1. Introduction

This report describes extensions to the profile refinement code first developed at the Rutherford Appleton Laboratory in the 1980s to treat time-of-flight powder neutron diffraction data collected at ISIS. The bulk of the earlier design and coding was carried out by W I F David and the late J C Matthewman, who chose to augment the basic subroutines for crystallographic calculations contained in the Cambridge Crystallographic Subroutine Library (CCSL)[1] by adding a new Profile Refinement (PR) library of subroutines, a library of Peak shape Functions (PF) and an associated set of Profile MAin programs (PMA) [2].

Early versions of these main programs (TF12LS, CN13LS, SR15LS etc) were limited to the treatment of diffraction patterns from a single-phase, non-magnetic sample. Moreover, they could only be used to analyse one type of data at a time, eg time of flight (ToF) neutron, constant wavelength neutron or X-ray data. Code for multiphase analysis was added by the same authors in the early 1990’s and many of the PR Library subroutines were modified in 1995-1997 by P J Brown & J B Forsyth to include neutron magnetic scattering from a single phase sample.

The present authors have now extended the CCSL code for profile refinement in two directions. Firstly, it may be used to fit neutron data from a multiphase sample in which some or all of the phases are magnetically ordered. Secondly, but perhaps equally importantly, data in more than one histogram of intensity versus angle or time-of-flight may be treated within a single refinement. The latter development is crucial to diffraction at pulsed neutron sources, where a powder diffractometer is usually equipped with a number of detector banks having significantly different resolution characteristics. Although the latter development was foreseen by earlier contributors to the profile refinement code [2], the premature death of Judy Matthewman in 1993 delayed further progress in this area.

We should also like to acknowledge the careful work carried out by K Shankland who subjected a 1995 version of the basic CCSL library to several different Fortran compilers running on a variety of computers. This exercise revealed a number of infelicities in the code which were removed. Shankland was also responsible for demonstrating the method of running the profile refinement code, and indeed any CCSL program, on a personal computer using G77 Fortran.

We have chosen to name the new computer program PRODD, which is an acronym for Profile Refinement of Diffraction Data. PRODD allows one to refine data from samples containing more than crystallographic phase and also to include more than one histogram of data in a single refinement. In addition to ferro-, ferri- and commensurate anti-ferromagnetic structures, the new program also allows incommensurate spiral and sine-wave amplitude modulated magnetic structures and their magnetic propagation vectors to be fitted to neutron diffraction data.

An executable program file is available for the Microsoft Windows (W) Intel platform (32 bit, W-95, W-98, W-NT are all tested, w-2000 ?; not alpha or earlier Windows versions). Source code is available upon request and will be offered for inclusion in future versions of CCSL [3].

The CCSL manual describes the input format for Q cards which must be added to the cystal data file, CDF, to define the magnetic structure of a phase. A Q PROP card, which describes the propagation vector of the magnetic structure, must be present if a phase is to be regarded as magnetic by PRODD. The remaining Q cards define the magnetic symmetry and the magnetic moments in magnitude and direction. In incommensurate magnetic structures, the phase angle of a magnetic moment must also be specified. Magnetic form factors are needed along with the rest of the F cards describing a phase. It is recommended that users also prepare input files for the program MAG3D, also part of CCSL, which can display a graphical representation of the magnetic structure described by a complete crystal data file for a single phase. The practice of splitting refinements into separate nuclear and magnetic phases is unnecessary and not recommended.

Additional features in the CDF not documented in the previous CCSL profile refinement manual include:

As in earlier versions of CCSL least-squares refinement, the choice of variables to be refined is made using the instructions L VARY parameter name, L FIX parameter name, L RELAte parameter names and L FUDGe parameter name cards in the CDF of the appropriate phase. However, in the case of parameters which can apply to more than one phase or data histogram, either *Pn or *Sn must precede the parameter name, where n is the number of the phase or histogram.

The component files required by PRODD are a CDF and possibly one or more histogram files (clearly, pattern profile simulation does not require any observed data, with NCYC 0). As with previous versions, the standard data file format is ToF or 2q, intensity and it's esd in free format.

When run, PRODD interactively asks for the name to be used for the output listing file (default extension .LIS) followed by the name of the CDF (default .CCL).

Finally, PRODD requires the names of the histogram data files which must be entered in the order * S1, * S2 etc.

