Amorphous Solid Forms: The Use of X-ray Powder Diffraction ... · diffraction. d 2π/d. Fourier transform. FT. transform, the Para-Crystalline diffraction transform . Diff ti S. Fourier

$Page 1: Amorphous Solid Forms: The Use of X-ray Powder Diffraction ... · diffraction. d 2π/d. Fourier transform. FT. transform, the Para-Crystalline diffraction transform . Diff ti S. Fourier$
Amorphous Solid Forms:pThe Use of X-ray Powder

Diffraction (XRPD)Simon Bates 2010

Diffraction (XRPD)

This document was presented at PPXRD -Pharmaceutical Powder X-ray Diffraction Symposium

Sponsored by The International Centre for Diffraction Data

This presentation is provided by the International Centre for Diffraction Data in cooperation with the authors and presenters of the PPXRD symposia for the express purpose of educating the scientific community.

All copyrights for the presentation are retained by the original authors.

The ICDD has received permission from the authors to post this material on our website and make the material available for viewing. Usage is restricted for the purposes of education and scientific research.

ICDD Website - www.icdd.comPPXRD Website – www.icdd.com/ppxrd

http://www.icdd.com/

http://www.icdd.com/ppxrd

Amorphous Forms: XRPDMethods You can Apply in Your Own Laboratory

• What do we mean by Amorphous Solid Forms?

• How to Collect the Best Powder Patterns?

• Simple Graphical Analysis Methods• Information Content of X-ray y

Amorphous data.• Direct Methods.

Simon Bates 2010

What do we mean by "Amorphous Solid Forms"?Amorphous Solid Forms ?

• Traditional view points:Traditional view points:– From classical thermodynamics, an

amorphous solid is one that manifests no long-range inter-molecular order.

– "X-ray amorphous" is a solid form whose powder pattern contains no crystallinepowder pattern contains no crystalline diffraction peaks.

• More extreme paradigm:• More extreme paradigm:– A kinetically frustrated form, with a

random and chaotic arrangement of

Simon Bates 2010

gmolecules


• Although lacking long-range order,Although lacking long range order, there is no fundamental restriction on the types of short range inter-yp gmolecular order that might exist.– The appearance of an X-ray Amorphous

powder pattern is driven by the characteristic short range order.The density of amorphous forms (usually– The density of amorphous forms (usually within a few percent of the crystalline density) implies significant close packing.

Simon Bates 2010


• Two traditional theoretical models of the amorphous state give some perspective on the types of local order that might exist.– Continuous Random Network (CRN)– Random Close Packed (RCP)( )

Simon Bates 2010

Amorphous Solid Forms?

CrystallineLow Temperature

X-ray Amorphous

GlassDefects

Ord

RCP

Melt

der/Entrop CRN

MeltAmorphous

py

High Temperature

Simon Bates 2010

Temperature/Energy

6

XRPD Data Collection• To collect the best powder patterns for

amorphous material analysis:amorphous material analysis:– Reduce all sources of background scatter as

far as possible.p– Accurately determine the background signal

over the analysis range and remove.– Collect data from background at low angles to

background at high angles (VIP).• Start at 1 or 2 degrees and measure up to 60 70• Start at 1 or 2 degrees and measure up to 60, 70,

80 or 90 degrees depending on where the diffraction signal from the sample falls to background

Simon Bates 2010

background.

XRPD Data Collection

4500 The modeling and

3000

3500

4000g

removal of a realistic background contribution is perhaps the most important

1000

1500

2000

2500

I (cn

ts) the most important

pre-processing step id analysis X-ray amorphous data.

0

500

1000

1 11 21 31 41 51 61 71 81

degrees 2Theta

Simon Bates 2010

Visual Analysis of Data

25000

X-ray amorphous halo widths increase with 2Theta according to universal equation: halo width = 4 E tan(θ) (E~0.125).

20000

25000

Universal halo width:

Delta 2Theta = 4 E tan(θ)

15000

(cnt

s)

Delta 2Theta 4 E tan(θ)

Ε = strain = 0.125 = (d1-d0)/d0.

5000

10000I

00 20 40 60 80 100 120

Simon Bates 2010

degrees 2Theta

Visual Analysis of Data3.5 Universal Halo width:

1.5

2.5 Crystallinity Index 7.5 4 E tan(θ)

E ~ 0.125

(∆d/d ~ 10%) by 10

-0.5

0.5

0 5 10 15 20PDF

(∆d/d ~ 10%) by 10 atomic steps, the atom position uncertainty is the size of a single

-2.5

-1.5

15 Ångstroms

step.

Corresponds to ~15Å maximum correlation

-3.5

Distance (A)length.

Crystallinity index ~ 7.5.

