********************************************************************************** ********************************************************************************** *************** ************************ *************** Documentation for MPREP5 and MPROFIL5 ************************ *************** ************************ ********************************************************************************** ********************************************************************************** PROGRAM AUTHORS - A. N. Fitch, A. D. Murray and A. Jouanneaux. A pair of programs which can be used sequentially to perform profile decomposition. The ".hkl" output file from an execution of MPROFIL5 can be used as input to the structure solution program "SIRPOW". TO RUN MPREP5 (UNIX implementation), TYPE mprep5 <"name".pre >mprep.out TO RUN MPROFIL5 (UNIX implementation), TYPE mprofil5 <"name".pro >mprofil.out The appropriate ".com" files for VMS systems are "mprep5.com" and "mprofil5.com", both of which are available in the current directory. N.B. The file "mpars.dat" ( see below ) containing the values of refineable parameters will be updated with each successive run of MPROFIL5. EXAMPLE FILES : The example files "cim.pre" (input to MPREP5), "cim.pro" (input to MPROFIL5) and "mpars.dat" (supplementary file to MPROFIL5) are available in the current directory. See original documentation below for detailed definition of the parameters contained in these input files ..... MANUAL FOR MULTIPHASE LEBAIL DECOMPOSITION PROGRAM MPROFIL version X14.6 MPREP version X5.0 1st August 1993 A.N. Fitch, A.D. Murray & A. Jouanneaux Manual for MPREP and MPROFIL LeBail Program Page 1 CONTENTS ________ SECTION PAGE The Rietveld and LeBail Methods 3 Possible Parameters 4 A) Overall Parameters 4 Refinement for Data Containing More Than One Phase 6 A Note on the Format of the Input Data 7 The MPREP Preprofile Preparation Program 8 Input Data for MPREP Program 8 Line: 1) Title 8 2) Number of Phasess and Background Type 8 3) Unit Cell Parameters for Each Phase 8 4) Profile Parameters 9 5) Halfwidth Parameters for Each Phase 9 6) Background Values 9 7) Excluded Regions 10 8) Number of Reflections 10 9) Denominators of Miller Indices for Each Phase 10 10) Reflection Data 10 11) Range of Profile Data or Datafile Name & Format 11 12) Profile Data 11 Input Data For MPROFIL LeBail Decomposition Program 13 Line: 1) Title 13 2) Overall Refinement Options 13 3) Text for Each Phase 15 4) Refinement Type for Each Phase 15 5) Output Options 16 Keyworded Input 16 6) Constraints Indicators 17 7) Structure Indicators for Each Phase 17 8) Wavelength(s) and Refinement Regulators 18 9) Preferred Orientation Axes 18 10) Unique Magnetic Axes 18 11) Symmetry Operators for Each Phase 19 Input of Scattering Factors 19 Optional Keyworded Line 20 12) Atomic Parameters 20 13) Scale Factors for Each Phase 20 14) Zeropoint, Specimen Displacement, Flat Plate Absorption Parameter and Depolarization Factor 20 Manual for MPREP and MPROFIL LeBail Program Page 2 CONTENTS (Contd.) _________________ SECTION PAGE 15) Halfwidth Parameters for Each Phase 21 16) Cell Parameters for Each Phase 21 17) Preferred Orientation and Asymmetry Parameters 22 18) Background Parameters 22 Refinement Codewords 22 19) Codewords for Atomic Parameters 23 20) Codewords for Scale for Each Phase 23 21) Codewords Zeropoint, Specimen Displacement, Flat Plate Absorption Parameter and Depolarization Factor 24 22) Codewords for Halfwidth Parameters for Each Phase 24 23) Codewords for Cell Parameters for Each Phase 25 24) Codewords for Preferred Orientation and Asymmetry Parameters 25 25) Codewords for Background Parameters 25 26) Lineprinter Profile Output 25 The Mprep and Mprof Commands 26 Acknowledgements 26 Enquiries About the Program 26 Disclaimer 26 Manual for MPREP and MPROFIL LeBail Program Page 3 The Rietveld and LeBail Methods _______________________________ Where extensive overlap occurs between adjacent reflections in a powder-diffraction pattern, it is not possible to obtain directly the integrated intensity of each of the contributing reflections. H.M. Rietveld in his paper "A Profile Refinement Method for Nuclear and Magnetic Structures", J. Appl. Cryst. 2, 65-71 (1969), describes the method which allows the refinement of a crystal structure from the composite profile of the powder-diffraction pattern. Rather than considering the individual integrated intensities of the Bragg peaks for structural refinement, the Rietveld method uses the method of least-squares to fit a calculated diffraction profile to the measured diffraction profile. The profile is calculated as a sum of overlapping peaks which are described by an assumed peak-shape function (often Gaussian, or pseudo-Voigt). The position of each peak is governed by the refined values of the unit-cell parameters (and the instrumental zero-point and any other geometric corrections such as specimen displacement etc.), the full-width at half maximum height follows a simple function of theta, controlled by three (or possibly four) refinable values, and the integrated intensity of each peak depends on the structure factor, and hence on the atomic parameters. The profile can therefore be described by the equation: y(i) = SUM(np)[SUM(k)[C(k)*F(k)*PSF(theta(i,k))]] + B(i) (1) Where: y(i) is the calculated profile at each point (i). SUM(np) is the sum over all phases contributing to the profile. SUM(k) is the sum over all reflections that contribute at each point (i) F(k) is the structure factor squared of each reflection (k). PSF(k) is the peak shape function of each reflection (k). C(k) is a modification term taking into account factors such as the. Lorentz, polarization, preferred orientation & asymmetry parameters etc. B(i) is the calculated background at each point (i). Thus the least-squares method can be used to obtain the best fit between observed and calculated profiles, by refining the values of the lattice parameters (zero-points etc.), the half-width parameters, and the atomic parameters. The quality of the fit is judged by the value the ratio of the "Weighted profile" & "Expected" R-factors, the "Chisq" value. For a good fit "Chisq" should be close to 1.0. The Rietveld method is for the refinement of a crystal structure. When solving structures from powder data it is necessary to extract the intensities of the overlapping peaks without a structural model. The LeBail method allows this to be done, given a starting set of unit cell parameters, and a list of possible reflections. The method is similar to Rietveld