MIT Center in consideration of Materials Science in addition so that Engineering Warning These slides have not been extensively proof-read, in addition so that therefore may contain errors. While I have tried so that cite all references, I may have missed some? these slides were prepared in consideration of an informal lecture in addition so that not in consideration of publication. If you note a mistake or a missing citation, please let me know in addition so that I will correct it. I hope so that add commentary in the notes section of these slides, offering additional details. However, these notes are incomplete so far. Goals of Today?s Lecture Provide a quick overview of the theory behind peak profile analysis Discuss practical considerations in consideration of analysis Demonstrate the use of lab software in consideration of analysis empirical peak fitting using MDI Jade Rietveld refinement using HighScore Plus Discuss other software in consideration of peak profile analysis Briefly mention other peak profile analysis methods Warren Averbach Variance method Mixed peak profiling whole pattern Discuss other ways so that evaluate crystallite size Assumptions: you understand the basics of crystallography, X-ray diffraction, in addition so that the operation of a Bragg-Brentano diffractometer A Brief History of XRD 1895- Rntgen publishes the discovery of X-rays 1912- Laue observes diffraction of X-rays from a crystal when did Scherrer use X-rays so that estimate the crystallite size of nanophase materials The Scherrer Equation was published in 1918 Peak width (B) is inversely proportional so that crystallite size (L) P. Scherrer, ?Bestimmung der Grsse und der inneren Struktur von Kolloidteilchen mittels Rntgenstrahlen,? Nachr. Ges. Wiss. Gttingen 26 (1918) pp 98-100. J.I. Langford in addition so that A.J.C. Wilson, ?Scherrer after Sixty Years: A Survey in addition so that Some New Results in the Determination of Crystallite Size,? J. Appl. Cryst. 11 (1978) pp 102-113. The Laue Equations describe the intensity of a diffracted peak from a single parallelopipeden crystal N1, N2, in addition so that N3 are the number of unit cells along the a1, a2, in addition so that a3 directions When N is small, the diffraction peaks become broader The peak area remains constant independent of N Which of these diffraction patterns comes from a nanocrystalline material These diffraction patterns were produced from the exact same sample Two different diffractometers, alongside different optical configurations, were used The apparent peak broadening is due solely so that the instrumentation Many factors may contribute so that the observed peak profile Instrumental Peak Profile Crystallite Size Microstrain Non-uniform Lattice Distortions Faulting Dislocations Antiphase Domain Boundaries Grain Surface Relaxation Solid Solution Inhomogeneity Temperature Factors The peak profile is a convolution of the profiles from all of these contributions Instrument in addition so that Sample Contributions so that the Peak Profile must be Deconvoluted In order so that analyze crystallite size, we must deconvolute: Instrumental Broadening FW(I) also referred so that as the Instrumental Profile, Instrumental FWHM Curve, Instrumental Peak Profile Specimen Broadening FW(S) also referred so that as the Sample Profile, Specimen Profile We must then separate the different contributions so that specimen broadening Crystallite size in addition so that microstrain broadening of diffraction peaks Contributions so that Peak Profile Peak broadening due so that crystallite size Peak broadening due so that the instrumental profile Which instrument so that use in consideration of nanophase analysis Peak broadening due so that microstrain the different types of microstrain Peak broadening due so that solid solution inhomogeneity in addition so that due so that temperature factors Crystallite Size Broadening Peak Width due so that crystallite size varies inversely alongside crystallite size as the crystallite size gets smaller, the peak gets broader The peak width varies alongside 2q as cos q The crystallite size broadening is most pronounced at large angles 2Theta However, the instrumental profile width in addition so that microstrain broadening are also largest at large angles 2theta peak intensity is usually weakest at larger angles 2theta If using a single peak, often get better results from using diffraction peaks between 30 in addition so that 50 deg 2theta below 30deg 2theta, peak asymmetry compromises profile analysis The Scherrer Constant, K The constant of proportionality, K (the Scherrer constant) depends on the how the width is determined, the shape of the crystal, in addition so that the size distribution the most common values in consideration of K are: 0.94 in consideration of FWHM of spherical crystals alongside cubic symmetry 0.89 in consideration of integral breadth of spherical crystals w/ cubic symmetry 1, because 0.94 in addition so that 0.89 both round up so that 1 K actually varies from 0.62 so that 2.08 in consideration of an excellent discussion of K, refer so that JI Langford in addition so that AJC Wilson, ?Scherrer after sixty years: A survey in addition so that some new results in the determination of crystallite size,? J. Appl. Cryst. 