In each diffusion reaction the flux of matter equals the conductivity multiplied by a driving force, with the conductivity being the mobility of the diffusing species (diffusivity) and the driving force being the presence of a concentration gradient as a function of distance in a direction (where a constant concentration gradient depicts a linear variation of concentration in one direction). A common example is the initial phase of explosive volcanic eruptions, in which diffusion controls bubble growth by allowing gas molecules to migrate into bubbles. Diffusion is a microscopic process, which can lead to macroscopic effects. In geology the study of diffusion is used to understand magmatic and metamorphic processes, mass transport, fluid/rock interactions, thermal and physico-chemical history of rocks and crystal growth, mineral zonation, atom ordering, exsolution features and isotopic characteristics. Diffusion has been of interest in a diversity of fields since then, such as physics, metallurgy and chemistry. Albert Einstein (1879-1955) continued working on the relationship between random atomic movement and the process of diffusion. In 1855 the German physician and physiologist Adolf Eugen Fick (1829-1901) introduced Fick's law of diffusion, describing diffusion of a gas across a fluid membrane, and thus the relationship between diffusion flux of a component and its concentration gradient. A value of D > 1 indicates that the element is compatible, it is preferentially accepted by the mineral. The partition coefficient can be calculated using the following equation: D = C A / C B, where C A is the concentration of an element in phase A and C B is the concentration of an element in phase B. The partition coefficient depends on factors such as composition, temperature and pressure, but is independent of the element concentration. Note that the letter 'D' is used both for diffusivity and partition coefficient but describes two totally different processes. Element partitioning can be described by the partition coefficient, D (sometimes K), which is the concentration ratio of an element between two phases. This process is called element partitioning. However, they can enter mineral structures, with certain elements being incorporated preferentially. Many elements occur in rocks in low concentrations and are not able to build their own minerals. Earth and Planetary Science Letters, 253, 307-327. Images modified after Watson & Baxter (2007) Diffusion in solid-Earth systems. Still debated are the exchange mechanism and grain-edge fluid diffusion.

Schematic illustrates common diffusion mechanisms and pathways, such as vacancies and interstitial atoms, and intragrain and grain-boundary diffusion.

Concentration gradient definition