1. PXRD AND RIETVELD REFINEMENT
By Saurav Chandra Sarma and Dundappa Mumbaraddi
Solid State and Inorganic Chemistry Lab, NCU,
JNCASR
2. 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).
7. 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).
8. 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.
10. CRYSTALLITE SIZE
Crystallites smaller than ~120nm create broadening of
diffraction peaks. (scherrer’s equation)
Where,
D-Size of ordered domains
K-dimentionless Shape factor
Lamda-X-ray wavelength
β-Line broading at FWHM
Theta-Brage angle
11. 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)
12. PREFERRED ORIENTATION (TEXTURE)
Preferred orientation of crystallites can create a systematic
variation in diffraction peak intensities.
DOI: 10.1038/srep03679
37. 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
38. 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
39. 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..N If 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
40. Uni:Scattering variable unit
0 2θ in degrees
1 TOF in sec
2 Energy in keV
Cor:Intensity correction
0 No correction is applied
1 File with intensity corrections
2 File with empirical function
Opt:Calculation optimization
0 General procedures used
1 Optimizes calculations to proceed faster
Aut: Automatic mode for refinement codes
numbering
0 Codewords treated as usual.
1 Codewords treated automatically by program
41. 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
42. 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
43. 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
44. 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
45. 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.
= 10X, Y, sigma format
= 11 Variable time XRD
= 12 GSAS
47. 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
48. 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
49. 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
50. 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_anRelaxation 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
51. NUMBER OF REFINED PARAMETERS
Maxs: Number of refined parameters (one
integer, one line)
52. 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
53. 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
54. 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
55. 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
56. 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)
57. 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
58. 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)