection Diffraction

Occurs from surface Occurs throughout the bulk

Takes place at any angle Takes place only at Bragg angles

~100 % of the intensity may be reflected

Small fraction of intensity is diffracted

Heat

Incident X-rays

SPECIMEN

Transmitted beam

Fluorescent X-raysElectrons

Compton recoil PhotoelectronsScattered X-rays

CoherentFrom bound charges

Incoherent (Compton modified)From loosely bound charges

X-rays can also be refracted (refractive index slightly less than 1) and reflected (at very small angles) Refraction of X-rays is neglected for now.

How does it work?How does it work?

In powder XRD method, a sample is ground to a powder In powder XRD method, a sample is ground to a powder ((±10µm) in order to expose all possible orientations to the X-ray ±10µm) in order to expose all possible orientations to the X-ray beam of the crystal values of beam of the crystal values of , , dd and and for diffraction are for diffraction are achieved as follows:achieved as follows:

1. 1. is kept constant by using filtered X- radiation that is is kept constant by using filtered X- radiation that is approximately monochromatic. approximately monochromatic. 2. d 2. d may have value consistent with the crystal structuremay have value consistent with the crystal structure3. 3. is the variable parameters, in terms of which the is the variable parameters, in terms of which the

diffraction peaks are measured.diffraction peaks are measured.

How does XRD Works???How does XRD Works??? Every crystalline substance Every crystalline substance

produce its own XRD pattern, produce its own XRD pattern, which because it is dependent on which because it is dependent on the internal structure, is the internal structure, is characteristic of that substance.characteristic of that substance.

The XRD pattern is often spoken The XRD pattern is often spoken as the “as the “FINGERPRINTFINGERPRINT” of a ” of a mineral or a crystalline substance, mineral or a crystalline substance, because it differs from pattern of because it differs from pattern of every other mineral or crystalline every other mineral or crystalline substances.substances.

Basic Component Of XRD MachineBasic Component Of XRD Machine

Therefore any XRD machine will consist of three basic component.

• Monochromatic X-ray source ()

• Sample-holder (goniometer).

• Data collector- such as film, strip chart or magnetic medium/storage.

By varying the angle , the Bragg’s Law conditions are satisfied by different d-spacing in polycrystalline materials. Plotting the angular positions and intensities of the resultant diffraction peaks produces a pattern which is characterised of the sample

X-ray Components

A typical X-ray instrument is built by combining high performance components such as X-ray tubes, X-ray optics, X-ray detectors, sample handling device etc. to meet the analytical requirements. A consequent modular design is the key to configure the best instrumentation. .

Diffraction Pattern Collected Diffraction Pattern Collected Where A Ni Filter Is Used Where A Ni Filter Is Used

To Remove K To Remove Kββ

K

02.6hchkeVE

Typical experimental data from Bruker XRDTypical experimental data from Bruker XRD

2-theta intensitas

20 405

20.05001 357

20.10002 381

20.15002 371

20.20003 376

20.25004 356

20.30005 370

20.35006 395

20.40006 373

20.45007 335

20.50008 397

I

2

TiO2

101 Anatase

110 Rutile

101 Anatase

110 Rutile

Examples of 3D Reciprocal Lattices weighed in with scattering power (|F|2)

Figures NOT to Scale

000

100

111

001

101

011

010

110

SC

Lattice = SC

Reciprocal Crystal = SC

No missing reflections


000

200

222

002

101

022

020110

BCC

Lattice = BCC

Reciprocal Crystal = FCC

220

011

202

100 missing reflection (F = 0)

22 4 fF

Weighing factor for each point “motif”


000200

222

002022

020

FCC

Lattice = FCC

Reciprocal Crystal = BCC

220

111

202

100 missing reflection (F = 0)110 missing reflection (F = 0)

22 16 fF

Weighing factor for each point “motif”

Sample preparationSample preparation

•

Make a mine powderMake a mine powder

Sample holderSample holder

Side Drift MountSide Drift Mount

Designed to reduce preferred orientation – great for clay samples, (and others with peaks at low 2-theta angles)

Film, pellets, crystalsFilm, pellets, crystalsmineral specimensmineral specimens

Sample holderSample holder

Specimen Holders for X-ray DiffractionSpecimen Holders for X-ray Diffraction

Match The Sample/Measurement Match The Sample/Measurement Conditions With The Diffraction PatternConditions With The Diffraction Pattern

1

2

3

Misinterpreting X-Ray Misinterpreting X-Ray Diffraction ResultsDiffraction Results

Why are peaks missing? Why are peaks missing?

