From the: Structure Determination by Powder Diffractometry (SDPD) mailing list

From: Armel Le Bail [armel@fluo.univ-lemans.fr]
Date: Fri, 15 Dec 2000 17:03:10 +0100
Reply-To: sdpd@egroups.com
Subject: Re: [sdpd] Best Cell?


>I wish to know what are criteria for 
>verifying the best cell suggested by 
>autoindexing. Especially, when there 
>are cells with V, 2V, 4V.

The principle is that you have to choose the proposition with the
highest symmetry explaining all your reflections.

It is always possible to index the reflections corresponding to a high
symmetry cell with a A, B, C, I, F or R Bravais lattice by a smaller 
symmetry P cell with smaller volume. Example, a rhombohedral
cell can always be described by a monoclinic C-centered cell with
2/3 volume ; a C-centered monoclinic cell is equivalent to a triclinic
cell with 1/2 volume, etc.

It is also always possible to index an hexagonal or trigonal cell
by an orthorhombic cell with a doubled volume.

Most indexing programs will recognize automatically such special
conditions. However, be very careful, having in mind the above
possibilities.

Hope Robin Shirley agrees, he is probably writing a better answer
than mine. A pity that so many experts prefer to stay at long distance
(almost infinite ;-) from the Internet.

Best,

Armel Le Bail
http://sdpd.univ-lemans.fr/course/

From the: Structure Determination by Powder Diffractometry (SDPD) mailing list

To: sdpd@egroups.com
From: "L. Cranswick" [L.M.D.Cranswick@dl.ac.uk]
Date: Fri, 15 Dec 2000 16:36:56 +0000 (GMT)
Subject: Re: [sdpd] Best Cell?


> I wish to know what are criteria for 
> verifying the best cell suggested by 
> autoindexing. Especially, when there 
> are cells with V, 2V, 4V.

Going via a graphical button pushing route
to help you select good cells:

One suggestion which may help is to make use
of the latest bleeding edge beta test of 
the Chekcell for Windows program:

  http://www.ccp14.ac.uk/ccp/web-mirrors/lmgp-laugier-bochu/bleeding_edge_beta_versions/chekcell.zip

The standard Chekcell uses "parsimony of extra"
reflections on all available cell and spacegroup
combinations as a selection criteria of useful
cells that could potentially be the "best cell".

The latest beta version also links
into LePage (using ported source code originally written 
by A.L. Spek and A. Meetsma) which suggests sub
and super cells that can be checked via 
"parsimony of extra" plus gives the true
"reduced" cell.  This (plus the enhanced Truecell
feature) can help get around the bias of indexing
programs to suggest low symmetry, low volume cells.

Many indexing programs do not reliably give
the "reduced" cell as they are based on the 
Delaunay reduction. 

Refer:
  http://www.ccp14.ac.uk/solution/indexing/reduced_cell.html

-----------

Check cell tutorials (now slightly out of date) are at:
  http://www.ccp14.ac.uk/tutorial/lmgp/#chekcell

Another new feature is a GUI based cell transformation
option similar to the WinGX transformation interface.
With this you can be performing common point and
click cell transformations (Hexagonal to Rhombohedral -
Obverse/Reverse, etc) as well as manually defining the
transformation matrix.

Lachlan.


-- 
Lachlan M. D. Cranswick

Collaborative Computational Project No 14 (CCP14)
    for Single Crystal and Powder Diffraction
Daresbury Laboratory, Warrington, WA4 4AD U.K
Tel: +44-1925-603703  Fax: +44-1925-603124
E-mail: l.cranswick@dl.ac.uk  Ext: 3703  Room C14
                           http://www.ccp14.ac.uk

From the: Structure Determination by Powder Diffractometry (SDPD) mailing list

Organization: Psychology Dept, Surrey Univ. U.K.
To: sdpd@egroups.com
Priority: normal
From: "ROBIN SHIRLEY (USER)" [R.Shirley@surrey.ac.uk]
Date: Fri, 15 Dec 2000 20:21:10 GMT
Subject: Re: [sdpd] Best Cell?

> Hope Robin Shirley agrees, he is probably writing a better answer
> than mine.

In fact I do pretty much agree, both with your reply and with
Lachlan's, (though don't hexagonal cells give alternative *V/2*
orthorhombic settings rather than 2V ones?).

