Accuracy-in-XRD.1, A. Kern © 1999 BRUKER AXS All Rights Reserved Accuracy and Precision in Powder Diffractometry A. Kern Bruker AXS GmbH Östliche Rheinbrückenstraße

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Accuracy-in-XRD.1, A. Kern© 1999 BRUKER AXS All Rights Reserved

Accuracy and Precisionin Powder Diffractometry

A. Kern

Bruker AXS GmbHÖstliche Rheinbrückenstraße 50

D-76187 Karlsruhe


Topics to be covered

Accuracy and Precision in Powder DiffractometryDefinition

Optimized Measurement and Evaluation Strategies: Early Decisions

Sample

Instrument

Data Colletion Strategies

Optimized Evaluation Procedures


Definition of Terms:“Accuracy” - “Precision”

Legend:

Z : Measurand = “true” value

A : Measurement result

AS : Accuracy

AR : Precision = standard

deviation

R

Z

|A -Z | = AA

A


Accurate Powder Diffractometry Precise or Accurate Results?

Tissue, 1996

High AccuracyHigh Precision

Low AccuracyLow Precision

Low AccuracyHigh Precision

High AccuracyLow Precision


Any diffraction experiment ca be devided in 5 parts:

Without a close consideration of each part, which must be repeated for each different experiment, one will most unlikely obtain an optimum analytical outcome

The Experiment:Overview

EarlyDecisions Sample Instrument Data

Collection Evaluation


Early Decisions: Step by Step

What is the aim of the experiment?

What accuracy and precision is necessary?

What are the sample properties?

What instrument and measurement parameters to use?

What evaluation methods and models to use?

By answering all these questions before executing any experiment on can save a whole lot of time as well as protect himself against erroneous results and frustration!


Early Decisions:General Conditions

What is the form of the sample?

How much sample is there?

What instruments are available?

Waht instrument setup are available?

Primary optics?

Sample holders?

Detectors?

What intensity / resolution is required?

...


Early Decisions: Accuracy / Precision needed

Methodical limits•Peak overlap•Scattering factors•Speed of analysis

Evaluation errors•Software errors•User errors•Quality of methods

Calibration errors•Uncalibratable errors•Use of standards•Quality of calibration

Measurement errors•Physical effects•Geometric effects•Alignment errors•Others...

Accuracy and precision

of results


Early Decisions:“Fitting the Experiment to the Need”

Identification and quantification of errors

Correction of errors by means of calibration

Minimizing of errors using optimized measurement and evaluation strategies

Checking of results


The Sample:General Considerations

One of the most important steps before data collection is the minimisation of systematic sample related effects. This is as important as the minimisation of instrumental aberations!

Avoid persisting with poor data - if possible

Re-prepare or remake the sample

Find a better sample

Change instrument or instrument setup

Improve instrument and measurement parameters


The Sample:Typical sample related problems

Not enough scattering particles (spotiness)

Sample not representative for the bulk

Bad sampling / particle heterogeneity / phase separation

Preferred orientation

Extinction

Microabsortion (multiphase samples)

“Sample problems” can also provide important informations:

preferred orientation degree of orientation

peak broadening crystallite size and strain


The Sample:Preparation

Back pressing, side drifting not effective on preferred

orientation in all cases

Use of capillary techniques most effective

intensity and resolution losses

not automatable

Addition of diluents contamination

enhanced transparency

amorphous scatter /additional peaks

Spray drying expensive equipment

large sample amount needed

lavish cleaning of equipment

Sample motion motion should be 90° to the

diffraction vector

improves particle statistics

no effect on preferred orientation in Bragg-Brentano reflection geometry

The grains in a powder should be randomly oriented:


The Sample:Number of Crystallites needed

Peak intensities for structure refinement required to be accurate to ±2%

Accurate, reproducible diffraction intensities require small crystallite size

typical intensity reproducibility for Quartz (113) reflection with CuK: is

15-20 m 5-50 m 5-15 m <5 m

18.2% 10.1% 2.1% 1.2%

The number of crystallites diffracting is related to size

diameter 40 m 10 m 1 m

crystallites / 20mm3 597.000 38.000.000 3.820.000.000

number diffracting 12 760 38.000

Smith, 1992


Non-Random Specimens:Particle Size or “Spotiness” Effect


The Sample:Sample Motion - Two Examples

Bragg-Brentano Reflection Debye-Scherrer Capillary

Rotation parallel to the scattering vector does not minimize preferred orientation effects!


The Instrument:General Considerations

The choice of the optimum instrument must consider the aim of the experiment as well as specific sample properties.

Whats the aim of the experiment

Radiation?

Geometry?

Instrumental setup (optics, sample carriers, detectors)?


Welches Instrument:Was ist das Ziel des Experiments?

