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Amorphous Solid Forms: The Use of X-ray Powder...
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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
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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.
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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
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gmolecules
What do we mean by "Amorphous Solid Forms"?Amorphous Solid Forms ?
• 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.
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What do we mean by "Amorphous Solid Forms"?Amorphous Solid Forms ?
• 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)( )
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Amorphous Solid Forms?
CrystallineLow Temperature
X-ray Amorphous
GlassDefects
Ord
RCP
Melt
der/Entrop CRN
MeltAmorphous
py
High Temperature
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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
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background.
XRPD Data Collection
4500 The modeling and
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4000g
removal of a realistic background contribution is perhaps the most important
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I (cn
ts) the most important
pre-processing step id analysis X-ray amorphous data.
0
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1 11 21 31 41 51 61 71 81
degrees 2Theta
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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
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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.
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Visual Analysis of Data
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
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-300
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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.
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y p
Visual Analysis of Data
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.
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Visual Analysis of Data
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
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800000
1000000
0
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400000
2.25A
4.4A9.5A
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degrees 2Theta0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
Visual Analysis of Data
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
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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
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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
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Diffuse profile extracted by f filt i
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7000Raffinose Pentahydrate frequency filtering
Use of equal area
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I(cnt
s)
rule to estimate ratio of crystalline to non-crystalline diffraction
0
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2000diffraction.
Digital filter used to isolate the crystalline from the0
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Degrees 2Theta
crystalline from the non-crystalline diffraction.
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Direct analysis: Crystalline -AmorphousAmorphous
• 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.
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Direct analysis: Crystalline -AmorphousAmorphous
100
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n
Thermodynamics and kinetics of re-crystallization to R5H
Amorphous dry Crystalline
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% 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%
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Direct analysis: Crystalline -AmorphousAmorphous
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
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1300
I(cnt
s)
defects
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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
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respect to crystalline diffraction.
Direct analysis: Crystalline -AmorphousAmorphous
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
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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
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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-
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suspension
Information Content of X-ray Amorphous DataAmorphous Data
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Information content:
4 halos P1, P2, P3,
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P3
4 halos P1, P2, P3, P4. Each halo has at least 3 parameters that d ib it
Intra-molecular order
30 degrees (~
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15000I (
cnts
)
P4
P3describe it:
- Position
- Width
30 deg ees (3Å) is an approximate divide between inter and intra
0
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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
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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.
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Due to the limited
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I (cn
ts) information content, refining
atom positions with respect to measured X-ray amorphous data will return
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amorphous data will return nonsense. The MCC pattern was calculated with just 8 atoms.
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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.
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Direct Methods I: Para-crystalline modelingcrystalline modeling
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
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presence of local short range order in the sample being studied. The short range order should be linear stacks.
Direct Methods I: Para-crystalline modelingcrystalline modeling
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Para-crystalline model with continuous structure factor
I(Q)
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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
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Each 1D stack forming in the solid state will give rise to a single primary halo.
Direct Methods I: Para-crystalline modelingcrystalline modeling
Component 1 real space
0.3
Direct Paracrystalline Modeling
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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
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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
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information as possible
Direct Methods I: Para-crystalline modelingcrystalline modeling
• 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.
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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
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X-ray Amorphous Form and Crystalline Parent FormCrystalline Parent Form
• Two common crystalline polymorphs:– Form BETA: Monoclinic P21/c (CCDC: BIYSEH01)– Form ALPHA: Orthorhombic Pca21 (CCDC:
BIYSEH02)BIYSEH02)
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X-ray Amorphous Form and Crystalline Parent FormCrystalline Parent Form
• 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).
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)
X-ray Amorphous Form and Crystalline Parent FormCrystalline Parent Form
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?
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X-ray Amorphous Form and Crystalline Parent FormCrystalline Parent Form
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.
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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
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The PDF and X-ray amorphous formsamorphous forms
• 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
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The PDF and X-ray amorphous formsamorphous forms
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distance Angstroms
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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
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p y yAlpha and Beta crystalline polymorphs.
The PDF and X-ray amorphous formsamorphous forms
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Amorphous
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Distance (A)
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Distance (A)
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Mill 1 Mill 2
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F
190 -1
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F
120
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Distance (A)-1.5
Distance (A)