in that a calculated profile is refined by least squares against the observed diffraction pattern. Hence lattice parameters, peak widths, peak-shape parameters are allowed to vary. The intensities are, however, unknown. In the Rietveld method, at the end of the least- squares cycles, overlapping intensity can be partitioned between the reflections in the ratios predicted by the structural model. In the LeBail method, the intensity is partitioned between overlapping peaks from arbitrarily assigned starting values - all equal say. At the end of the first cycle, the peaks no longer have equal intensities. The strong peaks will be strong, and the weak peaks weak. The process is repeated. The overlapping intensity is now partitioned using the new intensities such that the strong peaks take a larger fraction and another new set of intensities results. The process is cycled until a stable refinement is obtained. Hence the LeBail method uses the observed intensities directly to partition the intensity between overlapping peaks. Manual for MPREP and MPROFIL LeBail Program Page 4 Computationally, the method may be divided into two parts: Stage (1) Program MPREP _______________________ The (optional) subtraction of an estimated background, followed by the determination, (from consideration of the lattice parameters, zero- point, half-width parameters and peak-shape function), of which reflections may contribute to each of the observed points in the powder diffraction profile. This is the "pre-profile" step, and is carried out separately from least squares refinement since it involves considerable reorganisation of data which must be regrouped in the most convenient form. The value of the least-squares weight assigned to each profile point is also calculated in this stage. Stage (2) Program MPROFIL _________________________ The refinement of the profile and the extraction of the intensities from the data prepared in stage (1). The following documentation describes computer programs written in FORTRAN 77 and performing the functions required for stages (A) and (B) above. These programs are extensive modifications of those originally described by Rietveld. Possible Parameters ___________________ The parameters needed to refine a profile by the LeBail method include the following: (A) Overall Parameters: __________________ 1) The wavelength of the diffracted radiation. 2) The unit cell dimensions of the diffracting material, either as "a", "b", "c", "alpha", "beta", and "gamma" in Angstroms and degrees, or as the components of the reciprocal metric tensor, "aa", "bb", "cc", "bc", "ac", and "ab", where the reciprocal d- spacing is given [in Angstroms**-1] by: d* = sqrt( aa*h*h +bb*k*k +cc*l*l +bc*l*k +ac*l*k +ab*h*k) (6) where aa = a"*a"; bb = b"*b"; cc = c"*c"; bc = 2*b"*c"*cos(alpha"); ac = 2*a"*c"*cos(beta"); and ab = 2*b"*c"*cos(gamma"); the double prime (") is used to denote reciprocal cell parameters. The cell parameters actually refined are those formed by the reciprocal metric tensor. 3) A zero-point correction and corrections for peak-shifts caused by displacement of the sample from the axis of the diffractometer. 4) An arbitrary scale factor relating the observed and calculated diffraction profiles. 5) The peak shape function parameters Five functions to describe the peak shape are currently available: Manual for MPREP and MPROFIL LeBail Program Page 5 a) Gaussian G(theta(i)) = sqrt((4ln 2)/pi)/H(k)*exp(-4ln 2*(X/H(k))**2) Where: X = (2theta(i) - 2(theta(k)) (7) H(k) = sqrt(U*(tan(theta(k)))**2 + V*tan(theta(k)) + W + X/(cos(theta(k))**2 (8) theta(i) is the theta value of each profile point (i) 2theta(i) is twice theta(i) ie the two theta value of each profile point theta(k) is the expected theta value for each reflection (k) theta(k) is the expected theta value for each reflection (k) H(k) is the full width at half maximum for each reflection (k) U,V,W and X are the "halfwidth" parameters ln 2 is the natural log. of 2.0 (0.6931471806) pi is 3.141592654 Refinable parameters: U,V,W,X b) Variable Lorentzian (Pearson VII) L(theta(i) = (sqrt(C/pi)/(H(k)*([1 + C*(X/H(K))**2]**m)) (9) C = 4(2**(1/m) - 1) m is the Lorentzian order which varies between 0 and infinity. m = 1.0 gives the "pure" Lorentzian function m = 1.5 gives the "intermediate" Lorentzian function m = 2.0 gives the "modified" Lorentzian function Refinable parameters: U,V,W,X,m c) Pseudo-Voigt p-V(theta(i) = n*L(theta(i) + (1-n)*G(theta(i)) (10) n is the mixing parameter which varies between 0 and 1 Refinable parameters: U,V,W,X,n d) Split Pearson VII (Toraya,H. (1986) J. Appl. Cryst. 19,440) PVII(theta(i)) = Q/H(k)/[1 + (((1+As)/As)**2)*C1*(X/H(k))**2]**Lo for 2theta(i) less then or equal to theta(k) PVII(theta(i)) = Q/H(k)/[1 + ((1+As)**2)*C2*(X/H(k))**2]**Ho for 2theta(i) greater than theta(k) C1 = (2**(1/Lo) - 1) C2 = (2**(1/Ho) - 1) As(theta(k)) = As(1) + As(2)/sin(theta(k) + As(3)/(sin(theta(k))**2 Lo(theta(k)) = Lo(1) + Lo(2)*sin(theta(k) + Lo(3)/sin(theta(k) Ho(theta(k)) = Ho(1) + Ho(2)*sin(theta(k) + Ho(3)/sin(theta(k) (11) Q is a function of As, Lo and Ho Refinable parameters: U,V,W,X,As(1-3),Lo(1-3),Ho(1-3) e) Variable pseudo-Voigt p-V(theta(i)) = nv*L(theta(i) + (1-nv)*G(theta(i)) nv(theta(k)) = p(1) + p(2)*tan(theta(k) + p(3)/cos(theta(k)) (12) Refinable parameters: U,V,W,X,p(1-3) Manual for MPREP and MPROFIL LeBail Program Page 6 f) Parameterised pseudo-Voigt (Thompson,P., Cox,D.E. & Hastings,J.B. (1987) J. Appl. Cryst. 20,79) p-V(theta(i) = n*L(theta(i) + (1-n)*G(theta(i)) n = 1.36603*(Yl/Y) - 0.47719*(Yl/Y)**2 + 0.11116*(Yl/Y)**3 Y = [Yg**5 + 2.69269*Yl*Yg**4 + 2.42843*(Yl**2)*(Yg**3) + 4.47163*(Yg**2)*(Yl**3) + 0.07842*Yg*Yl**4 + Yl**5]**(1/5) Yg(theta(k)) = sqrt(U*(tan(theta(k)))**2) + V*tan(theta(k)) + W) Yl(theta(k)) = X/cos(theta(k)) (13) Refinable parameters: U,V,W,X 6) Correction factors for preferred orientation in the sample and asymmetry in the peak shape itself. The preferred orientation correction takes the form: exp(-G*alpha**2) (14) where "alpha" is the acute angle between the scattering vector and the preferred orientation axis, and "G" is the asymmetry parameter. The correction assumes a Gaussian distribution of the preferred orientation axes of the individual crystallites about the axis of the sample. The asymmetry correction takes the form: (1-[P*(2theta[i]-2theta[k])**2]*s/tantheta) (15) where "s" is a quantity of unit magnitude, but which takes the sign of "(2theta[i]-2theta[k])", and "P" is the asymmetry parameter. 