Structural Refinement based on the Rietveld Method

Transcription

1 Structural Refinement based on the Rietveld Method An introduction to the basics by Cora Lind Outline What, when and why? - Possibilities and limitations Examples Data collection Parameters and what to watch out for Step by step guide to GSAS Useful sources of information 1

2 History of the Rietveld method First introduced by Hugo Rietveld in Originally introduced for neutron data - Hardly any response from the scientific community after first presentation of the method in Hugo Rietveld shared his program as well as knowledge freely - First used for X-ray data in Became possible by increase in computing power Least squares based minimization algorithm to obtain the best fit between a structural model and a powder pattern - Demanding, as the algorithm is non-linear - User decides which parts of the model can be varied - You refine a crystal structure, not profiles! - Full pattern fitting Possibilities Works for simple and complicated structures - Thanks to today s computing power, even complicated structures can be refined rather rapidly Can be used to refine several phases as well as mixed occupancies - Use of internal standard possible - Quantitative analysis of mixture or versus a standard - Non-stoichiometry/partial occupancy can be refined Each point in the pattern can be regarded as an observation - No Bragg intensity tells you something about your crystal, too! Refinement of several data sets together - X-ray and neutron data - Several different wavelengths => changes scattering contrast between atoms

3 Limitations Parameters can sometimes be correlated - e.g. zero point and sample height For big structures, constraints or restraints can be necessary - Restrain bond distances or bond angles (define rigid bodies) - Constrain composition if known The method only works if you have a good starting model! - Divergence might be observed - A local instead of a global minimum may be found La 3 Ti 5 Al 15 O 37 How complicated can we get? - 60 atoms in the asymmetric unit - Cc, a =.57 Å, b = Å, c = 9.7 Å, β = independent structural parameters Ga (HPO 3 ) 3 4H O - 9 atoms in the asymmetric unit - P 1, a = 8.09 Å, b = Å, c = 7.67 Å, β = independent structural parameters T 3 R 3 insulin-zinc complex atom protein stereochemical restraints used step synchrotron pattern - R3, a = Å, c = Å 3

4 The most important part: Data collection! Without high quality data, even the best program can t help you! Choice of instrument - Resolution - Accessible angular range - Tricks you can play Sample preparation - Particle size - Surface roughness - Homogeneity - Preferred orientation Instrument alignment, sample height and other errors Choice of instrument In many cases, a well-aligned laboratory x-ray will do - Resolution is often sample limited (line broadening) For samples with closely spaced lines (due to symmetry or large unit cell), it might be an advantage to use synchrotron radiation - Tunable wavelength (lines can be spaced out) - Better instrument resolution - Larger accessible d-spacing range (commonly sample limited) - Absorption problems can be avoided - Methods like MAD (Multiple Anomalous Diffraction) phasing can help with locating atoms 4

5 Sample preparation Particle size needs to be small enough to avoid graininess problems (e.g. < 10 microns, preferably smaller) Large grains can result in unpredictable intensity spikes when the diffraction condition of one of these grains is fulfilled However, overgrinding should be avoided, as too small particles lead to line broadening! Avoid rocks or dust Sample surface needs to be smooth (particle size should be <5-10 microns), otherwise the intensity at low angles is reduced (surface roughness problem) The sample needs to be homogenous, so that every part is representative of the bulk sample (esp. if irradiated area changes with angle) Caution: Platelets or needles can lead to preferred orientation! Surface roughness effects 5