Simon Bates 2010


As a direct consequence of the universal peak width for X-ray amorphous materials the PDF transform performed on the

300 300 350

amorphous materials, the PDF transform performed on the measured powder pattern will show essentially the same damping and correlation length ~ 10 Å to 15 Å

0

100

200

0 5 10 15 20 25 30

100

0

100

200

0 5 10 15 20 25 30 -50

50

150

250

0 5 10 15 20 25 30

-300

-200

-100

-300

-200

-100

-350

-250

-150

Effective size Effective size Effective sizeEffective sizeIMC 1.1nm

Effective sizePVP 1.4nm

Effective sizepiroxicam 1.2nm

The PDF calculation gives a characteristic correlation length RpThat is consistently 10 Å to 15 Å for all amorphous materials tested.

Simon Bates 2010

y p


Rc, The correlation length determined from the universal width is <15Å.

Only atomic features defined by distances less than Rc will diffract coherently.

Rc

Rc effectively breaks the molecule into a series ofa series of small segments.

Simon Bates 2010


Human serum AlbuminModeling XRPD from the HSA molecule shows well defined low angle peaks below 6 degrees that correlate well with crystalline diffraction. The Human_serum_Albumin

Measured and Calculated

1600000

1800000

calculated single moleculemeasured powder

70.0Ap g ymeasured diffuse scattering shows nothing at low angles.

1000000

1200000

1400000

measured powderSingle Crystal Diffraction

cnts

600000

800000

1000000

0

200000

400000

2.25A

4.4A9.5A

Simon Bates 2010

degrees 2Theta0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60


The characteristic position of pa dominant halo in the measured data, can in principle be read straight from a graphical display of thea graphical display of the measured data.

However, the diffraction halo from randomly arranged smallfrom randomly arranged small local clusters will be shifted to high angles. The shift must be corrected for in order to determine 'd' values from X-ray amorphous halo positions.

d_effective ~ d/1.13

Simon Bates 2010

Visual Analysis of Data2 Amorphous raffinose profiles!

Change in x-ray amorphous profile as a precursor to re-crystallizationcrystallization.

Change in local order to accommodate water.

2500 0

3000.0

3500.0

4000.0

Chemometric Amorphous dry

PCRM chemometric analysis isolates 2 distinct X-ray 500.0

1000.0

1500.0

2000.0

2500.0

i (C

NTS

) PCRM

Amorphous wet

Simon Bates 201015

isolates 2 distinct X ray amorphous profiles

0.03.0 13.0 23.0 33.0 43.0 53.0 63.0

degrees 2ThetA

Direct analysis: Crystalline -AmorphousAmorphous

8000

Diffuse profile extracted by f filt i

6000

7000Raffinose Pentahydrate frequency filtering

Use of equal area

3000

4000

5000

I(cnt

s)

rule to estimate ratio of crystalline to non-crystalline diffraction

0

1000

2000diffraction.

Digital filter used to isolate the crystalline from the0

5 15 25 35 45 55

Degrees 2Theta

crystalline from the non-crystalline diffraction.

Simon Bates 2010


• The Equal Area Rule:The Equal Area Rule:– The relative total diffraction signal from

two phases is proportional to the electron density difference between the phases. (No preferred atomic absorption).For mixed organic systems with the same– For mixed organic systems with the same atoms and similar electron densities, the relative total diffraction will be proportional to the weight% of the phases present in the mixture.

Simon Bates 2010


100

120

n

Thermodynamics and kinetics of re-crystallization to R5H

Amorphous dry Crystalline

40

60

80

% p

hase

com

posi

tio

Amorphous wetTc

0

20

0 1 2 3 4 5 6 7 8 9Time

Re crystallization fromRe-crystallization from amorphous (dry) raffinose requires the addition of water. Amorphous dry amorphous wet crystalline. A 2 step phase transition. RH > ~45%

Simon Bates 2010


Extracted diffuse profiles for

S. Bates, R. Kelly, P. Shields, I. Ivanesvic, G. Zografi, A. W. Newman,J. Pharm. Sci., 96(5): 1418-1433, 2007.

X-ray

Drying

pdisordering raffinose pentahydrate

X ray amorphous

1500

1700

1900 Milling

900

1100

1300

I(cnt

s)

defects

500

700

5 15 25 35 45 55

Degrees 2Theta

Using rule of equal areas, diffuse scattering intensity can be quantified with

t t t lli diff ti

Simon Bates 2010

respect to crystalline diffraction.


Vacuum Oven @ 60ºC100

activated crystal?

80

random single amorphousl i

activated crystal?