111

200

220

311

222

•The sample is made from Morton’s Salt

•JCPDF# 01-0994 is supposed to fit it (Sodium Chloride Halite)

JCPDF# 01-0994

Rock Salt

It’s a single crystalIt’s a single crystal

2

At 27.42 °2, Bragg’s law fulfilled for the (111) planes, producing a diffraction peak.

The (200) planes would diffract at 31.82 °2; however, they are not properly aligned to produce a diffraction peak

The (222) planes are parallel to the (111) planes.

111

200

220

311

222

A random polycrystalline sample that contains thousands of A random polycrystalline sample that contains thousands of crystallites should exhibit all possible diffraction peakscrystallites should exhibit all possible diffraction peaks

2 2 2

• For every set of planes, there will be a small percentage of crystallites that are properly oriented to diffract (the plane perpendicular bisects the incident and diffracted beams).

• Basic assumptions of powder diffraction are that for every set of planes there is an equal number of crystallites that will diffract and that there is a statistically relevant number of crystallites, not just one or two.

111

200

220

311

222

66 67 68 69 70 71 72 73 74

2 (deg.)

Inte

ns

ity

(a

.u.)

Which of these diffraction patterns comesWhich of these diffraction patterns comes from a nanocrystalline material? from a nanocrystalline material?

These diffraction patterns were produced from the These diffraction patterns were produced from the exact same exact same samplesample

The apparent peak broadening is due solely to the instrumentationThe apparent peak broadening is due solely to the instrumentation 0.00150.0015° slits vs. 1° slits optical cofigurations° slits vs. 1° slits optical cofigurations Scan speed ( stepsize)Scan speed ( stepsize)

Hint: Why are the intensities different?

0.0015o

1o

http://prism.mit.edu/xrayhttp://prism.mit.edu/xray

Crystallite Size BroadeningCrystallite Size Broadening

Peak Width B(2Peak Width B(2) varies inversely with crystallite size) varies inversely with crystallite size The constant of proportionality, K (the Scherrer constant) depends The constant of proportionality, K (the Scherrer constant) depends

on the how the width is determined, the shape of the crystal, and on the how the width is determined, the shape of the crystal, and the size distributionthe size distribution

the most common values for K are 0.94 (for FWHM of spherical the most common values for K are 0.94 (for FWHM of spherical crystals with cubic symmetry), 0.89 (for integral breadth of spherical crystals with cubic symmetry), 0.89 (for integral breadth of spherical crystals with cubic symmetry, and 1 (because 0.94 and 0.89 both crystals with cubic symmetry, and 1 (because 0.94 and 0.89 both round up to 1). round up to 1).

K actually varies from 0.62 to 2.08K actually varies from 0.62 to 2.08 For an excellent discussion of K, refer to JI Langford and AJC Wilson, For an excellent discussion of K, refer to JI Langford and AJC Wilson,

“Scherrer after sixty years: A survey and some new results in the “Scherrer after sixty years: A survey and some new results in the determination of crystallite size,” determination of crystallite size,” J. Appl. Cryst.J. Appl. Cryst. 1111 (1978) p102-113. (1978) p102-113.

Remember: Remember: Instrument contributions must be subtractedInstrument contributions must be subtracted

cos

94.02

tB Scherrer’s FormulaScherrer’s Formula

t = thickness of crystallite / crystallite sizeK = constant dependent on crystallite shape (0.89) = x-ray wavelengthB = FWHM (full width at half max) or integral breadthB = Bragg Angle

Scherrer’s FormulaScherrer’s Formula

BcosB

Kt

Scherrer’s FormulaScherrer’s Formula

What is What is BB??

