The partition coefficient (D or Kd) quantifies how a trace element distributes between a mineral and a coexisting melt or fluid: D = C_mineral / C_melt. D depends on the element's ionic radius and charge (compatibility with the crystal site), the mineral's crystal structure, melt composition, temperature, and pressure. Elements whose ionic radius and charge match an available crystal site have high D (compatible); mismatches produce low D (incompatible). The bulk partition coefficient for a rock (D-bulk) is the weighted average of mineral D values, weighted by the modal abundance of each mineral. D-bulk controls whether an element is enriched or depleted during partial melting and fractional crystallization, making it the key parameter linking mantle mineralogy to magma composition.
Partition coefficients are the quantitative link between crystal chemistry and magma geochemistry. They encode, in a single number per element-mineral pair, whether and how strongly an element is incorporated into a crystal structure during magmatic processes.
The physical basis is crystal-chemical. Each mineral has specific crystallographic sites with defined sizes and charges. An element with the right ionic radius and charge for a site enters readily (high D). The lattice strain model formalizes this: D for an element depends on the strain energy penalty for fitting a foreign ion into the site. Elements whose radius matches the site's ideal radius have the highest D; elements too large or too small have exponentially decreasing D. This produces the characteristic parabolic D pattern when plotted against ionic radius -- the basis for predicting D values for elements without experimental data.
In practice, D values are determined experimentally (equilibrating mineral and melt at controlled T-P-X and analyzing both) or empirically (from natural mineral-glass pairs in volcanic rocks). The most important datasets for igneous petrology cover olivine, clinopyroxene, orthopyroxene, garnet, plagioclase, spinel, and amphibole in basaltic to rhyolitic melts. These values populate the melting and crystallization models (batch melting, fractional melting, Rayleigh fractionation) that predict how trace element concentrations evolve during magma genesis and differentiation.
The sensitivity of melt composition to source mineralogy, through D-bulk, is what makes trace elements such powerful probes of mantle processes. The presence or absence of garnet in the mantle source (controlled by pressure/depth) completely changes the HREE behavior and produces diagnostic REE slope differences between shallow and deep-derived magmas. Similarly, the presence of residual amphibole, phlogopite, or accessory phases (rutile, apatite, zircon) selectively retains specific elements, creating the characteristic depletion patterns that fingerprint source mineralogy and tectonic setting.