Tech Note 1016

Copyright XRD.US

                                         Amorphous Content Determination

 

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

 

Other Technical Notes are also available:

 

Note No

Title

Author

Link to TechNote

TN-101 Ab initio Structure Determination XRD.US http://www.xrd.us/technote/ab initio structure determination.htm
TN-102  Expert Witness XRD.US http://www.xrd.us/technote/expert witness.htm
TN-103  Grazing Incidence Diffraction XRD.US http://www.xrd.us/technote/grazing incidence diffraction.htm
TN-104  High Temperature Diffraction XRD.US http://www.xrd.us/high temperature diffraction.htm
TN-105  Neutron Diffraction XRD.US http://www.xrd.us/neutron diffraction.htm
TN-106  Percentage Crystallinity XRD.US http://www.xrd.us/technote/percentage crystallinity.htm
TN-107  Phase Identification XRD.US http://www.xrd.us/technote/phase identification.htm
TN-108  Precision Lattice Parameters XRD.US http://www.xrd.us/technote/precision lattice parameters.htm
TN-109  Preferred Orientation XRD.US http://www.xrd.us/technote/preferred orientation.htm
TN-1010  Quantitative Phase Analysis XRD.US http://www.xrd.us/technote/quantitative phase analysis.htm
TN-1011  Residual Stress XRD.US http://www.xrd.us/technote/residual stress.htm
TN-1012  Retained Austenite XRD.US http://www.xrd.us/technote/retained austenite.htm
TN-1013  Rietveld Structure Refinement XRD.US http://www.xrd.us/technote/rietveld structure refinement.htm
TN-1014 Crystallite size, size distribution and strain XRD.US http://www.xrd.us/technote/size and strain analysis.htm
TN-1015 Synchrotron Diffraction XRD.US http://www.xrd.us/technote/synchrotron diffraction.htm
TN-1016 Amorphous Content Determination XRD.US http://www.xrd.us/technote/amorphous content determination.htm

 

 

 

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