SHORT REFERENCE GUIDE
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Powder Diffraction Structure Analysis Program
DDM
Version 1.95
*************************************************
Includes Rietveld and Derivative Difference Minimization (DDM) methods
[L.A. Solovyov, J. Appl. Cryst. 37 (2004) 743-749]
Update/Download:
http://www.icct.ru/eng/content/persons/Sol_LA/ddm.html
http://sites.google.com/site/ddmsuite
http://l-solovyov.narod.ru/ddm.html
Leonid A. Solovyov
Institute of Chemistry and Chemical Technology
Academgorodok 50-24, 660036 Krasnoyarsk
Russia
E-mail: leosol@icct.ru
22 May 2012
General information
The program is designed for crystal structure analysis from powder diffraction data by making use of either Rietveld [H. Rietveld J.Appl.Cryst. (1969) 65], or Derivative Difference Minimization [L.A. Solovyov J.Appl.Cryst. (2004) 743] (DDM) method. In the DDM method the refinement is aimed not at minimizing the absolute difference between the experimental and calculated profiles but at minimizing the oscillations (or curvature) of the difference curve. The squared values of the difference curve derivatives are used in DDM as a measure of the difference curvature. The main advantage of this method is that it does not require the background line modeling or approximations. Eliminating the systematic errors caused by inadequate background definitions, DDM allows structure refinemet with increased stability and precision.
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COMMAND LINE: ddm.exe [Parameters file]
EXAMPLE: ddm.exe params.ddm
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I. Parameters
Parameters are stored internally in arrays XL(I,J), GLB(I), and PAR(I,J). XL contains the data for the atoms. The first index runs over the atoms; the second over the parameters for the atom. GLB contains those parameters which apply to all phases such as zero-point and background. PAR contains crystalline-phase dependent parameters such as lattice constants, scale factor, profile shape parameters n and m, preferred orientation parameters, etc. The first index runs over the phases. There are corresponding arrays LP, LGLB, and LPAR which map the parameters to the normal matrix elements. This mapping is determined by the user.
Codewords are entered for each parameter. A zero codeword means that the parameter is not being refined. Assume one wishes to vary the x,y,z coordinates of an atom and that y = x/2. If we let the codewords be given as:
x: 31.00
y: 30.50
z: 41.00
then x and y will be assigned to the third normal matrix parameter and z to the fourth. Also, 1.00 times the calculated shift in the third parameter will be applied to x and 0.50 times to y. The full calculated shift in the fourth parameter will be applied to z. In general, the codeword is formed as:
sign(A)*(10P + |A|)
where P is the parameter position in the matrix and A is the factor by which the computed shift will be multiplied before use. P is optional; a parameter will be refined if A is nonzero. The shifts are also multiplied by a relaxation factor before being applied to the parameters. The user may supply four different relaxation factors which apply to four different classes of parameters.
If P is zero, then the parameter position in the matrix is assigned by the program AUTOMATICALLY. Only those parameters which need to be restrained to have the same position in the matrix (as x and y in the above example) should be numbered by P in the codewords. Holes in the sequence of numbered codewords are removed automatically by the program. Making a line with codewords blank (in the Parameters file) is equivalent to assigning them zero values.
Starting from version 1.4 the manual numbering of symmetry related parameters is optional as the program imposes symmetry restrictions automatically.
MATHEMATICAL INFORMATION
1. Refinement method
The program uses the Newton-Raphson algorithm to minimize the quantity
, 
in the case of Rietveld refinement [Rietveld H. J. Appl. Cryst. (1969) 65], or
, 
in the case of Derivative Difference Minimization [Solovyov L.A. J. Appl. Cryst. (2004) 743],
where Yi and Yci are the observed and calculated profile intensities at the ith step, si is the variance in the observed profile intensity Yi and skj are the Savitzky-Golay (SG) coefficients for the derivative of order k with the convolution interval [-m, m]. The weights w depend on the exponent factor p that is chosen by the flag IWGHT in Line 7 of the Parameters file. In the Rietveld scheme p = 2(IWGHT+1); for DDM p = IWGHT.
