Abstract
Principal component analysis, using eigenvalues and eigenvectors, of the encountered variation in the chemistry of 153 garnets indicates the following: (1) In low grade metamorphic rocks, spessertite and almandine are distinctly isomorphous. The variability of pyrope content does not influence the binary Fe-Mn relationship. However there may be some influence of the grossularite content. (2) In high grade metamorphic rocks, pyrope and almandine are distinctly isomorphous. Variability of grossularite content does not affect the binary Mg-Fe relationship. However, variability in spessertite content may influence the linearity particularly when there is little pyrope.
Similar statistical analysis of the chemical data on 119 samples of clinopyroxenes indicates that only significant changes in the concentrations of Al in octahedral and/or of Al in tetrahedral sites and Ti could cause some change in the Fe∶Mg ratio in the mineral.
Principal component analysis of the data on coexisting garnet and clinopyroxene could be used to classify rocks into their petrogenetic types.
Distribution coefficient calculated by assuming ideal binary solution of Mg and Fe members in pyroxene and garnet is useful to indicate the P-T of the formation of the rocks.
Similar content being viewed by others
References
Banno, S.: Petrologic studies on Sanbagawa crystalline schists in the Bessi-Ino district, central Sikoku, Japan. J. Fac. Sci. Univ. Tokyo 15, 203–310 (1964).
Buddington, A. F.: Chemical petrology of some metamorphosed Adirondack gabbroic, syenitic and quartz-syenetic rocks. Amer. J. Sci. Bowen Vol., 37–84 (1952).
Challis, G. A.: The origin of ullramafic intrusions, New Zealand. J. Petrol. 6, 322–364 (1965).
Chinner, G. A.: Pelitic gneisses with varying ferrous/ferric ratio from Glenclova, Angus, Scotland. J. Petrol. 1, 178–217 (1960).
Coleman, R. G., D. E. Lee, L. B. Beatty, and W. W. Brannock: Eclogites and eclogites: their differences and similarities. Bull. Geol. Soc. Am. 76, 483–508 (1965).
Engel, A. E. J., and C. G. Engel: Progressive metamorphism and granitization of the major paragneiss, northwest Adirondack Mountains, New York, Part II, Mineralogy. Bull. Geol. Soc. Amer. 71, 1–58 (1960).
Ernst, W. G.: Petrochemical study of coexisting minerals from low-grade schists, Eastern Shikoku, Japan. Geochim. Cosmochim. Acta 28, 1631–1668 (1964).
Eskola, P.: On the granulites of Lapland. Am. J. Sci. Bowen Vol., 133–171 (1952).
Essene, E. J., W. S. Fyfe, and F. J. Turner: Petrogenesis of Fransiscan glaucophane schists and associated metamorphic rocks, California. Beitr. Mineral. Petrog. 11, 695–705 (1965).
Evans, B. W., and C. V. Guidotti: The sillimanite — potash feldspar isograd in western Maine, U.S.A. Contr. Mineral and Petrol. 12, 25–62 (1966).
Fiala, J.: The distribution of elements in mineral phases of some garnet periodites from the Bohemian Massif. Krystalinikum 4, 31–54 (1966).
Frost, M. J.: Metamorphic grade and iron-magnesium distribution between coexisting garnet-biotite and garnet-hornblende. Geol. Mag. 99, 429–438 (1962).
Green, D. H.: The petrogenesis of high temperature peridotite intrusion in the Lizard Area, Cornwall. J. Petrol. 5, 134–150 (1964).
Green, Tr. H.: An experimental investigation of sub-solidus assemblages formed at high pressure in high-alumina basalt, kyanite eologite and grospydite compositions. Contr. Mineral. and Petrol. 16, 84–114 (1967).
Himmelberg, G. R., and Wm. C. Phinney: Granulite facies metamorphism, Granite Falls, Montevideo Area, Minnesota. J. Petrol. 8, 325–348 (1967).
Kretz, R.: Chemical study of garnet, biotite and hornblende from gneisses of southwestern Quebec, with emphasis on distribution of elements in coexisting minerals. J. Geol. 67, 371–402 (1959).
Kuroda, Y., and Y. Ogura: Epidote amphibolite from the N. E. Abukuma Plateau, Japan. Sci. Rept. Tokyo Kyoiku Daigaku 8, 245–268 (1963).
Lee, D. E., R. G. Coleman, and R. C. Erd: Garnet types from the Cazadero area, California. J. Petrol. 3, 460–492 (1963).
Leelanandam, C.: Chemical study of pyroxenes from the charnockitic rocks of Kondapalli (Andhra Pradesh), India. Mineral. Mag. 36, 153–179 (1967).
Miyashiro, A.: Calcium-poor garnet in relation to metamorphism: Geochim. Cosmochim. Acta 4, 179–208 (1953).
Nixon, P. H., O. v. Knorring, and J. M. Rooke: Kimberlites and associated inclusions of Basutoland: A mineralogical and geochemical study. Am. Mineralogist 48, 1090–1132 (1963).
O'Hara, M. J., and E. L. P. Mercy: Petrology and petrogenesis of some garnetiferous peridotites. Trans. Roy. Soc. Edinburgh 65, 251–314 (1963).
Phinney, Wm. C.: Phase equilibria in the metamorphic rocks of St. Paul Island and Cape North, Nova Scotia. J. Petrol. 4, 90–130 (1963).
Reyment, R. A.: Multivariate statistical analysis in geology. European Meeting on Statistics, Econometrics and Management Science, Amsterdam (1968), Publ. No. 74 from the Plaeontological Institution, Uppsala.
Saxena, S. K.: Crystal-chemical aspects of distribution of elements among certain coexisting rock-forming silicates. Neues Jahrb. Mineral. Abhandl. 108, 292–323 (1968a).
—: Distribution of iron and magnesium between coexisting garnet and clinopyroxene in rocks of varying metamorphic grade. Am. Mineralogist 53, 2018–2024 (1968b).
—: Distribution of elements among coexisting minerals and the nature of solid solution in garnet. Am. Mineralogist 53, 994–1014 (1968c).
—: Chemical study of phase equilibria in charnockites, Varberg, Sweden. Am. Mineralogist 53, 1674–1695 (1968d).
—: Intracrystalline chemical variations in certain calcic pyroxenes and biotites. Neues Jahrb. Mineral. Abhandl. 107, 299–316 (1967).
—: Silicate solid solutions and geothermometry: 3. Distribution of Fe and Mg between co-existing garnet and biotite. Contr. Mineral. and Petrol. 22, 259–267 (1969).
—, and N. B. Hollander: Distribution of iron and magnesium in charnockitic rocks, Halmstad, Sweden. Neues Jahrb. Mineral. Monatsh. 2, 85–92 (1969).
Sobolev, N. V., Jr., I. K. Kuznetsova, and N. I. Zyuzin: The petrology of grospydite xenoliths from the zagadochnaya Kimberlite pipe in Yakutia. J. Petrol. 9, 253–280 (1968).
Yoder, H. S., Jr., and C. E. Tilley: Origin of basalt magmas. An experimental study of natural and synthetic rock systems. J. Petrol. 3, 342–532 (1962).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Saxena, S.K. Silicate solid solutions and geothermometry. Contr. Mineral. and Petrol. 23, 140–156 (1969). https://doi.org/10.1007/BF00375176
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00375176