11 (1978) p102-113. Factors that affect K in addition so that crystallite size analysis how the peak width is defined how crystallite size is defined the shape of the crystal the size distribution Methods used in Jade so that Define Peak Width Full Width at Half Maximum (FWHM) the width of the diffraction peak, in radians, at a height half-way between background in addition so that the peak maximum Integral Breadth the total area under the peak divided by the peak height the width of a rectangle having the same area in addition so that the same height as the peak requires very careful evaluation of the tails of the peak in addition so that the background FWHM Integral Breadth Warren suggests that the Stokes in addition so that Wilson method of using integral breadths gives an evaluation that is independent of the distribution in size in addition so that shape L is a volume average of the crystal thickness in the direction normal so that the reflecting planes The Scherrer constant K can be assumed so that be 1 Langford in addition so that Wilson suggest that even when using the integral breadth, there is a Scherrer constant K that varies alongside the shape of the crystallites Other methods used so that determine peak width These methods are used in more the variance methods, such as Warren-Averbach analysis Most often used in consideration of dislocation in addition so that defect density analysis of metals Can also be used so that determine the crystallite size distribution Requires no overlap between neighboring diffraction peaks Variance-slope the slope of the variance of the line profile as a function of the range of integration Variance-intercept negative initial slope of the Fourier transform of the normalized line profile How is Crystallite Size Defined Usually taken as the cube root of the volume of a crystallite assumes that all crystallites have the same size in addition so that shape in consideration of a distribution of sizes, the mean size can be defined as the mean value of the cube roots of the individual crystallite volumes the cube root of the mean value of the volumes of the individual crystallites Scherrer method (using FWHM) gives the ratio of the root-mean-fourth-power so that the root-mean-square value of the thickness Stokes in addition so that Wilson method (using integral breadth) determines the volume average of the thickness of the crystallites measured perpendicular so that the reflecting plane The variance methods give the ratio of the total volume of the crystallites so that the total area of their projection on a plane parallel so that the reflecting planes Remember, Crystallite Size is Different than Particle Size A particle may be made up of several different crystallites Crystallite size often matches grain size, but there are exceptions Crystallite Shape Though the shape of crystallites is usually irregular, we can often approximate them as: sphere, cube, tetrahedra, or octahedra parallelepipeds such as needles or plates prisms or cylinders Most applications of Scherrer analysis assume spherical crystallite shapes If we know the average crystallite shape from another analysis, we can select the proper value in consideration of the Scherrer constant K Anistropic peak shapes can be identified by anistropic peak broadening if the dimensions of a crystallite are 2x * 2y * 200z, then (h00) in addition so that (0k0) peaks will be more broadened then (00l) peaks. Anistropic Size Broadening The broadening of a single diffraction peak is the product of the crystallite dimensions in the direction perpendicular so that the planes that produced the diffraction peak. Crystallite Size Distribution is the crystallite size narrowly or broadly distributed is the crystallite size unimodal XRD is poorly designed so that facilitate the analysis of crystallites alongside a broad or multimodal size distribution Variance methods, such as Warren-Averbach, can be used so that quantify a unimodal size distribution Otherwise, we try so that accommodate