the diffusion coefficient

In both of Fick's laws there is a single number, D, that scales everything: give the same gradient a bigger D and atoms pour through faster. The diffusion coefficient (also called diffusivity) is that number — a compact measure of how easily a particular kind of atom moves through a particular material. Its units are area per time, square meters per second, which fits the idea that diffusion is about how much area an atom can spread across in a given time. A big D means fast, deep diffusion; a small D means atoms barely budge.

The single most important thing about D is that it is not a constant — it depends violently on temperature, following an Arrhenius law: D = D0 times exp(-Qd / (R times T)). Here D0 is a temperature-independent prefactor set by the crystal and jump geometry, Qd is the activation energy (the energy barrier an atom must clear to make one jump, in joules per mole), R is the gas constant (8.314 J/mol-K), and T is absolute temperature. The exponential means D is fiercely sensitive to temperature: a modest rise in T can multiply D by ten or a hundred. That single fact is why heat treatments are done hot, and why the very same part is dimensionally stable at room temperature — down cold, D is so tiny that atoms effectively never move.

Two levers set D. The activation energy Qd reflects the mechanism: small interstitial atoms (carbon, hydrogen) have a low Qd and diffuse fast; substitutional atoms moving by the vacancy mechanism face a higher Qd (they must both form and jump into a vacancy) and diffuse slowly. If you plot the natural log of D against 1/T you get a straight line whose slope is -Qd/R — the standard experimental way to measure the activation energy. Engineers read tabulated D0 and Qd values straight into Fick's laws to predict how long and how hot a process such as carburizing, doping, or sintering must run.