introduction to powder diffraction/practical data collection · 2 [email protected]...

$: Introduction to Powder Diffraction/Practical Data Collection · 2 Ivana.radosavljevic@durham.ac.uk PCG workshop January 2007 10 15 20 25 30 35 40 45 50 55 60 45,000 40,000 35,000$
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Durham

ChemistryDepartment

DurhamUniversity

Introduction to Powder Diffraction/Practical Data

CollectionDr Ivana Evans

Durham, January 2007

[email protected] www.durham.ac.uk/ivana.radosavljevic PCG workshop January 2007

Outline

• Information in a powder pattern• What is diffraction• How to collect (laboratory) data• Lab vs synchrotron vs neutron• What is Rietveld refinement

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Session 2 – Introduction

2θ - degrees

Cou

nts

1. Peak positions determined by size, shape, symmetry of unit cell – internal

structure

2 9 .52 95

2. Peak Intensities determined by

where atoms sit in unit cell – internal

structure

3. Peak widths influenced by size/strain of crystallites -

microstructure.

2θ


Historical background

1895: Röntgen discovers X-rays (Nobel Prize 1901)

1912: von Laue discovers X-ray diffraction on crystals (Nobel Prize1914)

1913: Bragg & Bragg discover structure analysis by XRD, NaCl (Nobel Prize 1915)

1916: Debye & Scherrer discover powder X-ray diffraction, LiF

1963: Zachariasen solves the structure of β-Pu from PXRD by direct methods

1969: Rietveld method

1990: direct space approaches to structure solution

2000: work on 100+ atom structures, proteins

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Diffraction: physical phenomenon

Crystalline state of matter• long-range 3D orderDiffraction• scattering on periodic arraysCrystallography• 2dhklsinθ = λ• Fhkl = Σfje2πi(hxj+kyj+lzj)


Samples

2-theta

I

(a) (b)

(d)(c)

Single crystal

Four differently oriented single crystals

Polycrystalline material

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Experiment

2θ

2θ

‘…data compressed into one dimension…’


Powder diffraction can give you

Powder DiffractionPowder Diffraction

Thermal expansion

Particle sizePhase

transitions

Ionic migration

PolymorphismIn-situ

chemistry

Particle strain

Structure determination

Kinetics studies

Crystallization/amorphization

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Laboratory Configurations

(a)(b)

1

2

4

5 16

2

33

2θθ

Reflection geometry Transmission geometry


Laboratory Bragg Brentano

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Laboratory Bragg Brentano

Tube

Divergence Slits/Sollers

Sample

AntiscatterSlits/Sollers

ReceivingSlit

Mono-chromator

Detector


PSD for Speed

7


Capillary Transmission Mode

12

3


Sample Preparation

• Dependent on experiment• Bulk holders• Single crystal Si wafers for low background• See examples on guided tour

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Data Collection

• Machine dependent• Make sure statistics are good enough for information you

need• Consider spending longer counting at higher 2θ to

compensate for intensity fall off in diffraction• Make sure you have sufficient points to define a peak (e.g.

10 across fwhm) – can rebin later but can’t create extra points

• Consider optical set up and whether it’s suited for your sample (see later tutorials)

• First guess on a “normal” lab instrument– 5-90º 0.02º step, 1 second per step ~ 1 hr


Common Crimes – Sample Prep

• Surface roughness• Intensities affected as f(2θ)• “Negative temperature factors”

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• Sample height

2θ offset = zero - 2*∆height*cos(θ)/radius;



• Infinite thickness• e.g. organic sample sprinkled on substrate

may not be infinitely thick• Intensities affected as f(2θ)

10


Common Problems – Sample Prep

• Preferred orientation• e.g. platelets with c-axis perpendicular to

sheets will give strong 00l reflections• Might be able to correct


Common Problems – Sample Prep

• Texture• Much harder to correct• Certain unrelated hkl reflections wrong

intensity

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Avoiding Preferred Orientation

• Capillary measurements• Flat plate reflection & transmission• Side/back mounting• Spray drying• Sieving• Neutron diffraction

http://www.ccp14.ac.uk/solution/powdermounts.htm


Common Crimes – Data Collection

• Beam overspill• Intensities affected as f(2θ)• High background at low 2θ due to sample holder

High 2θ Low 2θ

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Common Crimes – Data Analysis

• LP Factors – don’t ignore the geometry of the instrument you’re using

• Different configurations require different corrections

• e.g. Bragg-Brentano, incident monochromator

θθθθ

cossin2cos2cos1

2

22monoLP +

=


Common Crimes – Data Analysis

• Think about errors!• Poisson statistics sig(I)=I0.5 normally assumed• No longer true if you scale data • No longer true for psd’s where some parts of

pattern measured for longer• Use 2θ, I, sig(I) format – error propagation!

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Synchrotron vs Lab

• Pros– Far higher intensities– Choice of wavelength– Much sharper peak widths– Grenoble/Didcot/Japan/etc

• Cons– Sample damage– Must apply for beam time– Limited access– Grenoble/Didcot/Japan/etc


Neutrons vs X-rays

• Pros– Distinguish e.g. Mn/Fe– Information on O in metal oxides– Penetrating so can use complex sample environment– Grenoble/Didcot/Japan/etc

• Cons– Flux generally much weaker than X-rays– Large samples– Must apply for beam time– Limited access– Grenoble/Didcot/Japan/etc

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Refinement: pre Rietveld

Integrated intensity refinement• State of the art until late 60’s early

70’s

• Poor observation-to-parameter ratio

• Problems due to overlap

• Limited applicability

• Suitable for high symmetry systems

• Used extensively for high T nonstoichiometric phases

12 observations

4 variables• Scale factor• Uiso(Fe)• Uiso(O)• Occ(O)

Cheetham et al., 1971.


Refinement: the Rietveld method

Rietveld, 1969: diffraction pattern analysis by a curve fitting procedure

First proposed for constant wavelength neutron data

The difference between the observed and calculated profiles is minimized

• typical Rietveld plot:

Parameters refined:

• structural parameters (atomic positions,displacement parameters, occupancies,unit cell parameters)

• instrumental parameters (zero point, background parameters)

• peak shape function parameters

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Conclusions

• Overview/intro to diffraction/Rietveld• Many specific details will be covered in later

lectures/tutorials• Tour of instruments if you want

introduction to powder diffraction/practical data collection · 2 [email protected]...

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