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 50 D Karlsruhe

Accuracy-in-XRD.2, A. Kern © 1999 BRUKER AXS All Rights Reserved Topics to be covered Accuracy and Precision in Powder Diffractometry Definition Optimized Measurement and Evaluation Strategies: Early Decisions Sample Instrument Data Colletion Strategies Optimized Evaluation Procedures

Accuracy-in-XRD.3, A. Kern © 1999 BRUKER AXS All Rights Reserved Definition of Terms: “Accuracy” - “Precision” Legend: Z: Measurand = “true” value A: Measurement result  A S : Accuracy  A R : Precision = standard deviation

Accuracy-in-XRD.4, A. Kern © 1999 BRUKER AXS All Rights Reserved Accurate Powder Diffractometry Precise or Accurate Results? Tissue, 1996

Accuracy-in-XRD.5, A. Kern © 1999 BRUKER AXS All Rights Reserved 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 Early Decisions SampleInstrument Data Collection Evaluation

Accuracy-in-XRD.6, A. Kern © 1999 BRUKER AXS All Rights Reserved 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!

Accuracy-in-XRD.7, A. Kern © 1999 BRUKER AXS All Rights Reserved 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?...

Accuracy-in-XRD.8, A. Kern © 1999 BRUKER AXS All Rights Reserved 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

Accuracy-in-XRD.9, A. Kern © 1999 BRUKER AXS All Rights Reserved 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

Accuracy-in-XRD.10, A. Kern © 1999 BRUKER AXS All Rights Reserved 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

Accuracy-in-XRD.11, A. Kern © 1999 BRUKER AXS All Rights Reserved 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

Accuracy-in-XRD.12, A. Kern © 1999 BRUKER AXS All Rights Reserved 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:

Accuracy-in-XRD.13, A. Kern © 1999 BRUKER AXS All Rights Reserved 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  m5-50  m 5-15  m <5  m 18.2%10.1%2.1%1.2% The number of crystallites diffracting is related to size diameter40  m10  m1  m crystallites / 20mm number diffracting Smith, 1992

Accuracy-in-XRD.14, A. Kern © 1999 BRUKER AXS All Rights Reserved Non-Random Specimens: Particle Size or “Spotiness” Effect

Accuracy-in-XRD.15, A. Kern © 1999 BRUKER AXS All Rights Reserved The Sample: Sample Motion - Two Examples Bragg-Brentano Reflection Debye-Scherrer Capillary Rotation parallel to the scattering vector does not minimize preferred orientation effects!

Accuracy-in-XRD.16, A. Kern © 1999 BRUKER AXS All Rights Reserved 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)?

Accuracy-in-XRD.17, A. Kern © 1999 BRUKER AXS All Rights Reserved Welches Instrument: Was ist das Ziel des Experiments? Qualitative Analyse Quantitative Analyse Indexing 22 22 Intensität Auflösung Struktur Lösung Rietveld Analyse Wann werden folgende Profilparameter benötigt:

Accuracy-in-XRD.18, A. Kern © 1999 BRUKER AXS All Rights Reserved The Instrument: What Radiation to use? X-Ray Laboratory X-Ray Laboratory X-Ray Synchrotron X-Ray Synchrotron Neutrons Intensity Resolution Absorption problems Atom discrimination Light atoms small / reflection small / reflection small / reflection small / reflection Small samples Availability

Accuracy-in-XRD.19, A. Kern © 1999 BRUKER AXS All Rights Reserved The Instrument: What Geometry to use? BB DS Göbel Optics DS Conventional DS Conventional Intensity Resolution P/B Absorption Preferred orientation reflection reflection /  -2  capillary Sample amount capillary Non ambient Weak scattering reflection

Accuracy-in-XRD.20, A. Kern © 1999 BRUKER AXS All Rights Reserved The Instrument: Debye-Scherrer / Bragg-Brentano Bragg-Brentano Reflection Debye-Scherrer Capillary

Accuracy-in-XRD.21, A. Kern © 1999 BRUKER AXS All Rights Reserved 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 (  eff R) is crucial, if accurate intensities are needed

Accuracy-in-XRD.22, A. Kern © 1999 BRUKER AXS All Rights Reserved The Instrument: Fixed or variable Divergence Slits (I) Fixed Variable Beam divergence Fixed Variable Diffraction volume Constant Variable Illuminated sample length Fixed Variable Never use variable divergence slits for structure analysis! Fix them always to constant beam divergence!

