Thermal expansion is the increase in volume of a material as its temperature is increased, usually expressed as a fractional change in dimensions per unit temperature change. When a material is a solid, thermal expansion is described in terms of change in length, height, or thickness. If the material is a fluid, it is generally described in terms of a change in volume. Because the bonding forces among atoms and molecules vary from material to material, expansion coefficients are characteristic of elements and compounds. Softer metals exhibit a high coefficient of expansion (CTE); whereas harder materials, such as tungsten, exhibit a low CTE. A CTE mismatch between two workpieces can result in significant residual stresses at the joint which, when combined with the applied stresses can cause failure at lower pull strengths.