Profile Fitting For Analysis Of XRPD Data Using HighScore .
Profile Fittingfor Analysis of XRPD Datausing HighScore Plus v3Scott A Speakman, Ph.D.Center for Materials Science and Engineering at MITspeakman@mit.eduhttp://prism.mit.edu/xray
Profile fitting is a technique used to extract preciseinformation about the position, intensity, width, andshape of each individual peak in a diffraction pattern Profile fitting provides more precise peak information than anypeak search algorithm The peak information can be used in several calculations to quantifysample parameters such as unit cell lattice parameters, crystallitesize and microstrain, and relative weight fractions Many programs provide profile fitting capabilities– These slides describe how to use HighScore Plus, published by PANalyticalInc, to profile fit diffraction data– The general procedure can be used with other programs– Other commercial programs that offer profile fitting capabilities are: MDIJade, Bruker Topas, Rigaku PDXL, XPowder– Free programs, some of which are a bit older, include Xfit, Fourya, Winfit,Fullprof, FitSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Techniques to Quantify Diffraction Data Profile Fitting––– The position, intensity, width, and shape of each diffraction peak is empirically fitEach diffraction peak is fit independently of others unless constraints are explicitly imposedThis is a precise way to determine information about the peaks, but further work is required to extract meaning from thedataWhole Pattern Fitting––––An ideal diffraction pattern is calculated from a model of the sampleThe calculated diffraction pattern is compared to experimental data.The model is refined until the differences between the calculated and experimental diffraction patterns are minimized.The result is a refined model of the sample.–Rietveld Refinement The position and intensity of diffraction peaks are calculated from the crystal structure The width and shape of diffraction peaks are fit to functions that describes their systematic behavior related to 2theta The result is a refined model of the crystal structure and peak shape functions that can provide information about themicrostructure–Pawly or LeBail Fit The position of the diffraction peaks are calculated from, and constrained by, the unit cell lattice parameters The width and shape of diffraction peaks are fit to a function that describes their systematic behavior related to 2theta The peak intensities are empirically fitSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Profile Fitting models each diffraction peak with anempirical equation The experimental data areempirically fit with a series ofequations– Each diffraction peak is fit using aprofile function– The background is also fit, usuallyusing a polynomial function this helps to separate intensity inpeak tails from background Peak information is extracted fromthe profile equation rather thannumerically from the raw dataProfile fitting produces precisepeak positions, widths, heights,and areas with statistically validestimatesSlide ‹#› of 20In this example, the profile function modelsthe K alpha-1 & K alpha-2 peak doubletScott A Speakman, Ph.D.speakman@mit.edu
Diffraction peaks from laboratory diffractometers are amixture of Gaussian and Lorentzian profilesCountsCounts4000Gaussian profile shape2000Lorentzian profile shape300020001000100000 The profile function models this complex peak shape The same profile function is used for every peak in thediffraction patternSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Profile functions model the mixture of Gaussian andLorentzian contributions to the peak shape Diffraction data are most commonly modeled using a pseudoVoigt or Pearson VII function– A true Voigt curve is a convolution of the Gaussian and Lorentziancomponents This function is difficult to implement computationally– The pseudo Voigt is a linear combination of Gaussian andLorentzian components– The Pearson VII is an exponential mixing of Gaussian andLorentzian components Some techniques try to deconvolute the Gaussian andLorentzian contributions to the peak shape- this is difficult SA Howard and KD Preston, “Profile Fitting of Powder DiffractionPatterns,”, Reviews in Mineralogy vol 20: Modern Powder Diffraction,Mineralogical Society of America, Washington DC, 1989.Slide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Calculations are based on the peak informationextracted from profile fitting results Peak positions are used to calculate unit cell latticeparameters Peak widths are used to calculate crystallite size andmicrostrain– Peak shapes may also be used in crystallite size and microstrainanalysis Peak intensities are used to calculate the weight fractionof each phase in a mixtureSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Profile fitting procedurefor HighScore PlusThis tutorial assumes that you have a basic familiarity withHighScore Plus. Please review the %20Guide.pdffor some guidelines on the basics of HighScore Plus.Slide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Using Parameter Sets in HighScore Plus Each treatment or analysis in HighScore Plushas several parameters that can be adjusted tomodify the behavior of the program.