Here's a little chrismas story about quantitative Rietveld analysis.
Except for the last part this was printed in an internal company-news
magazine, so the level of the article is based on people that only have
a basic knowledge of this kind of analysis.
My company is cutting down on development activities, and I would like
to work more with QXRD based on Rietveld analysis. So good ideas are
very welcome. Personally I think that quantitative Rietveld - with
carefull consideration - has a great potential!
Have fun!! and a very merry christmas <:-)
Kristian
P.S. Hope the text and table are readable considering the different
kinds of mail programs out there!
P.P.S Hi Lachlan, here's the closest right now I get on publishing. Hope
it is of interest to you!
Faster Computers Offer Old Techniques Wider Scope
By Kristian Johnsen, .... , F.L.Smidth R&D Laboratory
X-ray diffractometry (XRD) has always been the chief method of
identifying minerals and performing swift semi-quantitative analyses.
Increasingly high-speed computers have made it easy to use XRD for
precise quantitative analysis.
F.L.Smidth+s laboratory has purchased an advanced computer program,
Siroquant, which calculates the mineralogical composition of clinker
samples based on X-ray diffractometric analysis. You merely need to know
what mineral phases the sample consists of, and it is not necessary to
have the minerals in physical form, for the program will calculate how
much of each of the substances is present without needing standard
values.
So far the program has been implemented for analysing the mineral
composition of cement clinker, but it can also be used to analyse the
mineralogical composition of other mixtures.
The Importance of Cement Mineral Composition
At the individual cement plant, there is an established relationship
between the chemical analysis and the mineralogical composition of the
cement clinker produced. But such relationships vary from one plant to
another due to the special characteristics of the raw materials used by
the individual plant. The reasons of such characteristics are often not
understood, so the variation between the chemical and the mineralogical
composition of the clinker produced at a cement plant still cannot be
fully explained. If one wants to compare different cement plants, it is
necessary to be able to analyse the actual mineralogical composition of
the clinker, because that will ultimately determine the properties of
the cement.
If problems arise with cement quality, one often hears the question:
Does the composition of the cement clinker correspond to that calculated
based on chemical analysis? To answer this question, direct measurement
of the composition is necessary. Such measurement normally takes place
under a microscope, by using a method called -point counting- on a
polished clinker sample.
The R&D Laboratory now has an alternative method called +Rietveld Full
Pattern X-Ray Analysis+. This method enables the Laboratory to measure
the quantitative mineral composition of the cement clinker and even of
cement powder because the actual X-ray analysis is made on a powder
sample.
This analysis of the composition is much more detailed than by using
microscopy. However, there is some uncertainty in defining the
relationship between two important phases in cement clinker, viz. alite
and belite, because their X-ray spectra are very alike. Analysing this
relationship by microscopy, on the other hand, is a very reliable
method, so the two methods complement each other.
Identifying Minerals by X-ray Diffraction
The mineral composition can be measured by chemical analysis or by using
the point counting method. X-ray diffractometric analysis uses the
crystalline properties of minerals to identify - and now also quantify -
the mineral composition. Crystals consist of atoms that are arranged in
a certain pattern which repeats itself periodically in three dimensions.
X-ray diffractometry are based on the nature of the X-rays and the
crystalline structure of the minerals. X-rays are electromagnetic waves
with a wave length of 0.1-100 =C5ngstr=F6m (10-10 m) which corresponds =
to
the typical spacing between the atoms of a crystal lattice. This
similarity means that crystals may act as three-dimensional diffraction
lattices for X-rays. The X-ray spectrogram provides information on the
crystal structure, composition, particle size, etc. of the mineral.
Quantitative Analysis with Siroquant
The Siroquant computer program can calculate the mineralogical
composition of a sample directly from an untreated X-ray spectrum.
Siroquant is based on a calculation method developed by H.M.Rietveld in
the late nineteen sixties. Initially, the Rietveld method was only used
at universities because they had access to strong computers that could
handle the heavy calculation work. But with the rapid development of
personal computers, the Rietveld method has now become commercially
available.
To be able to accurately quantify the mineral composition based on the
Rietveld method it is, first and foremost, necessary to know the crystal
structure of the minerals present in the sample. The calculations are
based on the fact that they include theoretical diffractograms for all
important mineral phases in the sample.
Siroquant calculates a synthetic X-ray spectrum for the sample and then
the program compares the synthetic spectrum with the spectrum measured.
This initial comparison usually shows a fairly large deviation. It is
therefore necessary to refine the synthetic spectrum to attain a
sufficient fit between the two spectra.
Siroquant enables individual refinement of the basic crystal structures
of the individual mineral phases. The refinement may take place in
several stages. During and after the refinement it is possible to assess
the fit between the measured and synthetic spectra both graphically and
statistically. Graphically, Siroquant indicates the fit by showing the
difference spectrum between the two spectra. Siroquant uses ordinary
statistical methods to improve the fit as much as possible.
Is there any difference between clinker from different kilns at the same
plant?
Clinker from kiln 1 Clinker from kiln 4
XRD Microscopy XRD Microscopy
C3S 52.3 53.5 58.7 62.0
d C3S =E6m 20 15
C2S 28.4 29.0 24.3 19.1
C3A 6.7 10.0=09
C4AF 10.9 6.9=09
C3A + C4AF 17.6 17 16.9 19.0
MgO 1.7 2.0=09
Porosity 12 20.0
Table 1: Comparison between results obtained by optical point count
(app. 1100 counts) and siroquant.
Siroquant was recently used to examine whether there was any difference
between clinker from two different kilns at the same plant. Two clinker
samples, one from each kiln, were crushed and an X-ray spectrum was made
from each sample. The clinker was also examined under the microscope.
The table shows that the two techniques match very well and that they
complement each other by giving different information on the clinker.
Additional results obtained on a rutine based refinement task
The above results were from a preprint later printed in FLS-news no. 6.
Table 2 shows later results, were it has been tried to follow t