Computers & Gwscicaces Vol. 7, pp. 27-34 009g-3004/81/0301-00271502.00/0 Pergamon Press Ltd.. 19~1. Printed in Great Britain MANTLE: A PROGRAM TO CALCULATE A 30 kbar NORM ASSEMBLAGE JOSEPH R. SMYTH Geological Research Group, Mail Stop 978, Los Alamos ScientificLaboratory,Los Alamos,NM 87545,U.S.A. (Received 27 August 1979) Abstract--MANTLE is a FORTRAN IV code to calculate mineral assemblages which would be expected at a pressure of 30 kbars from a bulk composition given in nine oxide components. The program also calculates the theoretical STP bulk density of the assemblages, and has been used for modelingmantles of the terrestrial planets. With some improvementsit may prove useful in modelingthe upper mantle of the earth. Key Words: Geochemistry,Mantle, Mars, Mineralogy,Planetology. INTRODUCTION In order to model the interiors of terrestrial planets, a FORTRAN IV program MANTLE was written to cal- culate a mineral assemblage and theoretical STP bulk density to be expected at 30 kbars (3.0 GPa) for a given rock composition. It is written for interactive cal- culations on DEC PDP-I1 series computers using the RT-11 operating system. The nine oxide components required for input are SiO2, AI203, TiO:, MgO, FeO, Fe203, CaO, Na20, and K20. The program casts the analyses into anhydrous phases which are known to be stable at 25-35kbar and 900-1300°C. The calculated phases correspond roughly to those observed in mantle- derived inclusions in kimberlites and basalts. The range of compositions accepted by the program exceeds that observed in terrestrial samples from high pressure ori- gins. In situations where observational and ther- modynamic data that would define stable phase assem- blages are lacking, a few assumptions are made concern- ing such a phase assemblage. The program was written to predict physical properties (especially densities) and mineral assemblages for various bulk compositions. It has proved useful in the modeling of terrestrial planets. It was used extensively to derive densities from trial compositions, and to predict partial melt compositions from calculated assemblages in modeling a hypothetical upper mantle for Mars (McGet- chin and Smyth, 1978). The 30 kbar pressure corresponds to a depth of 250 km in Mars, 90 km in Earth and Venus, 350 km in Mercury, and 500 km in the Moon, and so it is hoped that the program will be useful for modeling the upper mantle and all of the terrestrial planets. I have received several requests for copies of the program since the work of McGetchin and Smyth (1978), and feel publication of the program may lead to refinements of the algorithm and possibly to some needed investigations in experimental petrology. ALGORITHM Figure 1 is a flowchart of the algorithm. The oxide components are input as weight percents of SiO2, TiO~, AI203, MgO, FeO, Fe203, CaO, Na20, and K:O, which are converted immediately to relative numbers of cations. The first step is to remove Ti because it is assumed not to enter the silicate phases. Ti is removed either as futile (TiO2) if Ti exceeds Fe 2÷, or as ilmenite (FeTiO3) if Fe z+ exceeds Ti, as is usual. The second step is to remove K as a hypothetical pyroxene KAISi206. This is a bit arbitrary and is based on occurrence of pyroxenes containing up to 1.2 weight percent K20 as inclusions in diamonds (Rickard and Smyth, 1979, un- publ.). Compositions with K in excess of either AI or 2 x Si are rejected as implausible. The next step is to calculate ratios of Mg to Fe 2+ and AI to Fe3÷ for partitioning between various phases. All phases are assumed to have equal ratios of Mg to Fe 2÷ and AI to Fe 3+. Na is the next cation to be removed; as the pyroxenes, jadeite and acmite, in the ratio AI to Fe3+, respectively. Compositions with Na in excess of AI + Fe 3+ are rejected as being too alkalic. The remaining Fe 3+ then is removed as andradite garnet (Ca3Fe2~+Si3Ox:), with rejection if Fe3+ exceeds 1.5 times Ca or 1.5 times Si. After removal of andradite, all remaining compositions are accepted and a major branch occurs based on the ratio of Ca to Fe2++ Mg. If Ca exceeds Mg + Fe "+, the program branches to Ca-rich assemblages. Few, if any, of these assemblages have been recognized in terrestrial samples, or hypothesized for extraterrestrial occur- rences, and will not be dealt with further here, but are included in the program for completeness. The Ca-poor branch leads to the more common eclogite and peridotite assemblages. The next step in this branch is to remove the Ca as the clinopyroxenes, diopside, and hedenbergite, in the ratio of Mg to Fe:+. Then the path branches on the ratio of AI to Mg + Fe2+. On the AI-rich branch, there is a second branch to Si-rich and Si-poor compositions. In the Si- poor branch, pyrope (Mg3AI:Si30,2) and almandine (Fe3AI2Si30~,) garnets are removed, and the remainder then is Si-free with aluminium greater than twice the Mg + Fe. Spinel (MgAI:O4) and hercynite (FeAI204) then are removed according to the Mg to Fe 2+ ratio, and the remaining excess alumina is assigned to corundum (path ¢AGEO VoL 7, No. l--.c 27