rietveld-method part i - cefet-mg · 2017-11-06 · ifg, kit campus north - 2 - november 2017 dr....

Name of Institute, Faculty, Department1 10/31/17KIT – The Research University in the Helmholtz Association www.kit.edu

Dr. Peter G. Weidler Institute of Functional Interfaces IFG

Rietveld-Methodpart I

IFG, KIT Campus North - 2 - November 2017Dr. Peter G. Weidler Rietveld-Method I

Overview

➢ introduction, overview

➢ data collection

➢ background contribution,

➢ peak-shape function,

➢ refinement of profile parameters,

➢ refinement of structural parameters,

➢ use of geometric restraints,

➢ calculation of e.s.d.'s,

➢ interpretation of R values

➢ some common problems and possible solution

➢ QA with Rietveld


Hugo M. Rietveld (1932)

The Rietveld refinement

--> least squares approach --> refinement of theoretical line profile

(calculated from a known or postulated crystal structure) --> match with measured profile

"Line Profiles of Neutron Powder-diffraction Peaks for Structure Refinement." (Rietveld,H.M.(1967). Acta Crystallogr.,22,151-2.)

H. M. Rietveld (1969). "A profile refinement method for nuclear and magnetic structures". Journal of Applied Crystallography 2 (2): 65–71. doi:10.1107/S0021889869006558.

History


Gregori Aminoff Prize 1995

--> Ewald, Guinier, Kratky

History


History relevance of RM


Rietveld-Method what we want !

THIS !!!

good match of

your model with

the observed data

==>

amount/composition

crystallographic info

...


Rietveld Software and Utility Software or Features

DBWS (Free Dos Structure Refinement Software) FullProf (Free Dos and Mac Structure Refinement Software) RIQAS (Commercial Dos Quantitative Phase Analysis Software) GSAS (Free Dos Structure Refinement Software) SiroQuant (Commercial MS-Windows Quantitative Phase Analysis Software) Quasar (Commercial MS-Windows Quantitative Phase Analysis Software) FAT-Rietan (Free Dos and Mac Structure Refinement Software) ARITVE (Free Dos Glass Modelling Software)Riet7/SR5 (Dos Structure Refinement Software - No Quantitative Analysis) LHPM from ANSTO (Structure Refinement for DOS, WIN) XND (Structure Refinement for DOS) SIMREF and SIMPRO (Structure Refinement for DOS) Koalariet (Developmental Structure Refinement for Win95) BGMN fundamental parameters Rietveld (Structure Ref. WIN OS/2, Linux) XRS-82 Rietveld (Structure Refinement for DOS) ANSTO GUI LHPM-Rietica for Win32 Rietveld and Related Software BRASS - Bremen Rietveld Analysis and Structure Suite TOPAS - Alan Coelho

more info under http://www.ccp14.ac.uk/


Rietveld-Method Parameters refinable (simultaneously)

For each phase j present:

xj, y

j, z

j, B

j, N

j

● xj, y

j, z

j position coordinates,

● Bj an isotropic thermal parameter,

● Nj site-occupancy multiplier for all the

jth atom in the unit cell

● Scale factor (--> quantitative phase analysis)● Specimen-profile breadth parameters● Lattice parameters● Overall temperature factor● Individual anisotropic thermal parameters● Preferred orientation● Crystallite size and micorstrain (--> profile parameters)● Extinction

Global parameters:

● 2θ-Zero● Instrumental profile● Profile asymmetry● Background● Wavelength● Specimen displacement● Specimen transparency● Absorption


Rietveld-Method some formulas

The DREAM is Sy = 0 !!!


Rietveld-Method some formulas


Rietveld-Method finding a solution...


Rietveld-Method ...what a solution ?


Rietveld-Method ...some details


closer look on some details

➢ data collection

➢ background contribution,

➢ peak-shape function,








data collection

For Rietveld refinement, it is essential that the

powder diffraction data be collected appropriately

incorrect relative intensities and/or 2θ values

--> no amount of time spent on refinement will yield sensible results

For reflection geometry sample has to be `infinitely thick'

i.e. X-ray beam is totally absorbed by the sample

However, for highly absorbing materials, a potential source of

error is surface roughness.

--> can reduce the intensity of low-angle reflections

--> leads to anomalously low thermal parameters in refinement.


data collection: variable vs. fixed slits:

For Bragg-Brentano geometries incident beam to be kept on sample at all angles to ensure a constant-volume condition

However, varying slit leads to a progressive angular-dependent defocussing quality of the data deteriorates.

slit opening needs to have a precision of at least 1% (reproducible to a few microns over the entire 2θ range)

Recommendation: do not use variable slits for a Rietveld refinement


data collection: step width and time

Step width:

at least five steps (not more than ten) across the top of each peak (i.e. step size = FWHM/5)

Step time:

time per step should approximately compensate for the gradual decline in intensity with 2θ

maximum 2θ value should be chosen to give the maximum useful data (.e. as high as possible).

different counting times per ranges


data collection: preferred orientation PO

If intensities show strong dependence

e.g. all 00l reflections are strong and all hk0 weak

preferred orientation of the crystallites should be suspected.

