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 3.983 C 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 18 and 120 kelvin.[2] ALLVAR Alloy 30, a titanium alloy, exhibits anisotropic negative thermal expansion across a wide range of temperatures.[3]
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.[4] At the glass transition temperature, rearrangements that occur in an amorphous material lead to characteristic discontinuities of coefficient of thermal expansion and specific heat. These discontinuities allow detection of the glass transition temperature where a supercooled liquid transforms to a glass.[5] An interesting "cooling-by-heating" effect occurs when a glass-forming liquid is heated from the outside, resulting in a temperature drop deep inside the liquid.[6]
Absorption or desorption of water (or other solvents) 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.
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.
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 (not linear) 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.
When calculating thermal expansion it is necessary to consider whether the body is free to expand or is constrained. If the body is free to expand, the expansion or strain resulting from an increase in temperature can be simply calculated by using the applicable coefficient of thermal expansion.
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.
Linear expansion means change in one dimension (length) as opposed to change in volume (volumetric expansion).To a first approximation, the change in length measurements of an object due to thermal expansion is related to temperature change by a coefficient of linear thermal expansion (CLTE). It is the fractional change in length per degree of temperature change. Assuming negligible effect of pressure, we may write: α L = 1 L d L d T \displaystyle \alpha _L=\frac 1L\,\frac \mathrm d L\mathrm d T where L \displaystyle L is a particular length measurement and d L / d T \displaystyle \mathrm d L/\mathrm d T is the rate of change of that linear dimension per unit change in temperature.
The area thermal expansion coefficient relates the change in a material's area dimensions to a change in temperature. It is the fractional change in area per degree of temperature change. Ignoring pressure, we may write: α A = 1 A d A d T \displaystyle \alpha _A=\frac 1A\,\frac \mathrm d A\mathrm d T where A \displaystyle A is some area of interest on the object, and d A / d T \displaystyle dA/dT is the rate of change of that area per unit change in temperature.
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 α L \displaystyle \alpha _L in different directions. As a result, the total volumetric expansion is distributed unequally among the three axes. If the crystal symmetry is monoclinic or triclinic, even the angles between these axes are subject to thermal changes. In such cases it is necessary to treat the coefficient of thermal expansion as a tensor with up to six independent elements. 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.[8]
Thermal expansion coefficients of solids usually show little dependence on temperature (except at very low temperatures) whereas liquids can expand at different rates at different temperatures. However, there are some known exceptions: for example, cubic boron nitride exhibits significant variation of its thermal expansion coefficient over a broad range of temperatures.[9] Another example is paraffin which in its solid form has a thermal expansion coefficient that is dependent on temperature.[10]
The thermal expansion of liquids is usually higher than in solids because the intermolecular forces present in liquids are relatively weak and its constituent molecules are more mobile.[16][17] Unlike solids, liquids have no definite shape and they take the shape of the container. Consequently, liquids have no definite length and area, so linear and areal expansions of liquids only have significance in that they may be applied to topics such as thermometry and estimates of sea level rising due to global climate change.[18] However, αL is sometimes still calculated from the experimental value of αV.
In general, liquids expand on heating. However water is an exception to this general behavior: below 4 C it contracts on heating, leading to a negative thermal expansion coefficient. At higher temperatures water shows more typical behavior, with a positive thermal expansion coefficient.[19]
The expansion of liquids is usually measured in a container. When a liquid expands in a vessel, the vessel expands along with the liquid. Hence the observed increase in volume (as measured by the liquid level) is not the actual increase in its volume. The expansion of the liquid relative to the container is called its apparent expansion, while the actual expansion of the liquid is called real expansion or absolute expansion. The ratio of apparent increase in volume of the liquid per unit rise of temperature to the original volume is called its coefficient of apparent expansion. The absolute expansion can be measured by a variety of techniques, including ultrasonic methods.[20]
Historically, this phenomenon complicated the experimental determination of thermal expansion coefficients of liquids, since a direct measurement of the change in height of a liquid column generated by thermal expansion is a measurement of the apparent expansion of the liquid. Thus the experiment simultaneously measures two coefficients of expansion and measurement of the expansion of a liquid must account for the expansion of the container as well. For example, when a flask with a long narrow stem, containing enough liquid to partially fill the stem itself, is placed in a heat bath, the height of the liquid column in the stem will initially drop, followed immediately by a rise of that height until the whole system of flask, liquid and heat bath has warmed through. The initial drop in the height of the liquid column is not due to an initial contraction of the liquid, but rather to the expansion of the flask as it contacts the heat bath first. Soon after, the liquid in the flask is heated by the flask itself and begins to expand. Since liquids typically have a greater percent expansion than solids for the same temperature change, the expansion of the liquid in the flask eventually exceeds that of the flask, causing the level of liquid in the flask to rise. For small and equal rises in temperature, the increase in volume (real expansion) of a liquid is equal to the sum of the apparent increase in volume (apparent expansion) of the liquid and the increase in volume of the containing vessel. The absolute expansion of the liquid is the apparent expansion corrected for the expansion of the containing vessel.[21]
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