BB = (2 = (2θθ High) – (2 High) – (2θθ Low) Low)

BB is the difference in is the difference in angles angles at half max

2θ high

Noise

2θ low

Peak

When to Use Scherrer’s FormulaWhen to Use Scherrer’s Formula

Crystallite size <1000 ÅCrystallite size <1000 Å Peak broadening by other factorsPeak broadening by other factors

Causes of broadeningCauses of broadening• SizeSize• StrainStrain• Instrument Instrument

If breadth consistent for each peak then assured If breadth consistent for each peak then assured broadening due to crystallite sizebroadening due to crystallite size

K depends on definition of t and K depends on definition of t and BB Within 20%-30% accuracy at best Within 20%-30% accuracy at best

Sherrer’s Formula ReferencesSherrer’s Formula ReferencesCorman, D. Scherrer’s Formula: Using XRD to Determine Average Diameter of Corman, D. Scherrer’s Formula: Using XRD to Determine Average Diameter of

Nanocrystals.Nanocrystals.

Scherrer’s ExampleScherrer’s ExampleAu Foil

98.25 (400)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

95 95.5 96 96.5 97 97.5 98 98.5 99 99.5 100 100.5 101 101.5 102

2 Theta

Co

un

ts

Scherrer’s ExampleScherrer’s Example

BBt

cos

89.0

tt = 0.89*= 0.89*λλ / ( / (BB Cos Cos θθBB)) λλ = 1.54 Ǻ= 1.54 Ǻ

= 0.89*= 0.89*1.54 1.54 Ǻ / ( 0.00174 * Cos (98.25/ 2 ) ) Ǻ / ( 0.00174 * Cos (98.25/ 2 ) ) = 1200 Ǻ= 1200 Ǻ

BB = (98.3 - 98.2)* = (98.3 - 98.2)*ππ/180 = 0.00174/180 = 0.00174

Simple Right!Simple Right!Target Metal Of K radiation (Å)

Mo 0.71

Cu 1.54

Co 1.79

Fe 1.94

Cr 2.29

46.746.846.947.047.147.247.347.447.547.647.747.847.9

2 (deg.)

Inte

nsity

(a.

u.)

46.7 46.8 46.9 47.0 47.1 47.2 47.3 47.4 47.5 47.6 47.7 47.8 47.9

2 (deg.)

Inte

nsity

(a.

u.)

Methods used to Define Peak WidthMethods used to Define Peak Width

Full Width at Half Maximum Full Width at Half Maximum (FWHM)(FWHM)

the width of the diffraction the width of the diffraction peak, in radians, at a height peak, in radians, at a height half-way between background half-way between background and the peak maximumand the peak maximum

Integral BreadthIntegral Breadth the total area under the peak the total area under the peak

divided by the peak heightdivided by the peak height the width of a rectangle having the width of a rectangle having

the same area and the same the same area and the same height as the peakheight as the peak

requires very careful evaluation requires very careful evaluation of the tails of the peak and the of the tails of the peak and the backgroundbackground

FWHM


Remember, Crystallite Size is Remember, Crystallite Size is Different than Particle SizeDifferent than Particle Size

A particle may be made up of several different A particle may be made up of several different crystallitescrystallites

Crystallite size often matches grain size, but Crystallite size often matches grain size, but there are exceptionsthere are exceptions


Anistropic Size BroadeningAnistropic Size Broadening The broadening of a single diffraction peak is the product of the The broadening of a single diffraction peak is the product of the

crystallite dimensions in the direction perpendicular to the planes crystallite dimensions in the direction perpendicular to the planes that produced the diffraction peak. that produced the diffraction peak.


