Thermal expansion

Thermal expansion is the tendency of matter to increase in length, area, or volume, changing its size and density, in response to an increase in temperature.
In simple words, the change in size of a body due to heating is called thermal expansion. Substances usually contract with decreasing temperature, with rare exceptions within limited temperature ranges. The SI unit of thermal expansion is inverse Kelvin.
Temperature is a monotonic function of the average molecular kinetic energy of a substance. In simple words, temperature is the measure of kinetic energy of a body or the measure of hotness or coldness of a body. As energy in particles increases, they start moving faster and faster, weakening the intermolecular forces between them and therefore expanding the substance.
When a substance is heated, molecules begin to vibrate and move more, usually creating more distance between themselves.
The relative expansion divided by the change in temperature is called the material's coefficient of linear thermal expansion and generally varies with temperature.
The coefficient of thermal expansion is not constant but typically increases with temperature, as higher thermal energy reduces intermolecular forces and allows greater atomic displacement.

Prediction

If an equation of state is available, it can be used to predict the values of the thermal expansion at all the required temperatures and pressures, along with many other state functions.

Contraction effects (negative expansion)

A number of materials contract on heating within certain temperature ranges; this is usually called negative thermal expansion, rather than "thermal contraction". For example, the coefficient of thermal expansion of water drops to zero as it is cooled to and then becomes negative below this temperature; this means that water has a maximum density at this temperature, and this leads to bodies of water maintaining this temperature at their lower depths during extended periods of sub-zero weather.
Other materials are also known to exhibit negative thermal expansion. Fairly pure silicon has a negative coefficient of thermal expansion for temperatures between about. ALLVAR Alloy 30, a titanium alloy, exhibits anisotropic negative thermal expansion across a wide range of temperatures.

Factors

Unlike gases or liquids, solid materials tend to keep their shape when undergoing thermal expansion.
Thermal expansion generally decreases with increasing bond energy, which also has an effect on the melting point of solids, so high melting point materials are more likely to have lower thermal expansion. In general, liquids expand slightly more than solids. The thermal expansion of glasses is slightly higher compared to that of crystals. At the glass transition temperature, rearrangements that occur in an amorphous material lead to characteristic discontinuities of the coefficient of thermal expansion and specific heat. These discontinuities allow detection of the glass transition temperature where a supercooled liquid transforms into a glass.
Absorption or desorption of water can change the size of many common materials; many organic materials change size much more due to this effect than due to thermal expansion. Common plastics exposed to water can, in the long term, expand by many percent.

Effect on density

Thermal expansion changes the space between particles of a substance, which changes the volume of the substance while negligibly changing its mass, thus changing its density, which has an effect on any buoyant forces acting on it. This plays a crucial role in the convection of unevenly heated fluid masses, notably making thermal expansion partly responsible for wind and ocean currents.

Coefficients

The coefficient of thermal expansion describes how the size of an object changes with a change in temperature.
Specifically, it measures the fractional change in size per degree change in temperature at a constant pressure, such that lower coefficients describe lower propensity for change in size. Several types of coefficients have been developed: volumetric, area, and linear. The choice of coefficient depends on the particular application and which dimensions are considered important. For solids, one might only be concerned with the change along a length, or over some area.
The volumetric thermal expansion coefficient is the most basic thermal expansion coefficient, and the most relevant for fluids. In general, substances expand or contract when their temperature changes, with expansion or contraction occurring in all directions. Substances that expand at the same rate in every direction are called isotropic. For isotropic materials, the area and volumetric thermal expansion coefficient are, respectively, approximately twice and three times larger than the linear thermal expansion coefficient.
In the general case of a gas, liquid, or solid, the volumetric coefficient of thermal expansion is given by
The subscript "p" to the derivative indicates that the pressure is held constant during the expansion, and the subscript V stresses that it is the volumetric expansion that enters this general definition. In the case of a gas, the fact that the pressure is held constant is important, because the volume of a gas will vary appreciably with pressure as well as temperature. For a gas of low density this can be seen from the ideal gas law.

For various materials

This section summarizes the coefficients for some common materials.
For isotropic materials the coefficients linear thermal expansion α and volumetric thermal expansion α_V are related by.
For liquids usually the coefficient of volumetric expansion is listed and linear expansion is calculated here for comparison.
For common materials like many metals and compounds, the thermal expansion coefficient is inversely proportional to the melting point.
In particular, for metals the relation is:
for halides and oxides
In the table below, the range for α is from 10⁻⁷ K⁻¹ for hard solids to 10⁻³ K⁻¹ for organic liquids. The coefficient α varies with the temperature and some materials have a very high variation; see for example the variation vs. temperature of the volumetric coefficient for a semicrystalline polypropylene at different pressure, and the variation of the linear coefficient vs. temperature for some steel grades. The highest linear coefficient in a solid has been reported for a Ti-Nb alloy.
The formula is usually used for solids. Volumetric coefficients shown which do not follow that rule are highlighted.

Material	Material type	Linear coefficient CLTE α	Volumetric coefficient α_V	Notes
ALLVAR Alloy 30	Metal alloy	−30	Anisotropic	Exhibits negative thermal expansion in broad range of temperatures
Aluminium	Metal	23.1	69
Brass	Metal alloy	19	57
Carbon steel	Metal alloy	10.8	32.4
CFRP	Composite	–0.8	Anisotropic	Fiber direction
Concrete	Aggregate	12	36
Copper	Metal	17	51
Diamond	Nonmetal	1	3
Douglas fir	Biological	27	75	Radial
Douglas fir	Biological	45	75	Tangential
Douglas fir	Biological	3.5	75	Parallel to grain
Ethanol	Liquid	250	750
Gasoline	Liquid	317	950
Glass	Glass	8.5	25.5
Glass	Glass	3.3	9.9	Matched sealing partner for tungsten, molybdenum and kovar.
Glycerine	Liquid		485
Gold	Metal	14	42
Granite	Rock	35–43	105–129
Ice	Nonmetal	51
Invar	Metal Alloy	1.2	3.6
Iron	Metal	11.8	35.4
Kapton	Polymer	20	60	DuPont Kapton 200EN
Lead	Metal	29	87
Macor		9.3		-
Mercury	Liquid	60.4	181
Nickel	Metal	13	39
Oak	Biological	54		Perpendicular to the grain
Platinum	Metal	9	27
Polypropylene	Polymer	150	450
PVC	Polymer	52	156
Quartz	Nonmetal	12–16/6–9		Parallel to a-axis/c-axis T = –50 to 150 °C
Quartz	Nonmetal	0.59	1.77
Rubber	Biological	Disputed	Disputed	See Talk
Rock salt	Rock	40	120
Sapphire	Nonmetal	5.3		Parallel to C axis, or
Silicon carbide	Nonmetal	2.77	8.31
Silicon	Nonmetal	2.56	9
Silver	Metal	18	54
"Sitall"	Glass-ceramic	0±0.15	0±0.45	Average for −60 °C to 60 °C
Stainless steel	Metal alloy	10.1 ~ 17.3	30.3 ~ 51.9
Steel	Metal alloy	11.0 ~ 13.0	33.0 ~ 39.0	Depends on composition
Titanium	Metal	8.6	26
Tungsten	Metal	4.5	13.5
Water	Nonmetal	69	207
"Zerodur"	Glass-ceramic	≈0.007–0.1		From 0 °C to 50 °C