“Parameter Sets” are saved values for theparameters that can used during analysisIf you do not know what parameters to use,the “Default” parameter set is usually a goodstarting point.To access a parameter set:– In any dialogue window, click the “More” button This button is usually in the lower right-handcorner– Select the parameter set from the drop-down menu To save a parameter set:– Set the parameters to values that you want to use– Click on the “More” button to open the parameter setarea– Click the floppy disk icon– Give the parameter set a unique nameSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Do not process the data before profile fitting Do not subtract the background before profile fitting– The background will be modeled during the profile fit process Do not strip K alpha-2 peaks before profile fitting– The K alpha-1 and K alpha-2 peak doublet will be modeled bythe profile function Do not smooth the data before profile fitting– Profile fitting relies on a statistically comparison to your rawdata which will be invalid if your data are smoothedSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
The Steps for Profile Fitting1.2.3.4.5.Fit the backgroundIdentify the peaks (ie peak search)Profile Fit the dataEvaluate the quality of the profile fitDo calculations based on the resultSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Setting Program Defaults before Profile Fitting HighScore Plus has severalpreconfigured desktop layouts– The best desktops for profile fitting are Profile Fitting Line Profile Analysis– To change the desktop go to the menu View Desktop Select the desired desktop from the listin the menu Do not select the desktop from the dropdown menu in the Desktop submenu; thisis used for selecting a filename when savinga customized desktopSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
You might want to restore Program and DocumentSettings to default if working on a shared computer Go the menu Customize Program Settings– Click on the button Reset All to Default– Click on the OK button to close the window– You can also explore Program Settings to modify the look, feel, andperformance of the program such as options for display behavior, automaticbacking up of analysis files, behavior during pattern simulation or Rietveldrefinement, and data treatments applied automatically when you open a file Go to the menu Customize Document Settings––––Click on the button Reset All to DefaultClick on the OK button to close the windowNote: this menu is only available after you have opened a fileYou can also explore the Document Settings to change options for thegraphic display, the analyze view, and labeling for legends and peakmarkersSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
The Steps for Profile Fitting1.2.3.4.5.Fit the backgroundIdentify the peaks (ie peak search)Profile Fit the dataEvaluate the quality of the profile fitDo calculations based on the resultSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Step 1. Fit the Background In most cases, the background fit is only required to aidthe peak search The background will usually be modeled and refinedduring the profile fit process– A perfect background is not necessary at this point To fit the background in HighScore Plus– Go to Treatment Determine Background– You may want to change the y-axis scale to Square Root so thatyou can see the background betterSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Background Fit Options: AutomaticOverfit: bending factortoo large or granularitytoo small Adjust parameters until green background line is agood fit to the data, without overfitting the dataUse the slider to adjust Bending factor to fitnonlinearity and curvature– If made too large, background may fit peak intensityGranularity controls the sampling interval– A smaller number will fit the data more closely, butmay overfit the dataUse smoothed input data to avoid oversampling dataand noiseUnderfit: granularity toolarge or bending factortoo smallTypically use parameters:– Granularity: 10 to 30– Bending Factor: 0 to 2When the background is a good fit, click Accept. Do NOT Subtract the background.Slide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Background Fit Options: ManualToo many base pointstoo close together tendto create poor fits Use cubic spline interpolation to fitcurves between each base pointThe base points are shown as black dotson the green background curveThe Mode (add, move, delete)determines what happens when you leftclick on the base point– Add and Delete base points tocreate an accurate background fit– The first and last base points canonly be MovedThe best background fitis usually accomplishedby using the fewest basepoints possibleWhen the background is a good fit, click Accept. Do not Subtract the background.Slide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Step 2: Peak Search Start a Peak Search from the menu Treatment Search Peaks Use the Default parameter setWhen starting with the Defaultparameter set, you may need to increasethe “Minimum Significance” for noisy dataSlide ‹#› of 20If the sample is nanocrystalline, you will needto increase the Maximum tip width andPeak base width in order to account for thebroader diffraction peaksScott A Speakman, Ph.D.speakman@mit.edu