> The standard Chekcell uses "parsimony of extra" reflections on all
> available cell and spacegroup combinations as a selection criteria
> of useful cells that could potentially be the "best cell".

Regarding this criterion, used in Chekcell and referred to by
Lachlan...

Something very similar was tried around 1970, by early zone-indexing
programs from the Delft group, for selecting zones according to what
they called "maximum coverage".  When these programs evolved into
ITO, this was abandoned and a (somewhat over-optimistic) probability
estimate used instead.  In its turn, this became supplanted in LZON
and FJZN6 by the Japanese PM criterion.

This "parsimony" or "coverage" criterion has its attractions, but
can also sometimes mislead, since it makes little use of the 
quantitative goodness of fit between the observed and calculated 
patterns.

Another methodological problem (shared by those versions of M20 that 
allow the exclusion of "unindexed lines") is that the decision as to 
whether or not an observed line is "indexed" by a theoretical 
(calculated) one is essentially arbitrary, involving some threshold 
or cut-off point in Q or 2Theta difference, beyond which, quite 
abruptly, indexing is disallowed.

By contrast, criteria like PM make a much smoother transition and
handle unindexed lines more gracefully.

I hope to have time, next year perhaps, to explore the potential of
PM (or related criteria) for solution evaluation, and perhaps
implement them in further releases of Crysfire.

> A pity that so many experts prefer to stay at long distance (almost
> infinite ;-) from the Internet.

Not personally guilty, I hope.

I'm a moderately frequent contributor to these discussions (when I
feel I have have something relevant to say), and of course the free
non-profit release of Crysfire is published entirely on the Internet
via the CCP14 website.

Best wishes and a merry Xmas to all sdpd indexers

Robin Shirley

P.S.  If you index protein powder patterns (or any cells with
volumes greater than c.5000 A**3), check out my new UNSCALE program
which restores the original scaling to rescaled Crysfire summary
files.  This will be available shortly from the CCP14 website.

To: sdpd@egroups.com
From: Armel Le Bail [armel@fluo.univ-lemans.fr]
Date: Fri, 15 Dec 2000 22:47:42 +0100
Subject: Re: [sdpd] Best Cell?


>(though don't hexagonal cells give alternative *V/2*
>orthorhombic settings rather than 2V ones?).

in lenght
a(o)=a(h)
b(o)=a(h)x1.732
c(o)=c(h)

or in vectors :
a(o)=a(h)+b(h)
b(o)=b(h)-a(h)
c(o)=c(h)

V(o)=2V(h)

And many compounds like beta-AlF3 in the large HTB
(Hexagonal Tungsten Bronze) family are really
orthorhombic, pseudo hexagonal : very hard to determine
the exact structure either from powder or single crystal 
(systematically twinned) data. A well known pathology.
The orthorhombic cell is C-centered (Cmcm space
group in the beta-AlF3 case).

Apart from the V, 2V, 2/3V, 3V, 4V pitfall, another one is
to not recognize I-centered cells in monoclinic settings, etc.
A good one is also the rhombohedral cell with large c
parameter, and first reflection being the 006 when programs
have max l value = 2 or 4 for the first tested hkl... You have
to fall down in all these pitfalls in order to known them.

Programs need help sometimes. An advice is to test
a/b, a/c, etc, ratios in order to see if there are not 1.414 or 1.732
values.

Best regards,

Armel Le Bail
http://sdpd.univ-lemans.fr/course/

To: sdpd@egroups.com
From: Robin Shirley [R.Shirley@surrey.ac.uk]
Date: Thu, 21 Dec 2000 14:41:41 GMT
Subject: Re: [sdpd] Best Cell?

Robin Said:
>> (though don't hexagonal cells give alternative *V/2*
>> orthorhombic settings rather than 2V ones?).

Armel Said:
> in length
> a(o)=a(h)
> b(o)=a(h)x1.732
> c(o)=c(h)

> or in vectors :
> a(o)=a(h)+b(h)
> b(o)=b(h)-a(h)
> c(o)=c(h)

> V(o)=2V(h)

I wasn't using sufficiently careful terminology.  I should have referred
to the V/2 orthorhombic cell of a *derivative* lattice rather than just 
an alternative orthorhombic setting of the hexagonal lattice.

The distinction is an important one, since, as I shall show, this issue
*always* arises when trying to index a hexagonal powder pattern, and can
easily result in the hexagonal cell being overlooked.