7) Background Parameters. A refinable background function is available, consisting of a 5th order polynomial. B(i) = BK0 + BK1*theta(i) + BK2*theta(i)**2 + BK3*theta(i)**3 + BK4*Theta(i)**4 + BK5*theta**5 (16) B(i) is the background at each profile point BK0-BK5 are the refinable background parameters theta(i) is in radians Refinement for Data Containing More Than One Phase __________________________________________________ Data containing more than one diffracting phase may arise in a number of ways; for example: 1) high or low temperature studies in which the sample environment (container, cryostat or furnace) gives a diffraction pattern. 2) samples which almost invariably contain a secondary phase, e.g. impurity or genuine multi-phase behaviour. 3) experiments in which the preferred orientation of plate-like crystallites is reduced by mixing the sample with a powder - usually one giving relatively few Bragg peaks. Manual for MPREP and MPROFIL LeBail Program Page 7 4) gas adsorption studies where the substrate gives a pattern. Secondary experiments are sometimes performed to subtract the subsidiary pattern(s). However, this is usually not possible. This version of the program allows calculation and refinement of a profile with contributions from up to three phases. A Note on the Format of the Input Data ______________________________________ All of the input instructions are read in a "free-format" mode, in which all numeric values must be terminated by at least one space character or a comma. Certain defined values are expected to be integers and should therefore not include decimal points, but there is no requirement to insert a decimal point in a decimal value unless there are figures following it. The program also recognises simple fractions (e.g. 1/2, 1/6) and exponential format (1.6D-10, -3.2E+4). For the most part, the program scans one line of input data at a time searching for a definite number of values. If not all of these values are found then those not specified are set to zero. Hence, if the program expects to read five decimal values from a line of input data, the following representations are equivalent: 1 2 1 2 0 0 0 1.0 2.0 0.0 0.0 0.0 as are the combinations possible with or without decimal points: 1 2.0 etc. In the above example, note that the specification of the fifth value, but not the third or fourth, would require one of the following: 1 2 0 0 3 1.0 2.0 0.0 0.0 3.0 Lines beginning with a "#" symbol (Ascii 45) are treated as comments and will normally be ignored by the programs. Comments cannot be included in the input diffraction data. In the description of the input data required by the program given in the remainder of this document, the following conventions are used: ivalue - indicates that input of an integer value is reqired. value - indicates that input of a real (floating point) number is required. char - indicates that input of a character string is required. Lines marked "For Each Phase" must be repeated for each phase. Manual for MPREP and MPROFIL LeBail Program Page 8 MPREP Preprofile Preparation Program ____________________________________ Before the refinement can be carried out, it is necessary to determine which reflections contribute to which parts of the powder pattern. This task may be carried out more than once during the course of refinement because alteration of the unit cell and profile parameters changes the relationship between the reflections and the profile. It is recommended that the profile preparation stage should be repeated if significant changes in the unit cell or profile parameters occur. ************************************************************ ********* ************ ****** Input Data for MPREP5 Program ********* ********* ************ ************************************************************ Line 1. Title _____________ A title consisting of up to 80 hollerith characters which will be output as a heading for the printed results. Line 2. Number of Phases and Background Type ____________________________________________ ivalue(2.1) the number of phases in the scan. ivalue(2.2) background type. allowed values: 0 a background is subtracted and only those parts of the pattern contributing to the Bragg reflections are passed to the profile refinement program. 1 no background is subtracted and the whole pattern is passed to the profile refinement program. 2 a background is subtracted and the whole pattern is passed to the profile refinement program. Line set 3. Unit Cell Parameters for Each Phase _______________________________________________ value(3.1) > a < > aa. > < > value(3.2) > b < > bb. > < > value(3.3) > c < > cc. > < or > value(3.4) > alpha < > bc. > < > value(3.5) > beta < > ac. > < > value(3.6) > gamma < > ab. When value(3.1) is greater than 1.0, the input is assumed to contain the real cell dimensions, "a", "b", and "c" in angstroms, and "alpha", "beta", and "gamma" in degrees. otherwise, the unit cell is input as the components of the reciprocal metric tensor, "aa", "bb", "cc", "bc", "ac", and "ab". This line must be repeated for each phase. Manual for MPREP and MPROFIL LeBail Program Page 9 Line 4. Profile Parameters __________________________ value(4.1) the zeropoint error relating the true two theta value to that indicated by the counter arm scale (in units of hundredths of a degree). The zero point error is subtracted from the scale reading in calculating the true two theta value. value(4.2) the neutron or synchrotron-radiation wavelength, or for conventional x-ray refinement, the wavelength of the x-ray alpha-1 radiation. value(4.3) the two theta range over which a reflection is assumed to yield a significant contribution to the profile is calculated from: 2*value(4.3)*H(k), where H(k) is the halfwidth calculated from the profile parameters, "U", "V", and "W" using equation (7). The remaining two values should only be supplied when conventional x- ray refinement is carried out. value(4.4) the wavelength of the x-ray alpha-2 radiation. value(4.5) the monochromator polarisation constant, (cos(twotheta-m))**2. value(4.6) is reset to 1.0 if input as zero. Line set 5. Halfwidth Parameters for Each Phase _______________________________________________ value(5.1) > < U. > < value(5.2) > halfwidth parameters (in units < V. > of hundredths of a degree). < value(5.3) > < W. As defined in equation (7) Line set 6. Background Values _____________________________ Up to 100 background values may be given in the form: value(6.1) two theta in units of hundredths of a degree. value(6.2) background count at two theta equals value(6.1). The input of background values is terminated by a line