40

60

perc

ent amorphous%

nucleation events

0

20

p

defects%

defects normalised to crystalline%

random single defect nucleation events

-20

00 5 10 15 20 25 30

Hours

Simon Bates 2010

Hours

Dextran-Trehalose:Miscible or Phase SeparatedMiscible or Phase Separated

DSC Trehalose

Nano Suspension

composition ratio: calculated v known

Single Tg

PCRM

PCRM1Trehalose

PCRM2Dextran

PCRM chemometric method finds NO inter-species molecular interaction

Simon Bates 201021

Dextran-Trehalose: Re-crystallization eventcrystallization event

• Re-crystallization of the trehalose-dextran dispersion gives another measure of the phase separated domaingives another measure of the phase separated domain size. The width of crystalline peaks can be used to calculate the effective size of the crystalline regions.calculate the effective size of the crystalline regions.

Re-crystallization out of T-D dispersion

P k idth

Width of crystalline peaks implies a crystalline domain size

f b t 10 dPeak widths crystal domain sizes

of between 10nm and 30nm.

Phase separated i i thregions in the

amorphous state will likely be of similar size or smaller nano-

Simon Bates 2010

suspension

Information Content of X-ray Amorphous DataAmorphous Data

25000

Information content:

4 halos P1, P2, P3,

15000

20000 P1P2

P3

4 halos P1, P2, P3, P4. Each halo has at least 3 parameters that d ib it

Intra-molecular order

30 degrees (~

10000

15000I (

cnts

)

P4

P3describe it:

- Position

- Width

30 deg ees (3Å) is an approximate divide between inter and intra

0

5000

0 20 40 60 80 100 120

- Relative Intensity

That is 9 variables for inter molecular

inter and intra molecular order.

degrees 2Thetafor inter-molecular order. Potentially enough information to place 3 or 4 Due to limited information content of the

measured data Data MUST be modeled within

Simon Bates 2010

atoms at most. measured data. Data MUST be modeled within physically realistic limits.

Information Content of X-ray Amorphous DataAmorphous Data

Modeling the atom positions of MCC using the Rietveld component of Topas, returns just eight (8) ll d fi d t MCC i h ith(8) well defined atoms. MCC is a mesophase with more information in the measured data than in the X-ray amorphous powder pattern.

600

700

800

900

Due to the limited

200

300

400

500

I (cn

ts) information content, refining

atom positions with respect to measured X-ray amorphous data will return

0

100

5 15 25 35degrees 2Theta

amorphous data will return nonsense. The MCC pattern was calculated with just 8 atoms.

Simon Bates 2010

Direct Methods I: Para-crystalline modelingcrystalline modeling

d 2π/d

Bragg diffraction models are the

FT

Bragg diffraction models are the most commonly used to calculate theoretical powder patterns.

However model is based upon

real-space diffraction-space

However, model is based upon discrete scattering events at integer (HKL) points of diffraction space.

X-ray amorphous scattering isr

Fourier transform matching pair –identity transform

Qd act o space X ray amorphous scattering is

continuous and significant error may be introduced by using a model based upon discrete diffraction

tidentity transform events.

Simon Bates 2010


Real Space

W(r)*W(r) |D(Q)|2Like the Bragg diffraction

d 2π/d

Fourier transform

FT

diffraction transform, the Para-Crystalline diffraction transform

Diff ti S

Fourier transform matching pair –identity transform

is a Fourier identity pair (essentially the same in diffraction

Diffraction Space

real-spacediffraction-space

and real space.).

The utility of the Para-Crystalline

rp

Qspaceydiffraction transform is its continuous nature. The para-crystalline diffraction model is based upon the

presence of local short range order in the sample being

Simon Bates 2010

presence of local short range order in the sample being studied. The short range order should be linear stacks.


40004500

Para-crystalline model with continuous structure factor

I(Q)

20002500300035004000

Basic unit

provides a total diffraction theory for amorphous/glassy systems.

0500

100015002000Basic unit

00.00 1.00 2.00 3.00 4.00Q

1D para-crystalline stack

Simon Bates 2010

Each 1D stack forming in the solid state will give rise to a single primary halo.


Component 1 real space

0.3

Direct Paracrystalline Modeling

4.55

5 8Å

0

0.05

0.1

0.15

0.2

0.25

Prob

abili

ty

1.52

2.53

3.54

I(cnt

s)

~5.8Å~3.8Å~5.8Å

00 5 10 15 20 25 30 35 40

Distance A

Component 2 real space0

0.51

0 10 20 30 40 50 60

Degrees 2Theta

0 5

1

1.5

2

Prob

abili

ty

Limited information content in

~3.8Å

0

0.5

0 5 10 15 20 25 30 35 40

Distance A

P Limited information content in x-ray amorphous pattern –use para-crystalline model to directly extract as much i f ti ibl

Simon Bates 2010

information as possible


• Para-crystalline modeling treats the X-Para crystalline modeling treats the Xray amorphous sample as being a sum of up to 3 non interacting linear stacksof up to 3 non interacting linear stacks. The 'd' value of the para-crystalline model is often related to the heightmodel is often related to the height, width or length of the molecule.