The choice of the convolution interval [-m, m] for each data-point is controlled by the variables WDDM and CDDM specified in Line 7 of the Parameters file. The interval selection consists in finding the widest interval for which the deviations of the profile intensities from the fitted SG polynomial PSG satisfies certain criterion defined by the value of WDDM. This procedure generates narrower convolution intervals for profile regions with sharp features. CDDM limits the maximal interval width allowed (in degrees 2q).
If WDDM > 0, the selection criterion is based on the counting statistics:
< WDDM
If WDDM < 0, the selection is done according to the Durbin-Watson correlational statistics:
> 4 + 2WDDM + 2/(m-1) - 1/(2m+1)
The optimal ranges are: 1 < WDDM < 3 and -1.7 < WDDM < -1.3.
The variable structural and profile parameters vr are refined by solving the normal equations
for Rietveld refinement, or
for DDM.
The standard uncertainties of the variable parameters are estimated from the diagonal elements of a residual-related variance-covariance matrix Vx. In the Rietveld refinement Vx is calculated as
, 
, 
,
where A is the inverted normal matrix, Dn is the residual (Yn - Yñn), and x is the variable parameter. In the DDM mode the matrix Vx is derived as follows:
,
, 
, 
,
, 
, 
, 
, 
,
where 
and 
are the SG coefficients, and the summation in the expression for Lni
is done for all the profile points whose convolution interval [-m,
m] includes the nth point.
The refinement reliability factors are calculated as:
Rp = 100 S|Yi - Yci| / S(Yi - Ybi), the profile R-factor;
Rwp = 100 [Swi(Yi - Yci)2 / Swi(Yi - Ybi)2]1/2, the weighted profile R-factor;
Rexp = 100 [(N - P + C) / Swi(Yi - Ybi)2]1/2, the expected weighted R-factor;
RB = 100 S|I - Ic| / SIo, the Bragg R-factor;
where Ybi is the background intensity at the ith step, I and Ic are the "observed" (estimated from the observed profile) and the calculated integral reflection intensities;
RDDM = 
, DDM
R-factor;
DDM-Rw = 
,
simplified weighted DDM R-factor.
2. Calculated profile
The profile intensities Yci are calculated by summing the contributions from neighboring Bragg reflections, k, for all phases, p, plus the background, Ybi:
Yci = Sp sp {Sk [ |Fk|2 f(2qi - 2qk) Lk Pk Sa ]}p + Ybi,
where sp is the scale factor for phase p, Fk is the structure factor, f is a reflection profile function which approximates the effects of both instrumental and, possibly, specimen features, Lk contains the Lorentz, polarization and multiplicity factors, Pk is a preferred orientation function, and Sa includes the surface roughness, finite sample thickness and absorption corrections. The ratio of the intensities for the two wavelengths (if used) is absorbed in the calculation of |Fk|2, so that only a single scale factor is required for each phase.
The currently available profile functions are:
NPROF FUNCTION NAME
(0) exp[-Co(2qi - 2qk)2 /Hk2] ÖCo /HkÖp Gaussian (`G')
(1) [1+C1(2qi - 2qk)2 /Hk2]-1 ÖC1 /pHk Lorentzian (`L')
(2) [1+C2(2qi - 2qk)2 /Hk2]-2 2ÖC2 /pHk Lorentzian Mod 1
(3) [1+C3(2qi - 2qk)2 /Hk2]-1.5 ÖC3 /2Hk Lorentzian Mod 2
(5) nL + (1 - n)G, pseudo-Voigt ('pV')
n = NA + NB*2q
(6) (C4/Hk) [1 + 4(21/m - 1) (2qi - 2qk)2 /Hk2]-m, Pearson VII (`PVII')
m = NA + NB/2q + NC/(2q)2
for NPROF < 7: Hk = [(U + Aniso2)tan2q +V tanq +W + (Z + Aniso1Fder)/cos2q ]1/2
(7) nL + (1 - n)G, Thompson-Cox-Hastings (TCH) pseudo-Voigt
n = 1.36603q - 0.47719q2 + 0.1116q3 [Thompson P., Cox D.E., Hastings J.B.