where value(6.1) is given as -100. The first background value should be given either before or at the point where the first profile intensity was measured. Background counts at intermediate points are obtained by linear interpolation. Manual for MPREP and MPROFIL LeBail Program Page 10 Optional line set 7. Excluded Regions _____________________________________ Up to 10 regions of the measured profile may be omitted from the calculation. These regions are defined by lower and upper bounds in two theta given in units of hundredths of a degree. value(7.1) -(lowest two theta value of the excluded region) value(7.2) -(highest two theta value of the excluded region) Note that the minus signs are obligatory. When regions to be excluded are specified, the input of such values is terminated by a line where value(7.1) is given as -100. This terminator should be omitted when no excluded regions are given. Line 8. Number of Reflections _____________________________ ivalue(8.1) the number of reflections To be supplied in line set 10. (Maximum 3000). Line set 9. Denominators of Miller Indices for Each Phase _________________________________________________________ The denominators of the Miller indices are included to eliminate the need for non-integral Miller indices in the case of cell enlargement. The program interprets the Miller indices supplied in line set 9 as: [ivalue(10.2)/ivalue(9.1)]; [ivalue(10.3)/ivalue(9.2)]; [ivalue(10.4)/ivalue(9.3)]. ivalue(9.1) > < > < ivalue(9.2) > the denominators of the Miller indices. < > < ivalue(9.3) > < Line set 10. Reflection Data ____________________________ Ivalue(8.1) reflections must be supplied. the data required for each is: ivalue(10.1) composite code number: (10*phase serial number)+reflection code number. For phase no.1 the serial number may be omitted. Allowed values of this reflection code number are: 1 reflection arising solely from neutron nuclear scattering, or from synchrotron-radiation. 2 reflection arising solely from neutron magnetic scattering. 3 reflection arising from both neutron nuclear and magnetic scattering. 4 conventional x-ray alpha-1 reflection. 5 conventional x-ray alpha-2 reflection. ivalue(10.2) > < h. > < ivalue(10.3) > Miller indices < k. > < ivalue(10.4) > < l. ivalue(10.5) multiplicity of reflection. Manual for MPREP and MPROFIL LeBail Program Page 11 Line 11. Range of Profile Data or Datafile Name and Format __________________________________________________________ EITHER; char(11.1) DATA char(11.2) 30 characters maximum char(11.3) where is the name of the file containing the profile data, and is one of D1A, PDS, or HAR, depending on the format of the profile data, value(11.4) start angle for reading the data from the file. value(11.5) finish angle for reading the data from the file (angles in degrees * 100). If value(11.4) or (11.5) is omitted then the maximum range of profile data is used. OR; ivalue(11.1) profile type indicator. When ivalue(11.1) is greater than 10, then it is taken as the two theta value in units of hundredths of a degree at which the profile data commences, and the data must be supplied according to the specifications of line set 12a. Otherwise, the profile data is assumed to comply with the specifications of line set 12b, and the precise value of ivalue(11.1) is unimportant. ivalue(11.2) two theta interval between consecutive profile points in units of hundredths of a degree. ivalue(11.3) two theta value of the last profile point in units of hundredths of a degree. Optional line set 12a. Profile Data ___________________________________ To be supplied only when ivalue(11.1) is greater than 10 Formatted input in format (10(F2.0,F6.0)) Ten counter readings must be supplied on each line, with the possible exception of the last line in the set. These values must be sorted on two theta, and must be recorded from an initial two theta value of ivalue(11.1) in constant steps of ivalue(11.2) until a two theta value of ivalue(11.3). The very first counter reading input is assumed to be that measured at a two theta value of ivalue(11.1), the second at ivalue(11.1) + ivalue(11.2), and the nth at ivalue(11.1) + (n-1)*ivalue(11.2). The last counter reading input is that where two theta equals ivalue(11.3). For data with intensities as counts per counter & number of counters, the latter occupy the first two columns of every eight for a data point. Data from the D1A diffractometer at I.L.L. Grenoble is usually obtained in this format. Manual for MPREP and MPROFIL LeBail Program Page 12 Optional line set 12b. Profile data ___________________________________ To be supplied only when ivalue(11.1) is less than or equal to 10 Formatted input in format(I8,F8.0) Each line of input contains two values: ivalue(12b.1) two theta value in units of hundredths of a degree at which a count of value(12b.2) was recorded. ivalue(12b.2) the count measured at two theta equals ivalue(12b.1). The data points supplied must be sorted on two theta in increasing order. The last point input is that where ivalue(12b.1) equals ivalue(11.3). Data from AERE, Harwell is normally converted to this format after processing (by the "Collate" program). Manual for MPREP and MPROFIL LeBail Program Page 13 ************************************************************************** ******** ********* ***** Input Data for MPROFIL LeBail Decomposition Program ****** ******** ********* ************************************************************************** Line 1. Title _____________ a title consisting of up to 80 characters which will be used as a heading for printed output, or, up to twenty lines of 80 characters each, preceded by a line whose first five characters are TITLE, and terminated by a line whose first three characters are END. Line 2. Overall Refinement Options __________________________________ ivalue(2.1) number of refinement cycles. If specified as zero, then structure factors and profile intensities will be calculated and may be output. (Maximum 99). ivalue(2.2) number of phases (Maximum 3). ivalue(2.3) number of parameters To be refined. (Maximum 300) ivalue(2.4) a non-zero value indicates that an asymmetry parameter is to be applied to the pattern and requires inclusion of value(2a.1). ivalue(2.5) allowed values of this parameter are: 0 a normal single zero-point correction will be applied. A non-zero value leads to the application of a correction to the peak positions arising from displacement of the sample from the axis of the diffractometer. 