Qualitative AnalyseQualitative Analyse

Quantitative AnalyseQuantitative Analyse

IndexingIndexing

22 IntensitätIntensität

AuflösungAuflösung

Struktur LösungStruktur Lösung Rietveld AnalyseRietveld Analyse

Wann werden folgende Profilparameter benötigt:


The Instrument:What Radiation to use?

X-Ray Laboratory

X-Ray Laboratory

X-RaySynchrotron

X-RaySynchrotron NeutronsNeutrons

IntensityIntensity

ResolutionResolution

Absorption problemsAbsorption problems

Atom discriminationAtom discrimination

Light atomsLight atoms

small / reflection

small / reflection

small / reflection

small / reflection

Small samplesSmall samples

AvailabilityAvailability


The Instrument:What Geometry to use?

BBBB DSGöbel Optics

DSGöbel Optics

DSConventional

DSConventional

IntensityIntensity

ResolutionResolution

P/BP/B

AbsorptionAbsorption

Preferred orientationPreferred orientation

reflectionreflection



reflection / -2reflection / -2

capillarycapillary Sample amountSample amount capillarycapillary

Non ambientNon ambient

Weak scatteringWeak scattering reflectionreflection


The Instrument:Debye-Scherrer / Bragg-Brentano

Bragg-BrentanoReflection

Debye-ScherrerCapillary


The Instrument:Effect of Absorption

Bragg-Brentano Absorption is independent of 2:

Constant diffraction volume

Transparency effect may cause problems High absorption : Use reflection geometry

Low absorption : Use transmission geometry

Debye-Scherrer Absorption is 2-dependent:

Variable diffraction volume

An intensity correction (effR) is crucial, if accurate intensities are needed


The Instrument:Fixed or variable Divergence Slits (I)

FixedFixed VariableVariable

Beam divergenceBeam divergence FixedFixed VariableVariable

Diffraction volumeDiffraction volume ConstantConstant VariableVariable

Illuminated sample length Illuminated sample length FixedFixed VariableVariable

Never use variable divergence slits for structure analysis!

Fix them always to constant beam divergence!


The Instrument:Fixed or variable Divergence Slits (II)

Fixed divergence slits Variable divergence slits


The Instrument:Point-, Line- and Area-Detectors

Scintillation detector

small spot measured scan necessary long measuring time

PSD

large 2range measured simultaneously

medium measuring time

HI-STAR / CDD

large 2 and chi range measured simultaneously

very short measuring times measurement of oriented

samples and very small sample amounts


The Instrument:Powder Diffraction using 2-D Detectors

Amorphous Sample Crystalline Sample Heavily oriented crystalline sample with amorphous content


Data Collection:General Considerations

A very crucial step in each experiment is the choice of optimum instrument and measurement parameters. Important examples are:Sample carrier material

Receiving slit

Divergence and anti-scatter slits

Soller slit(s)


Data Collection:Sample Carrier Material

0 .0 0 5 .0 0 1 0 .0 0 1 5 .0 0 2 0 .0 0 2 5 .0 0 3 0 .0 0

0

1 0 0

2 0 0

3 0 0

4 0 0

In te n s ity[cp s]

Plastic

S ingle crysta l (S i)


Data Collection:Counting Statistics - Detection Limit

20

40

60

80

100

t = 1 0 s2 = ±4,5c/s

t = 5 s2 = ±6,3c/s

t = 1 s2 = ±14,1c/s

t = 0 ,5 s2 = ±20c/s

Av e ra g e b a c k g ro u n d le v e l= 5 0 c/s;

Jenkins, 1989


Data Collection:Influence of Divergence Slit

2 6 .3 0 2 6 .4 0 2 6 .5 0 2 6 .6 0 2 6 .7 0 2 6 .8 0 2 6 .9 0

0

2 0

4 0

6 0

8 0

1 0 0

IR e l

Q u a rz , 10 1

R ec e iv in g S lit: 0 .0 5 °

D iv e rg e n c e S lit:

1 °

0 .3 °


Data Collection:Flat Specimen Error


Data Collection:Influence of Receiving Slit

2 8 .0 0 2 8 .2 0 2 8 .4 0 2 8 .6 0 2 8 .8 0 2 9 .0 0

0

2 0

4 0

6 0

8 0

1 0 0

I re l

Si, 111 Receiving slit:

