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IUCr Computing School Siena 18-23 August 2005
Dealing with overlapped data
Bill David, ISIS Facility,Bill David, ISIS Facility,Rutherford Appleton Laboratory, UKRutherford Appleton Laboratory, UK
IUCr Computing School Siena 18-23 August 2005
Powder diffraction: issues and algorithms
Bill David, ISIS Facility,Bill David, ISIS Facility,Rutherford Appleton Laboratory, UKRutherford Appleton Laboratory, UK
IUCr Computing School Siena 18-23 August 2005
WIFD - standard disclosure
• 1983-5 (Oxford to ISIS)– GENIE – data manipulation and analysis package
• based on VMS command line interpreter – still in use• (I still have my VAX (called JARAK) in the basement )
• 1983-– CCSL – FORTRAN77 crystallographic subroutine library – (www.iill.fr/dif/ccsl/html/ccsldoc.html) Rubbia effect
– basis of all Rietveld analysis at RAL until 1992• 1997-
– DASH - structure solution from powders• SA5TOR (VAX VMS) -2 weeks• GUI (Winteracter – all FORTRAN – 6 months)• CCDC – α and β testing – 18 months
IUCr Computing School Siena 18-23 August 2005
858075706560555045403530252015
110,000
100,000
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,000
0
-10,000
MgH2 11.15 %LiBH4 0.04 %MgO 31.55 %MgHx 55.00 %fcc-Mg-Li 2.26 %
858075706560555045403530252015
11.511
10.5109.5
98.5
87.5
76.5
65.5
54.5
43.5
32.5
MgH2 11.15 %LiBH4 0.04 %MgO 31.55 %MgHx 55.00 %fcc-Mg-Li 2.26 %
Major advances in instrumentation
log-scale
Note width differences
IUCr Computing School Siena 18-23 August 2005
Outline
Massive overlap:proteins & powders
Overlapping impurities
Overcoming overlap in structure solution
Overlap in time: dealing with millions of datapoints
IUCr Computing School Siena 18-23 August 2005
High Throughput Phase Diagram Mapping via Powder Diffraction: a case-study of HEWL versus pH.S. Basso, A. N. Fitch, G. C. Fox, I. Margiolaki & J. P. Wright
Proteins and powders
IUCr Computing School Siena 18-23 August 2005
Proteins and powders
IUCr Computing School Siena 18-23 August 2005
Colour representation of ID31 powder diffraction data from the pH variation experiment, from pH 6.56 – 3.33 of HEWL crystallised at (a) 4°C and (b) RT. At low temperature the tetragonal phase is favoured and a smooth anisotropic shift in the peak position is apparent.
Proteins and powders
See Jon Wright / Jeremy Cockcroft
IUCr Computing School Siena 18-23 August 2005
after Baerlocher &
McCusker
powder diffraction - standard disclosure
IUCr Computing School Siena 18-23 August 2005
powder diffractionradial reciprocal space distance only - d-spacing
*********
2*22*22*2
cos2cos2cos2 γβα bhkachlacklb
clbkahQhkl
+++
++=
a*
c*
β*
bottlenecks in the maze
IUCr Computing School Siena 18-23 August 2005
V*
d*
ΔV*=4πd*2Δd*ΔN=4πVd*2Δd*
ΔN=2πVA d*2Δd*
TRAFFIC JAM in the maze!
IUCr Computing School Siena 18-23 August 2005
( )( ) ( )xxp
Nx
NN −∝
Δ×Δ=ΔΔ=
exp2222 θθθθ
peak density - TRAFFIC JAM in the maze!
IUCr Computing School Siena 18-23 August 2005
( )( ) ( )xxp
Nx
NN −∝
Δ×Δ=ΔΔ=
exp2222 θθθθ
( )asymasym
asym
NV
dVddN
20
2 *2**
≈
Δ=Δ π
( )
(S) 3601.0)20tan((L) 1606.0)45tan(
2tan
≈≈
≈≈
Δ≈
o
o
oasymN θθ
peak density - TRAFFIC JAM in the maze!
IUCr Computing School Siena 18-23 August 2005
( )( ) ( )( ) ( )xxxp
xxpNx
NNN
NN
−∝−∝
Δ×Δ=ΔΔ=
expexp
2222 θθθθ
peak density - TRAFFIC JAM in the maze!
