The separation of isotopes of an element during naturally occurring processes as a result of the mass differences between their nuclei. Although the chemical properties of the isotopes of an element are the same, there are differences in their physical properties (e.g. density, vapour pressure, boiling point, and melting point) due to the greater vibrational energy of the lighter isotope. Separation (fractionation) of isotopes will occur during such processes as evaporation or condensation, melting or crystallization, diffusion through crystals, and isotopic exchange reactions between water in a melt and minerals or mineral pairs. The extent of fractionation is dependent on temperature and is more pronounced the greater the mass difference between isotopes in relation to their individual isotopic mass. Significant fractionation occurs naturally with carbon, oxygen, sulphur, and hydrogen-deuterium. Fractionation ratios and isotopic ratios are useful in determining palaeotemperatures, geologic processes, and the modes of formation of rocks and minerals. See d/h ratio; oxygen-isotope ratio; oxygen-isotope analysis; stable-isotope studies; isotope geochemistry.