1 Debye-Scherrer geometry, Delta 2theta = a/R*cos(2theta) - b/R*sin(2theta) 2 Flat plate, theta - 2theta geometry, Delta 2theta = b/R*cos(theta) 3 Flat plate at fixed sample angle alpha, delta 2theta Delta 2theta = b/R*sin(2theta/R)*sin(alpha) 4 Flat plate transmission geometry, Delta 2theta = -a/R*sin(2theta) where a and b are sample displacement in the directions parallel with and perpendicular to the incident beam, respectively, and R is the sample to detector distance. The parameters To be entered are value(14.2) and possibly value(14.3). ivalue(2.6) a non-zero value leads to calculation of an empirical background determined as a polynomial of order 5 and requires inclusion of optional line 18. Manual for MPREP and MPROFIL LeBail Program Page 14 ivalue(2.7) a non-zero value leads to the application of an absorption correction. allowed values are: 0 Debye-Scherrer geometry, or a fully absorbing flat plate specimen in theta - 2theta geometry. No correction for absorption is applied. 1 Partially absorbing flat plate specimen in theta - 2theta geometry. 2 Fully absorbing flat plate specimen at fixed sample angle alpha. 3 Partially absorbing flat plate specimen at fixed sample angle alpha. 4 Symmetric scanning transmission geometry. 5 Transmission geometry at fixed sample angle alpha. 6 Capillary Sample All non-zero options require input of the absorption parameter(value 14.4). Options 2, 3 and 5 additionally require the sample angle alpha, value(2a.2). ivalue(2.8) a non-zero value leads to correction for depolarisation of the incident synchrotron radiation, when the beam is not 100% polarised in the plane perpendicular to the incident and diffracted beams. 0 incident beam is 100% plane polarised. 1 incident radiation is on average value(16.5)x100% depolarised. 2 incident radiation is on average value(16.5)x100% depolarised and the diffracted beam is incident upon an analyser crystal (whose normal lies in the plane of the incident and diffracted radiation) which acts as a receiving slit before the detector. Option requires the further input of the two theta angle of the analyser crystal, value(2a.3). Note this option only applies to synchrotron radiation. ivalue(2.9) a non-zero value leads to Fourier filtering of the residual background and requires inclusion of values(2a.4) to (2a.7). If ivalue(2.9) equals 2 the values from a previous refinement will be read in from the file (see keyword options). ivalue(2.10) a non-zero value leads to correction to the intensities arising from absorption of a covering film over a flat plate sample, and requires the absorption parameter of the film values(2a.8). ivalue(2.11) a non-zero value leads to minimisation using proportionate discrepancies. This option should be set when performing a multi-phase refinement using different scale factors for each phase, when refining conventional alpha1 alpha2 X-ray radiation, and is set automatically when refining a background function. Manual for MPREP and MPROFIL LeBail Program Page 15 Optional line set 2a. _____________________ value(2a.1) the 2theta angle in degrees below which the asymmetry correction is to be applied. To be supplied only when value(2.4) is non-zero. value(2a.2) the fixed angle in degrees of a flat plate specimen. To be supplied only if ivalue(2.5) equals 3, or ivalue(2.7) equals 2, 3 or 5. value(2a.3) the 2theta angle of the analyser crystal before the detector when synchrotron radiation is used. To be supplied only when ivalue(2.8) equals 2. value(2a.4) starting value for the summation in real space for Fourier filtering (in Angstrom - recommended value = 0.0). value(2a.5) end value for the summation. value(2a.6) step value for the summation. value(2a.7) number of data points To be used in the inverse Fourier transform (a zero value uses all profile points). Values(2a.4) - (2a.7) are To be supplied only if ivalue(2.9) is non-zero. value(2a.8) the absorption parameter (mu x t) of the covering film. To be supplied only when ivalue(2.10) is non-zero. Line set 3. Text for Each Phase _______________________________ Up to 16 characters which will be used as a heading on output. Line set 4. Refinement Type for Each Phase [Use only 0,4 or 5 for LeBail __________________________________________ decomposition] ivalue(4.1) refinement type indicator. 0 neutron nuclear scattering only. 1 neutron nuclear scattering plus magnetic scattering calculated from the formula given by O. Halpern and M. H. Johnson (Physical Review 1939, vol. 55, p. 898). 2 neutron nuclear scattering plus magnetic scattering calculated from the special formula for uniaxial configuration spin symmetry (Shirane, loc.cit. This option requires the inclusion of optional line 10.) 3 neutron nuclear scattering plus magnetic scattering calculated from the special formula for cubic configurational spin symmetry (Shirane, loc. cit.). 4 diffraction of synchrotron radiation. 5 conventional x-ray diffraction, alpha-1 and/or alpha2. ivalue(4.2) peak-shape function indicator. 0 Gaussian peak-shape. 1 Variable Lorentzian (Pearson VII). 2 Pseudo-Voigt. 3 Split Pearson VII (Toraya). 4 Variable pseudo-Voigt. 5 Parameterised pseudo-Voigt (Thompson, Cox & Hastings). ivalue(4.3) a non-zero value leads to the application of the preferred orientation correction, and requires the inclusion of optional line 9 and optional value (17.1). Manual for MPREP and MPROFIL LeBail Program Page 16 Line 5. Output Options ______________________ ivalue(5.1) a non zero value leads to the output of the least-squares parameters, in a form suitable for re-input, to the new parameters file. 1 output the parameters. 2 output the parameters and R-factors. ivalue(5.2) a non-zero value leads to output of the observed and calculated profiles in a form suitable for the PLOT plotting program. ivalue(5.3) a non-zero value produces output of a file containing the final observed and calculated F squared for phase abs(ivalue(5.3)) in a form suitable for input to SIRPOW (ivalue(5.3) positive) or SHELXS (ivalue(5.3) negative) ivalue(5.4) a non-zero value produces output of the final observed and calculated peak intensities (and optionally, profile intensities) to the lineprinter file. allowed values are: 1 output peak intensities. 