IUCr Computing School Siena 18-23 August 2005
dealing with the TRAFFIC JAM of peak overlap
IUCr Computing School Siena 18-23 August 2005
Dehydration of pharmaceutical compounds
Zopiclone hydratesC17H17ClN5O3.2H2Ohypnotic – insomnialine phases: dihydrate - anhydrous
Paracetamol hydratesC8H9NO2.nH20pain-killer, analgesic, antipyretic4'-hydroxyacetanilide, acetaminophen, tylenol
IUCr Computing School Siena 18-23 August 2005
Key points
• Analysing all the data as fully as possible– Managing a million data-points
• 130 patterns• 8520 points per pattern• 1,107,600 points
• Identifying change– Principal component analysis / clustering
• Quantitative phase analysis• Structure determination• Rietveld refinement
– Structure, microstructure & inhomogeneity
IUCr Computing School Siena 18-23 August 2005
time2θ 0oC
35oC
30oC30oC
IUCr Computing School Siena 18-23 August 2005
water+dissolvedparacetamol
crystallisation + ice formation
ice melting
trihydrate
step-function inwater background
trihydrate – monohydratetransformation
novel paracetamol
phaseformation
new intermediate phase
monohydrate
time2θ 2 mins
IUCr Computing School Siena 18-23 August 2005
Comparing paracetamol trihydrate structures
IUCr Computing School Siena 18-23 August 2005
Dehydration of pharmaceutical compounds
Zopiclone hydratesC17H17ClN5O3.2H2Ohypnotic – insomnialine phases: dihydrate - anhydrous
Paracetamol hydratesC8H9NO2.nH20pain-killer, analgesic, antipyretic4'-hydroxyacetanilide, acetaminophen, tylenol
IUCr Computing School Siena 18-23 August 2005
Zopiclone dehydration and phase transformations
TGA
DSC
-7.17ww% = 2H2O
IUCr Computing School Siena 18-23 August 2005 2 theta
dihy
drat
e
anhy
drou
s
T(o C
)
IUCr Computing School Siena 18-23 August 2005
IUCr Computing School Siena 18-23 August 2005 2 theta
Tem
pera
ture
(o C)
Complex anisotropic sample line-shape
IUCr Computing School Siena 18-23 August 2005
2H2O
xH2O
no H2O
IUCr Computing School Siena 18-23 August 2005
TOPASzopiclone dihydratestandard line-shape (axial divergence …)
IUCr Computing School Siena 18-23 August 2005
TOPASzopiclone dihydratestandard line-shape (axial divergence …)
IUCr Computing School Siena 18-23 August 2005
diff
Δ (2 θ )
-0 .0 3 -0 .0 2 -0 .0 1 0 .0 0 0 .0 1 0 .0 2 0 .0 3
Inst
rum
enta
l pea
k sh
ape
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 .2
Δ (2 θ )
0 .0 0 0 0 .0 0 5 0 .0 1 0 0 .0 1 5 0 .0 2 0 0 .0 2 5
sam
ple
peak
sha
pe
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 .2
⊗
obscalc
Complex anisotropic sample line-shape
IUCr Computing School Siena 18-23 August 2005
( )hklfwidth =
*1
*1
2*1
2*1
22*1
*0
*0
2*0
2*0
2
*0
*0
*0
2*0
22*0
22*0
22*0
2
2
cos2
hlEClBkAhd
hlEClBkAh
chlaclbkahd
+++=
+++=
+++= β
( ) **2*2*2max
2* 2 EhlClBkAhd Δ+Δ+Δ+Δ=Δ
( ) ( ) ( ) θπθ tan21802 **2*2*22max EhlClBkAhd Δ+Δ+Δ+Δ=Δ
( )hkld *0 ( )hkld *
1
There is a distribution of water content leading to a distribution of lattice constants
Complex anisotropic sample line-shape
IUCr Computing School Siena 18-23 August 2005
Δ 2θ/Δ 2θmax
-1.0 -0.5 0.0 0.5 1.0po
lyno
mia
l com
pone
nts
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
constant termlinear termquadratic termcubic term
0.0 1.00.50.25 0.75
33xa
22 xa
xa1
0a
Δ 2θ
-1.0 -0.5 0.0 0.5 1.0
poly
nom
ial c
ompo
nent
s
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
combined lineshape
Δ 2θ/Δ 2θmax
-1.0 -0.5 0.0 0.5 1.0
poly
nom
ial c
ompo
nent
s
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
combined lineshapetruncated exponential
0.0 1.00.50.25 0.75
we have defined the limits of the sample line-shape
but we don’t know the lineshape
construct a generalised lineshape using polynomials / orthogonal polynomials
cubic polynomial
( ) ( ) ( ) θπθ tan21802 **2*2*22max EhlClBkAhd Δ+Δ+Δ+Δ=Δ
( )( ) ( )( )max
33
2210
2212
2
θθ
θ
ΔΔ=−
+++=Δ
x
xaxaxaa
Complex anisotropic sample line-shape
IUCr Computing School Siena 18-23 August 2005
TOPAS screenshot
hkl-dependent polynomial line-shape
hkl-dependent exponential convolution
IUCr Computing School Siena 18-23 August 2005
TOPASzopiclone dihydratestandard line-shape (axial divergence …) convoluted with hkl-dependent exponential
IUCr Computing School Siena 18-23 August 2005
with thanks …
M Brunelli, A Fitch, J Wright (ESRF)A CoelhoN Shankland, A Kennedy (Strathclyde)C Pulham (Edinburgh)K Shankland, A J Markvardsen (ISIS)
Zopiclone
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