q = HL / Hk, J. Appl. Cryst. (1987) 79]
Hk = (HG5 + 2.69269HG4HL + 2.42843HG3HL2 + 4.47163HG2HL3 + 0.07842HGHL4 + HL5)0.2,
for IAN3 > 0: HL = (X + Aniso21/2)tanq +(Y + Aniso11/2Fder)/cosq,
HG = [U tan2q +V tanq +W +Z/cos2q]1/2,
for IAN3 < 0: HL = X tanq +(Y + Aniso11/2Fder)/cosq,
HG = [(U + Aniso2)tan2q +V tanq +W +Z/cos2q]1/2,
where Hk is the full-width-at-half-maximum (FWHM) of the kth Bragg reflection, NA, NB, NC, U, V, W, Z, X, and Y are refinable parameters, and
Co = 4ln2, C1 = 4, C2 = 4(Ö2 - 1), C3 = 4(22/3 - 1), and C4 = 2G(m)(21/m - 1)1/2 / G(m - 0.5)Öp.
The anisotropic peak broadening terms are calculated as follows:
the size term, Aniso1 =d2(SIZ1h2 + SIZ2k2 + SIZ3l2 + SIZ42hk + SIZ52hl + SIZ62kl)/100
the strain term depends on IAN3 flag,
if IAN3=1, Aniso2 = d2(STR1h2 + STR2k2 + STR3l2 + STR42hk + STR52hl + STR62kl)/100
if IAN3=2, Aniso2 = d4[STR1h4 + STR2k4 + STR3l4 + 3(STR4h2k2 + STR5h2l2 + STR6k2l2) +
+ 2(STR7kh3 + STR8hl3 + STR9lk3 + STR10hk3 + STR11lh3 + STR12kl3) +
+ 4(STR13klh2 + STR14hlk2 + STR15khl2)]/10000
The term Fder responsible for the selective anisotropic broadening due to structural defects is calculated as described in ref [Solovyov L.A. J. Appl. Cryst. (2000) 338]. Its calculation involves the structure factor derivative with respect to a refinable parameter responsible for the defects (pseudo-position occupancy, for instance). The codeword number of the defect-responsible parameter is specified in the variable NDPAR (Line 13.2). If NDPAR=0, no broadening related to defects is considered.
The background intensity Ybi at the ith step may be obtained by any of several methods. The user's choice is indicated by the value of NBCKGD entered in the fourth position in Line 3 of the Parameters file. The choices are: (1) an operator-supplied file with background intensities Ibi (NBCKGD = 1), or (2) linear interpolation between operator-selected points in the pattern (NBCKGD = n, where n is the number of points), or (3) the background function (NBCKGD = 0):
where BKPOS is user-specified in Line 5 of the Parameters file. Note that the operator-supplied background intensities Ibi are optional; they are added to the background function when NBCKGD = 1.
The diffraction peak asymmetry is allowed for by giving the left side of a peak an additional broadening:
FWHM_left = FWHM_right + 2P1exp(-2q*0.084) + P2tanq,
where P1 and P2 are refinable parameters. Additionally, the peak asymmetry may be introduced by the approach of Finger, Cox & Jephcoat (1994) J. Appl. Cryst. 892. The respective refinable parameter FCJ (Line 13.8) is related to an effective slit_height/diffractometer_radius ratio that is considered to be equal to the sample_height/diffractometer_radius ratio.