Step 2: Peak Search (cont.) Click on Search Peaks to see a preview ofthe result– A calculated pattern based on the peaksearch is shown over the experimentaldata.– The “Set Display of Peaks” button willallow you to place the orange peak linemarkers in the data, above the data, orboth. Click on the triangle next to the button inorder to see the drop-down menu. Slide ‹#› of 20If necessary, modify the peak searchparameters and click Search Peaks buttonto see the new result.Click Accept when the peak search issatisfactoryScott A Speakman, Ph.D.speakman@mit.edu
If a reference pattern exists for your phase, use it tohelp you edit the peak listCounts8000nanoTiO2 with LaB6In this example, the peak search only found 3peaks (solid orange lines), while thereference card shows that there are 4 peaks(solid red lines).600040002000036CountsThe profile fitting will use the peaksavailable to fit the data as best as possible.In this case, the second peak is modeled asmuch too wide in order to compensate forthe missing first peak at 37 2θ. This alsocauses the last peak to disappear.Counts8000373839Position [ 2Theta] (Copper (Cu))nanoTiO2 with LaB660004000200008000nanoTiO2 with LaB636373839Position [ 2Theta] (Copper (Cu))When all four peaks are properly included,the profile fitting accurately separates thecontributions of the overlapping peaks.600040002000036373839If the peak list is incorrect, the profile fitting will be inaccurate.Position [ 2Theta] (Copper (Cu))Slide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
If a reference pattern exists for your phase, use it tohelp you edit the peak list Select the Peak List tab in the Lists Pane To delete a peak, select its line in the Peak List and either:– Press Delete on your keyboard– Right-click and select Delete Peak– If you move your mouse cursor above a peak line marker, that peak willautomatically be highlighted in the Peak List– Remember that lines shaded gray in the Peak List are K-alpha2 peaks. These areshown as dotted orange lines in the Main Graphics. You do not have to edit these–they will be corrected automatically during profile fitting. To insert a peak:– Right-click in the Main Graphics window and select Insert Peak– Position the cursor to match the height and position of the peak, and thenleft-click to insert the peak– Right-click in the Main Graphics window and select Insert Peak to turn thepeak insertion cursor offSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Step 3. Profile Fit the data Inspect the Program Settings for the Profile Fitting– Select the Refinement Control tab in the Lists Pane– Left-click on the phrase Global Variables in the RefinementControl pane (circled in red)– Look in the Object Inspector pane for the Global Settings.Slide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Inspect the most relevant profile fitting preferences Background:– The Method can be changed using the drop-down menu– The most common settings are: Polynomial: fit the background using a polynomial curve Shifted Chebyshev: fit the background using a curve that isuseful for samples with amorphous content Use Available Background: fix the background to the curvecreated in step 1 and do not refine it during profile fitting–This is a useful selection when the background is complex orwhen the pattern features many overlapping peaks. Profile Function:– The function can be changed using the drop-down menu– This determines the equation used to fit each diffraction peak– Pseudo Voigt and Pearson VII are the most common For settings with a text-based value, you click on the worddescribing what is being used (such as the “Polynomial” forBackground Method or “Pseudo Voigt” for ProfileFunction) and a drop-down menu will appear to allow youto change the setting.Slide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Inspect the most relevant profile fitting preferences Profile Fit Peak Base Width– This number determines the cut-off wherethe peak intensity is no longer calculated– If the profile fit does not extend for the fulllength of the tails of the peak, thenincrease this 200000048.504949.50Position [ 2Theta] (Copper (Cu))Peak Based Width small ( 10)Slide ‹#› of 20504848.5049Position [ 2Theta] (Copper (Cu))49.50Peak Based Width larger ( 25)Scott A Speakman, Ph.D.speakman@mit.edu50