For every hexagonal lattice, there exists a derivative orthorhombic
lattice with a unit cell having half the volume of the hexagonal cell:
V(o) = V(h)/2.  This forms what Mighell & Santoro called a "geometrical
ambiguity" - two different though related lattices that have distinct
reduced forms but give identical powder patterns.

For the theoretical basis of this, see Mighell & Santoro (1975),
"Geometrical Ambiguities in the Indexing of Powder Patterns",
J.Appl.Cryst.,8,372-374, and specifically Table 1 on p.373.

The Hexagonal to Derivative Orthorhombic transformation matrix is given
there as [.5,.5,0 / .5,-.5,0 / 0,0,-1], the determinant of which is 0.5,
hence V(o) = V(h)/2 as stated.

This result can readily be verified by indexing any convenient hexagonal
powder pattern using an exhaustive program such as DICVOL or TAUP
(=POWDER).

Provided that the search is continued far enough, these programs should
find the correct hexagonal solution of volume V, plus an orthorhombic
solution of volume V/2.  If monoclinic searches are enabled, one or more
additional V/2 monoclinic settings of that orthorhombic cell are also
likely to be found.

For example, the first 20 lines to Qmax = 7500 QU. of a constructed
hexagonal pattern with cell 4x4x5A (hence volume 69.282A**3) also gives a
V/2 orthorhombic solution (with volume 34.641A**3).

The dimensions of the derivative orthorhombic cell are 2 x 3.4645 x 5A
(i.e. a/2, a*sqrt(3)/2, c).

For this test pattern (which has also been given a few small, simulated
measurement errors to keep the figures of merit manageable), and using 
all Crysfire defaults, TAUP v3.2c gave the following solutions:

I20  Merit  Volume  V/V1 BL Pedig    a       b       c     al   be   ga
 20 167.46  34.639  1.00 P  Ort_1  1.9997  3.4644  5.0000  90   90   90
 20  85.67  69.277  2.00 P  Hex_1  3.9999  3.9999  5.0000  90   90  120

Similarly, DICVOL91 reports as the two best solutions:

I20  Merit  Volume  V/V1 BL Pedig    a       b       c     al   be   ga
 20  220.8  34.646  1.00 P  Mon_1  3.4646  5.0000  2.0000  90 89.975 90
 20  202.6  69.278  2.00 P  Hex_1  3.9999  3.9999  5.0000  90   90  120

For reasons of its own that I didn't have time to investigate, DICVOL91
missed the V/2 orthorhombic cell during its orthorhombic search, then
found it later in a monoclinic approximation.  But one can see from the
values reported for the cell constants that is actually orthorhombic.

DICVOL91 reports two further monoclinic settings of this V/2 cell.  Both
programs also report a 5V tetragonal supercell.  If TAUP is allowed to
pursue a hexagonal pattern into low symmetry (not recommended), it
usually reports copious additional monoclinic and triclinic settings of
these cells.

The differences in the figures of merit variously reported by the
programs carry no significance, and result from minor details such as
different policies regarding how far symmetry-equivalent lines should be
eliminated before reporting that result and moving on to the next.

The complete logfile for the two runs is attached as HEXDTEST.LOG, and
the CRYS dataset as HEXDTEST.CDT, in case anyone wishes to verify these
calculations (apologies for including them as [ASCII] attachments, which 
are generally discouraged in postings, but this was necessary to stop 
them being corrupted by word-wrap, and in any case they are quite small).

In this example, because the cell volumes are so small, both the V/2 and
V solutions lie within DICVOL's first 400A**3 volume shell, so both are
found automatically.

However, one cannot rely generally on hexagonal cells being small enough
for this to happen.  More usually, DICVOL91 will halt after the first
volume shell that contains the V/2 orthorhombic cell, and won't go on to
report the presence of a hexagonal solution.

A manual restart starting from the next volume shell is thus usually 
required to check that no hexagonal solution with twice that cell volume 
(i.e. with volume V) is present.

Anyone using DICVOL91 on patterns that may well give hexagonal cells
(and other analogous high-symmetry cases - see Mighell & Santoro) needs
to be aware of this consequence of DICVOL's strategy of searching
outwards through solution space in successive volume shells.  It is a
very efficient strategy for the majority of situations, but can cause
confusion in high-symmetry cases where lower-volume derivative cells
exist that can cause the search to halt prematurely.

Robin Shirley