The absorption and microabsorption correction for a flat sample is
Sak = m/mk + (1 - m/mk) exp(-0.0002PARSkmk/3) + ABSORP1exp[-0.0002PARSk(m - mk)/3-ABSORP2/sinq]
where ABSORP1 and ABSORP2 are adjustable parameters, m and mk are the linear absorption coefficients of the sample and the kth phase, and PARSk is the particle size [um]. ABSORP1 = -1 holds for the finite sample thickness effect and ABSORP1 > 0 holds for the surface roughness effect (equivalent to the Suortti model [Suortti P. J.Appl. Cryst. (1972) 325]). For a cylindrical sample:
Sa = exp[-(1.7133 - 0.0368sin2q)ABSORP3 + (0.0927 + 0.375sin2q)ABSORP32]
The preferred orientation function is:
Pk = G2 + (1-G2)P[1 + d2(EPR1h2 + EPR2k2 + EPR3l2 + EPR42hk + EPR52hl + EPR62kl)/100]-3/2,
with P = G2 + (1-G2) (G12cos2a + sin2a/G1)-3/2 (March-Dollase model chosen by IPREF=1)
or P = G2 + (1-G2)exp(-G1a2) (Rietveld-Toraya model chosen by IPREF=0)
where G1, G2, and EPR1...EPR6 are refinable parameters, a is the acute angle between the scattering vector and the preferred orientation direction in reciprocal space, and d is the reflection d-spacing. When the EPR coefficients are refined without restraints, the scale-factor SF is fixed.
3. Size-strain calculations
When the TCH profile function is used (NPROF = 7), the crystallite size and micro-strain calculations are performed based on the refined FWHM parameters. The estimated size and strain values are written to the Output file. The volume-weighted and area-weighted domain sizes DV and DA, and the maximum (upper limit) of strain e are calculated as:
DV = 1/bS, DA = 1/ 2bSL, e = bD/4,
bS = [2bSL + (bSL2 + 9bSG2)1/2]/3, bD = [2bDL + (bDL2 + 9bDG2)1/2]/3,
bSL = (Y - Ys)p2/360l, bDL = (X - Xs)p2/360,
bSG = [(Z - Zs)/pln2]1/2p2/ 360l, bDG = [(U - Us)/pln2]1/2p2/ 360,
where bS and bD are the approximations of the integral breadth of the size- and strain-broadened profiles derived from their Gaussian and Lorentzian components, Y, Z, X and U are the refinable parameters of the FWHM components HL and HG of the TCH function, Ys, Zs, Xs and Us are the respective FWHM parameters for an instrumental broadening standard (entered in Line 12 of the Parameters file), and l is the wavelength. An estimation of the average crystallite diameter <D> and its distribution dispersion s<D> is done using equations
<D> = DA+ (DADV)1/2 / 4 and s<D> = <D> (DV/DA - 1/2)/2
found empirically from fitting TCH function to simulated profiles for the model of spherical crystallites with different size distribution dispersions. The anisotropic diameter <D>aniso and strain eaniso are calculated similarly, but the Lorentzian breadth components are given by:
bSLaniso = (Y - Ys + Aniso11/2)p2/360l, bDLaniso = (X - Xs + Aniso21/2)p2/360.
4. Quantitative phase analysis calculations
In a mixture of N crystalline phases the net weight fraction Wi of phase i is given by:
Wi = SiMiViNi2 / S(SjMjVjNj2) (4.1)
where S is the scale factor, M and V are the unit cell mass and volume, N is the space group multiplicity.
If the internal standard with the weighted fraction Ws is used, the phase fractions are corrected:
Wi* = WiWs / W0, WR = 1 - S Wi* (4.2)
where W0 is the standard fraction calculated from (4.1), and WR is the residual “amorphous” fraction.
The external standard based calculations are performed as follows:
Wi* = mSiMiViNi2 / CT, WR = 1 - S Wi* (4.3)
where m is the sample mass absorption coefficient, C is the diffractometer constant (DIFC) determined from the external standard measurement, and T is the counting time of the current scan (TPS).