2 output structure factor squared. -1 output peak intensities and observed and calculated profiles. -2 output structure factor squared and observed and calculated profiles. Keyworded Input _______________ Optional keyworded input can be supplied. The format of this input is KEYWORD -------- parameter list If any keyword is not supplied, the default values shown will be used. Allowed keywords are: CHEC check validity of input data only. No refinement or calculation of intensities will be carried out. INPU filename (30 characters) Binary input file created by MPREP program. Default: for003.dat NEWP filename (30 characters) Output file for refined parameters (and R-factors). Default: mpars.dat PLOT filename (30 characters) Output file for observed and calculated profiles. Default: for007.dat SOUN turn on sound option. Manual for MPREP and MPROFIL LeBail Program Page 17 Line 6. Constraints Indicators [both zero for LeBail decomposition] ______________________________ ivalue(6.1) a non- zero value indicates that ivalue(6.1) "strict" constraint function(s) will be supplied, and requires the inclusion of optional line set 26. ivalue(6.2) a non-zero value indicates that ivalue(6.2) chemical constraint function(s) will be supplied, and requires the inclusion of optional line set 27. Line set 7. Structure Indicators For each Phase [all zero for LeBail _______________________________________________ decomposition] ivalue(7.1) [non] centrosymmetric key. allowed values of this parameter are: 1 the structure is non-centrosymmetric. 2 the structure is centrosymmetric. ivalue(7.2) the number of spacegroup symmetry operators which define the nuclear structure. Exclude the identity operation (x,y,z), operations related by a centre of symmetry and those due to centred cells. The maximum number of operators which may be supplied is therefore 23. ivalue(7.3) the number of atoms contained in the asymmetric unit of the structure. (Maximum 99). ivalue(7.4) the number of different types of atom which give rise to neutron nuclear scattering. (Maximum 8). ivalue(7.5) the number of different types of atom which give rise to neutron magnetic or normal x-ray scattering, or to neutron paramagnetic background scattering. (Maximum 8). ivalue(7.6) (applicable only when the structure gives rise to neutron magnetic scattering). The number of rotation matrices associated with each of the ivalue(7.2) spacegroup symmetry operators. These rotation matrices are applied to the magnetic vectors in order to transform them from the reference position in the asymmetric unit to other sites which are structurally, but not necessarily magnetically, related. When ivalue(7.6) is non-zero, optional line set 11a must be supplied. Manual for MPREP and MPROFIL LeBail Program Page 18 Line 8. Wavelength(s) and Refinement Regulators _______________________________________________ value(8.1) the neutron or synchrotron wavelength, or for x-ray refinement, the wavelength of the alpha-1 radiation. value(8.2) To be supplied only when x-ray refinement is carried out. The wavelength of the alpha-2 radiation. Note: this value should not be supplied when refining with data from synchrotron radiation. value(8.3) the refinement will be terminated if all of the shifts in the refined parameters are less than the product of value(8.3) and the standard deviations of the parameters. A typical value is 0.3; The remaining five values specify the fraction of the calculated shift which is To be applied to the type of parameters specified below. If any of these relaxation factors is input as zero, it is immediately set to 0.8; value(8.4) applies to atomic coordinates. value(8.5) applies to the temperature factors and the preferred orientation parameter. value(8.6) applies to the scale and site occupation factors, and to the components of the magnetic vector. value(8.7) applies to the zeropoint and the halfwidth, cell, depolarisation, absorption and asymmetry parameters. value(8.8) applies to background parameters. Optional line set 9. Preferred Orientation Axes _______________________________________________ To be supplied for each phase for which ivalue(4.2) is non-zero. value(9.1) > < > < value(9.2) > Zone axis of the preferred-orientation axis. < > < value(9.3) > < Optional line set 10. Unique Magnetic Axes __________________________________________ To be supplied for each phase for which ivalue(4.1) is equal to 2; value(10.1) > < > < value(10.2) > Zone axis of the unique magnetic axis. < > < value(10.3) > < Manual for MPREP and MPROFIL LeBail Program Page 19 Line set 11. Symmetry Operators for Each Phase [omit for LeBail ______________________________________________ decomposition] Ivalue(7.2) symmetry operators must be supplied for each phase in verbatim form according to the keyworded scheme: SYMM X, Y, Z e.g. #Spacegroup number 19, P 21 21 21 SYMM 0.5-X,-Y, 0.5+Z SYMM 0.5+X, 0.5-Y,-Z SYMM -X, 0.5+Y, 0.5-Z Input of Scattering Factors [omit all but "END" for LeBail ___________________________ decomposition] The input of scattering factors is controlled by keyworded input. The three character keyword determines which type of scattering factor is to be read in. Termination of scattering factor input occurs when the keyword "END" is read in. A) Neutron Nuclear Scattering lengths _____________________________________ To be supplied only when ivalue(4.1) is less than 3 Keyword - NEU e.g. NEU 0.72 0.588 0.62 C) X-ray Atomic Scattering Factor Curves ________________________________________ To be supplied only when ivalue(4.1) is greater than 3 and ivalue(7.5) is greater than zero. Keywords - XRA, F0, F1, F2 e.g. The following example shows how to input two X-ray scattering curves. For the first curve 15 individual pairs of sin(theta)/lambda and f0 values are supplied and for the second the nine coefficients for the calculation of f0 are given. The atoms are U and O and the values come from "International Tables for X-ray Crystallography" Volume IV 1974. XRA F0 15 0.00 90.000 0.05 88.085 0.10 83.867 0.15 79.294 0.20 74.922 0.25 70.798 0.30 66.951 0.35 63.405 0.40 60.143 0.45 57.127 0.50 54.317 0.55 51.684 0.60 49.211 0.70 44.716 1.00 34.413 F1 1 0.0 -5.359 F2 13.409 XRA F0 3.04850 13.2771 2.28680 5.70110 1.54630 0.3239 0.8670 32.9089 0.2508 F1 1 0.0 0.047 F2 0.032 "END" Keyword _____________ One "END" keyword must be supplied to terminate the input of scattering factors. After the "END" keyword the next line of the input data should be the optional keyworded line, or the atomic parameters, line 12. Manual for MPREP and MPROFIL LeBail Program Page 20 Optional Keyworded Line _______________________ PARS filename (30 characters) File containing information which must otherwise be supplied in line set 12 - line set 18. If supplied, lines 12-18 are omitted from the input data set. Line set 12. Atomic Parameters [omit for LeBail decomposition] ______________________________ The data required for each of the ivalue(7.3) atoms is: name An alphanumeric identifier assumed to consist of the first