Subduction Factory 3: An Excel worksheet and macrofor calculating the densities, seismic wave speeds,and H2O contents of minerals and rocks at pressureand temperatureBradley R. HackerDepartment of Geological Sciences, University of California, Santa Barbara, California 93106, USA([email protected])Geoffrey A. AbersDepartment of Earth Sciences, Boston University, Boston, Massachusetts 02215, USA ([email protected])[1] An Excel macro to calculate mineral and rock physical properties at elevated pressure and temperatureis presented. The workbook includes an expandable database of physical parameters for 52 rock-formingminerals stable at high pressures and temperatures. For these minerals the elastic moduli, densities, seismicvelocities, and H2O contents are calculated at any specified P and T conditions, using basic thermodynamicrelationships and third-order finite strain theory. The mineral modes of suites of rocks are also specifiable,so that their predicted aggregate properties can be calculated using standard solid mixing theories. A suiteof sample rock modes taken from the literature provides a useful starting point. The results of thesecalculations can be applied to a wide variety of geophysical questions including estimating the alteration ofthe oceanic crust and mantle; predicting the seismic velocities of lower-crustal xenoliths; estimating theeffects of changes in mineralogy, pressure and temperature on buoyancy; and assessing the H2O contentand mineralogy of subducted lithosphere from seismic observations.Components: 3919 words, 1 dataset.Keywords: Equation of state; density; P wave; Poisson’s ration; S wave.Index Terms: 3919 Mineral Physics: Equations of state; 3660 Mineralogy and Petrology: Metamorphic petrology; 8124Tectonophysics: Earth’s interior—composition and state (1212).Received 30 July 2003; Revised 2 December 2003; Accepted 3 December 2003; Published 20 January 2004.Hacker, B. R., and G. A. Abers (2004), Subduction Factory 3: An Excel worksheet and macro for calculating the densities,seismic wave speeds, and H2O contents of minerals and rocks at pressure and temperature, Geochem. Geophys. Geosyst., 5,Q01005, doi:10.1029/2003GC000614.1. Introduction[2] Addressing many geodynamic problemsrequires calculating the densities and wavespeeds of rocks at elevated pressure and tem-perature. Hacker et al. [2003] presented a data-base of mineral physical p roperties and aformalism for such calculations. Here we presentan Excel workbook that includes that databaseof mineral physical properties and a macro1thatuses that formalism to calculate mineral and1Auxiliary materi al is available at ftp://ftp.agu.org/apend/gc/2003GC000614.G3G3GeochemistryGeophysicsGeosystemsPublished by AGU and the Geochemical SocietyAN ELECTRONIC JOURNAL OF THE EARTH SCIENCESGeochemistryGeophysicsGeosystemsTechnical BriefVolume 5, Number 120 January 2004Q01005, doi:10.1029/2003GC000614ISSN: 1525-2027Copyright 2004 by the American Geophysical Union 1 of 7rock physical properties at elevated pressure andtemperature.2. Database[3] The mineral physical properties databasecomprises t he ‘‘database’’ worksheet of the work-book. It includes the formula weight (‘‘gfw’’column), molar volume (‘‘V’’), H2O content(‘‘H2O’’), expansivity a (‘‘a0’’) parameterizedto vary with temperature [Holland and Powell,1998], isothermal bulk modulus KT(‘‘KT’’), K0T=@KT/@P (‘‘KT prime’’), shear modulus G (‘‘G’’),G0= @G/@P (‘‘G prime’’),  =(@lnG/@lnr)P(‘‘gamma’’), the first thermodynamic Gru¨neisenparameter gth=(@lnT/@lnr)S(‘‘gth’’), and secondGru¨neisen parameter dT=(@lnKT/@lnr )P(‘‘dT’’)for common minerals [e.g., Anderson et al.,1992; Bina and Helffrich, 1992]. (Here, P =pressure, T = temperature, and S = entropy.)See Hacker et al. [2003] for a brief discussionof uncertainties in these data. Explanations of themineral abbreviations as well as mineral formulaecan b e found in the ‘‘rock mineral modes’’worksheet.[4] Many of these parameters have not beenmeasured directly for all the minerals in thedatabase, a nd have been approximated froma variety of scaling relationships [see alsoHelffrich, 1996]. The most critical approxima-tions are of the shear moduli (G) of hydrousphases, which have been measured directly forfew hydrous minerals. Where G has not beenmeasured, we estimate it from KTby assumingthat the Poisson ratio matches that of a mineralof similar structure for which G is known. Avariety of observed relations among , dT, gth,K0T, and G0[Anderson et al., 1992] allow some ofthe other needed parameters to be estimated fromothers, or we make other standard assumptions(e.g., K0T= 4). If no derivative terms are avail-able, they are scaled from those of similarminerals. All of these approximations are speci-fied on a case-by-case basis in the Notes onParameter Values section below, which are keyedto notes next to each parameter value in the‘‘database’’ worksheet.3. Mineral Properties at Pressure andTemperature[5] The ‘‘minerals’’ worksheet contains single-crystal physical properties calculated at elevatedtemperature and pressure (T, P). To calculate prop-erties at elevated temperature and pressure, indi-vidual properties are first extrapolated from STP(standard temperature and pressure) in temperatureand then in pressure. The specific values calculatedare: the thermal expansivity at temperature(‘‘alpha(T, 0)’’ column), density at temperature(‘‘rho(T, 0)’’), isothermal bulk modulus at temper-ature (‘‘Kt(T, 0)’’), shear modulus at temperature(‘‘G(T, 0)’’), isothermal bulk modulus at tempera-ture and pressure (‘‘Kt(T, P)’’), thermal expansivityat temperature and pressure (‘‘alpha(T, P)’’), adia-batic bulk modulus at temperature and pressure(‘‘Ks(T, P)’’), shear modulus at temperature andpressure (‘‘G(T, P)’’), density at temperature andpressure (‘‘rho(T, P)’’), bulk wave speed at tem-perature and pressure (‘‘V bulk’’), P wave speed attemperature and pressure (‘‘Vp’’), S-wave speed attemperature and pressure (‘‘Vs’’), and Poisson’sratio (‘‘Poisson’s ratio’’). The methodology, basedon that of Bina and Helffrich [1992], was describedby Hacker et al. [2003] and is repeated below withminor modification (principally, we now uniformlyapply a third-order approximation for finite strain,producing