II. Description of input files
A. The Parameters file This file contains the control variables and the structural parameters. If output of a new input file is selected, the current input file will be updated at the end of the last cycle (see flag NXT in Line 4). A star (*) before a line number indicates that the line's existence depends on the value of a control variable. The parameters are entered in free format and should be separated by at least one space. In the mathematical expressions Q denotes the diffraction angle Theta. Line Par.N Description 1. Title - any 70 characters to be used to label the printout. 2. Data file name 3. 1 JOBTYP - 0 - X-ray case 1 - Neutron case(nuclear scattering only) 2 NPROF - profile selection 0 - Gaussian 4 - [Not used] 1 - Lorentzian (Cauchy) 5 - pseudo-Voigt(pV) 2 - Mod 1 Lorentzian 6 - Pearson VII 3 - Mod 2 Lorentzian 7 - Thompson-Cox-Hastings pV 3 NPHASE - number of phases in the sample 4 NBCKGD - background correction control 0 - polynomial background -1 - background to be estimated by weighted difference smoothing (see BKCURV, Line 5.10). The resultant curve is output to ddm_bckgr file 5 NEXCRG - number of excluded regions read from Line 10. 6 NSCAT - number of extra scattering sets read from Line 11. 7 INSTRM - data type 0 - laboratory Q-2Q X-ray data, or single detector neutron data (the Data file contains only profile intensities, see section B.) 1 - the Data file contains profile intensities and squared variances 2 - PANalytical XRDML data (multiple scans are summed) 3 - XY (2Theta Intensity) format 4 - XYE (2Theta Intensity Sigma) format 8 IPREF - preferred orientation function type 0 - Rietveld-Toraya function 1 - March-Dollase function 9 ISZSTR - size-strain instrumental standard used (for NPROF=7) If ISZSTR=1, instrumental broadening parameters US ZS XS YS are read from Line 12. 4. Output control flags (0 for off, >0 for on) 1 IWP =1: prf-file for WinPLOTR =2: weighted prf-file for WinPLOTR 2 IPL =1: text-files with calculated and observed intensities =2: text-files with weighted profile intensities 3 IPC =1: list of reflections =2: list of |F|obs, |F|calc & R-F 4 MAT =1: correlation matrix output 5 NXT =1: parameters file is updated after the last cycle 6 LST1 number of last refinement cycles to output 7 LST2 not used 8 LST3 not used 9 LST4 not used Line Par.N Description 5. 1 Lamda(1) - Wavelength1 2 Lamda(2) - Wavelength2 3 RATIO - Alpha2/Alpha1 intensity ratio 4 BKPOS - origin of background polynomial (in °2Q) 5 WDT - range of calculated peak profile in units of FWHM (beyond this the calc. profile is set to zero) 6 CTHM - monochromator coefficient in polarization correction [1 + CTHM*(cos2Q)2]/[sin2Q sinQ] 7 TMR - convolution interval for R-Bragg calculation and profile decomposition in units of FWHM 8 RLIM - peaks below this angle (2Q) are corrected for asymmetry by the Finger-Cox-Jephcoat approach 9 SAMPLE - angle (2Q) below which the intensities are corrected for the effect of the primary beam falling beyond the sample edges (Bragg-Brentano geometry only) An empirical correction is applied: Icor=I/(1+(.0128+.0106*(SAMPLE-2Q))*(SAMPLE-2Q)) 10 BKCURV - number ofvalues in the weighted difference smoothing estimation of the background curve 6. 1 MCYCLE - number of refinement cycles (starting from 0) 2 EPS - refinement convergence precision: run terminates when all parameter shifts are < EPS*e.s.u. RELAX - relaxation factors for parameter shifts 3 (1) - coordinates & isotropic displacement factors 4 (2) - anisotropic displacement parameters 5 (3) - profile, asymmetry, overall atomic displacement and preferred orientation parameters 6 (4) - peak shift and lattice parameters, overall scale factor, site occupancies 7. 