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Introduction
Not all solids, powders independently from
origin -natural, industrial or laboratory made specimens are very often do not
contain all the phases present in crystalline form. Amorphous or poorly
crystalline material does not contribute to diffraction peaks, and so is
not determined by Rietveld quantification formula. It has been suggested
that there may be a significant fraction of amorphous surface material in
chemically pure powders, especially in samples that have undergone
extensive milling. Experience gained with real world samples at XRD.US
tells us that probably more 80% of all samples initially considered to be
crystalline contains some amounts of amorphous component at quantities
more 3-4%. The amount of amorphous material in a mixture may be
determined by the addition of a known weight of (crystalline) internal
standard prior to the phase analysis
Why important
The
most of samples initially considered to be 100% crystalline are containing
some amounts of amorphous (non-diffracting) components. The origin of
present amorphous components could be highly variable: ball milling of
crystalline samples will generate some amounts of amorphous materials;
spontaneous crystallization from highly concentrated solutions, gels will
generate an amorphous materials etc.
Presence of amorphous component along with crystalline components of
pharmaceuticals will essentially effect the pharmokinetics, distribution,
dissolution etc.
Phase quantification without taking into account the amorphous content
will result in inaccurate determination the quantities of the crystalline
phases.
Theoretical consideration
The
weight of a phase in a mixture is proportional to the product of the scale
factor, as derived in a multi-component Rietveld analysis of the powder
diffraction pattern, with the mass and volume of the unit cell. If all
phases are identified and crystalline, the weight fraction
W of phase P
is given by
where S, Z, M and V
are, respectively, the Rietveld scale factor, the number of formula units
per unit cell, the mass of the formula unit and the unit-cell volume. This
is the basis of a method providing accurate phase analyses without the
need for standards or for laborious experimental calibration procedures.
The
amount of of amorphous content in spiked sample is given by the simple
equation
An example
Let's device an example mixture-A consisting of amorphous (Am) and crystalline (Cr=Cr1+Cr2+Cr3)
components.
Weight percentage of present phases apriori known to be:
Amorphous Phase (Am) - 25wt% (0.25 part)
Crystalline Phase #1 (Cr1) - 5wt% (0.05 part)
Crystalline Phase #2 (Cr2) - 25wt% (0.25 part)
Crystalline Phase #3 (Cr3) - 45wt% (0.45part)
The
total amount of crystalline phases (Cr1, Cr2 and Cr3) is 75%. If we
compute the percentage of each crystalline phases using by Rietveld
formula while ignoring the hump (fitting it as a background) caused by
present amorphous (non-diffracting) component we will get the following
Crystalline Phase #1 (Cr1) - 6.6667wt%
Crystalline Phase #2 (Cr2) - 33.3333wt%
Crystalline Phase #3 (Cr3) - 60.0000wt%
The
obtained result shows the correct ratio of the crystalline components
(Cr), however, the real concentration of obtained components are
incorrect. For now we are not concerned with the correct weight
percentages of the crystalline components. The goal is to find the weight
percentage of amorphous component (Am).
Now
we need to create a new mixture-B, made by simple mixing of mixture-1 and
crystalline internal standard (Cr4), let's say in the following
weight ratio.
Mixture-A -
66.6667 wt% (2/3 part)
Crystalline Phase #4 (Cr4)-33.3333
wt% (1/3 part)
Similar Rietveld analysis (without background
hump modeling as a Bragg scatterer) of this new mixture-B will give the
following results:
Crystalline Phase #1 (Cr1) - 4.0000wt%
Crystalline Phase #2 (Cr2) - 20.0000wt%
Crystalline Phase #3 (Cr3) - 36.0000wt%
Crystalline Phase #4 (Cr4) -
40.0000wt%
To determine the weight percentage of
amorphous component Am we need only two numbers highlighted in yellow.
Again, by simply determining the weight percentage of the newly added and
pre-weighted crystalline internal standard we have determined the
concentration of amorphous component in initial mixture-A. We did not use
any other than the weight percentage of weighed (WIS)
internal standard and Rietveld analyzed concentration of the internal
standard (WRIT)
References
calibration procedures
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