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Thermal expansion is the change in shape and volume of a system due to a temperature change. For liquids, gases, and isotropic solids, thermal expansion is isotropic, involving only a change in volume and requiring, therefore, the measurement of a single parameter to uniquely specify the expansion. Crystalline solids with symmetries other than cubic have anisotropic expansions. In the hexagonal and tetragonal systems, a sphere expands to an ellipsoid of revolution, the unique axis of the ellipsoid coinciding with the unique, or c, crystallographic axis. Two parameters must be measured to uniquely specify the expansion of tetragonal and hexagonal compounds. In the orthorhombic, monoclinic, and triclinic systems a sphere expands to a triaxial ellipsoid. The three principal axes coincide with the three crystallographic axes in the orthorhombic systems, and hence only three parameters are needed to uniquely specify the thermal expansion. In the monoclinic system, the only symmetry requirements are that one axis of the spheroid coincides with the b, or twofold crystallographic axis. Thus, four parameters must be measured to specify the expansion of a monoclinic solid, three giving the axial lengths of the spheroid and one specifying its orientation. In the triclinic system there are no symmetry requirements controlling the orientation of the spheroid of expansion. Consequently, six parameters must be measured to uniquely specify the thermal expansion, three giving the axial lengths of the spheroid, and three specifying their orientations with respect to the crystallographic axes. Complete discussions of the crystallographic relationships of thermal expansions can be

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