The Gibbs method is a technique to apply the change in mineral composition, which is preserved as compositional zoning, to decipher the pressure temperature path of metamorphic rocks. This method involves deriving a system of equations composed of a Gibbs-Duhem equa tion for each phase, stoichiometrical relations among the chemical potentials of phase components, and relationship between compositional term, dX, and other intensive variables. To solve these equations random mixing of substitution and constant molar entropy and volume are assumed. The continuous pressure-temperature path during garnet growth can be inferred by choosing garnet composition as monitor parameters.

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There are many ultramafic complexes in the Sangun zone in central Chugoku district, Southwest Japan: they are Shiratakiyama, Tari-Misaka, Inazumiyama, Mochimaru, Yagami, Kasamatsu, Takase, Mimuro, Ashidachi, Yufune, Yanomine, Suishoyama, Niimi, Osa, Tajibe, Fuse, Taguchi, Harashige, and Ochiai-Hokubo. Lithological variations in these complexes were determined for both primary and thermal metamorphic mineral assemblages.
     With one exception (the Ochiai-Hokubo complex) they consist of harzburgite, dunite and chromitite, and are intruded by some gabbroic dikes. Harzburgite is always dominant over dunite. Chromitite is closely associated with dunite: a chromitite body is enclosed by a dunite envelope and large chromitite bodies are exclusively found in relatively dunite-dominant complexes. The lithological features indicate their derivation from the transition zone or the uppermost mantle member of ophiolitic suites.
     The complexes are frequently suffered from the thermal metamorphism by some younger granitic masses. The contact aureole is divided into five mineral zones, Ia (chrysotile/lizardite), Ib (antigorite), II (olivine-talc), III (olivine-anthophyllite) and IV (olivine-orthopyroxene) in order of increasing metamorphic grade. The highest metamorphic grade attained is different dependent on the distance from and rock facies (temperature) of granitic magmas.

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The Orikabe plutonic complex in the Kitakami Mountains is divided into Main and North plutons. The Main pluton is composed of three rock types; i.e., the Tokusenjo type (gabbro), Orikabe type (monzodiorite-monzogranite) and Sasamori type (granodiorite). The oxidation states of magmas around solidus are estimated from coexisting Fe-Ti oxides as follows; near the FMQ and NNO buffers in the Tokusenjo type, in the range from the FMQ to HM buffer in the Orikabe type, and intermediate between the NNO and HM buffer in the Sasamori type. The total pressure for the Orikabe and Sasamori type magmas at their solidus temperatures is estimated to be about 2-3 kb by hornblende geobarometer. Hornblende of the Sasamori type has cores rich in A1^IV and Ti, whereas that of the Orikabe type is generally poor in them. It indicates that hornblende in the Orikabe type began to crystallize at lower temperature than that in the Sasamori type, which is concordant with microscopic observation of the Orikabe type rocks, suggesting crystallization of hornblende simultaneous with or later than biotite. The delay of hornblende appearance in the Orikabe type is due to lower water content of the magma than that of the Sasamori type. In gabbros of the Tokusenjo type, the coexistence of Fe-rich olivine and Ca-poor plagioclase and scarcity of hornblende are characteristic, indicating a H₂O poor magma (less than 3 wt. %) of the Tokusenjo type. Chemical composition of the minerals in the Tokusenjo type rocks is continuous to that of the Orikabe type with increase in SiO₂ of host rocks, suggesting continuous differentiation of magmas of the both types.

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