Measurement of thermal expansion of solids

The thermal expansion (or thermal dilatation) of a sample corresponds to the fact that it expands or contracts under the effect of temperature. In order to quantify this effect, a coefficient of linear expansion α is defined, expressed in K-1, which varies according to the temperature. The order of magnitude for usual materials is 10-6 K-1.

Some samples exhibit isotropic thermal expansion; that is to say equivalent in all directions of space. Conversely, others have an anisotropic behavior: they expand in different ways depending on the direction. This behavior can be caused by a composition itself anisotropic (multilayer materials, etc.), the manufacturing process, the thermal history of the sample, etc.

Some examples of coefficients of thermal expansion

Here are in the table below some orders of magnitude of coefficient of thermal expansion of common materials

Measurement method

The coefficient of linear thermal expansion is often measured by TMA or dilatometry. The length or thickness of a sample is measured continuously while it is subjected to a controlled temperature variation.

The thermal expansion of materials can be measured from -150°C to over 1000°C. This measurement provides access to the variation of the coefficients of thermal expansion as a function of temperature, but also, where appropriate, to the glass transition temperature, etc.

Jean-Claude Neyt, COO and Lab Manager, Calnesis

Several measurement geometries can be used:

• Traction between two jaws
• Compression a fixed plane and a flat probe
• Penetration between a fixed plane and a fine probe

The sample is often placed under a flow of inert gas (helium) during the measurement. Most often, two measurements are carried out: the first to allow the thermal relaxation of the sample, and the second for the measurement as such.