Thermal expansion

Fairly pure silicon has a negative coefficient of thermal expansion for temperatures between about 18 and 120 kelvins (−255 and −153 °C; −427 and −244 °F).

[4] Unlike gases or liquids, solid materials tend to keep their shape when undergoing thermal expansion.

[5] At the glass transition temperature, rearrangements that occur in an amorphous material lead to characteristic discontinuities of coefficient of thermal expansion and specific heat.

This plays a crucial role in convection of unevenly heated fluid masses, notably making thermal expansion partly responsible for wind and ocean currents.

In the general case of a gas, liquid, or solid, the volumetric coefficient of thermal expansion is given by

For common materials like many metals and compounds, the thermal expansion coefficient is inversely proportional to the melting point.

Common engineering solids usually have coefficients of thermal expansion that do not vary significantly over the range of temperatures where they are designed to be used, so where extremely high accuracy is not required, practical calculations can be based on a constant, average, value of the coefficient of expansion.

In the field of continuum mechanics, thermal expansion and its effects are treated as eigenstrain and eigenstress.

For a solid, one can ignore the effects of pressure on the material, and the volumetric (or cubical) thermal expansion coefficient can be written:[28]

If the volumetric expansion coefficient does change appreciably with temperature, or the increase in volume is significant, then the above equation will have to be integrated:

Thus, in an isotropic material, for small differential changes, one-third of the volumetric expansion is in a single axis.

This ratio can be found in a way similar to that in the linear example above, noting that the area of a face on the cube is just

Materials with anisotropic structures, such as crystals (with less than cubic symmetry, for example martensitic phases) and many composites, will generally have different linear expansion coefficients

If the crystal symmetry is monoclinic or triclinic, even the angles between these axes are subject to thermal changes.

A good way to determine the elements of the tensor is to study the expansion by x-ray powder diffraction.

The thermal expansion coefficient tensor for the materials possessing cubic symmetry (for e.g. FCC, BCC) is isotropic.

There are some exceptions: for example, cubic boron nitride exhibits significant variation of its thermal expansion coefficient over a broad range of temperatures.

[30] Another example is paraffin which in its solid form has a thermal expansion coefficient that is dependent on temperature.

[31] Since gases fill the entirety of the container which they occupy, the volumetric thermal expansion coefficient at constant pressure,

From 1787 to 1802, it was determined by Jacques Charles (unpublished), John Dalton,[32] and Joseph Louis Gay-Lussac[33] that, at constant pressure, ideal gases expanded or contracted their volume linearly (Charles's law) by about 1/273 parts per degree Celsius of temperature's change up or down, between 0° and 100 °C.

In October 1848, William Thomson, a 24 year old professor of Natural Philosophy at the University of Glasgow, published the paper On an Absolute Thermometric Scale.

In general, liquids expand on heating, except cold water; below 4 °C it contracts, leading to a negative thermal expansion coefficient.

At higher temperatures it shows more typical behavior, with a positive thermal expansion coefficient.

[42] The expansion and contraction of the materials must be considered when designing large structures, when using tape or chain to measure distances for land surveys, when designing molds for casting hot material, and in other engineering applications when large changes in dimension due to temperature are expected.

The steam for heating the rod is supplied by a boiler which is connected by a rubber tube to the inlet.

The control of thermal expansion in brittle materials is a key concern for a wide range of reasons.

Ceramics need to be joined or work in concert with a wide range of materials and therefore their expansion must be matched to the application.

Good example of products whose thermal expansion is the key to their success are CorningWare and the spark plug.

In addition or instead the formulation of the body can employ materials delivering particles of the desired expansion to the matrix.

The thermal expansion of glazes is controlled by their chemical composition and the firing schedule to which they were subjected.