Diamond is a metasomatic mineral that forms during migration of carbon-bearing fluids, which means that it forms from fluids and melts that move through the mantle.
Generally, two conditions are needed for diamond formation: Carbon must be present in a mantle fluid or melt in sufficient quantity, and the melt or fluid must become reduced enough so that oxygen does not combine with carbon.
Traditional models for diamond formation from fluids in the mantle invoke either carbonate (CO3) reduction or methane (CH4) oxidation to remove the elements bonded to carbon. Both these mechanisms require some oxygen exchange with the surrounding rocks—peridotite or eclogite at the site of diamond precipitation so that elemental carbon can be produced to crystallize diamond (Smit & Shirey, n.d.).
These processes occur at high pressures and temperatures of at least 2000 degrees Fahrenheit (How Diamonds Are Formed?).
Diamonds can form in both peridotite (predominant rock type in the mantle that contains the minerals orthopyroxene, clinopyroxene, and olivine) and eclogite (rock type in the lithospheric mantle, a bimineralic rock consisting of a sodium-rich clinopyroxene known as omphacite and garnet with pyrope (Mg-rich), grossular (Ca-rich), and almandine (Ferich) components.) in the cratonic lithospheric mantle, as well as their higher pressure equivalents in the much deeper transition zone and lower mantle.
Reference:
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Smit, K. V., & Shirey, S. B. (n.d.). Diamonds from the Deep.
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Melodye Gordon English 5181 User Document 3