Instrumental Peak ProfileInstrumental Peak Profile A large crystallite size, defect-free powder A large crystallite size, defect-free powder

specimen will still produce diffraction peaks specimen will still produce diffraction peaks with a finite widthwith a finite width

The peak widths from the instrument peak The peak widths from the instrument peak profile are a convolution of:profile are a convolution of:

X-ray Source ProfileX-ray Source Profile

• Wavelength widths of KWavelength widths of K11 and K and K22 lines lines

• Size of the X-ray sourceSize of the X-ray source

• Superposition of KSuperposition of K11 and K and K22 peaks peaks Goniometer OpticsGoniometer Optics

• Divergence and Receiving Slit widthsDivergence and Receiving Slit widths• Imperfect focusingImperfect focusing• Beam sizeBeam size• Penetration into the samplePenetration into the sample

47.0 47.2 47.4 47.6 47.8

2 (deg.)

Inte

nsity

(a.

u.)

Patterns collected from the same sample with different instruments and configurations at MIT

...)( SFsci BBBBFWHMB


What Instrument to Use?What Instrument to Use? The instrumental profile determines the upper limit of crystallite The instrumental profile determines the upper limit of crystallite

size that can be evaluatedsize that can be evaluated if if the the Instrumental peak width is much larger than the than the

broadening due to crystallite size, then we cannot accurately broadening due to crystallite size, then we cannot accurately determine crystallite sizedetermine crystallite size

For analyzing larger nanocrystallites, it is important to use the For analyzing larger nanocrystallites, it is important to use the instrument with instrument with the smallest instrumental peak width

Very small nanocrystallites produce weak signals the specimen broadeningthe specimen broadening will be significantly larger than the will be significantly larger than the

instrumental broadeninginstrumental broadening the signal:noise ratio is more important than the instrumental the signal:noise ratio is more important than the instrumental

profileprofile

Smaller Crystals Produce Broader XRD Peaks Smaller Crystals Produce Broader XRD Peaks


Comparison of Peak Widths at Comparison of Peak Widths at Crystallite SizesCrystallite Sizes

Rigaku XRPD is better for very small nanocrystallites, <80 nm (upper limit 100 nm)Rigaku XRPD is better for very small nanocrystallites, <80 nm (upper limit 100 nm) PANalytical X’Pert Pro is better for larger nanocrystallites, <150 nmPANalytical X’Pert Pro is better for larger nanocrystallites, <150 nm

Crystallite Size FWHM (deg)

100 nm 0.099

50 nm 0.182

10 nm 0.871

5 nm 1.745

Decrease Decrease crystallite sizecrystallite size

A = anatase, R = rutile, B = brokite, (B)=TiO2(B)

Wahyuningsih, S., 2009

CeOCeO22

19 nm19 nm

45 46 47 48 49 50 51 52

2 (deg.)

Inte

nsity

(a.

u.)

ZrOZrO22

46nm46nm

CexZr1-xO2

0<x<1

Polycrystalline films on Silicon Polycrystalline films on Silicon

Solid Solution InhomogeneitySolid Solution Inhomogeneity Variation in the composition of a solid solution can create a Variation in the composition of a solid solution can create a

distribution of d-spacing for a crystallographic planedistribution of d-spacing for a crystallographic plane

Why do the peaks broaden toward each other?


Many factors may contribute toMany factors may contribute to the observed peak profile the observed peak profile

Instrumental Peak ProfileInstrumental Peak Profile Crystallite SizeCrystallite Size MicrostrainMicrostrain

Non-uniform Lattice DistortionsNon-uniform Lattice Distortions FaultingFaulting DislocationsDislocations

Solid Solution InhomogeneitySolid Solution Inhomogeneity

The peak profile is a convolution of the profiles from all of The peak profile is a convolution of the profiles from all of these contributionsthese contributions

Thank you for your attending!Thank you for your attending!

Workshop & Analysis Informations:

Dr. Sayekti Wahyuningsih, M.SiDr. Yoventina Iriani, M.Si

Laboratorium MIPA Terpadu FMIPA Universitas Sebelas MaretPhone / fax : (0271) 663375

X-ray diffraction. Equipment Bruker D8 Analytical X-ray Systems.

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Transcript of X-ray diffraction. Equipment Bruker D8 Analytical X-ray Systems.