1 NDEC - number of cycles for profile decomposition run (either DDM or Le Bail methods depending on CDDM) If NDEC > 0, the structure model is ignored and the squared structure factors F2 are read from ddm_ffobs file which is overwritten with the refined F2s after the final run cycle. If ddm_ffobs is absent, a set of equal F2 is applied at the first decomposition cycle. If both MCYCLE and NDEC > 0, the refinement of profile parameters is followed by NDEC decomposition cycles 2 MAXS - refined parameters control flag MAXS = 0 denotes refinement of all parameters with nonzero codewords MAXS = -1 removes all refinement codewords 3 WDDM - DDM convolution interval selection threshold If WDDM>0, the counting statistics is used (optimal WDDM=3) If WDDM<0, the Durbin-Watson statistics is used If WDDM=0, all convolution intervals are equal to CDDM 4 CDDM - maximal DDM convolution interval in degrees 2Q If CDDM=0, Rietveld refinement is performed instead of DDM 5 IWGHT - weighting scheme flag: for DDM IWGHT = 0, 1, 2; for Rietveld IWGHT = 0, 1 Line Par.N Description 8. Global parameters 8.1 1 ZER - zero-point for 2Q (in degrees) 2 DISP - sample displacement 2Q correction parameter 3 SHASM - asymmetry-related peak shift correction parameter 4 ABSORP1, 5 ABSORP2 - absorption correction coeffs. for flat sample: Icor=I*[1 + ABSORP1*exp(-ABSORP2/sinQ)] ABSORP1 = -1 holds for the finite sample thickness effect ABSORP1 > 0 holds for the surface roughness effect 6 ABSORP3 - absorption correction coeff. for cylindrical sample: Icor = I*exp[-(1.7133 - 0.0368*sin2Q)* ABSORP3 + + (0.0927 + 0.375*sin2Q)*ABSORP32] 8.2 Codewords for ZER, DISP, SHASM, ABSORP 8.3 BACK - polynomial background coefficients (six values) 8.4 FBACK - codewords for background coefficients *9. Not used *10. If NEXCRG > 0, there are NEXCRG lines ALOW - low angle bound of excluded region AHIGH - high angle bound of excluded region NOTE: A reflection will be excluded if any part of its calculated tail falls in this range. *11. If NSCAT > 0, there are NSCAT sets of lines for extra scatterers not included in the incorporated table of scattering factor coefficients *11.1 NAM - symbol identifying this set DFP - f', DFPP - f'', XMAS - Molecular mass, AMAC - mass absorption coefficient *11.2 Either one line of the form A1 B1 A2 B2 A3 B3 A4 B4 C, the coefficients for the analytic approximation to f, or a set of lines of the form Posi - Scat, where Posi = sinQ/lambda and Scat = f The set is terminated by a line with -100 in the first position. If the first form is desired, A2 can not = 0 *12. If ISZSTR = 1, there are instrumental broadening parameters US, ZS, XS, YS for size-strain calculations (only for NPROF=7). ******************************************************************************** At this point optional code-lines may be added beginning from $ symbol followed by the line-code and parameters: $QPA SWT DIFC TPS OMAC - quantitative phase analysis constants SWT - internal standard weight percent DIFC - diffractometer constant derived from external standard TPS - counting time of current data scan OMAC - overall sample mass absorption coefficient (if known) If SWT>0, the 1st phase is assumed as the internal standard If DIFC=0, TPS>0, the DIFC constant will be calculated If OMAC=0, the MAC will be derived from the atomic composition $BFILE Filename - background curve file name The program will read the background point positions and intensities in free format from the specified file. ******************************************************************************** 13. Phase parameters: NPHASE sets of lines (see Line 3) 13.1 PHSNM - name of phase (maximum 70 characters) 13.2 1 NATOM - number of atoms 2 IFUR - Fourier output flag If IFUR=1, F-factors are written to ddm_cif.cif If IFUR=2, F-squared are written to ddm_cif.cif 3 NDPAR - codeword number of the parameter responsible for structural defects (pseudoposition occupancy parameter, for instance) in the selective anisotropic broadening model [Solovyov (2000) J.Appl.Cryst. 