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
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.
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.
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
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.
4. Heating rate affects the test results.
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.
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.
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
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 email@example.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.