initio Ab structure solution from
powder diffraction data
Angus P. Wilkinson
School of Chemistry and Biochemistry
Georgia Institute of Technology
Outline
The problem
General procedure
Instrument selection
An example - Ga2(HPO3)3.4H2O
Recent developments
How far can we go ?
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The problem
Single crystals not available:
Synthesis route does not provide crystals.
Material undergoes a phase transition that
destroys single crystals.
Rietveld refinement requires a model.
Standard structure solution methods require
integrated intensities.
We have to live with overlap or get smart.
Ab initio structure solution
through the ages
Powder diffraction data has long been used
for structure solution.
Most of the early successes were with simple
structures
Some atom positions fixed by density and space
group - UF5 Zachariasen
Model building can be useful
Patterson and direct methods were adopted
later
Early examples include, Pu by Zachariasen and
Ellinger in 1963.
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RuF4
Solved by inspection and Fourier maps
Solving a structure
Index powder pattern and determine lattice.
Treor, Dicvol, Ito etc.
Check data bases for related structures.
NIST crystal data and ICSD
Determine space group
Can be difficult due to overlap
Use information such as SHG
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Gather as much supporting information as
possible.
Chemical composition.
Density.
Solid state NMR.
Extract integrated intensities / structure
factors.
Often done using Le Bail or Pawley method.
Solve structure.
Direct methods or Patterson.
Defaults often do not work. Look at output
carefully !
Develop the model
If solution attempt gives a large fragment of the
structure transfer model to Rietveld package
and develop using Fourier techniques.
If only a small fragment
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Choice of instrument
Many powder ab initios are carried out
using high resolution laboratory
diffractometers.
Synchrotron data can give you a lot of extra
information.
Neutron diffractometers have been used in
special cases.
Combined X-ray and neutron data sets are
becoming increasingly popular.
Ab initio structure solution of
Ga2(HPO3)3.4H2O
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Strategy
Index lab X-ray data set using Treor
a = 8.13, b = 10.02, c = 7.70, = 111.5o
Get supporting information
TGA shows weight loss of ~ 15% at about 180oC
31P MAS NMR shows three distinct phosphorus sites
SHG demonstrates non-centrosymmetric
Assign unit cell contents
On basis of above plus an estimate of the density,
Ga2(HPO3)3.3H2O and Z = 2.
Collect synchrotron X-ray pattern.
Used beam line X7A at NSLS, = Collected 1.29915(2)
data in range 6 < 2 < 75o
Capillary sample
Assign space group on the basis of systematic
absences and SHG.
Use the Le Bail method within GSAS to extract
551 structure factors.
Input Fs into CRYSTALS.
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Run SHELXS-86 TREF
produced two large peaks in E map, presumably Ga.
Difference Fourier maps calculated with
CRYSTALS located two phosphorus and two
oxygen atoms.
Use GSAS for combined Rietveld / Fourier maps
to locate 10 more oxygen atoms.
Low temperature neutron data was collected at
NIST so the hydrogen positions could be located.
A deuterated sample was used
Use the x-ray model as a starting point for neutron
refinement.
The fit was lousy !
Locate as many deuterons as possible using
geometric arguments.
Refine model and locate additional oxygen and
several deuterons.
Final model
29 atoms in the asymmetric unit.
132 positional parameters.
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BT-1 data for Ga2(DPO3)3.4D2O
Problems !
Direct methods requires large numbers of reliable
integrated intensities
reflections around ~ 1 - 1.2 are very important
The number of unique reflections that can be
obtained is limited by:
low instrument resolution
poor sample quality
exact overlap of inequivalent reflections
We have severe problems in cases with high
metric and low Laue symmetry
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Recent developments
Better ways of deconvoluting overlaps.
Statistical deconvolution of overlaps
Maximum entropy processing of Patterson maps
Fast Iterative Patterson Squaring (FIPS)
Improved direct methods procedures.
Use weights to allow for reliability of E values.
Use a structure solution strategy that does not
require a lot of separate structure factors.
Simulated annealing
Rietveld refinement needs a good starting model
because of the poor convergence of least squares
methods
Simulated annealing has very good convergence
properties and can produce structural information
from minimal models:
Unit cell
Space group
Unit cell contents
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Approaches to simulated annealing
Refine the model with respect to the
diffraction pattern.
Solovyov et al., Mat. Sci. For. 133-136, 195 (1993)
Refine the model using bond-strength
bond-length relationships.
Limited applicability. May get more than one
structure.
Pannetier et al., Nature 346, 343 (1990).
Refine the model with respect to a geometric
cost function.
Shows a lot of promise for zeolitic materials.
Deem and Newsam, JACS 114, 7198 (1992).
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What are the limits to ab initio
structure solution ?
If you can refine it, you should be able to
solve it!
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