6 Preferred orientation For a known structural model (e.g. Rietveld analysis only), preferred orientation can sometimes be accounted for Spherical harmonics model is best unless you have a good idea of what kind of preferred orientation you have Refinement often unstable For an unknown structure (e.g. need to extract integrated intensities), preferred orientation is a killer! To avoid preferred orientation, the sample can be side packed To check whether you might have preferred orientation in a sample, run patterns: One of a loosely or side packed sample, one of a sample that has been pressed down, compare the relative intensities! Experimental setup Make sure that the instrument is well aligned before collecting data! Zero point Footprint Choose slits that will keep the full beam footprint on the the sample at all angles (otherwise your low angle intensities will be off)! The sample height needs to be correct, as incorrect sample height shifts the peaks Long counting times improve the signal to noise ratio and facilitate the extraction of integrated intensities Choose a low background sample holder (e.g., metal, not plastic) In some cases, an internal standard can be useful 6

7 Effects of sample height displacement Rietveld programs Plenty of good packages available from the authors or as free download GSAS (General Structure Analysis System) Fullprof DBWS (named after D. B. Wiles and A. Sakthivel, who wrote the code together with R. A. Young) Rietan In the US, GSAS (Larson and von Dreele, LANL) is most widely used 7

8 Parameters to be varied (GSAS) Automatically varied: Scale factor and 3 background terms Lattice parameters Specimen displacement Zero point Peak shape parameters Atomic positions and thermal parameters Extinction Surface roughness Preferred orientation Parameters Structural variables - Atom positions, fractional occupancies, thermal parameters - Only these parameters are refinable in most single crystal software Profile parameters - Unit cell constants, wavelength - Peak shape, including width and asymmetry - Diffractometer zero point - Sample height and transparency - Background Correction terms - Absorption, extinction - Surface roughness, preferred orientation 8

9 What to watch out for Some parameters can be highly correlated - Unit cell constants and wavelength - Thermal parameters and partial occupancy - Sample height and zero point - Look at correlation matrix! Check whether your results are physically meaningful! - If you know the wavelength, fix it - Does your occupancy agree with your chemical composition? - Bond lengths? Use an internal standard if possible - Known lattice constant - Constrain sample height, zero point, asymmetry etc. to be identical for standard and sample Peak shape models Several different peak shape models are available in most Rietveld packages, as the peak shape is determined by - sample characteristics - instrument characteristics Convolution of several different factors, but in many cases, one factor will be dominant Laboratory x-rays will usually give Lorentzian peak shape Medium resolution CW neutron diffractometers give Gaussian peak shape TOF instruments give highly asymmetric peak shapes In high resolution data, sample characteristics determine the peak shape - can be very challenging to model the peak shape properly 9

10 Gaussian peak shape Examples of peak shapes Lorentzian peak shape ( t) 1 t exp σ G ( ) = πσ Γ 1 L( t) = π Γ / + t Pseudo-Voigt peak shape P( t) = η L( t, Γ) + (1 η) G( t, σ ) How to judge your refinement Several different indices: - R wp - R w - R F w ( ( ) ( )) i yi obs yi calc wi ( yi ( obs)) y ( obs) y ( calc) i ( I ( obs)) K y ( obs) 1/ i i ( I ( calc)) ( I ( obs)) K K 1/ 1/ 1/ - Goodness of fit Chi The easiest way to get low Chi values is to collect noisy data R F is not minimized during the refinement, but gives information about the agreement between the structural model and the pattern The most important judgment is in all cases the visual judgment! - Low indices mean nothing if the fit does not look convincing 10

11 A good fit Example: Wrong lattice constant 11

12 Example: Wrong peak shape model Example: Preferred orientation 1

13 Modern instrumentation High resolution diffractometers and synchrotron data can provide extra information - Better peak resolution (FWHM can be as low as in some cases) - High peak to background ratios However, there is a price to pay for this: - Peak shape often determined by the sample - TOF diffractometers have asymmetric peaks Modeling of high resolution data can be very demanding Refining several patterns simultaneously Refinement of several patterns simultaneously can provide additional information X-ray and neutron data - X-rays usually give better resolution, but the intensity falls off at small d- spacings - Good for resolving small lattice distortions - Neutron data provide much higher intensities at small d-spacings - More reliable atomic positions and thermal parameters, esp. for light atoms X-ray data of several different wavelengths - Can be used to change the scattering contrast between atoms - More reliable refinement of partial occupancies 13