Although many Rietveld refinement programs allow refinement

of a preferred-orientation parameter with respect to a specific

crystallographic vector based on the March model (Dollase, 1986),

this is usually only a crude approximation to reality,

so elimination (or minimization) of the problem experimentally

is to be preferred.


data collection: particle size

ideal particle size approx. 1±5 µm

If crystallites larger --> non-randomness may become a problemi.e. not all crystallite orientations are equally represented

...some calculations yielding the number of particlesin diffraction conditions:

example: quartz α-SiO2 10x10x0.2mm³


data collection: diffractometer

Calibration of diffractometercareful calibration of 2θ-values with standard material e.g. NIST Si SRM 640b and/or fluorophlogopite mica SRM 675

Any diffractometer can be adjusted so that the deviations of the measured peak positions from the correct ones are less than 0.01(2).

Set-up:diffractometer should give a

low background andmaximum peak resolution (small peak widths)

monochromatic radiation e.g. Cu Kα1 rather than Cu Kα1,2

if possible → Synchrotron radiation

Although longer data-acquisition times are required with monochromatic radiation, its use is particularly advantageous:

number of lines in pattern is halved


data collection: data pretreatment

Any temptation to smooth the diffraction data before doing a

Rietveld refinement must be resisted.

Smoothing introduces point-to-point correlations

conclusion : only best data yields best refinement results


Background

basically two approaches

● estimation by linear interpolation btw. selected points btw. peaks ● modelled by an empirical or semi-empirical function containing several

refinable parameters.

Both have advantages and disadvantages

For simple patterns where most peaks are resolved to the baseline, both methods tend to work well and the fit is easily verified with a plot.

This means if background-subtraction approach is used, the background usually has to be

re-estimated and re-subtracted several times during a refinement


Refining the background appears to be the preferred methodbecause background and structural parameters can be refined simultaneously (and std. deviations estimated in the usual way).

However, polynomial functions are largely or entirely empirical. If the polynomial happens to describe the background well, then, as might be expected, this procedure also works well;

but if it does not, no amount of refining coefficients of polynomial (or increasing the order of the polynomial) can correct the problem and refinement will not proceed satisfactorily.

In such a case, background subtraction is the better approach

Background


Peak Shape Functions

The accurate description of the shapes of the peaks in a powder pattern is critical to the success of a Rietveld refinement.

If the peaks are poorly described, the refinement will not be satisfactory

The peak shapes are a function of both ● sample e.g. domain size, stress/strain, defects

and ● instrument e.g. radiation source, geometry, slit sizes

and ● vary as a function of 2θ.

In certain cases, they can also vary as a function of indices (hkl).

Accommodating all of these aspects in a single peak-shape description is nontrivial and compromises are often made


Peak Shape Functions: pseudo-Voigt

pseudo-Voigt function: linear combination of Lorentzian and Gaussian with η/(1- η) the pseudo-Voigt mixing parameter

Diffraction lines dominated by instrumental broadening, usually vary in a linear manner, from a dominant Gaussian component at low angles to a Lorentzian trend at high angles.


Peak Shape Functions: Pearson type VII


Peak Shape Functions: TCHZ Thompson-Cox-Hasting pseudo-Voigt


Profile Parameterstructure-free approach

If only a partial structural model is available, it is probably best to usea structure-free approach, in which the intensities of the reflections are simply adjusted to fit the observed ones.

--> Le Bail- or Pawley-Method--> whole pattern methods

Pawley method enables the e.s.d.'s of the reflection intensities to be estimated more correctly and calculates the covariances between overlapping reflections.--> Pawley method of choice

--> fast check/estimation of model, amount, additional phases, background-function

--> input: space group, lattice parameters, peak shape function


Space Groups


Profile Parameterstructure-free approach

Pawley-Method

CeO: a (Å) 5.41301 +/- 0.00002GOF 1.63TCHZbgr: polynomial 2 order


closer look on some details...... to be continued








Literature

R.A. Young The Rietveld MethodIUCr, Oxford University Press, 1993, pp.299 40€ 95BRL

D.L. Bish & J.E. Post (Eds) Modern Powder DiffractionReviews in Mineralogy Vol 20Mineralogical Society of America, 1989, pp.369 30€ 70BRL

W.I.F. David, K. Shankland, L.B. McCusker, Ch. BaerlocherStructure Determination from Powder Diffraction DataIUCr, Oxford Science Publications, 2002 (2011 reprint), pp. 337

68€ 160BRL

International Union of Crystallographywww.iucr.org


Literature


CEFET

Bruker AXS do Brasil and Bruker AXS Germany, Knielingen

UMFG

Acknowledgment

INCT-Acqua

rietveld-method part i - cefet-mg · 2017-11-06 · ifg, kit campus north - 2 - november 2017 dr....

Documents