338] 4 PREF(3) - preferred orientation direction h k l 5 PARS - Particle size [um] for the microabsorption correction 13.3 SYMB - space group symbol, e.g. P-1, P63/m, P21/n, P 1 1 2/b, I41/acd, Pmmn, Pmmn S, R-3c, R-3c R, HALL -P 3* 2N, ... ending R means RHOMBOHEDRAL setting, S means ORIGIN CHOICE 1 By default (if S is omitted) the ORIGIN CHOICE 2 with the inversion centre at (0,0,0) is selected Line Description ******************************* NATOM line sets ******************************** 13.4 4 lines for each of the N atoms 13.41 LABEL - identification characters for atom (4 characters) NTYP - link to scattering data for atom: either name from 11.1 or chemical symbol and valence to access the incorporated list of f-coefficients taken from the International Tables. x,y,z - fractional atomic coordinates B - isotropic temperature parameter N - occupation number (number of atoms in the unit cell) NOTE: if N = -1, the occupation number will be calculated by the program IANIS - isotropic (0) or anisotropic (1) temp. factor flag ADIST - maximal interatomic distance for GEOMETRY output If ADIST<0, ANGLES will not be output to CIF for this atom 13.42 CX,CY,CZ - codewords for the fractional atomic coordinates CB - codeword for the isotropic temperature parameter CN - codeword for the occupation number Lines 13.43 and 13.44 are entered only if IANIS = 1 *13.43 Beta11, Beta22, Beta33, Beta12, Beta13, Beta23 anisotropic temperature parameters *13.44 CB11, CB22, CB33, CB12, CB13, CB23 codewords for anisotropic temperature parameters ******************************************************************************** 13.5 13.51 SF - scale factor If SF = 0, it will be estimated by the program BQ - overall isotropic temperature factor 13.52 CSF, CBQ - codewords for SF and BQ 13.6 13.61 U,V,W,Z,X,Y - FWHM ("H") parameters For NPROF = 0...6 H2 = U*tan2Q + V*tanQ + W + Z/cos2Q X & Y are used only when NPROF = 7, where HGauss = [U*tan2Q + V*tanQ + W + Z/cos2Q]1/2 HLorentz = X*tanQ + Y/cosQ 13.62 CU,CV,CW,CZ,UX,UY - codewords for FWHM parameters 13.7 13.71 A, B, C, Alpha, Beta, Gamma - lattice parameters LAUE - reflection generation flag When LAUE = 1, the set of reflections is generated as for Laue class -1 disregarding the actual lattice symmetry. This option is required when the preferred orientation or anisotropic broadening directions are inconsistent with the crystal symmetry. 13.72 CA,CB,CC,CAlpha,CBeta,CGamma - lattice parameters codewords 13.8 13.81 G1, G2 - preferred orientation parameters, PO = G2 + (1 - G2)* PrefCorrr(G1) With IPREF=0, setting G1 to any number > 99.0 for a phase causes the program to generate for that phase only those reflections for which d* is parallel to the preferred orientation vector PREF specified in Line 13.2 P1, P2, FCJ - peak asymmetry parameters P1 and P2 are the split-FWHM asymmetry parameters: FWHM_left = FWHM_right + 2P1*EXP(-2 *0.084) + P2tan FCJ is an effective slit_height/diffractometer_radius ratio in the Finger, Cox & Jephcoat asymmetry model. The convergence of FCJ refinement may be slow and/or unstable for strongly overlapped and noisy data. Use an appropriate starting value (0.01-0.02), RLIM (Line 5) and relaxation factors (Line 6) 13.82 CG1, CG2, CP1, CP2, CFCJ - codewords for G1, G2, P1, P2, FCJ Line Description 13.9 Profile Shape parameters 13.91 NA, NB, NC For the usual pseudo-Voigt (NPROF=5) the Shape parameter n = NA + NB*2Q For the Pearson VII (NPROF=6) the Shape parameter m = NA + NB/2Q + NC/(2Q)2 For all other profiles listed (1 - 3, 7), NA, NB, NC, and their codewords must all be set to zero. 13.92 codewords for NA, NB, NC 13.10 FWHMmin, FWHMmax - lower and higher FWHM limits for the FWHM estimation procedure (undocumented) IAN3 - anisotropic strain model flag = 1 or -1 indicates 2nd rank anisotropy tensor: Aniso2 = (STR1*h2 + STR2*k2 + STR3*l2 + STR4*2hk + + STR5*2hl + STR6*2kl)*0.001*d2 = 2 or -2 indicates 4th rank anisotropy tensor: Aniso2 = [STR1*h4 + STR2*k4 + STR3*l4 + + 3(STR4*h2k2 + STR5*h2l2 + STR6*k2l2) + + 2(STR7*kh3 + STR8*hl3 + STR9*lk3 + + STR10*hk3 + STR11*lh3 + STR12*kl3) + + 4(STR13*klh2 + STR14*hlk2 + STR15*khl2)]*0.00001*d4 For NPROF < 7, H(a)2 = H2 + Aniso2*tan2Q For NPROF = 7 only: if IAN3 > 0, HLorentz(a) = HLorentz + Aniso21/2*tanQ if IAN3 < 0, HGauss(a) = HGauss + Aniso2*tanQ2 13.11 13.111 EPR(6) - six preferred orientation coefficients for the Ellipsoidal IPREF = 2) function: Icorr = Iobs[1 + (EPR1*h2 + EPR2*k2 + EPR3*l2 + + EPR4*2hk + EPR5*2hl + EPR6*2kl)*0.001d2]-1.5 NOTE: When EPR coefficients are refined without restrains, the scale-factor SF should be fixed. 