PXRD AND RIETVELD REFINEMENT

By Saurav Chandra Sarma and Dundappa MumbaraddiSolid State and Inorganic Chemistry Lab, NCU,

JNCASR

What Rietveld can do..???

• Analysis of the whole diffraction pattern.• Phase purity and identification.

• Refinement of the structure parameters from diffraction data.• Quantitative phase analysis.• Lattice parameters.• Atomic positions and Occupancies.• Isotropic and anisotropic thermal vibrations.

• Grain size and micro-strain calculation.• Magnetic moments (Neutron diffraction).

PHASE PURITY

Lattice parameter

sCe2AgGe3 Pr2AgGe3 Nd2AgGe3

  Single crystal XRD

Reitveld refinement

Single crystal XRD

Reitveld refinement

Single crystal XRD

Reitveld refinement

a = b 4.2754(3) 4.2733(1) 4.2401(6) 4.2270(1) 4.1886(6) 4.1876(3)

c 14.6855(16) 14.7976(1) 14.611(3) 14.6457(1) 14.557(3) 14.5343(2)

PHASE IDENTIFICATION

What Rietveld can do..???

• Analysis of the whole diffraction pattern.• Phase purity and identification.

• Refinement of the structure parameters from diffraction data.• Quantitative phase analysis.• Lattice parameters.• Atomic positions and Occupancies.• Isotropic and anisotropic thermal vibrations.

• Grain size and micro-strain calculation.• Magnetic moments (Neutron diffraction).

QUANTITATIVE PHASE ANALYSIS

With high quality data, you can determine how much of

each phase is present

The ratio of peak intensities varies linearly as a function

of weight fractions for any two phases in a mixture.

Experimental Data

Fitted Data

Model 1

Model 2

Difference between experimental and fitted data

CRYSTALLITE SIZE

Crystallites smaller than ~120nm create broadening of diffraction peaks. (scherrer’s equation)

Where,D-Size of ordered domainsK-dimentionless Shape factorLamda-X-ray wavelengthβ-Line broading at FWHMTheta-Brage angle

MICROSTRAIN

Ref:A. Khorsand Zak et al. / Solid State Sciences 13 (2011) 251-256

Microstrain may also create peak broadening (analyzing the peak widths over a long range of 2theta using a Williamson-Hull plot can let you separate microstrain and crystallite size)

PREFERRED ORIENTATION (TEXTURE)

Preferred orientation of crystallites can create a systematic

variation in diffraction peak intensities.

DOI: 10.1038/srep03679

PREFERREDCRYSTALLOGRAPHIC ORIENTATION

AVAILABLE FREE SOFTWARE

GSAS- Rietveld refinement of crystal structures

FullProf- Rietveld refinement of crystal structures

Rietan- Rietveld refinement of crystal structures

PowderCell- crystal visualization and simulated

diffraction patterns

JCryst- stereograms

PANalytical HighScore Plus

FULLPROF- RIETVELD REFINEMENT OF CRYSTAL STRUCTURES

REITVELD REFINEMENT USING FULLPROF SOFTWARE

Necessary files: High quality PXRD pattern

.dat file.xy file .raw file

Structural model.cif (from database)

Step 1:Create a new folder and paste the .dat and .cif files in that folderStep2:In the FullProf window click on ‘WinPlotr’ option.

OPEN WINPLOTR

SELECT DATA FILE

SELECT BACKGROUND

SELECTION OF PEAKS

OPEN EDITOR OF PCR FILE

Click on <Ed PCR> followed by cif PCR.

Click on <X ray> , <Default Values>, write the space group with proper spacing

PROFILE FITTING BY USING PCR FILE

PROFILE FITTING

Red line => observed dataBlack line => Calculated pattern by the programme.Blue line => Difference pattern

AFTER PROFILE FITTING

REITVELD REFINEMENT

REITVELD REFINEMENT

REITVELD REFINEMENT

AFTER FITTING

DESCRIPTION OF THE .PCR FILE

Title (lines 1-3) COMM:Will use original, single phase format Job parameter flags (line 4) Job: Radiation type

0 X-rays1 Neutrons, CW-1 Neutrons, TOF2 Pattern calc (X-rays)3 Pattern calc (neutrons, CW)-3 Pattern calc (neutrons, TOF)

Npr: Default profile shape0 Gaussian1 Cauchy (Lorentzian)2 Modified 1 Lorentzian3 Modified 2 Lorentizian4 Tripled pseudo-Voigt5 pseudo-Voigt6 Pearson VII7 Thompson-Cox-Hastings8 Numerical profile9 TOF conv. pseudo-Voigt10 TOF, similar to 911 Split pseudo-Voigt12 conv. Pseudo-Voigt13 TOF Ikeda-Carpenter

Nph:Number of phases Nba: Background type 0 Refine with polynomial 1 Read from CODFIL.bac N >1Linear interpolation -1 Refine with Debye+polynomial -2 Treated iteratively with Fourier filtering -3 Read addition 6 additional polynomial coeffs. Nex:Number of regions to exclude Nsc:Number of user defined scattering factors Nor:Preferred orientation function type 0 Function No. 1 1 Function No. 2