14 A step by step guide to GSAS SETUP - Expnam enter experiment name * (up to 8 characters) - Expedt edit *.exp experiment file - Cnvfile convert data file to correct format - Exit COMPUTE - Powpref powder data preparation - Genles general least squares refinement GRAPHICS - Powplot powder pattern plotting UTILITIES - Rawplot to plot your raw data EXPEDT Y Q D 1) Data setup P Flowchart for EXPDT I Quit Use X to travel up the flowchart Delete last *.exp file 6) Least squares L (see nd part of flow chart) ) Powder data preparation P T H Edit experiment title 4) Histogram data editing Read data from 3) Phase edit R 5) Edit powder histogram n another *.exp file E I Insert a new phase Edit excluded regions D Set minimum d-spacing E n Edit phase n T Set maximum θ I J Insert a new histogram (data) Insert a dummy histogram 14

15 6) Least squares menu O L A Flowchart for EXPDT II L-S control editing E C n 8) Overall parameter editing A B C E F H L O P S Set maximum number of cycles Change Fobs extraction flag Absorption coefficients Background coefficients Diffractometer constants Extinction parameters X-ray f and f parameters Histogram scale Lattice constants Preferred orientation parameters Profile coefficients Phase fractions 7) Atom editing L P n K C s E s I s Change parameter of atom s Erase atom s Insert atom s List atom parameters Use X to travel up the flowchart V turns refinement flags on/off D n damps parameter refinement by n0% <return> shows you all options Change to phase n Edit atom parameter constraints How to run GSAS I Start PC-GSAS.exe Choose experiment name (up to 8 characters) in EXPNAME Start EXPEDT answer Y to question Do you wish to create this file? enter a title for the experiment Go to box 3) [phase edit], insert new phase information Go to box 4) [histogram data editing], insert new histogram use *.gs file (sometimes needs to be run through CNVFILE first) instrument parameter files end in.prm, copy them from the GSAS directory to your directory; laboratory X-ray data: inst_xry.prm for bank number desired, enter 1 set maximum θ or minimum d-spacing (REQUIRED for new histograms) enter 0 on second bank question to exit histogram editing menu 15

16 How to run GSAS II Go to box 7) [atom editing], insert atom parameters choose I (isotropic thermal parameter) for FLAG Go to box 8) [overall parameters] pick suitable background and profile functions for our instrument: Background function # (default), peak profile type # (default), change peak shape from Gaussian to Lorentzian, e.g. set GU and GV to 0, GW to 0.1, LX and LY to 5 (sharp peaks, like Si standard) or any value up to ~0 (rather broad peaks) Exit EXPEDT Run POWPREF, then GENLES Start POWPLOT enter A N N M T D P to plot next histogram, reflection markers and difference curve as a function of θ Look at your refinement and figure out what you need to vary to improve it! How to run GSAS III If you refine several phases, constrain changes in parameters like sample height or asymmetry to be identical for all phases before varying them! in the profile menu, type K, then 8 (for parameter SHFT, which is the sample height), enter <return> 1 1 <return> etc. until you reach the last phase number Suggested order for turning on parameters automatically varied: 3 background parameters, histogram scale if necessary, insert more background parameters lattice constants (make sure the starting point isn t too far off!) profile parameters LX, LY, SHFT; if necessary also ASYM, GW preferred orientation, diffractometer constants, absorption, extinction etc. should only be varied if absolutely necessary! 16

17 Useful resources CCP14: Free software including tutorials and examples Rietveld mailing list GSAS download ftp://ftp.anl.gov/public/gsas/ R. A. Young; The Rietveld method Comprehensive text including history, description of several Rietveld programs, as well as details about certain parameters (e.g. background modeling, peak shapes, pattern decomposition ) 17