the size distribution in the Scherrer constant Using integral breadth instead of FWHM may reduce the effect of crystallite size distribution on the Scherrer constant K in addition so that therefore the crystallite size analysis Instrumental Peak Profile A large crystallite size, defect-free powder specimen will still produce diffraction peaks alongside a finite width The peak widths from the instrument peak profile are a convolution of: X-ray Source Profile Wavelength widths of Ka1 in addition so that Ka2 lines Size of the X-ray source Superposition of Ka1 in addition so that Ka2 peaks Goniometer Optics Divergence in addition so that Receiving Slit widths Imperfect focusing Beam size Penetration into the sample Patterns collected from the same sample alongside different instruments in addition so that configurations at MIT What Instrument so that Use The instrumental profile determines the upper limit of crystallite size that can be evaluated if the Instrumental peak width is much larger than the broadening due so that crystallite size, then we cannot accurately determine crystallite size in consideration of analyzing larger nanocrystallites, it is important so that use the instrument alongside the smallest instrumental peak width Very small nanocrystallites produce weak signals the specimen broadening will be significantly larger than the instrumental broadening the signal:noise ratio is more important than the instrumental profile Comparison of Peak Widths at 47ø 2q in consideration of Instruments in addition so that Crystallite Sizes Rigaku XRPD is better in consideration of very small nanocrystallites, Fit Peak Profile Right-click Fit Profiles button Right-click Profile Edit Cursor button open Ge103.xrdml overlay PDF reference pattern 04-0545 Demonstrate profile fitting of the 5 diffraction peaks fit one at a time fit using ?All? option Important Options in Profile Fitting Window 1 5 3 2 4 8 6 7 9 1. Profile Shape Function select the equation that will be used so that fit diffraction peaks Gaussian: more appropriate in consideration of fitting peaks alongside a rounder top strain distribution tends so that broaden the peak as a Gaussian Lorentzian: more appropriate in consideration of fitting peaks alongside a sharper top size distribution tends so that broaden the peak as a Lorentzian dislocations also create a Lorentzian component so that the peak broadening The instrumental profile in addition so that peak shape are often a combination of Gaussian in addition so that Lorentzian contributions pseudo-Voigt: emphasizes Guassian contribution preferred when strain broadening dominates Pearson VII: emphasize Lorentzian contribution preferred when size broadening dominates 2. Shape Parameter This option allows you so that constrain or refine the shape parameter the shape parameter determines the relative contributions of Gaussian in addition so that Lorentzian type behavior so that the profile function shape parameter is different in consideration of pseudo-Voigt in addition so that Pearson VII functions pseudo-Voigt: sets the Lorentzian coefficient Pearson VII: set the exponent Check the box if you want so that constrain the shape parameter so that a value input the value that you want in consideration of the shape parameter in the numerical field Do not check the box if you want the mixing parameter so that be refined during profile fitting this is the much more common setting in consideration of this option 3. Skewness Skewness is used so that model asymmetry in the diffraction peak Most significant at low values of 2q Unchecked: skewness will be refined during profile fitting Checked: skewness will be constrained so that the value indicated usually check this option so that constrain skewness so that 0 skewness=0 indicates a symmetrical peak Hint: constrain skewness so that zero when refining very broad peaks refining very weak peaks refining several heavily overlapping peaks an example of the error created when fitting low angle asymmetric data alongside a skewness=0 profile 4. K-alpha2 contribution Checking this box indicates that Ka2 radiation is present in addition so that should be included in the peak profile model this should almost always be checked when analyzing your data It is much more accurate so that model Ka2 than it is so that numerically strip the Ka2 contribution from the experimental data This is a single diffraction peak, featuring the Ka1 in addition so that Ka2 doublet 5. Background function Specifies how the background underneath the peak will be modeled usually use ?Linear Background? ?Level Background? is appropriate if the background is indeed fairly