Inspect the most relevant profile fitting preferences Asymmetry Type– When set to “No Asymmetry Function”, the peaks will bemodeled as symmetric– If peaks are asymmetric (usually at low angle) , you can modelusing Split Width (most common), Split Shape, or both. For settings with a text-based value, you click on the worddescribing what is being used (such as “No AsymmetryFunction” for Asymmetry type) and a drop-down menuwill appear to allow you to change the setting.Counts1000025000345Position [ 2Theta] (Copper (Cu))Slide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
You can customize or restore default values for profilefitting preferences Go to the menu Customize Defaults Select the Default GlobalSettings tab The Profile Fitting Preferences,such as background methodand asymmetry type, are listedhere. Changes made to thesepreferences will change thedefault starting values for allnew profile fitting analysesSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Adjust the Automatic Profile fit parameters Many items for profile fitting are found in the menuTreament Profile Fit Make sure the Profile Fit Mode is set to Automatic Select “Edit Automatic Profile Fit Steps” to adjust theway that your data will be fitSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Edit the profile fit parameters Go to the menu Treatment Profile Fit Edit Automatic Profile FitSteps For normal profile fitting, select the Default parameter set The only item to modify is the More Background term– You can change the No. of Additional Background Terms– You can choose whether or not to use the 1/x background term If you changed the parameter set, you will need to save it as a newparameter setWhen using a backgroundfunction such as a polynomial,the “No of additional backgroundterms” will determine the orderof the polynomialThe 1/x background term iseffective at modelingbackground the increasesexponentially at low anglesSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
To execute the profile fit Many items for profile fitting are found in the menu Treament Profile FitYou can execute different profile fitting treatments from the menuTreatment Profile Fit Fit Profile or by using the toolbar (circled inred above, which is from the Line Profile Analysis desktop)– If you click on theicon, HSP will run the “Default” parameter set– If you click on the black triangle to the right of theicon, you will beable to select which parameter set you want to runSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
The Residual Plot shows how many refinement cyclesran and how the residual fit improved By default the profile fit is limited to 20 refinement cycles. If the profile fitting ran for 20 cycles and then stopped, it maynot have reached the optimal refinement. You should run theprofile fit again. If the profile fitting stops before it reaches 20 cycles (as shownabove), then it found a minimum in the least-squares residualSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
How to determine if the profile fit is good First, compare the calculatedprofile to the experimental data In HSP, make sure that the option“Show Calculated Profile inAnalyze View is selected” (circledin red). The experimental data is usuallyplotted in red and the calculatedprofile in blue, though this colorscheme can change. There should be good agreementbetween both of these plots.Slide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Use the difference plot to determine if the fit is good The difference plot shows is a plot of (Iexp-Icalc) vs 2theta,and shows where the greatest differences between theexprimental and calculated plots are. The difference plot is shown in the Additional Graphicsarea– Right-click in the Additional Graphics area.– Select the menu Show Graphics Difference PlotSlide ‹#› of 20Scott A Speakman, Ph.D.speakman@mit.edu
Agreement Indices quantify the difference between theexperimental and calculated profiles To see the Agreement Indices–––– Rexpected is a statistical evaluation of the noise of the data. A smaller Rexpectedindicates better quality data.Rprofile is the residual difference between observed and calculated plots.Weighted Rprofile (Rwp) uses a weighting function to place more emphasis ongood fit between high intensity data points (such as intense peaks) and lessemphasis on low intensity data points (such as background).– Select the Refinement Control tab in the Lists PaneLeft-click on the entry Global VariablesLook in the Object Inspector paneExpand the area “Agreement Indices”In a good fit, Rwp should be less than 10Goodness of Fit isSlide ‹#› of 20𝑅𝑤𝑝2.𝑅𝑒𝑥𝑝2In a good fit, the GOF should be less than 4.Scott A Speakman, Ph.D.speakman@mit.edu
Look at the Peak List for anomalous values, such aslarge FHWM values For each phase in a sample, valuessuch as FHWM and Shape shouldbe similar, with
HighScore Plus has several preconfigured desktop layouts –The best desktops for profile fitting are Profile Fitting Line Profile Analysis –To change the desktop go to the menu View Desktop Select the desired desktop from the list in the menu Do not select the des
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