It's All Relative

October 31, 2008
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Test results for dilatometers are always relative to calibration and testing conditions.



A common perception regarding analytical instruments is that the operator places a sample into the instrument, closes the door, presses the start button and walks away. In a short time, a multicolored graph emerges with the desired number that reveals the intrinsic nature of the sample. Television shows like CSI have only reinforced this impression.

In an analogous fashion, dilatometry is also considered an absolute science in which any sample can be placed into the dilatometer and the intrinsic thermal expansion nature will emerge. However, operators of dilatometers (or any other analytical instrument) realize that test results are relative to calibration and testing conditions.

Figure 1. Hahn and Kirby platinum thermal expansion values.

Calibration is Key

Like other instruments, the dilatometer must be calibrated with a sample of known properties. High-purity platinum is a common calibration material. Many years ago, Hahn and Kirby (National Bureau of Standards) performed a series of elaborate measurements on rods of high-purity platinum and published papers that are widely accepted as the thermal expansion properties of high-purity platinum.

The measurements were made with an interferometer at a series of isothermal temperatures, and the consensus data points were used to determine a best-fit equation to describe the thermal expansion behavior properties of high-purity platinum. Figure 1 is a graph of the Hahn/Kirby data (percent length change vs. temperature) that is used for dilatometer calibration. Their efforts and techniques are a characterization of the intrinsic thermal expansion properties of high-purity platinum.

Unless they read the fine print in the Hahn and Kirby papers, the person using the table of thermal expansion values may gloss over the fact that these measurements were 1) made with an interferometer under a series of isothermal conditions and 2) curve fitted. The sample was allowed to soak at a specific temperature for a sufficient time to allow the sample to reach its equilibrium length for that temperature.

Today, R&D and manufacturing QC labs do not want to wait days or weeks to generate thermal expansion data at a series of isothermal temperatures. The dilatometer was developed to generate thermal expansion data quickly by monitoring the expansion or shrinkage of a sample while subjecting it to a heating and cooling cycle. Decisions are routinely made using data generated from this dynamic thermal cycle method. However, significant differences exist between the data generated by the isothermal and dynamic test methods.

Figure 2. A typical dilatometer.

Figure 2 is a concept drawing of a typical dilatometer. The sample is held between the sample holder and push rod, and the cold end of the push rod is connected to a displacement sensor. As the sample is heated and cooled during a dynamic thermal cycle, the sample holder and push rod are also heated and cooled. The displacement sensor records the combined movement of the sample, sample holder and push rod. The amount of movement by the sample holder and push rod must be removed from the displacement sensor signal to isolate the movement of the sample. The purpose of the calibration process is to determine the amount of sample holder and push rod movement that must be removed from the displacement sensor output.

Figure 3. Percent linear change vs. temperature for a 1-in. high-purity platinum rod.

Test Conditions Make a Difference

Figure 3 is a graph displaying percent linear change vs. temperature. The red curve is the isothermal platinum data and the blue curve is the displacement sensor (LVDT) output for a 1-in. rod of high-purity platinum during a heating rate of 3°C/minute. The blue curve is the raw LVDT output, which is the combined result of sample, sample holder and push rod movement. The green curve is the difference between the isothermal platinum data and the raw LVDT output, and it represents the amount of correction that must be removed from the LVDT output in order to generate the isothermal platinum value. This amount of correction is attributed to the combined affect of the sample holder and probe rod movement.

Since the temperature of the sample is constantly increasing due to the heating rate, the sample never has enough time to reach its equilibrium length for that instantaneous temperature. The green correction curve contains one more component, the thermal lag of the sample.

Figure 4. Heating rate affects the test results.

Figure 4 is similar to Figure 3, but in this case the same 1-in.-long platinum rod was heated at different rates. Note how the raw LVDT output is different for different heating rates. The only variable that changed was the heating rate of the furnace. The intrinsic expansion characteristic of the platinum did not change, but its apparent expansion characteristic did. The variable output of the LVDT was due to relative abilities of the sample, sample holder, and probe rod to absorb heat and expand during that heating rate. The thermal lag effect of the sample, sample holder and probe rod during the heating rate influenced the measured expansion values.

Figure 5. Different sample cross-sections result in different test results.

In Figure 5, the dilatometer was calibrated with a rod of high-purity platinum that was 1 in. long by 1/8 in. diameter. After calibration, two rods of 99.8% high alumina were run at the same heating rate using the same correction values. Even though the sample lengths were the same, the expansion values for the same 99.8% high alumina were different. The difference was the cross-section of the two samples; one sample had more thermal mass than the other, which influenced the measured expansion values.

Figure 6. Sample diameter affects the test results.

In the final example, Figure 6 , the dilatometer was calibrated with two rods of high-purity platinum. Both were 1 in. long, but one was 1/8 in. diameter and the other was 1/4 in. diameter. After calibration, two rods of 99.8% high alumina were run at the same heating rate using different correction values. Even though the sample lengths were the same, their cross-sections were different. Note how the expansion values for the same 99.8% high alumina were different based on the relative testing conditions.

Making Sense of the Results

These examples show how thermal expansion measurements are significantly influenced by calibration and testing conditions. Both the high alumina and platinum were not altered during the previous tests, yet it was clear how the measured expansion values appeared to be different.

If we can see expansion differences in inert materials as a result of differences in the testing conditions, it is easy to envision that analogous expansion differences are present in materials that change over the testing cycle. How do we separate the actual ceramic changes from the changes that occur due to the testing conditions? The key is to recognize that dilatometry is a relative test method, not an absolute test method. If the testing conditions are controlled and repeated, the test results are reliable as long as they are compared to the test results that were generated from the same testing conditions.

When comparing the data generated from one dilatometer to another, or from one company to another, it is common to encounter different expansion values. Even though the expansion values may be different, it would be wrong to automatically conclude that one is correct while the other is wrong. It is possible that both values are correct because of the relative nature of dilatometry.

For additional information regarding dilatometers, contact the Edward Orton Jr. Ceramic Foundation, 6991 Old 3C Highway, Westerville, OH 43082-9026; (614) 818-1331; fax (614) 895-5610; e-mail slevin@ortonceramic.com; or visit www.ortonceramic.com.

Editor’s note: This article is based on a paper given at the Ceramic Manufacturers Association (CerMA) conference held May 2008 in Columbus, Ohio.


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