The program then proceeds to complete the required number of cycles of refinement unless, at some earlier stage, the refinement converges or the least-squares matrix becomes ill- conditioned. It will also ask for names for any optional files (.HKL, .PRO, .FOU etc) that have been specified and, before beginning the last cycle, for the name of the new crystal data file ( default extension .CCN) to which the new values of the parameters are to be written. A recent development within CCSL is that the estimated standard deviations of positional and unit cell parameters can be written to the .CCN file in the form of an A SD atom name, esd(x), esd(y), esd(z), esd(ITF), esd(site) and similarly for a C SD card.

Assuming an I card with an appropriate value for PRPR has been supplied then the program will write out a .PRO file, containing the observed and calculated data. The format of the file is lines containing x back obs calc esd where x is the ToF or 2q specified in the input data file for each obs and esd. For profile fits to more than one histogram of data, the .PRO file contains each fit in the same sequential order as the data files were supplied, with a couple blank lines separating them. Currently it falls to the user to create plots of this data, using a scientific graphing package such as Kaleidagraph. Calculated positions of hkl reflection markers can be included in the .LIS file through the I PRFC card. The .LIS file also contains information from each least-squares cycle giving the new, esd, shift, old and shift/esd values for each variable in the refinement.

For example to plot a Rietveld fit of multi-pattern data using the free "gnuplot" program (Reference????????? ) use the command:

The x-axis is the ToF or 2q value, the index 0 refers to the first histogram, use index 1, 2 etc to examine the subsequent histograms. Reflection marker positions can be added if the PRFC option was set on the I CARD in the refinement. Taking the list of reflections from the .LIS file gives a set of points which can be over plotted with gnuplot (or any other package).

A number of examples of refinements carried out using PRODD form an Appendix to this document.

Assuming a mistre.ss file and the perl scripts ccsl and get_split have been obtained then executables can be built on a system with working perl and fortran installations. Extraction is a two stage process, the script ccsl takes the mistre.ss file and performs parameter substitutions for array dimensions to suit the user (see jbfpar.mk4) and then get_split separates the large output files into individual fortran subroutines and main programs. To build PRODD one needs to extract the pr, pf, pma and lib sections of the mistre.ss file. The directory structure which is assumed below and in the supplied makefile places the mistre.ss in the root directory, extracted fortran in ./extract and the sections lib, pr etc in directories ./lib, ./pr etc. To use the ccsl script, issue the commands….

which should create the files libmk4.f, prmk4.f, pfmk4.f and pmamk4.f in a directory called extract, using the values in jbfpar.mk4 for parameter substitutions. These large files can either be compiled directly or split up by get_split. Eg

This splits the file extract/libmk4.f into individual subroutines in a directory called lib. Each subroutine needs to be compiled and the main program prodd.f is found in the pma section of the mistre.ss files. Rather than splitting the entire file pmamk4.f the source can be extracted with the get mode of the get_split script.

The file prodd.got will be found in the pma directory (for many compilers it may be necessary to rename this to prodd.f). Compilation of the Fortran source code is system dependant, we give two examples here.

9.1 Compaq Visual Fortran running under MSWindows.

• Install the source code (see above)
• Run developer studio
• Create a new workspace – for example called CVF_CCSL (file > new > workspace)
• Create a new project for a fortran static library and add all the source code files except prodd.f to it (the contents of ./pr, ./pf, ./lib).
• Create a new project for a fortran console application and add the file prodd.f to it (from ./pma).
• Adjust the project settings for both projects to turn off array bounds checking and add the /static compiler switch. (project > settings > fortran)
• Add a dependency to the prodd project so that it depends on the library project
• Click build
• Test the exectuable !

9.2 G77 running under MSWindows.

A popular free compiler available for a variety of systems, these instructions should be appropriate for the majority of unix systems as well as windows, possibly with minor modifications to the makefile.

• Install the source code (see above)
• Obtain the compiler and make utility (see www.mingw.org)
• Edit and use the supplied makefile and build with "make –r prodd".
• Test the executable !

Alex Hannon for collecting the GEM data (A3), Steve Hull for the CuBr multiphase example (A2)

[1] CCSL Website

[2] W I F David, R M Ibberson Ibberson & J C Matthewman (1992) Rutherford Appleton Laboratory Report RAL Report 92-032.

