Read deeply chapters 2.2 to 2.3, included, of the SDPD tutorial (CD). Another way is to access to the Kunming Workshop (CD) conference text (beginning of part 2). Some examples of indexation are given, with solutions. You should play with those data (CD: Na₂C₂O₄, [Pd(NH₃)₄]Cr₂O₇, t-AlF₃, beta-BaAlF₅ and cimetidine C₁₀H₁₆N₆S) before to try to solve the exercise given below.

Remember : indexing is more art than science. That step is frequently qualified of  "bottleneck". Many people cannot even think to do invest time in something which has not a unique solution, which supposes that the compound under study is pure, that purity being uncertain, etc. If you can survive to that session of the course, you should be able to finish the whole course. 

You may also consider to look at (see the full book references given at the first session of the course) :

B5 : Chapter 6 (pages 419-504). This will allow you to measure the change in indexing techniques, 25 years later.

B7 : Chapter 7 (pages 118-135). The more recent views of Per-Erik Werner (author of TREOR) about autoindexing.

The SDPDRR-2 (CD) (Structure Determination by Powder Diffractometry Round Robin - 2) first step concerns indexing. You will find there how people really cope with data today.

Even more recent (2004), see the UPPWs and the Powder Diffraction Indexing Benchmarks where indexing programs are compared through a series of tests (article on the CD: PDF).

And, do not forget the Course FAQ (CD).

Most indexing programs use the peak positions extracted from a powder pattern. So, you need first (having recorded the powder pattern)  to extract these peak positions.

Most diffractometers are delivered with their own commercial system for peak position extraction (for instance EVA with the Bruker/Siemens powder diffractometers). But you may want to try some others. 

- You may find more details on some of the peak position extraction programs at the CCP14 page on that topic (CD). You may already have downloaded some of them the previous week for data conversion purpose. Those programs can even do much more.

Already seen last week : Powder by Nita Dragoe. WinFIT by Stefan Krumm. PowderX by Cheng Dong.

New this week : Winplotr by T. Roisnel and J. Rodríguez-Carvajal (CD: winplotr.zip).

Recommended for peak position extraction in this course : PowderX (see on the CD the demos 1 and 2) and Winplotr. 

Indexing software

- Indexing software may be found in several places. The most up to date versions should always be obtained from the authors themselves. However, the latest versions may also be found at some repository places. The versions below were compiled by A. Le Bail, they are distributed with Fortran sources, and TREOR and DICVOL were modified for accepting a zeropoint value.

Treor by P.E. Werner (CD: treor90.zip + paper to read in PDF), Ito by J.W. Visser (CD: ito13.zip + paper to read in PDF), Dicvol by D. Louër (CD: dicvol91.zip + paper to read in PDF)

You may have a look at the full list (CD) of indexing programs (and other programs) that were used in successful SDPD, and verify that few others are really in use, and also look at the CCP14 page on indexing (CD). Note that the Crysfire program will be used next week -so wait before using it.

Very recent approaches make use of Monte Carlo, genetic algorithm (CD: see paper in PDF), for indexing, either on the raw data or applied to extracted peak positions. The problem with this approach is calculation time which can be prohibitive in low symmetries. One simple software in this new category is :

McMaille by A. Le Bail (open Fortran source code) - version 3 recommended (CD). (CD: see paper in PDF),

Other useful software

- Other software that you may need at this time are those who can generate the whole list of reflections for a given cell. For instance, if you choose to add a standard compound like NAC (Na₂Ca₃Al₂F₁₄) to your sample, in order to calibrate, then you need the full list of the NAC reflections.

Hklgen by A. Le Bail (open Fortran source code)(CD).

Eradis (open Fortran source code)(CD).

In fact, many programs can deliver such hkl list of reflections together with angular positions (for instance some Rietveld codes, etc), but you will have hyperlinks to them in a few weeks.

Space groups - systematic extinctions
- Informations about space groups will be obtained at several places. The Bible is : International Tables for Crystallography, Volume A, Space Group Symmetry, D. Reidel Publishing Company : Dordrecht (1983). 
You may have a look at these Websites :
The 230 space groups, Java Applet by J.J. Rousseaux, Université du Maine. See  the Crystallography Server - Bilbao. 
See also http://www.calidris-em.com/archive.htm. 
SGInfo can be run both stand alone and via the web: 
http://www.csb.yale.edu/sginfo/
http://www.csb.yale.edu/user-cgi-bin/sginfo-query
(is also part of the WinGX single crystal suite: 
http://www.chem.gla.ac.uk/~louis/wingx/ 
http://www.ccp14.ac.uk/ccp/web-mirrors/farrugia/~louis/wingx/ )
Quite a few web-databases are available: 
ALTWYK - "Symmetry equivalent positions generator" is a very good one: http://ylp.icpet.nrc.ca/altwyk/default.htm
A cheaper alternative to the International Tables that can be obtained on CD-ROM : A Hypertext Book of Space Group Diagrams and Tables :
http://img.cryst.bbk.ac.uk/sgp/mainmenu.htm
(example spacegroups are visible via the above web address)

Cell parameters refinement
- Unit cell refinement is an important step in the process of indexing powder patterns. Both for calibration when a standard compound is mixed with the unknown, or for refining the cell parameters as proposed by the indexation (though a more sophisticated way exists now, which will be seen in a future week during this course).

Lapod by J.I Langford (CD: lapod.zip)

Celref in the LMGP suite (CD: celref.zip)

Eracel by Jean Laugier & Alain Filhol (old celref version) (CD: eracel.zip)

...

You may find more details on some of the unit cell refinement software at the CCP14 page on that topic (CD).
 

Next week, you will have other software to download on the same indexing topic. So that, even if you find other quite interesting software, please wait for next week before to inform us.

Some software are free for non-commercial use but cannot be obtained without contacting their authors. You will need some of these softwares during the SDPD Internet Course, so that we suggest that it could be time already for trying now to obtain them. Here is the list :

Expo by the SirWare group (get also SIR97, by the way) (CD: old-expo.zip, sir97.zip, CCP14 pages)

Shelx by G.M Sheldrick (CD: shelx.zip)

WinGX by L. Farrugia (CD: CCP14 pages)

We expect from you here an exact result, because a wrong one is simply false. You should produce your unique cell proposition (we do not want 200 hypothetical cells, only one).

A compound was synthesized in the NaF/CrF₃ system. Although some data exist in the JCPDS-ICDD PDF-2 database, the proposed indexation seems to be wrong (verify if this is correct). Two patterns were recorded on a D8 diffractometer (CuKalpha), one with the pure sample (na5.raw, na5.uxd, na5.dat, na5.udf) and one with the sample mixed with a standard (NAC, cubic a=10.2533A, space group I2₁3) (na5+nac.raw, na5+nac.uxd, na5+nac.dat, na5+nac.udf).

- Propose a zeropoint for both powder patterns (to be added, so care to the sign).
- Propose one (only one) indexation for the unknown compound. Produce the same result from TREOR, DICVOL and ITO, if possible. If you wish, apply a "modern" program like McMaille.

The solutions must be returned by email. Copy-paste the condensed results (should not exceed 50-100 lines for each of the 3 indexing programs, including figures of merit and direct cell parameters, together with the list of dobs/dcalc and 2theta-obs/calc). At this stage, we do not ask you for more (do not give space group).