Dum:Control of divergence 1 If some phases are treated in Profile Matching,

convergence criterion with stand. dev. not applied 2 Program stopped for local divergence: chi2(i-

cycle+1)>chi2(i-cycle) 3 Reflections near excluded regions excluded from

Bragg R-factor Iwg:Refinement weighting scheme 0 Standard least squares 1 Maximum likelihood 2 Unit weights Ilo: Lorentz and polarization corrections 0 Standard Debye-Scherrer or Bragg Brentano 1 Flat plate PSD geometry -1 Lorentz-polarization correction not performed 2 Transmission geometry 3 Special polarization correction

Ias: Reflections reordering 0 Reordering performed only at first cycle 1 Reordering at each cycle Res: Resolution function 0 Not given 1—4 For CW data, profile is Voigt function and different

functions available Ste: Number of data points reduction factor 1,2..NIf Ste>1, number of data points and therefore step size

reduced by factor Ste Nre: Number of constrained parameters Cry: Single crystal job 0 Only integrated intensity given, no profile parameters 1 Refinement with single crystal data or int. intensities 2 Montecarlo search for starting configuration, no least

squares 3 Simulated annealing optimization method

Uni:Scattering variable unit 0 2θ in degrees 1 TOF in sec 2 Energy in keV Cor:Intensity correction0 No correction is applied1 File with intensity corrections2 File with empirical function Opt:Calculation optimization0 General procedures used1 Optimizes calculations to proceed faster Aut: Automatic mode for refinement codes

numbering0 Codewords treated as usual.1 Codewords treated automatically by program

REFINEMENT OUTPUT CONTROLS (LINE 7)

Ipr: Profile integrated intensities 0 No action 1 Observed and calculated profiles in .out

file 2 Calculated profiles for each phase in

n.sub files 3 Like 2 but background added to each

profile Ppl: Types of calc output-I 0 No action 1 Line printer plot in .out file 2 Generates background file 3 Difference pattern included in .bac file

Ioc: Types of calc output-II 0 No action 1 List of observed and calculated

integrated intensities in .out file 2 Reflection from 2nd wavelength if

different Mat:Correlation matrix 0 No action 1 Correlation matrix written in .out file 2 Diagonal of LS matrix printed before

inversion at every cycle

Pcr: Update of .pcr 0 after refinement 1 .pcr re-written with updated parameters 2 New input file generated called .new Ls1: Types of calc output-III 0 No action 1 Reflection list before starting cycles

written in .out file Ls2: Types of calc output-IV 0 No action 1 Corrected data list written in .out file 4 Plot of diffraction pattern displayed on

the screen at each cycle

LS3:Types of calc output-V 0 No action 1 Merged reflection list written in .out file Prf: Output format of Rietveld plot file 0 1 For WinPLOTR 2 For IGOR 3 For KaleidaGraph and WinPLOTR 4 For Picsure, Xvgr

Ins: Data file format 0 Free format, 7 comments ok = 1 D1A/D2B, original Rietveld = 2 D1B old format = 3 ILL instruments D1B, D20 = 4 Brookhaven, pairs of lines with 10 items = -4 DBWS program = 5 GENERAL FORMAT for TWO AXIS = 6 D1A/D2B format prepared by SUM, ADDET

or MPDSUM = 7 From D4 or D20L = 8 DMC at Paul-Scherrer Inst. = 10 X, Y, sigma format = 11 Variable time XRD = 12 GSAS

Rpa:Output .rpa/.sav file = 0 = 1 Prepares output file CODFIL.rpa = 2 Prepares file CODFIL.sav Sym:Output .sym file = 0 = 1 Prepares CODFIL.sym Hkl: Output of reflection list = 0 No action = 1 Code, h, k, l, mult, d_hkl, 2, FWHM, I_obs,

I_calc, I_obs-calc = 2 h, k, l, mult, sinq/l, 2, FWHM, F2, s(F2) = 3 Real and imaginary parts of structure factors,

h, k, l, mult, F_real, F_imag, 2, intensity = 4 h, k, l, F2, (F2) = 5 h, k, l, mult, F_calc, T_hkl, d_hkl, Q_hkl

Fou:Output of CODEFIL.fou = 0 No action = 1 Cambridge format = 2 SHELXS format = 3 FOURIER format = 4 GFOURIER Sho:Reduced output during refinement = 0 = 1 Suppress out from each cycle, only last

printed

EXPERIMENTAL SET UP CONTROLS (LINE 8) Lamda1:wavelength 1 Lamda2:wavelength 2 Ratio:I2/I1 If <0, parameters U,V,W for l2 read

separately Bkpos: Origin of polynomial for background Wdt:Cut off for peak profile tails in FWHM

units ~4 for Gaussian ~20-30 for Lorentzian ~4—5 for TOF Cthm:Monochromator polarization correction

muR:Absorption correction m = effective absorption coeff. R= radius or thickness of sample AsyLim: Limit angle for asymmetry

correction Rpolarz:Polarization factor Iabscor:Absorption correction for TOF data = 1 Flat plate perp. to inc. beam = 2 Cylindrical