[3] PRODD Website

[4] Cagliotti

[5] Voigt with vL& Y asymmetry correction.

[6] L Finger J. Appl. Cryst. 27, 892, 1992.

[7] Pawley refinement CAILS

[8] Kaleidagraph

[9] gnuplot

The following examples are designed to illustrate both the differences and the similarities between the input file formats for previous CCSL-based refinement programs and the program PRODD. The structure of the input file is still very similar to the format required for the program MULTI, which was able to perform multi-phase refinement [2]. Cards containing the instructions concerning the number of least-squares cycles to be performed and printing control information are placed at the beginning of the crystal data file. These are followed by cards describing the instrumental parameters for each histogram in a block which starts with a L PKCN *Sn TYPE m card. A further block of cards in the input file then describes each crystallographic phase present in the sample. These blocks are separated by a line beginning with **. These blocks are referred to as phase 0, phase 1, etc – where phase 0 contains the instrumental information.

A simple ToF refinement using the silicon standard sample measured on the HRPD instrument at the spallation neutron source ISIS. Two data sets are being refined, histogram 1 (*S1) is from the 90° bank and histogram 2 (*S2) is from the backscattering detector. The parameters describing the shape of the moderator pulse are constrained to be the same for both histograms and are described by the TAUS, TAUF and SWCH parameters. Only a single phase (silicon) is included in this example. Figure 1 shows the fit obtained and table 1 shows the input file along with explanatory comments.

Figure A1: Profile fit to HRPD silicon standard for the backscattering bank (upper) and 90° bank (lower). Red dots – observed data, green line – calculated, blue line – difference.

Table A1 Commented listing of the CDF which produced the profile for Example A1

Table 1: Input file for NBS standard silicon on HRPD.

A multiphase refinement of POLARIS ToF neutron data for a sample of CuBr in a clamped pressure cell. This fit was originally carried out using the old CCSL based program ‘MULTI’, we reproduce it here to demonstrate the necessary changes to the crystal data file.

Figure 2: Three phase fit to POLARIS data.

Crystal data file for example A2 (CuBr phases).

A3 Weighed multiphase, multi-histogram magnetic sample on GEM

Data were collected for sample containing a mixture of NiO, CeO₂ and NaCl in weighed proportions to test the capabilities of the program with respect to determination of phase fractions in the mixture. At the time of the experiment the commissioning of the GEM instrument was in progress and three data banks were available, giving ToF data from detectors centered around 2q values of 90° , 70° and 20° . Figure 3 shows the profile fit to the data., table 3 gives the input file.

The refined values of SPHA for NiO, CeO₂ and NaCl were 0.3312(4), 0.3329(5) and 0.3360(7) respectively. These reflect the relative number of each kind of unit cell in the sample. By looking at the site multiplicities in the .lis file, the number of each kind of atom in the unit cell can be calculated and hence the mass of the unit cell. The weight and atomic fractions are then simply:

wt. fraction = at. fraction =

where M_cell is the mass of the unit cell. For this example the SPHA values have been constrained such that they sum to 1.0 and there are equal numbers of formula units in the unit cells of each phase. Hence, the atomic fractions are just the SPHA values and the wt fractions are calculated as: NiO = 24.33(3)% , CeO₂ = 56.34(6) and NaCl = 19.33(4). These favourably with the measured values of 24.6%, 56.2% and 19.1%, with due uncertainty in the purity of the starting materials and the presence or otherwise of amorphous phases.

The input file for this fit is shown below. It is rather long, but the main new feature is the addition of a group of Q cards to describe the magnetic structure in NiO. See the CCSL manual [] for further details relating to Q cards. The refined moment of 1.840(8) m_B is in good agreement with the value expected for Ni²⁺, allowing for covalency and zero point spin deviation.

Figure 3: Profile fits to the GEM multiphase sample. Top left: 20° bank, top right 70° bank, bottom: 90° bank.

A4 Rb₂S₂O₆ synchrotron x-ray diffraction at ambient temperature on beamline BM16 at ESRF.

Sharp diffraction profiles are well fitted by peakshape number 4, which is based on the source code of L. Finger[6]. Note that L SORC CN has been used although this is clearly x-ray diffraction data. The Lorentz-Polarisation correction is the same in both instances.

Crystal data file for Rb₂S₂O₆, note the temperature factors are incorrect since no the absorbtion correction has yet to be applied.