13.112 CEPR(6) - codewords for EPR 13.113 SIZ(6) - six anisotropic size broadening coefficients The anisotropic broadening term is calculated as: Aniso1 = (SIZ1*h2 + SIZ2*k2 + SIZ3*l2 + SIZ4*2hk + + SIZ5*2hl + SIZ6*2kl)*0.001*d2 For NPROF < 7, H(a)2 = H2 + Aniso1/cos2Q For NPROF = 7, HLorentz(a) = HLorentz + Aniso11/2/cosQ 13.114 CSIZ(6) - codewords for SIZ 13.115 STR(1-6) - anisotropic strain broadening coefficients 13.116 CSTR(1-6) - codewords for STR Lines 13.117 - 13.120 are entered if IAN3 = 2 *13.117 STR(7-12) - anisotropic strain broadening coefficients *13.118 CSTR(7-12) - codewords for STR *13.119 STR(13-15) - anisotropic strain broadening coefficients *13.120 CSTR(13-15) - codewords for STR B. The Data file This file contains the data from the diffractometer. The first line contains the variables START, STEP, STOP and DATAID in free format: START - beginning angle in degrees 2Q STEP - step size in degrees 2Q STOP - last angle in degrees 2Q DATAID - alphanumeric string identifier The rest of the file consists of the data themselves in free format. Depending on the INSTRM parameter (Line 3) for each data-point either the profile intensity alone or both the intensity and its squared variance should be given. NOTE: The START angle assigned here must correspond to that of the first datum. The STOP angle can be any angle less than that of the last datum in the file. Any desired angular range can be selected for the refinement by (i) declaring an excluded region (NEXCRG in Line 3 and bounds in Line 10) from the START angle to the desired beginning and (ii) assigning the desired ending angle to STOP. C. Optional files 'ddm_ffobs', and 'ddm_fwobs' These files, if used, should be placed to the same folder from which the program was run. The file 'ddm_ffobs' contains estimated observed squared structure factors after the last refinement (or decomposition) run. It is rewritten automatically by the program. It can be created and/or edited manually if the structure factors need to be entered at the initial step of the profile decomposition procedure (see NDEC description in Line 7). The file 'ddm_fwobs' is optional. It may contain fixed FWHM values for selected reflections. Five parameters should be specified for each selected reflection: h, k, l, FWHM, Nphase where hkl are the indexes and Nphase is the number of phase to which the reflection belongs. The file format is free. EXAMPLE: 1 0 0 0.149 1 1 3 -1 0.209 1 1 0 1 0.242 2 ...................... If 'ddm_fwobs' file exists in the folder from which the program was run the FWHM values for the selected reflections are read from it and fixed (not refined). This option may be useful in difficult cases of anisotropic peak broadening when it can not be satisfactorily modeled. III. Description of output files File 'ddm_out.txt' contains detailed output listing File 'ddm_prf.prf' contains the observed and calculated patterns, which can be viewed by the popular program WinPLOTR. WinPLOTR is freely downloadable from: http://www-llb.cea.fr/fullweb/winplotr/winplotr.htm File 'ddm_prf.txt' is a text file with the observed, calculated, difference, and background profile intensities and the DDM convolution interval widths (in degrees 2Q). File 'ddm_ref.txt' contains positions and integral intensities of reflections. File 'ddm_cif.cif' is the Crystallographic Information File, which can be read by many programs for crystal structure visualization and analysis.