dealing with overlapped data powder diffraction: issues ...€¦ · topas screenshot hkl-dependent...

$: Dealing with overlapped data Powder diffraction: issues ...€¦ · TOPAS screenshot hkl-dependent polynomial line-shape hkl-dependent exponential convolution IUCr Computing School$
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


Powder diffraction: issues and algorithms

Bill David, ISIS Facility,Bill David, ISIS Facility,Rutherford Appleton Laboratory, UKRutherford Appleton Laboratory, UK


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


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


Outline

Massive overlap:proteins & powders

Overlapping impurities

Overcoming overlap in structure solution

Overlap in time: dealing with millions of datapoints


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




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.


See Jon Wright / Jeremy Cockcroft


after Baerlocher &

McCusker

powder diffraction - standard disclosure


powder diffractionradial reciprocal space distance only - d-spacing

*********

2*22*22*2

cos2cos2cos2 γβα bhkachlacklb

clbkahQhkl

+++

++=

a*

c*

β*

bottlenecks in the maze


V*

d*

ΔV*=4πd*2Δd*ΔN=4πVd*2Δd*

ΔN=2πVA d*2Δd*

TRAFFIC JAM in the maze!


( )( ) ( )xxp

Nx

NN −∝

Δ×Δ=ΔΔ=

exp2222 θθθθ

peak density - TRAFFIC JAM in the maze!


( )( ) ( )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



( )( ) ( )( ) ( )xxxp

xxpNx

NNN

NN

−∝−∝

Δ×Δ=ΔΔ=

expexp

2222 θθθθ



dealing with the TRAFFIC JAM of peak overlap


Dehydration of pharmaceutical compounds

Zopiclone hydratesC17H17ClN5O3.2H2Ohypnotic – insomnialine phases: dihydrate - anhydrous

Paracetamol hydratesC8H9NO2.nH20pain-killer, analgesic, antipyretic4'-hydroxyacetanilide, acetaminophen, tylenol


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


time2θ 0oC

35oC

30oC30oC


water+dissolvedparacetamol

crystallisation + ice formation

ice melting

trihydrate

step-function inwater background

trihydrate – monohydratetransformation

novel paracetamol

phaseformation

new intermediate phase

monohydrate

time2θ 2 mins


Comparing paracetamol trihydrate structures


Dehydration of pharmaceutical compounds

Zopiclone hydratesC17H17ClN5O3.2H2Ohypnotic – insomnialine phases: dihydrate - anhydrous

Paracetamol hydratesC8H9NO2.nH20pain-killer, analgesic, antipyretic4'-hydroxyacetanilide, acetaminophen, tylenol


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 2 theta

Tem

pera

ture

(o C)

Complex anisotropic sample line-shape


2H2O

xH2O

no H2O


TOPASzopiclone dihydratestandard line-shape (axial divergence …)


TOPASzopiclone dihydratestandard line-shape (axial divergence …)


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



( )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



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



TOPAS screenshot

hkl-dependent polynomial line-shape

hkl-dependent exponential convolution


TOPASzopiclone dihydratestandard line-shape (axial divergence …) convoluted with hkl-dependent exponential


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

dealing with overlapped data powder diffraction: issues ...€¦ · topas screenshot hkl-dependent...

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