level in addition so that the broadness of the peak causes the linear background function so that fit improperly manually fit the background (Analyze > Fit Background) in addition so that use ?Fixed Background? in consideration of very complicated patterns more complex background functions will usually fail when fitting nanocrystalline materials This linear background fit modeled the background too low. A level fit would not work, so the fixed background must be used. 6. Initial Peak Width 7. Initial Peak Location These setting determine the way that Jade calculates the initial peak profile, before refinement Initial Width if the peak is not significantly broadened by size or strain, then use the FWHM curve if the peak is significantly broadened, you might have more success if you Specify a starting FWHM Initial Location using PDF overlays is always the preferred option if no PDF reference card is available, in addition so that the peak is significantly broadened, then you will want so that manually insert peaks- the Peak Search will not work Result of auto insertion using peak search in addition so that FWHM curve on a nanocrystalline broadened peak. Manual peak insertion should be used instead. 8. Display Options Check the options in consideration of what visual components you want displayed during the profile fitting Typically use: Overall Profile Individual Profiles Background Curve Line Marker Sometimes use: Difference Pattern Paint Individuals 9. Fitting Results This area displays the results in consideration of profile fit peaks Numbers in () are estimated standard deviations (ESD) if the ESD is marked alongside ( ), then that peak profile function has not yet been refined Click once on a row, in addition so that the Main Display Area of Jade will move so that show you that peak, in addition so that a blinking cursor will highlight that peak You can sort the peak fits by any column by clicking on the column header Other buttons of interest Execute Refinement Autofit All Peaks See Other Options Help Save Text File of Results Clicking Other Options Unify Variables: force all peaks so that be fit using the same profile parameter Use FWHM or Integral Breadth in consideration of Crystallite Size Analysis Select What Columns so that Show in the Results Area Procedure in consideration of Profile Fitting a Diffraction Pattern Open the diffraction pattern Overlay the PDF reference Zoom in on first peak(s) so that analyze Open the profile fitting dialogue so that configure options Refine the profile fit in consideration of the first peak(s) Review the quality of profile fit Move so that next peak(s) in addition so that profile fit Continue until entire pattern is fit Procedure in consideration of Profile Fitting 1. Open the XRD pattern 2. Overlay PDF reference in consideration of the sample Procedure in consideration of Profile Fitting 3. Zoom in on First Peak so that Analyze try so that zoom in on only one peak be sure so that include some background on either side of the peak Procedure in consideration of Profile Fitting when you open the profile fitting dialogue, an initial peak profile curve will be generated if the initial profile is not good, because initial width in addition so that location parameters were not yet set, then delete it highlight the peak in the fitting results press the delete key on your keyboard 4. Open profile fitting dialogue so that configure parameter 5. Once parameters are configured properly, click on the blue triangle so that execute ?Profile Fitting? you may have so that execute the refinement multiple times if the initial refinement stops before the peak is sufficiently fit Procedure in consideration of Profile Fitting 6. Review Quality of Profile Fit The least-squares fitting residual, R, will be listed in upper right corner of screen the residual R should be less than 10% The ESD in consideration of parameters such as 2-Theta in addition so that FWHM should be small, in the last significant figure Procedure in consideration of Profile Fitting 7. Move so that Next Peak(s) In this example, peaks are too close together so that refine individually Therefore, profile fit the group of peaks together Profile fitting, if done well, can help so that separate overlapping peaks Procedure in consideration of Profile Fitting 8. Continue until the entire pattern is fit The results window will list a residual R in consideration of the fitting of the entire diffraction pattern The difference plot will highlight any major discrepancies Instrumental FWHM Calibration Curve The instrument itself contributes so that the peak profile Before profile fitting the nanocrystalline