Simon Bates 2010

X-ray Amorphous Form and Crystalline Parent FormCrystalline Parent Form

Measured Form A melting point ~

KINETIC Evolution in XRPD patterns

203 C

Calculated powder tt l ti

Crystalline Form A

Kinetic disorder

C t lli pattern evolution based on inheritance of Form A unit cell

ki tif

20nm

10nm5nm Micro-crystalline

Crystalline

Measured X-ray Amorphous

packing motif5nm1.8nm Glassy

Glassy Form A

Predicted X-rayAmorphous

Simon Bates 2010


• Two common crystalline polymorphs:– Form BETA: Monoclinic P21/c (CCDC: BIYSEH01)– Form ALPHA: Orthorhombic Pca21 (CCDC:

BIYSEH02)BIYSEH02)

Simon Bates 2010


• When a crystalline powder pattern shows some correlation to an X-ray amorphous y ppowder pattern, it is tempting to use Rietveld methods to solve for the local structure.structure.– However: - Bragg calculation method not suited

to X-ray amorphous powder patterns.– Too many variables in a typical Rietveld model– Too many variables in a typical Rietveld model

when compared to the actual information content.

– Limited refinement: reduce structure to P1Limited refinement: reduce structure to P1 restrict refinement to the micro-structure and a single lattice parameter (maybe acceptable in some cases).

Simon Bates 2010

)


Indomethacin Rietveld modeling in Maud:modeling in Maud:

a: 9.302 9.137

b: 10.968 10.644

c: 9.756 10.241

al:69.36 68.68

be: 110.83 106.21

ga: 92.75 85.29

Volume: 867 872 (0 5%)Many X-ray amorphous forms exhibit an apparent Volume: 867 872 (0.5%)

Mean crystal size ~20Å

Many X ray amorphous forms exhibit an apparent relationship to one of the crystalline polymorphs (usually the high temperature form). Can Rietveld modeling give realistic information?

Simon Bates 2010


FelodipinePiroxicam beta

p

Piroxicam alphaPiroxicam alphaBecause a Rietveld model is able to describe the measured data, this in itself is not proof that the punderlying molecular model is correct.

Simon Bates 2010

The PDF and X-ray amorphous formsamorphous forms

• The Pair wise Distribution Function is a transformed powder pattern displayed as a function of distance.– Shows common atom-atom pair

distances as a peak.L t diti l f li id d– Long traditional use for liquid and amorphous systems to determine local coordination numbers.coordination numbers.

– PDF matching often used as verification for molecular modeling and form similarity

Simon Bates 2010


• Calculation of the PDF from a measuredCalculation of the PDF from a measured powder pattern:– The PDF transform is just a Fourier sine

transform and is straight forward to execute.– Derivation of the required reduced structure

factor from a powder pattern is the difficult partfactor from a powder pattern is the difficult part. • Requires correction for all instrumental sources of

background and intensity modification.• Lorentz – Polarization, Compton Scattering,

Absorption, Illuminated sample volume, air-scatter etc.• Best addressed by optimizing the diffractometer

Simon Bates 2010


1234

1

2

3

4

-5-4-3-2-1

00 5 10 15 20 25 30

PDF

-4

-3

-2

-1

0

1

0 5 10 15 20 25 30PDF

-6

distance Angstroms

-5

distance Angstroms

PDF study of the solid forms of Piroxicam. The X-ray amorphous form shows just 3 NN PDF peaks before the signal damps out. The location of these 3 peaks and relative intensity closely matches the PDF of both the

Simon Bates 2010

p y yAlpha and Beta crystalline polymorphs.


2

2.5

4 AmorphousAs made

-0.5

0

0.5

1

1.5

0 50 100 150 200PDF

-2

0

2

0 5 10 15 20PDF

Amorphous

-2.5

-2

-1.5

-1

Distance (A)

300-6

-4

Distance (A)

10

0.5

1

1.5

0.5

1

1.5

Mill 1 Mill 2

-1

-0.5

00 50 100 150 200PD

F

190 -1

-0.5

00 50 100 150 200PD

F

120

Simon Bates 2010

-1.5

Distance (A)-1.5

Distance (A)

Documents

Amorphous Solid Forms: The Use of X-ray Powder Diffraction ... · diffraction. d 2π/d. Fourier transform. FT. transform, the Para-Crystalline diffraction transform . Diff ti S. Fourier