On the structure of liquid PBr3

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On the structure of liquid PBr3

• Barbara J Gabrys and Laszlo Pusztai
• Department of Materials and OUDCE
• University of Oxford
• Research Institute for Solid State Physics and
  Optics
• Hungarian Academy of Science

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Outline

• Why study molecular liquids?
• Liquid phosphorus tribromide (PBr3) low symmetry
  trigonal pyramidal molecule
• Method in a capsule RMC with fnc
• Results
• Conclusions

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Meet our molecule

• vital statistics in solid state
• 2.24 Å distance P-Br
• 3.44 Å distance Br-Br
• 101 Br-P-Br angle
• a colourless liquid at RT
• lethal!
• useful e.g. for extinguishing fires

• photogenic...

Enjalbert R and Galy J 1979 Acta Crystallogr.
B35 546
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Methodology

• get number density (molecular)
• place points randomly in a box at correct nr
  density
• construct spheres around points
• optimise centre-centre distance ? no overlap
  between centres, most dense packing
• define the molecule
• address topology construct fixed neighbours
  constraint (fnc) file
• get other data, e.g. neutrons

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Methodology ctd

• include real data
• run the RMC program
• dont forget the consistency check the hard
  sphere check (are any special features present
  prior to using fnc constraints?)
• carry out data analysis
• interpret results

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What we have for our system

• one set of data available a total structure
  factor from ns measurements (Misawa et al.) ?
• S(Q) provides averaged information
• molecular liquid no Bragg peaks
• the molecular structure from x-rays at low temp.
  (Enjalbert and Galy) ?
• ability to set fixed neighbour constraints (fnc)

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P
P Br 2.2 Å
Br-P-Br 101º
Br
P atom in the centre (0,0,0)
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Programs used 1st stage
I
O
Random
starting configurations _.cfg
Euler angles (0) nr of particle types (1) density
generate and randomly distribute particles
1 component system
I
O
MoveOut
increasing complexity
name_.cfg
_.cfg
initial configuration of hard spheres (hs)
I
O
RMCPP
name_hs.cfg .out .hgm .hst
name_hs.dat name_.cfg run_rmcpp_name_.bat
equilibrium configuration 1-component hs
configuration
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Programs used 2nd stage
I
O
AddAtomRel.exe
.cfg molecular geometry in terms of vectors
.cfg
add physical constraints ? define the molecule
2-component system
I
O
generate fnc file
increasing complexity
.scratch
.fnc
obtain reference system - hard spheres (hs)
I
O
RMCPP
name_fnc.cfg .out .hgm .hst
name_. fnc name-.dat name_.cfg
name_.add run_rmcpp_name_.bat
equilibrium configuration 2-component (molecular)
hs configuration
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Programs used final stage
having got the reference system, the program can
be run with real data
I
O
RMCPP
.out .cfg .hgm .hst
name. fnc name.dat name.cfg name.add name.fqd
(exp.data) run_rmcpp_name_.bat
increasing complexity
2-component system with data
partials g(r) total structure factor S(Q)
I
O
programs for data analysis
.cfg
.cos, ...
data for plotting various comparisons
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Results RMC details
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Results RMC details

• system size (nr of particles) 6000
• maxd 0.1Å (max displacement per atomic move)
• the role of cut-offs if any feature changes with
  the change of cut-off value ? likely artefact

rc intermolecular cut-off distance
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Representation of molecular structure

• rather than subtract the intra-molecular part of
  the structure factor (error-prone procedure)...
• ...use fixed neighbours constraints (fnc)
• fncs a special neighbour list
• it fixes the number and identity of neighbours
  of a given type
• they must be kept within specified distance
  limits from a given centre

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Basic equations
The total structure factor S(Q) is determined
from neutron diffraction
The partial pair correlation function is
calculated from particle coordinates
It is related to the real space total pair
correlation function
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What does it mean?

• comparison of the RMC with Misawa et al. data
  (scanned)
• discrepancies may be due to experimental errors,
  resolution of digitalisation etc.
• interpretation of the total structure factor is
  hard
• resort to working with gij(r)
• having real structure helps possibility of
  informed change of different parameters
• M.Misawa, T. Fukunaga, K. Suzuki J. 1990 Chem.
  Phys. 92, 5486

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red RMC with fnc black
red hs black RMC with fnc
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Are we any wiser?

• gPP(r) the same cut-off for RMC and hs
• most interesting gBrBr(r) showing strong
  orientational correlation between Br-Br
• a peak around 4Å not present in hard sphere
  simulation
• validate this feature by changing values of
  cut-offs

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a nice example a well-defined Q value where the
two curves start to diverge - below this Q the
intra-molecular part dominates
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P-Br-Br intra dominates, but non-negligible
inter-correlations
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Br-Br-Br intra dominates (sharp peak eq. to
?61.6)
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What are most probable orientations of molecules?
something like that...
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Conclusions

• first sharp diffraction peak has predominantly
  intra-molecular origin
• orientational correlations need refining we need
  to find bond angles for the hard sphere system
• use of fnc allows for modelling of the total
  structure factor, thus making use of both
  intra-and inter-molecular parts of the measured
  data

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Acknowledgments

• the Royal Society for supporting LP
• Department of Materials and Hungarian Academy of
  Science for their hospitability
• the Schouten Foundation for supporting BJG
• OUDCE

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Details of determination of coordinates
Cross-sections in planes
z
y
P
b
b
a
60
Br
?
x
y
2b/?3
2b
ratio 2/31/3
Co-ordinates