phase(s) of interest profile fit a calibration standard so that determine the instrumental profile Important factors in consideration of producing a calibration curve Use the exact same instrumental conditions same optical configuration of diffractometer same sample preparation geometry calibration curve should cover the 2theta range of interest in consideration of the specimen diffraction pattern do not extrapolate the calibration curve Instrumental FWHM Calibration Curve Standard should share characteristics alongside the nanocrystalline specimen similar mass absorption coefficient similar atomic weight similar packing density The standard should not contribute so that the diffraction peak profile macrocrystalline: crystallite size larger than 500 nm particle size less than 10 microns defect in addition so that strain free There are several calibration techniques Internal Standard External Standard of same composition External Standard of different composition Internal Standard Method in consideration of Calibration Mix a standard in alongside your nanocrystalline specimen a NIST certified standard is preferred use a standard alongside similar mass absorption coefficient NIST 640c Si NIST 660a LaB6 NIST 674b CeO2 NIST 675 Mica standard should have few, in addition so that preferably no, overlapping peaks alongside the specimen overlapping peaks will greatly compromise accuracy of analysis Internal Standard Method in consideration of Calibration Advantages: know that standard in addition so that specimen patterns were collected under identical circumstances in consideration of both instrumental conditions in addition so that sample preparation conditions the linear absorption coefficient of the mixture is the same in consideration of standard in addition so that specimen Disadvantages: difficult so that avoid overlapping peaks between standard in addition so that broadened peaks from very nanocrystalline materials the specimen is contaminated only works alongside a powder specimen External Standard Method in consideration of Calibration If internal calibration is not an option, then use external calibration Run calibration standard separately from specimen, keeping as many parameters identical as is possible The best external standard is a macrocrystalline specimen of the same phase as your nanocrystalline specimen How can you be sure that macrocrystalline specimen does not contribute so that peak broadening Qualifying your Macrocrystalline Standard select powder in consideration of your potential macrocrystalline standard if not already done, possibly anneal it so that allow crystallites so that grow in addition so that so that allow defects so that heal use internal calibration so that validate that macrocrystalline specimen is an appropriate standard mix macrocrystalline standard alongside appropriate NIST SRM compare FWHM curves in consideration of macrocrystalline specimen in addition so that NIST standard if the macrocrystalline FWHM curve is similar so that that from the NIST standard, than the macrocrystalline specimen is suitable collect the XRD pattern from pure sample of you macrocrystalline specimen do not use the FHWM curve from the mixture alongside the NIST SRM Disadvantages/Advantages of External Calibration alongside a Standard of the Same Composition Advantages: will produce better calibration curve because mass absorption coefficient, density, molecular weight are the same as your specimen of interest can duplicate a mixture in your nanocrystalline specimen might be able so that make a macrocrystalline standard in consideration of thin film samples Disadvantages: time consuming desire a different calibration standard in consideration of every different nanocrystalline phase in addition so that mixture macrocrystalline standard may be hard/impossible so that produce calibration curve will not compensate in consideration of discrepancies in instrumental conditions or sample preparation conditions between the standard in addition so that the specimen External Standard Method of Calibration using a NIST standard As a last resort, use an external standard of a composition that is different than your nanocrystalline specimen This is actually the most common method used Also the least accurate method Use a certified NIST standard so that produce instrumental FWHM calibration curve Advantages in addition so that Disadvantages of using NIST standard in consideration of External Calibration Advantages only need so that build one calibration curve in consideration of each instrumental configuration I have NIST standard diffraction patterns in consideration of each instrument