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The elusive silicon value in Iron
The elusive silicon value
by David Sparkman January 10th
2011 all rights reserved
Different elements raise and lower the arrest temperatures. This can be seen in the article on “Thermodynamic Properties of Iron-Bases Alloys” by Doru Stephenescu, in the ASM handbook on Castings, volume 15. The problem with silicon stems from the mathematical rule called the degrees of freedom rule.
http://en.wikipedia.org/wiki/Degrees_of_freedom_%28statistics%29 . The rule boils down to saying, if we are only measuring two properties (liquidus and eutectic), we can only
calculate two values (carbon and silicon). While the carbon calculation has proven quite robust, the silicon is
calculation is more elusive. The reason is that the silicon calculation is actually calculating residuals and not just
silicon. These residuals are the net effect of silicon, manganese, chrome, copper, sulfur, phosphorus and a host of
other minor elements. Going back to Stephenescu, he suggests that the equation tying some of the effects
together is CE = C + Si/3 + P/2 + Mn/5 – Cr/9. We simplify that equation by saying CE = Carbon + Si/k1 + k2 and
achieve this by assuming that the other residuals P, Mn, CR, Cu, S etc., remain relatively constant as compared to
the fluctuations in Silicon.
Some high chrome foundries have successfully used a similar technique to measure chrome by assuming that the
other residuals remain relatively constant, and chrome is the main reason for the fluctuations in the arrests when
measuring 9 to 16% chrome levels.
With MeltLab we provide the ability to have 20 different metal types. That is meant to be overkill, not to be
necessarily practical. If your foundry is making iron grades with different levels of Manganese, the usual problem
maker, consider having a separate curve for each of those different grades. For example, Ductile iron generally will
have a low level of manganese 0.25-0.35%, while grey iron often has a level of 0.30-0.40%, and high strength grey
often goes higher in manganese and chrome. A 10 point difference in manganese will cause about a 6 point shift in
the silicon curve.
When the Grey Iron Research Institute (Now ICRI or Iron Casting Research Institute) first introduced using thermal
analysis for carbon and silicon analysis, they used a residual technique to calculate silicon. Since CE = C + factor * Si
+ offset, according to their method, solving for Silicon gave Si = k1*(CE – C) + k2.
Not to be out done, the BCIRA (British Cast Iron Research Association) tried to go them one better and issued their
own solution. Since the CE was calculated as CE = a constant * Liquidus + an offset, and C = a different constant *
Liquidus + another constant * Eutectic + another offset, the equations could be simplified by just saying there was
a relationship between Silicon, Liquidus and Eutectic expressed as Silicon = k1*Liquidus + k2* Eutectic + k3. Note
that the k’s in different equations are not the same values.
To further complicate matters, the Americans used the 1948 ITPS (International Temperature Preliminary
Standard), and the British used the 1968 ITPS which differ by about 2 degrees F in the area of interest. Even today,
some calibrators sold by certain cup manufactures in the USA are calibrated to the 1948 standard, while the
temperature industry has moved on to the 1990 ITS (International Temperature Standard with the term
“preliminary” being dropped).
The elusive silicon value in Iron
The elusive silicon value
by David Sparkman January 10th
2011 all rights reserved
Which technique is best? The AFS (residuals) technique makes it easy to see the relationship, and can be checked
for accuracy by looking for a reasonable slope between 2.5 and 3.3. (Different irons can have different slopes.) The
BCIRA method gives a standard error that is about 25% smaller but is more susceptible to a kind of error from not
enough spread in the data. We recommend the following precautions when calculating values for your silicon
calculation:
1. You should have at least 6 or more data points of the same grade of iron for the calculation and they
should be spread out and not clustered. Never believe an equation based on less than 6 points. Two data
points in the AFS method always makes a straight line with no error, and 3 data points in the BCIRA always
makes a straight line with no error. It is why we say statistics don’t lie, but statisticians do. Less than 6
data points is a statistical lie – don’t do it. More different data points are always better. 2. The data points should be spread over a 0.30 to 0.40 range of silicon. The difference between your
highest data point and your lowest data is your spread in data. 3. The data point spread should be equal to or greater than 8 to 10 times the resulting standard error. 4. The thermal couple wire in the cups can introduce variance if you change batches of cups (and therefore
batches of thermal couple wire). Unless you are correcting for the wire bias of the cups, try to run all the
data points on the same batch of cups. 5. Be careful that your spectrometer does not increase the standard error because of the instrument’s drift.
If the standard error for the spectrometer is +/- 0.02, which Is common, you want to be able to achieve a
+/- 0.03 to 0.04 for the MeltLab. Whatever standard error you have in your spectrometer is carried over
into the MeltLab. Mathematically, according to standard statistics, the standard error of the MeltLab is
the square root of the sum of all the errors squared going into the measurement. StdErr = Square Root (
SpectrometerError^2 + WireError^2 + MeltLabError^2). To make this easier, we are introducing a tool into the latest version of MeltLab called Chemistry Calibration
Currently this is limited to Silicon for Iron Chemistries, but it will be expanded over time.
The first step is to select the grade of iron you want to work with. Pull down the drop box you see here in the
upper right of the above graphic when you are in the program, and pick the grade from the grades you have
created in MeltLab. The table without data will appear as you see above. Fill in the three critical data colums
The elusive silicon value in Iron
The elusive silicon value
by David Sparkman January 10th
2011 all rights reserved
circled in red: Liquidus, Eutectic and Spectrometer Silicon. The calculated fields will be filled in by the computer.
The Spectrometer Mn, Ni, and Cr will be used in later versions as we expand our research. The system uses both
bivariant (AFS method) and trivariant (BCIRA method) regression equations.
This table can be saved to disk at any time by pressing the familiar Checkbox button. There is a
table saved to disk for each metal grade you fill in.
Next you have a few things you can play with. The commuter looks at the liquidus temperature and guesses that a
Liquidus below 2000 must be Centigrade, and above 2000 must be Fahrenheit. Then you can select either the AFS
method or the BCIRA method we discussed above.
Don’t be fooled by the spread of the light blue lines (+/- 2*standard error). The vertical scale on the AFS Silicon is
naturally 3 times larger than the BCIRA scale making that graph look like it has more spread. Look instead at the
standard error of the two methods in the equations grid.
AFS Method
BCIRA Method
There it becomes obvious that in this case the BCIRA method is better. You can then take the slopes calculated and
enter them into the equation editor for your iron. For BCIRA, Slope 1 is the Liquidus slope and slope 2 is the
eutectic slope. For the AFS method, Slope 1 is the silicon slope. The intercept is another name for the offset.
This utility is activated when your MeltLab service contract is current starting with service contracts and program
updates from January 1st
2011.