REFINEMENT CONTROLS (LINE 9) NCY:Number of refinement cycles Eps:Control of convergence precisionForced termination when

shifts < EPS x e.s.d R_at Relaxation factor of shifts of atomic parameters: coordinates, moments, occupancies, Uiso’s R_an Relaxation factor for shifts of anisotropic displacement

parameters R_pr: Relaxation factor of profile parameters, asymmetry,

overall displacement, cell constants, strains, size, propagation vectors, user-supplied parameters

R_gl: Relaxation factor of Global parameters, zero-shift, background, displacement and transparency

Thmin:Starting scattering variable value (2θ/TOF/Energy) Step:Step in scattering variable Thmax: Last value of scattering variable PSD: Incident beam angle Sent0: Maximum angle at which primary beam completely

enlightens sample

NUMBER OF REFINED PARAMETERS

Maxs: Number of refined parameters (one integer, one line)

REFINEMENT CONTROLS II (LINE 14, REFINABLE)

Zero:Zero point for T Sycos: Systematic shift with cosθ

dependence Sysin:Systematic 2 shift with sin2θ

dependence Lambda:Wavelength to be refined More: Flag to read micro-absorption

coefficients ≠ 0 Line 15 is read to define

microabsorption

JASON-HODGES FORMULATION FOR TOF DATA (LINE 16)

Zerot: Zero shift for thermal neutrons Dtt1t: Coeff. #1 for d-spacing calc Dtt2t: Coeff. #2 for d-spacing

calculation x-cross:Position of the center of the

crossover region Width:Width of crossover region

REFINEMENT PARAMETERS FOR EACH PHASE (LINE 19)

Nat: Number of atoms in asymmetric unit Dis: Number of distance constraints Mom:Number of angle constraints or number of magnetic

moment constraints Jbt: Structure factor model and refinement method = 0 Rietveld Method = 1 Rietveld Method but purely magnetic phases = -1 Like 1 but with extra parameters in spherical coordinates = 2 Profile matching mode with constant scale factor = -2 Like 2 but modulus instead of intensity given in .hkl file = 3 Profile matching with constant relative intensities = -3 Like 3 but modulus instead of intensity given in .hkl file = 4 Intensities of nuclear reflections are calculated from Rigid

body groups = 5 Intensities of magnetic reflections calculated from conical

magnetic structures in real space = 10 Phase can contain nuclear and magnetic contributions = 15 Phase is treated as commensurate modulated crystal

structure 

Pr1, Pr2, Pr3: Preferred orientation in reciprocal

space for all three directions Irf: Method of reflection generation = 0 List of reflections for the phase

generated by space group = 1 h, k, l, mult read from .hkl file = 2 h, k, l, mult, intensity read from .hkl file = 3 h,k,l, mult, F_real, F_imag read

from .hkl file = 4 list of integrated intensities given as

observations

Isy: Symmetry operators reading control code = 0 Operators automatically generated from Space

Group = 1 Symmetry operators read below (use for

magnetism) = 2 Basis functions of irreducible representations of

propagation vector group instead of symmetry operators Str: Size-strain reading control = 0 Strain/size parameters correspond to selected

models = 1 Generalized formulation of strain used = 2 Generalized formulation of size used = -1 Options 1 and 2 simultaneously, size read before

strain = 3 Generalized formulation of size and strain

parameters Furth:Number of user defined parameters (only when

Jbt=4)

ATZ:Quantitative phase analysis coefficient ATZ = ZMwf2/t Z: Formula units per cell Mw: Molecular weight f: Site multiplicity t: Brindley coefficient for microabsorption Nvk: Number of propagation vectors Npr Specific profile function for the phase More: If not 0, then line 19-1 read

ATOMIC PARAMETERS (LINE 25) Atom:Atom name Typ:Atom type X, Y, Z:Coordinates Biso:Isotropic B factor Occ:Occupancy In/Fin:Ordinal number of first and last symmetry operator

applied to the atom (when users supply own list of reflections)

N_t: Atom type = 0 Isotropic atom = 2 Anisotropic atom = 4 Form-factor of atom is calculated Spc: Number of chemical species (For bond valence calcs.) betaij:6 numbers (i,j =1,2) for anisotropic factors (line

25b)

PROFILE SHAPE PARAMETERS Scale:Scale factor Shape 1:Profile shape parameter Bov:Overall isotropic B factor Str1, Str2, Str3:Strain parameters Strain Model: U,V,W:Half-width parameters X: Lorentzian isotropic strain param. Y: Lorentzian isotropic size param. GauSiz:Isotropic size parameter of Gaussian

character LorSiz:Anisotropic Lorentzian contribution of particle

size Size-Model:Size model selector

DATA RANGE PARAMETERS (LAST LINE)

2Th1/TOF1:First value for x-axis 2Th2/TOF2:Last value for x-axis