four characters in the line, including spaces. ivalue(12.1) the serial number of the phase to which this atom contributes. ivalue(12.2) the serial number of the neutron scattering factor, or x-ray scattering curve to be used. value(12.3) x-coordinate > > value(12.4) y-coordinate > in fractions of the unit cell edge. > value(12.5) z-coordinate > value(12.6) isotropic temperature factor. value(12.7) site occupation factor - (actual number of atoms rather than fractional occupancy). Line set 13. Arbitrary Scale Factor for Each Phase __________________________________________________ value(13.1) scale factor for neutron diffraction data, or x-ray alpha-1 radiation or synchrotron radiation. value(13.2) To be supplied only when x-ray refinement is carried out. Scale factor for x-ray alpha-2 radiation. Line 14. Zeropoint, Specimen Displacement, Flat Plate Absorption ________________________________________________________________ Parameter and Depolarisation Factor ___________________________________ value(14.1) the zeropoint error relating the true two theta value to that indicated by the counter arm scale (in units of hundredths of a degree). The zero point error is subtracted from the counter reading in calculating the true two theta value. value(14.2) To be supplied only if ivalue(2.5) is equal to 1 or 4 a/R as described in line 2. value(14.3) To be supplied only if ivalue(2.5) is equal to 1, 2 or 3 b/R as described in line 2. value(14.4) flat plate sample absorption parameter mu * t, where mu is the linear absorption coefficient of the powder and t is the thickness of the sample. To be supplied only when ivalue(2.7) is not equal to 0 nor equal to 2. value(14.5) depolarisation fraction, To be supplied only when ivalue(2.8) is non-zero. Manual for MPREP and MPROFIL LeBail Program Page 21 Line set 15. Halfwidth Parameters for Each Phase ________________________________________________ value(15.1) > < U. > halfwidth parameters according to < value(15.2) > equation (8) (in units of < V. > hundredths of a degree). < value(15.3) > < W. value(15.4) To be supplied only when ivalue(4.2) is equal to 1, the Lorentzian order parameter, m as described in Equation (9) value(15.5) To be supplied only when ivalue(4.2) is equal to 2, the mixing parameter, n of the pseudo-Voigt function as defined in Equation (10) value(15.6) halfwidth parameter X, according to Equation (8). Optional line set 15a, b, c. ____________________________ To be supplied only when ivalue(4.2) is equal to 3 Split Pearson VII parameters as defined by Equation (11). value(15a.1)-(15a.3) asymmetry parameters, As(1-3). value(15b.1)-(15b.3) low angle order parameters, Lo(1-3) value(15c.1)-(15c.3) high angle order parameters, Ho(1-3) Optional line 15d. __________________ To be supplied only when ivalue(4.2) is equal to 4 Variable pseudo-Voigt parameters as defined by Equation (12). value(15d.1)-(15d.3) mixing parameters, p(1-3). Line set 16. Cell Parameters for Each Phase ___________________________________________ value(16.1) > a < > aa > < > value(16.2) > b < > bb > < > value(16.3) > c < > cc > < or > value(16.4) > alpha < > bc > < > value(16.5) > beta < > ac > < > value(16.6) > gamma < > ab When value(16.1) is greater than 1.0, the input is assumed to contain the cell edges "a", "b", and "c" in angstroms, and the angles "alpha", "beta", and "gamma" in degrees. Otherwise, the cell is input as the components of the reciprocal metric tensor "aa", "bb", "cc", "bc", "ac", and "ab" (see equation (6)). Manual for MPREP and MPROFIL LeBail Program Page 22 Optional line 17. Preferred Orientation and Asymmetry Parameters ________________________________________________________________ For Each Phase ______________ To be supplied only when ivalue(2.4) or ivalue(4.3) is non-zero value(17.1) To be supplied only when ivalue(4.2) is non-zero. The preferred orientation parameter - see equation (14). value(17.2) To be supplied only when ivalue(2.4) is non-zero. The asymmetry parameter - see equation (15). Optional line set 18. Background Parameters ___________________________________________ To be supplied only when ivalue(2.5) is non-zero value(20.1) background coefficients, BK0-BK5 as described by -value(20.6) equation (16). Refinement Codewords ____________________ The program provides the user with the facility to relate directly the parameters being refined and the way in which the least squares matrix is calculated. This is achieved by requiring the user to specify which row of the least squares matrix is associated with which of the structure parameters. Parameters which are independent of one another are assigned different row numbers, (irow), whereas parameters which are linearly dependent are assigned the same row number. The number of row numbers supplied must be equal to the number of variables (ivalue(2.2)), but the row numbers may take on any value, and need not be sequentially ordered. In order to allow simple linear relationships to be maintained between parameters, the user is also required to specify for each parameter a shift multiplier (frac) by which the shift calculated from the least squares equations will be multiplied before it is applied to the parameter to which it refers. This shift multiplier is given in addition to the blanket relaxation factors supplied for different types of parameter on line 6. The row number in the least squares matrix and the shift multiplier are combined to form a refinement codeword (code) for each parameter according to: code = [irow*10 + abs(frac)]*sign(frac) (20) where "abs(frac)" means the absolute value of "frac" and "sign(frac)" i s +1 if frac is positive, and -1 if "frac" is negative. A zero codeword means that the parameter with which it is associated will not be refined. If two parameters of the structure are related by: parameter(1) = f*parameter(2) + constant (16) (21) this relationship may be preserved during refinement by allocating each parameter the same row number (say, "ir") in the least squares Manual for MPREP and MPROFIL LeBail Program Page 23 matrix, and setting the appropriate codewords to: for parameter(1): code = 10*ir + 1.0 (17) (22) (that is apply the calculated shift directly to parameter(1)) for parameter(2): code = (10*ir + abs(f))*sign(f) (18) (23) (that is apply (the calculated shift)*f to parameter(2)) Note that the codewords are constructed without reference to the constant term in equation (21). A common situation in which codewords are of use is that in which an atom resides on a special position such as (x, 2x, z). In this case, the x and y coordinates are