0.015°0.05°0.15°0.6°


Instrument Resolution (I):D500 with Ge-Primary Monochromator

Scintillation counter

FWHM = 0.038° 2

Position sensitive detector

FWHM = 0.046° 2

2 5 .0 0 2 5 .2 0 2 5 .4 0 2 5 .6 0 2 5 .8 0 2 6 .0 0

0

2 0

4 0

6 0

8 0

1 0 0

IR e l

D 5 0 0 S ZS R M 1 9 7 6 , 0 1 2

F W H M : 0 ,0 3 8 ° 2

2 5 .0 0 2 5 .2 0 2 5 .4 0 2 5 .6 0 2 5 .8 0 2 6 .0 0

0

2 0

4 0

6 0

8 0

1 0 0

IR e l

D 5 0 0 O E DS R M 1 9 7 6 , 0 1 2

F W H M : 0 ,0 4 6 ° 2


Instrument Resolution (II):D8 ADVANCE

Scintillation counter

FWHM = 0.030° 2

2 4 .7 5 2 5 .0 0 2 5 .2 5 2 5 .5 0 2 5 .7 5 2 6 .0 0 2 6 .2 5 2 6 .5 0

0

1 0 0 0

2 0 0 0

3 0 0 0

In te n s ity[c o u n ts ]

D 8 A D V A N C E S ZS R M 1 9 7 6 , 0 1 2

FW H M = 0.030° 2


Evaluation:

Most important Errors

Software errors

User errors, e.g. Smoothing

Background subtraction

Quality of methods, e.g. 2-Determination

2nd derivative

Profile fitting


Evaluation:Errors due to smoothing

2 8 .0 0 2 8 .2 0 2 8 .4 0 2 8 .6 0 2 8 .8 0 2 9 .0 0

0

2 0

4 0

6 0

8 0

1 0 0

I re l

Si, 111

R AW data5 poin t sm ooth ing9 poin t sm ooth ing17 point sm ooth ing


Evaluation:Gaussian and Lorentzian Function

28.00 28.20 28.40 28.60 28.80 29.00

0

20

40

60

80

100

IRel

GaussianSi 111

28.00 28.20 28.40 28.60 28.80 29.00

0

20

40

60

80

100

IRel

LorentzianSi 111


Evaluation:Split-PearsonVII Function

28.00 28.20 28.40 28.60 28.80 29.00

0

20

40

60

80

100

IRel

Split-PearsonVIISi 111


Evaluation:Comparison of Peak Profile Functions

2 0 .0 0 2 0 .0 5 2 0 .1 0 2 0 .1 5 2 0 .2 0 2 0 .2 5 2 0 .3 0

0

2 0

4 0

6 0

8 0

1 0 0

IR e l

(L o re n tz )m = 1m = 1 .5m = 2m = 1 0G a u ß

(M o d ifiz ie rte L o re n tz )(M ittle re L o re n tz )


Evaluation:Calibration

Instrument alignment Crucial for alignment checking and alignment. Use always the

same sample!

Internal calibration Standard added to the sample. Almost all errors can be

corrected

External calibration Standard used external to the sample. Does not correct for

important errors like sample displacement and transparency!


Evaluation:List of recent NIST XRD Standards

Material SRM Number Certified forSilicon SRM 640b d-value calibration

Fluoro-Phlogopite SRM 675 d-value calibration

-Al2O3 SRM 1976 intensity calibration,instrument alignment

LaB6 SRM 660 profile analysis

-Al2O3 SRM 676 quantitative analysis

-Si3N4, -Si3N4 SRM 656 quantitative analysis

-Quartz SRM 1978a quantitative analysis

Cristobalite SRM 1979a quantitative analysis

-Al2O3, ZnO, TiO2, SRM 674a quantitative analysis

Cr2O3, CeO2


Evaluation:Typical Intensity Calibration Function

2 0 .0 0 4 0 .0 0 6 0 .0 0 8 0 .0 0 1 0 0 .0 0 1 2 0 .0 0 1 4 0 .0 0 1 6 0 .0 0

0 .7 0

0 .8 0

0 .9 0

1 .0 0

1 .1 0

1 .2 0

1 .3 0

IA / I B

In s tru m e n t R esp o n se F u n c tio nS R M 1 9 7 6

S Z


Evaluation:Typical Angle Calibration Function

2 0 .0 0 4 0 .0 0 6 0 .0 0 8 0 .0 0 1 0 0 .0 0 1 2 0 .0 0 1 4 0 .0 0 1 6 0 .0 0

-0 .0 3

-0 .0 2

-0 .0 1

0 .0 0

0 .0 1

0 .0 2

0 .0 3

A n g le C a lib ra tio n F u n c tio nS R M 1 9 7 6

S Z


Evaluation:Accuracy of XRD results

Lattice parameters : ~ 0.001% 2 ~ 0.003° 2

Thermal expansion L/L : < 3%

Atom coordinates : < ± 1 Temperature factors : < 50%


Bruker AXS:Diffraction Solutions

Diffraction solutions is our comprehensive, application oriented package consisting of

High-precision, fast and innovative analysis technology for all your needs

Hardware Software

Supply of analytical and technical expertise - knowledge transfer between customer and supplier

Application support, consulting User trainings Workshops User meetings

Documents

Accuracy-in-XRD.1, A. Kern © 1999 BRUKER AXS All Rights Reserved Accuracy and Precision in Powder Diffractometry A. Kern Bruker AXS GmbH Östliche Rheinbrückenstraße