The linear coefficient of thermal expansion (CLTE, or CTE or α) is often measured by a thermomechanical analyzer (TMA). There are two standard test methods that we are often asked to follow: one is the ASTM E 831 test method and the other is the IPC-TM-650 2.4.24 test method. To help clients prepare samples for testing and interpret test results, I compile a FAQ for your references in this blog.
Q. Can you describe briefly how the test is done?
A. In a TMA, the specimen is placed in the sample holder at ambient temperature. The sample height is measured by the probe with a minimal amount of force to maintain contact throughout the experiment. The furnace is closed around the sample stage to control temperature. The initial temperature is usually 20 oC below the lowest temperature of interest. The specimen is then heated at a specified heating rate, for example, 5 oC/min, over the desired temperature range. A thermograph is produced where the sample height dimensional change is tracked over the entire temperature range of interest.
Q. What are the specimen dimension requirements for testing?
A. Each specimen is a cube or a cylindrical shape. The base (i.e., x – y dimensions) should be 5 to 8 mm by 5 to 8 mm. The measuring direction (may be called height, or length, or z-direction) should be 5 to 8 mm and flat and parallel. The ASTM test method specifies length to be between 2 and 10 mm. The IPC test method specifies thickness to be greater than 0.51mm.
Q. Why a wide range in specimen height is allowed in test method?
A. There are several reasons for this. One reason is dependent on the sample shape. For example, the IPC method is specific for printed circuit boards which is flat and thin. Another reason is the expected thermal expansion of the sample. For samples with low thermal expansion, a longer length is preferable to improve measurement accuracy. However, specimen longer than 10 mm is discouraged to minimize specimen temperature gradients.
Q. Can I use a different heating rate than specified in the standard test method?
A. Yes. A different heating rate is allowed as long as any deviation from the standard test method be reported in the test report.
Q. How many specimens should be tested of the same material?
A. It all depends… The ASTM test method recommends at least three specimens. The IPC test method recommends two specimens. Each test should use a fresh specimen. Bottom line, do at least one!
Q. What is the precision of the TMA CTE test?
A. 5 to 10% is typical. The precision depends on imprecisions of measurements (i.e., temperature and length measurements from the TMA equipment), sample preparations (i.e., surface parallelism), and sample type (i.e., specimen thickness and expected thermal expansion).
Q. What is the dimensional unit for values of CTE, α
A. The unit for α is length change over total length per temperature scale. The following expressions in SI units are frequently used:
Q. How is CTE calculated
A. The coefficient of linear thermal expansion (CLTE or CTE or a) is length change over temperature change over total initial length. In math expression,
α = (ΔL/ΔT) x (1 / Lo)
Determine CTE values from TMA thermograph; graph from ASTM E831 test method
CTE values are expressed either as “mean” value over a temperature range or as “instantaneous” value at a specific temperature. The mean CTE value is the slope of direct line between two points on a TMA thermograph. For example, in the TMA thermograph shown below, the mean CTE value between temperature of interest 0 to 100 oC is 24.26 mm/m.oC. The instantaneous value is the right y-axis a value at a temperature. This right y-axis (the blue line) is the derivative values of the left y-axis (the green line). For example, the instantaneous CTE value at 150 oC is 26.3 mm/m.oC.
A typical TMA thermograph from TMA CTE testing