XRDpresentation

8/8/2019 XRDpresentation

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X-Ray Diffraction(XRD)

Ulrike TroitzschDepartment of Earth and Marine Sciences Australian National University

For teaching purposes ONLY (ANU 2007)


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W hat is X-ray diffraction?

Scattering phenomenon, X-rays passingthrough crystalAtool for the characterisation of solid materials

based on their crystal structure

Used byEarth ScientistsChemistsPhysicists

Material Scientists ArchaeologistsBiologists

Rosalind E. Franklin 1952


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XRD complementsother analytical methods

Visual(colour, streak, cleavage, symmetry )Need large crystals! cm

Optical microscopy(colour, birefringence,pleochroism )Need large crystals! m to mm

SEM(composition: wt.% SiO2, CaO )W hat about polymorphs? (Calcite, Aragonite = CaCO3)

Need large crystals!> 3 mXRF(composition: wt.% SiO2, CaO )W hat about polymorphs? (Calcite, Aragonite = CaCO3)

W hat is X-ray diffraction?


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H istory

Discovery of X-raysby W . C. Rntgen in 1895o X- ray radiography (relative absorption of X-rays is

function of average atomic number and density of matter)Max von Laue in 1912: X-rays have dual character of

particle and wave [Nobel prize 1914 for his discovery of the diffraction of X-rays by crystals]

o X- ray crystallography (interaction of X-rays with crystal structures)Single crystal or powder XRD!

L. Bragg 1913, analysed KCl and NaCl with X-raycrystallography and developed B raggs Law [Nobel Prize1915]Technological improvements (last 40 years)

o Computers (20 atom structure took 1-2 years, now 200 atoms canbe refined in 1-2 days)

o X- ray spectrometry (characteristic X-rays from each element)SEM, XRF


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W hat are X-rays?Beams of electromagnetic radiationo Short wavelength, high energy

W ave (sinusoidal, oscillatingelectric fieldwith, atright angles to it, a magnetic field)wavelength frequency Particle (photon)Photon energy E E = h(h is Plancks constant: 6.625 x 10-34 Js)

In teractswith

electro n s!


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Properties of a wave

W ave = c / (c=300.000 km/s)


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Electromagneticradiation

(n gstrm) is non-SI unit of lengthX-rays: 10-8 to 10-11 m1 = 10-10 m= 0.1 to 100

0.1 nm dimension of atoms, bonds, unit-cells


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H ow are X-raysgenerated?

1.Radioactive materialsundergo decay (too manynuclear particles or too highneutron/proton ratio)

1532P -> 1632S + X-ray

2.Machines (acceleratedparticles hit target matter)

o X-ray tube (accelerateselectrons which interact withelectrons of target)

o Particle accelerator

e -


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X-ray tube

Tu n gste n Filame n t

Target (Co,

Cu)

Electro nb eam

1. W filament isheated, electronsboil off

2. Electrons areaccelerated inelectric field

3. Electrons interactwith target (anode),producing X-rays

X- rays


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Typical X-ray spectrum

Continuousradiation

Spikes


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Two types of X-radiation are produced:

1. Bremsstrahlung (braking radiation, white radiation),produces a continuous spectrum of X-raywavelengths


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Two types of X-radiation are produced:

2. Characteristic Radiation (X-rays of distinctwavelengths, unique for each element)

1. Incoming electronknocks inner shellelectron out of its place

2. Empty site is filled by anelectron from a higher shell

3. The difference in binding

energy between inner and outer shell electronsis released as X-ray of characteristic wavelength


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Typical X-ray spectrum

Continuous radiation= Bremsstrahlung

Spikes =Characteristic radiation

Characteristic radiatio n is used i n XRD , whichrequires monoc hr omatic r adiation(eg. CuK = 1.5418 )


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Interaction of X-rays with crystal structures

Unit-cell of NaCl

ClNa

Crystal structure :three-dimensional,periodicarrangementof atoms in space.

Many different layers of atoms exist in a crystal structure.Each set of layers has a distinct interplanar distance (d -spaci n g) .


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Interaction of X-rays with crystal structures

X-rays (electromagnetic wave) interact with theelectrons of the atoms in the crystal

Cohere n t Scatter : elastic collision between aphoton (X-ray) and and electron (in crystal)

o outgoing photons (X-ray) have samewavelength, frequency and energy asincoming photons [XRD!]

In cohere n t Scatter (= Compton scatter):inelastic collision between photon and electron- outgoing photons have lower energy


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Interaction of X-rays with a scattering center

Every electron/atom in structure acts as ascattering center, and is a source of sphericalwaves of the same wavelength and frequency as

the incoming wave.

Incomingwave

+

+

-

-

In terfere n ce


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Positive NegativeInterference Interference

Crests and troughs add up andform a wave with twice the

amplitude.

Crests and troughs are offsetand cancel each other out.

This happens to most X-rays scattered in crystalsdue to the large number of scattering centers ...


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X-rays passing through a crystal lattice

X- raysout of phase!


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DiffractionHowever : There is an exception, allowingsomeX-rays to experience positive (or constructive)interference in crystals. This is calleddiff r action .

W hen a periodic array of objects each scatter radiation cohere n tly , the concerted co n structivein terfere n ce at specific a n gles is calleddiff r action .