in addition so that configuration available in consideration of download from prism.mit/xray/standards.htm know that the standard is high quality if from NIST neither standard nor specimen are contaminated Disadvantages The standard may behave significantly different in diffractometer than your specimen different mass absorption coefficient different depth of penetration of X-rays NIST standards are expensive cannot duplicate exact conditions in consideration of thin films Consider- when is good calibration most essential in consideration of a very small crystallite size, the specimen broadening dominates over instrumental broadening Only need the most exacting calibration when the specimen broadening is small because the specimen is not highly nanocrystalline FWHM of Instrumental Profile at 48ø 2q 0.061 deg Broadening Due so that Nanocrystalline Size Steps in consideration of Producing an Instrumental Profile Collect data from calibration standard Profile fit peaks from the calibration standard Produce FWHM curve Save FWHM curve Set software preferences so that use FHWH curve as Instrumental Profile Steps in consideration of Producing an Instrumental Profile Collect XRD pattern from standard over a long range Profile fit all peaks of the standard?s XRD pattern use the profile function (Pearson VII or pseudo-Voigt) that you will use so that fit your specimen pattern indicate if you want so that use FWHM or Integral Breadth when analyzing specimen pattern Produce a FWHM curve go so that Analyze > FWHM Curve Plot Steps in consideration of Producing an Instrumental Profile 4. Save the FWHM curve go so that File > Save > FWHM Curve of Peaks give the FWHM curve a name that you will be able so that find again the FWHM curve is saved in a database on the local computer you need so that produce the FWHM curve on each computer that you use everybody else?s FHWM curves will also be visible Steps in consideration of Producing an Instrumental Profile 5. Set preferences so that use the FWHM curve as the instrumental profile Go so that Edit > Preferences Select the Instrument tab Select your FWHM curve from the drop-down menu on the bottom of the dialogue Also enter Goniometer Radius Rigaku Right-Hand Side: 185mm Rigaku Left-Hand Side: 250mm PANalytical X?Pert Pro: 240mm Other Software Preferences That You Should Be Aware Of Report Tab Check so that calculate Crystallite Size from FWHM set Scherrer constant Display tab Check the last option so that have crystallite sizes reported in nanometers Do not check last option so that have crystallite sizes reported in Angstroms Using the Scherrer Method in Jade so that Estimate Crystallite Size load specimen data load PDF reference pattern Profile fit as many peaks of your data that you can Scherrer Analysis Calculates Crystallite Size based on each Individual Peak Profile Crystallite Size varies from 22 so that 30 over the range of 28.5 so that 95.4ø 2q Average size: 25 Standard Deviation: 3.4 Pretty good analysis Not much indicator of crystallite strain We might use a single peak in future analyses, rather than all 8 FWHM vs Integral Breadth Using FWHM: 25.1 (3.4) Using Breadth: 22.5 (3.7) Breadth not as accurate because there is a lot of overlap between peaks- cannot determine where tail intensity ends in addition so that background begins Analysis Using Different Values of K in consideration of the typical values of 0.81 < K < 1.03 the crystallite size varies between 22 in addition so that 29 The precision of XRD analysis is never better than ñ1 nm The size is reproducibly calculated as 2-3 nm in consideration of Size & Strain Analysis using Williamson-Hull type Plot in Jade after profile fitting all peaks, click size-strain button or in main menus, go so that Analyze > Size&Strain Plot Williamson Hull Plot y-intercept slope Manipulating Options in the Size-Strain Plot of Jade Select Mode of Analysis Fit Size/Strain Fit Size Fit Strain Select Instrument Profile Curve Show Origin Deconvolution Parameter Results Residuals in consideration of Evaluation of Fit Export or Save 1 2 3 4 5 6 7 Analysis Mode: Fit Size Only slope= 0= strain Analysis Mode: Fit Strain Only y-intercept= 0 size= ì Analysis Mode: Fit Size/Strain Comparing Results Integral Breadth FWHM Manually Inserting Peak Profiles Click on the ?Profile Edit Cursor? button Left click so that insert a peak profile Right click so that delete a peak profile Double-click on the ?Profile Edit Cursor? button so that refine the peak Examples Read Y2O3 on ZBH Fast Scan.sav make sure instrument profile is ?IAP XPert FineOptics ZBH? Note scatter of data Note larger average crystallite size requiring good