linearly dependent and must be given the same row number in the least squares matrix. In order to maintain the relationship "y = 2x", the shift applied to y must be twice that applied to x. If x is designated the 5th parameter of the refinement, and z the 6th, then the codewords required for the coordinates x, y, and z respectively are: 51; 51; and 61; Another case requiring correctly specified codewords is exemplified by refinement of the cell parameters in a hexagonal crystal. In this case, the cell parameters (see equation (6)) are related by: bc = ac = 0; aa = bb = ab; cc independent thus "bc" and "ac" should not be refined, and "aa", "bb", and "ab" should be given the same codeword. The codewords for the structure parameters are specified in the same order as the parameters themselves. All of the codewords should be omitted when ivalue(2.1) is zero. Line 19. Codewords for Atom Parameters [omit for LeBail decomposition] ______________________________________ Codewords must be supplied for each of the atoms as follows: value(19.1) > < x-coordinate. > < value(19.2) > codeword for < y-coordinate. > < value(19.3) > < z-coordinate. value(19.4) codeword for the isotropic temperature factor. value(19.5) codeword for the site occupation factor. Line set 20. Codewords for Scale Factors for Each Phase [zero for LeBail __________________________________________ decomposition] value(20.1) codeword for the scale factor for neutron diffraction or x-ray alpha-1 reflections. value(20.2) To be supplied only when x-ray alpha1-alpha2 refinement is carried out. Codeword for the scale factor for x-ray alpha-2 reflections. Manual for MPREP and MPROFIL LeBail Program Page 24 Line 21. Codewords for Zeropoint, Specimen Displacement, Flat Plate ___________________________________________________________________ Absorption Parameter and Depolarization Factor ______________________________________________ value(21.1) codeword for zeropoint error and eccentricity corrections. value(21.2) To be supplied only if ivalue(2.5) is equal to 1 or 4 Codeword for a/R as described in line 2. value(21.3) To be supplied only if ivalue(2.5) is equal to 1, 2 or 3 Codeword for b/R as described in line 2. value(21.4) Codeword for the flat plate sample absorption parameter mu x t, where mu is the linear absorption coefficient of the powder and t is the thickness of the sample. To be supplied only when ivalue(2.7) is not equal to 0 nor equal to 2. value(21.5) Codeword for the depolarisation fraction, to be supplied only when ivalue(2.8) is non-zero. Line set 22. Codewords for Halfwidth Parameters for Each Phase ______________________________________________________________ value(22.1) > < U. > < value(22.2) > codeword for < V. > < value(22.3) > < W. value(22.4) to be supplied only when ivalue(4.2) is equal to 1. Codeword for the Lorentzian order parameter as described in Equation (9). value(22.5) to be supplied only when ivalue(4.2) is equal to 2. codeword for the mixing parameter of the pseudo-Voigt function as defined in Equation (10). value(22.6) codeword for the halfwidth parameter X, according to Equation (8). Optional line set 22a, b, c. ____________________________ To be supplied only when ivalue(4.2) is equal to 3 Codewords for split Pearson VII parameters as defined by Equation (11). value(22a.1)-(22a.3) codewords for asymmetry parameters, As(1-3). value(22b.1)-(22b.3) codewords for low angle order parameters, Lo(1-3) value(22c.1)-(22c.3) codewords for high angle order parameters, Ho(1-3) Optional line 22d. __________________ To be supplied only when ivalue(4.2) is equal to 4 Codewords for variable pseudo-Voigt parameters as defined by equation (12). value(22d.1)-(22d.3) codewords for mixing parameters, p(1-3). Manual for MPREP and MPROFIL LeBail Program Page 25 Line set 23. Codewords for Cell Parameters for Each Phase _________________________________________________________ The cell parameters actually refined are the components of the reciprocal metric tensor defined in equation (6). value(23.1) > < aa. > < value(23.2) > < bb. > < value(23.3) > < cc. > codewords for < value(23.4) > < bc. > < value(23.5) > < ac. > < value(23.6) > < ab. Optional line set 24 Codewords for the Preferred Orientation and ________________________________________________________________ Asymmetry Parameters for Each Phase ___________________________________ To be supplied only when ivalue(2.4) or ivalue(4.3) is non-zero value(24.1) To be supplied only when ivalue(4.3) is non-zero. Codeword for the preferred orientation parameter. value(24.2) To be supplied only when ivalue(2.4) is non-zero. Codeword for the asymmetry parameter. Optional line 25. Codewords for Background Parameters ______________________________________________________ value(25.1) Codewords for background coefficients, BK0-BK5 as -value(25.6) defined in equation 15. Optional line 26. Profile Output ________________________________ To be supplied only when ivalue(5.10) is non-zero. ivalue(26.1) the count interval corresponding to one lineprinter column in the plot of observed and calculated profiles. the suggested value is: (maximum observed count/120). If input as zero, ivalue(28.1) is set 50. ivalue(26.2) the count interval corresponding to one lineprinter column in the plot of the difference between the observed and calculated profiles. The suggested value is 50. If input as zero, ivalue(28.2) is set to 50. ivalue(26.3) the minimum count that will be plotted in the observed profile. The suggested value is zero. Optional line 26 is the last line of data required by the program. Manual for MPREP and MPROFIL LeBail Program Page 26 The Mprep and Mprof Commands ____________________________ Within the PDPL, the commands "mprep" and "mprofil" can be used to run the programs. (Type "pdhelp mprof" and "mprep" for further details). Acknowledgements ________________ The program authors are: H.M. Rietveld ----> A.W. Hewat ----> P.J. Clarke ----> P.J. Bendall & -------- A.N. Fitch, J.K. Cockcroft & A.D. Murray <---- M.W. Thomas | A. Jouanneaux, A.N. Fitch and A.D. Murray This version of the manual was typed by J. Lampard then ruined by A. Fitch Enquiries About The Program ___________________________ should be addressed to: Dr. A.D. Murray, OR A.N. Fitch, Computer Centre, Department of Chemistry, University College London, Keele University, Gower Street, Staffordshire. ST5 5BG London WC1E 6BT Tel. 01-380 7358 EMAIL: A.Murray@UK.AC.UCL cha40@uk.ac.kl.seq1 Disclaimer __________ While the program has been tested by the authors, no guarantee is given concerning its proper functioning.