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Crystal struCture determInatIOn frOm X-ray POwder dIffraCtIOn data fOr POlyCrystallIne materIals
E. Moreno, C. Conesa-Moratilla, T. Calvet, M. A. Cuevas-Diarte, I. Morrison.
X-ray diffraction is one of the most powerful
techniques for characterizing the structural
properties of crystalline solids; single crystal
X-ray diffraction, in particular, is widely
used. Unfortunately, for many important
crystalline solids it is difficult to grow a
single crystal of sufficient size and quality
for analysis by this method. High-quality
polycrystalline samples are often easier
to obtain, allowing the option of using
powder diffraction patterns to determine
crystal structures. However, the information
content in such patterns is significantly
reduced in comparison with single crystal
X-ray diffraction, and data problems can
make solving a crystal structure difficult.
Palmitic acid is a long chain compound
from the family of n-carboxylic acids
with a general formula CH3(CH2)14COOH.
Four different forms, named A, B, E and
C are mentioned in the literature.1-2
The knowledge of the structure of
compounds like these is crucial for gaining
understanding of more complex systems
such as polymers, or biological substances
such as lipids. The C polymorph consists
of a monoclinic unit cell (P21/c, Z=4) that
InaposterpresentedattheAbInitioModelinginSolidStateChemistry2004
conference,London,researchersreportedonthestructuredeterminationoftheC
polymorphofpalmiticacidfromconventionalX-raypowderdiffractiondata.Using
Accelrys’ReflexPlusandCASTEPsoftware,theywereabletovalidatetheresultsof
powderanalysisagainstthetheoreticalstructureoftheCpolymorphofpalmiticacid,
andsoestablishamethodtosolvethestructuresofthelongermembersofthefamily.
materials studio enables the complete workflow of structure solution from X-ray powder data in one integrated environment alongside atomistic simulation
CASE STUDY: MATEriAlS STUDio
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contains two dimers held together by hydrogen bonds. In this
form, the hydrocarbon chains assume an all-trans conformation3.
The powder diffraction pattern of the C polymorph of palmitic
acid was indexed with X-Cell4. Among others solutions, a
monoclinic unit cell (P21/c) was obtained, in agreement with
that in the literature. After Pawley refinement of the P21/c cell,
the structure solution was attempted by a direct space Monte
Carlo simulated-annealing approach, and full-profile comparison
method implemented in Powder Solve5. Following the global
optimization algorithm, the trial structures are continuously
generated by modifying specified degrees of freedom in order
to find the trial structure that yields the best agreement between
calculated and experimental patterns. In this case, the molecules
have been treated as a quasi-rigid body with one internal degree
of freedom involving the torsion angle between O-C1-C2-C3.
After the structure solution step, Rietveld6 refinement is
done. Usually the information contained in the pattern is not
enough to refine all the discrete atomic coordinates; instead,
the refinement has to be assessed considering the molecule
as a rigid body. In such cases, the use of first-principles DFT
calculations7-8 are a valuable tool to optimize the crystal structure,
since they provide fairly accurately atomic positions, which are
a valuable guidance in a subsequent Rietveld refinement.
Indexing, refinement and structure solution steps were carried out using the Reflex Plus software package for crystal structure determination from powder X-ray
figure 1: Structure obtained after optimization with CASTEP (K 1x4x2 PW480eV cutoff GGA-PBE) and X-ray powder diffraction comparison with experimental data.
figure 2: Structure obtained after Rietveld refinement and X-ray powder diffraction comparison with experimental dat
CASE STUDY: MATEriAlS STUDio
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CS-8067-1211
diffraction, implemented in the PC modeling environment Materials Studio. The input files for the DFT calculations were generated with CASTEP module, implemented in the same Materials Studio modeling environment.
In summary, elucidation of the crystal structure was possible with systematic use of software tools:
• Unit cell index with X-Cell2
• Space group determination, based on systematic absences and density considerations
• Pawley refinement
• Simulated annealing using PowderSolve (Reflex Plus)
• Structure refinement using the Rietveld method
• Optimization of atomic coordinates by DFT calculations using DMol3 or CASTEP
• Rietveld refinement with fixed atomic coordinates
The final structure was validated by comparing the results with those obtained by single crystal X-ray diffraction2.
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referenCe
1. Moreno, E.; Calvet, T. et al, (Awaiting publication).
2. Von Sydow, E., Arkiv for Kemi; 1955, 9, 231-254.
3. Moreno, E., et al, (Awaiting publication).
4. Neumann, M.A., J. Appl. Cryst. 2003, 36, 356-365.
5. Engel, G. E., et al. J. Appl. Cryst. 1999. 32, 1169-1179.
6. Young, R. A., The Rietveld Method, Oxford University Press; Oxford, 1995.
7. Hohenberg, P., Kohn,W., Phys. Rev. 1964, 136, B864-871.
8. Kohn,W., Sham, L., Phys. Rev. 1965, 140, A1133-1138.
9. Delley, B., J. Chem. Phys. 1990, 92, 508-517.
10. Delley, B., J. Chem. Phys. 2000,113, 7756-7764.
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