Accuracy-in-XRD.23, A. Kern © 1999 BRUKER AXS All Rights Reserved The Instrument: Fixed or variable Divergence Slits (II) Fixed divergence slits Variable divergence slits

Accuracy-in-XRD.24, A. Kern © 1999 BRUKER AXS All Rights Reserved The Instrument: Point-, Line- and Area-Detectors Scintillation detector small spot measured scan necessary long measuring time PSD large 2  range 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

Accuracy-in-XRD.25, A. Kern © 1999 BRUKER AXS All Rights Reserved The Instrument: Powder Diffraction using 2-D Detectors Amorphous SampleCrystalline SampleHeavily oriented crystalline sample with amorphous content

Accuracy-in-XRD.26, A. Kern © 1999 BRUKER AXS All Rights Reserved 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)

Accuracy-in-XRD.27, A. Kern © 1999 BRUKER AXS All Rights Reserved Data Collection: Sample Carrier Material

Accuracy-in-XRD.28, A. Kern © 1999 BRUKER AXS All Rights Reserved Data Collection: Counting Statistics - Detection Limit Jenkins, 1989

Accuracy-in-XRD.29, A. Kern © 1999 BRUKER AXS All Rights Reserved Data Collection: Influence of Divergence Slit

Accuracy-in-XRD.30, A. Kern © 1999 BRUKER AXS All Rights Reserved Data Collection: Flat Specimen Error

Accuracy-in-XRD.31, A. Kern © 1999 BRUKER AXS All Rights Reserved Data Collection: Influence of Receiving Slit

Accuracy-in-XRD.32, A. Kern © 1999 BRUKER AXS All Rights Reserved Instrument Resolution (I): D500 with Ge-Primary Monochromator Scintillation counter FWHM = 0.038° 2  Position sensitive detector FWHM = 0.046° 2 

Accuracy-in-XRD.33, A. Kern © 1999 BRUKER AXS All Rights Reserved Instrument Resolution (II): D8 ADVANCE Scintillation counter FWHM = 0.030° 2 

Accuracy-in-XRD.34, A. Kern © 1999 BRUKER AXS All Rights Reserved Evaluation: Most important Errors Software errors User errors, e.g. Smoothing Background subtraction Quality of methods, e.g. 2  -Determination 2nd derivative Profile fitting

Accuracy-in-XRD.35, A. Kern © 1999 BRUKER AXS All Rights Reserved Evaluation: Errors due to smoothing

Accuracy-in-XRD.36, A. Kern © 1999 BRUKER AXS All Rights Reserved Evaluation: Gaussian and Lorentzian Function  I Rel Gaussian Si  I Rel Lorentzian Si 111

Accuracy-in-XRD.37, A. Kern © 1999 BRUKER AXS All Rights Reserved Evaluation: Split-PearsonVII Function  I Rel Split - PearsonVII Si 111

Accuracy-in-XRD.38, A. Kern © 1999 BRUKER AXS All Rights Reserved Evaluation: Comparison of Peak Profile Functions

Accuracy-in-XRD.39, A. Kern © 1999 BRUKER AXS All Rights Reserved 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!

Accuracy-in-XRD.40, A. Kern © 1999 BRUKER AXS All Rights Reserved Evaluation: List of recent NIST XRD Standards MaterialSRM NumberCertified for SiliconSRM 640bd-value calibration Fluoro-PhlogopiteSRM 675d-value calibration  -Al 2 O 3 SRM 1976intensity calibration, instrument alignment LaB 6 SRM 660profile analysis  -Al 2 O 3 SRM 676quantitative analysis  -Si 3 N 4,  -Si 3 N 4 SRM 656quantitative analysis  -QuartzSRM 1978aquantitative analysis CristobaliteSRM 1979aquantitative analysis  -Al 2 O 3, ZnO, TiO 2,SRM 674aquantitative analysis Cr 2 O 3, CeO 2

Accuracy-in-XRD.41, A. Kern © 1999 BRUKER AXS All Rights Reserved Evaluation: Typical Intensity Calibration Function

Accuracy-in-XRD.42, A. Kern © 1999 BRUKER AXS All Rights Reserved Evaluation: Typical Angle Calibration Function

Accuracy-in-XRD.43, A. Kern © 1999 BRUKER AXS All Rights Reserved Evaluation: Accuracy of XRD results Lattice parameters: ~ 0.001%  2  ~ 0.003° 2  Thermal expansion  L/L:< 3% Atom coordinates :< ± 1  Temperature factors :< 50%

Accuracy-in-XRD.44, A. Kern © 1999 BRUKER AXS All Rights Reserved 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