Diffraction in crystalline materials is best describedwith

Braggs Law: n = 2 dhkl sin


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Braggs LawX-

raysin phase!

dhk l

For positive interference to occur, the path -differe n cemust be equal to one wavelength ( or multiplewavelengths (n .

n = 2 dhkl sin

hkl


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The X-ray diffractometer

Powder diffractometer with Bragg-Brentano geometry. Analyst controls (choice of target in X-ray tube)

(positions of X-ray tube/sample/detector

n = 2 dsin


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SampleW e are choosing incoming angle = outgoing angle.Therefore only diffraction from atomic planes in the crystal structurethat are parallel to the flat sample surface are detected

muscovite

(001)

For example, if we analysed this singlemuscovite crystal with XRD, lying flat on thesample holder with its 001 plane, only (001)planes would diffract.

H owever, we want ALL crystallographic planesto contribute to the XRD pattern.

sample

All samples need to be ground up very finely(ideally 1-10 m grain size), and the grainsoriented randomly in the sample holder.

Powder X-ray Diffraction


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Typical XRD scan

B ackgrou n dPeaks (at certain ang le and with certain i nt e ns i ty ) resulting frompositive interference of X-rays with crystal structure of one or more minerals

H ow do we know which minerals caused the peaks?

B ackgrou nd


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Typical XRD scan

32 1

4

5

6

7

8

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PeakNo

2 angle AbsoluteIntensity

RelativeIntensity

d spacing

12349

20.32 20.66

21.07 28.12

32.88

32 counts40 counts

173 counts192 counts

590 counts

5 %7 %

29 %32 %

100 %

= 2 d sin sin = d

X-ray wavelengthused:CoK = 1.7889

5.07 4.98

4.89 3.68

3.16


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ICDD (International Centre for Diffraction Data)publishes the datasets called P D F (Powder Diffraction

File)

Compare with the d-spacings and relative intensities of your sample.


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ICDD (International Centre for Diffraction Data)publishes the datasets called P D F (Powder Diffraction

File)

Compare with the d-spacings of the strongest peaks in your sample.


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Mineral Identification

Baddeleyite ZrO2H ematite Fe2O3Pseudobrookite Fe2TiO5Rutile TiO2

The XRD pattern of a mineral is like its fingerprint


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Mineral Quantification

Baddeleyite 40 wt.%H ematite 30 wt.%Pseudobrookite 25 wt.%Rutile5 wt.%

Sample A

Sample BBaddeleyite 20 wt.%H ematite 2 wt.%Pseudobrookite 18 wt.%Rutile60 wt.%

I mpo r tant : The intensity of XRD reflections dependsn ot o n ly on theabundance of a mineral in the sample, but on elemental composition

(atomic scattering factors), hkl , grain size, crystal structure strain


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The lower the symmetry, the more complex the diffraction pattern

Triclinic: a b c,

Cubic: a=b=c, = =


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Order of reflection

n = 2 dhkl sinn : Order of ReflectionMultiply n withhkl , for example:hkl Plane 100 produces reflections 100 (1st order, n=1)200 (2nd order, n=2)300 (3rd order, n=3) etc.

= 2 d/n sinReflections are produced by plane dhkl andfictitious planes dhkl /2, dhkl /3, etc

100200

300 400

2theta


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Systematic absences or extinctionsRecap:1. Every plane with its characteristic d-spacing can diffract at

a specific angle (Braggs Law)2. A single plane can cause several reflections (n=1, 2, 3,)H owever, not all reflections of one plane are necessarilypresent due to systematic a b se n ces caused by

Centering of the lattice (I, F, A )Screw axesGlide planes

n = 2 dhkl sin changes ton = 2 (dhkl/2) sin or 2n = 2 dhkl sin

Only even order reflections are present! Eg. Plane 100: reflections 200, 400,


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Relationship between d spacing and unit celldimensions

peak positions > d-spacing > unit celldimensions

(providedhkl is known)

cubic systemtetragonalorthorhombic(after that it gets reasonably complicated )

n = 2 dhkl sin


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Effect of solid solution: eg. Calcite

CalciteCaCO3

Mg-rich CalciteMg0.064Ca0.936CO3 Ionic radii:

(6-fold coordination)

Ca2+ 1.00 Mg2+ 0.72

Same crystal structure, different cation sizes change in d-spacing


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Effect of strain on peak shapeFor example: annealedbrass

H ighstrain

Lowstrain


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Effect of grain size on peak shape

1 m

Sample: 3minerals

For g r a i n s ize s less t han ~100 m:

The larger the grain size, the sharper thepeako eg. clay minerals are typically very fine

grained, their peaks small and broadGrains


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W hat determines intensity of a peak I hkl ?Atomic scattering factor f : the ability of an

atom (or ion) to scatter X-rayso Depends on number of electrons, ie atomic

number Light elements scatter little, heavy elements scatter a lot.

o Depends on angle o Look up in tablesAtom positionsin unit cell (x,y,z coord.)

hkl All combined inStructure factor F (sum over all atoms)

If enough reflections are available, one can use the intensities of the peaks

to determine the position of every atom in the unit cell, their thermal motionetc. (Rietfeld refinement)

(Among other things )


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Information in a diffraction pattern

Peak positio n s give unit cell size andshapeSystematic a b se n ces give type of unitcell and space group informationPeak i n te n sities tell you about

o the electron density inside the unit cell, i.e.where the atoms are located

o the abundance of a mineral in a mineralmixturePeak shapes a n d widths tell youabout any deviation from a perfectcrystal; crystallite size (

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