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What is CTE?

CTE is the abbreviation for Coefficient of Thermal Expansion.  It is a thermal property of materials that is a measurement of how much a material expands when it is heated.  It is a common property of materials that heat added to the material will cause the material to expand.  This is due to the greater energy the molecules have when they are heated.  Because they have more energy, they will expand their volume as they move more rapidly.  There are some materials that actually contract or don’t change at all when they are heated, but these materials are the exception.  Zirconium tungstate (ZrW₂O₈) has a negative thermal expansion of - 6 ppm/C in the temperature range of 150°C – 700°C.  Below 150C the expansion is - 9 ppm/C.

Thermal expansion is most often measured with an instrument that can run Thermomechanical Analysis (TMA).   The resin sample is either molded as or cut into a small rod or prism shape with parallel ends.  A probe sits on the top of the sample and as the sample expands, the probe movement is measured.  The heat is supplied by a heating element that surrounds the sample and the probe.

Expansion is typically measured in units of 0.00001 mm.  CTE is expressed as the expansion for a standard unit of length so that values can be compared.  If a sample of 12.36mm expands by 0.00021mm, the expansion is expressed as .00021mm/12.36mm.  This = 0.000017 mm per mm unit length.  Because CTE values are usually very small, it is common to express the expansion as ‘part per million’, i.e. ppm.  The value of 0.000017mm per mm would be written as 17 ppm.

The measurement of CTE occurs over a temperature range so the ‘ppm’ of expansion must be converted to a ‘ppm/T’ value where T is the temperature unit.  This is typically °C (for degrees Celsius) but expansion could also be expressed as ‘ppm/°F’ if the temperature range is measured in degrees Fahrenheit. 
By reporting the dimension change per unit of temperature it is possible to compare values for different materials using the same temperature unit.

This is a typical chart of expansion change as the temperature of the material is increasing.    The initial slope and the final slope are different because the thermoset resin sample has gone through its Tg (glass transition temperature) during the test.   In this temperature region the change in length is not linear.  It is common to report the CTE as two values.  One is below the Tg and the other is above the Tg.   The customer can then know how the material behaves if it is being used below its Tg or if it is being used above its Tg.  It is important that the CTE is provided with reference to what temperature or temperature range applies to the CTE value.  If the Tg is determined to be below ambient temperature, e.g. if it is -33°C, then the CTE will have just one value (one slope) if it is measured from ambient temperature, i.e. 25°C to a higher temperature.

Knowing the CTE of a resin is helpful in analyzing stresses that might occur when a system consists of resin plus some other solid component, e.g. metal, ceramic, mineral filler, glass fiber.  The system will expand at a different rate for each component, which could create stresses in the resin.  Resin systems can also contain liquid materials, e.g. plasticizers, which will expand more than the cured resin when heated.

Some typical CTE’s are shown below.  These values are at temperatures around 25°C.

Epoxy resins have CTE’s around 50 ppm/°C below the Tg.  If the system has filler in it, the CTE can be lower due to the very low expansion of the filler component.  Above the Tg the CTE can be around 100 – 150 ppm/°C. 

If a material is flexible, such as a silicone or a flexible epoxy, the CTE can be above 200 ppm/°C.  This might not be a problem, however, because the flexible resin can more easily absorb stresses than a rigid resin.   Mereco has an epoxy material which has very good flexibility at or above 25°C.  This is the 1650 series (with different viscosities ranging from 350 cps for 1650-00 to 270,000 cps for 1650-90.  The Tg of this material is around - 34°C and the CTE above this temperature is 225-250 ppm/°C.  This flexible material has an elastic modulus of 1,600 psi (11MPa) which puts it in the class of flexible silicones.

Thermoplastics can have varying CTE based on the rigidity or flexibility of their polymer backbone.   Polyethylene has CTE around 200 ppm/°C and polycarbonate has CTE around 60 ppm/°C.