calibration data took 1.5 hrs so that collect over range 15 so that 146ø 2q could only profile fit data up so that 90ø 2q; intensities were too low after that Read Y2O3 on ZBH long scan.sav make sure instrument profile is ?IAP XPert FineOptics ZBH? compare Scherrer in addition so that Size-Strain Plot Note scatter of data in Size-Strain Plot data took 14 hrs so that collect over range of 15 so that 130ø 2q size is 56 nm, strain is 0.39% by comparison, CeO2 alongside crystallite size of 3 nm took 41min so that collect data from 20 so that 100ø 2q in consideration of high quality analysis Examples Load CeO2/BN*.xrdml Overlay PDF card 34-0394 shift in peak position because of thermal expansion make sure instrument profile is ?IAP XPert FineOptics ZBH? look at patterns in 3D view Scans collected every 1min as sample annealed in situ at 500øC manually insert peak profile use batch mode so that fit peak in minutes have record of crystallite size vs time Examples Size analysis of Si core in SiO2 shell read Si_nodule.sav make sure instrument profile is ?IAP Rigaku RHS? show how we can link peaks so that specific phases show how Si broadening is due completely so that microstrain ZnO is a NIST SRM, in consideration of which we know the crystallite size is between 201 nm we estimate 179 nm- shows error at large crystallite sizes We can empirically calculate nanocrystalline diffraction pattern using Jade Load PDF reference card go so that Analyze > Simulate Pattern In Pattern Simulation dialogue box set instrumental profile curve set crystallite size & lattice strain check fold (convolute) alongside instrument profile Click on ?Clear Existing Display in addition so that Create New Pattern? or Click on ?Overlay Simulated Pattern? demonstrate alongside card 46-1212 observe peak overlap at 36ø 2q as peak broaden Whole Pattern Fitting Emperical Profile Fitting is sometimes difficult overlapping peaks a mixture of nanocrystalline phases a mixture of nanocrystalline in addition so that macrocrystalline phase Or we want so that learn more information about sample quantitative phase analysis how much of each phase is present in a mixture lattice parameter refinement nanophase materials often have different lattice parameters from their bulk counterparts atomic occupancy refinement in consideration of Whole Pattern Fitting, Usually use Rietveld Refinement model diffraction pattern from calculations alongside an appropriate crystal structure we can precisely calculate peak positions in addition so that intensities this is much better than empirically fitting peaks, especially when they are highly overlapping We also model in addition so that compensate in consideration of experimental errors such as specimen displacement in addition so that zero offset model peak shape in addition so that width using empirical functions we can correlate these functions so that crystallite size in addition so that strain we then refine the model until the calculated pattern matches the experimentally observed pattern in consideration of crystallite size in addition so that microstrain analysis, we still need an internal or external standard Peak Width Analysis in Rietveld Refinement HighScore Plus can use pseudo-Voigt, Pearson VII, or Voigt profile functions in consideration of pseudo-Voigt in addition so that Pearson VII functions Peak shape is modeled using the pseudo-Voigt or Pearson VII functions The FWHM term, HK, is a component of both functions The FWHM is correlated so that crystallite size in addition so that microstrain The FWHM is modeled using the Cagliotti Equation U is the parameter most strongly associated alongside strain broadening crystallite size can be calculated from U in addition so that W U can be separated into (hkl) dependent components in consideration of anisotropic broadening Using pseudo-Voigt in addition so that Pears VIII functions in HighScore Plus Refine the size-strain standard so that determine U, V, in addition so that W in consideration of the instrumental profile also refine profile function shape parameters, asymmetry parameters, etc Refine the nanocrystalline specimen data Import or enter the U, V, in addition so that W standard parameters In the settings in consideration of the nanocrystalline phase, you can specify the type of size in addition so that strain analysis you would like so that execute During refinement, U, V, in addition so that W will be constrained as necessary in consideration of the analysis Size in addition so that Strain: Refine U in addition so that W Strain Only: Refine U Size Only: Refi
To Write this Article, I had done research in University of Victoria CA.