For petrological calculations, including geothermobarometry and the calculation of phase diagrams (for example, P–T petrogenetic grids and pseudosections), it is necessary to be able to express the activity–composition (a–x) relations of minerals, melt and fluid in multicomponent systems Although the symmetric formalism—a macroscopic regular model approach to a–x relations—is an easy-to-formulate, general way of doing this, the energetic relationships are a symmetric function of composition We allow asymmetric energetics to be accommodated via a simple extension to the symmetric formalism which turns it into a macroscopic van Laar formulation We term this the asymmetric formalism (ASF) In the symmetric formalism, the a–x relations are specified by an interaction energy for each of the constituent binaries amongst the independent set of end members used to represent the phase In the asymmetric formalism, there is additionally a "size parameter" for each of the end members in the independent set, with size parameter differences between end members accounting for asymmetry In the case of fluid mixtures, for example, H2O–CO2, the volumes of the end members as a function of pressure and temperature serve as the size parameters, providing an excellent fit to the a–x relations In the case of minerals and silicate liquid, the size parameters are empirical parameters to be determined along with the interaction energies as part of the calibration of the a–x relations In this way, we determine the a–x relations for feldspars in the systems KAlSi3O8–NaAlSi3O8 and KAlSi3O8–NaAlSi3O8–CaAl2Si2O8, for carbonates in the system CaCO3–MgCO3, for melt in the melting relationships involving forsterite, protoenstatite and cristobalite in the system Mg2SiO4–SiO2, as well as for fluids in the system H2O–CO2 In each case the a–x relations allow the corresponding, experimentally determined phase diagrams to be reproduced faithfully The asymmetric formalism provides a powerful and flexible way of handling a–x relations of complex phases in multicomponent systems for petrological calculations

Activity–composition relations for phases in petrological calculations: an asymmetric multicomponent formulation

This textbook provides a basic understanding of the formative processes of igneous and metamorphic rock through quantitative applications of simple physical and chemical principles. The book encourages a deeper comprehension of the subject by explaining the petrologic principles rather than simply presenting the student with petrologic facts and terminology. Assuming knowledge of only introductory college-level courses in physics, chemistry, and calculus, it lucidly outlines mathematical derivations fully and at an elementary level, and is ideal for intermediate and advanced courses in igneous and metamorphic petrology. The end-of-chapter quantitative problem sets facilitate student learning by working through simple applications. They also introduce several widely-used thermodynamic software programs for calculating igneous and metamorphic phase equilibria and image analysis software. With over 350 illustrations, this revised edition contains valuable new material on the structure of the Earth's mantle and core, the properties and behaviour of magmas, recent results from satellite imaging, and more.

Principles of igneous and metamorphic petrology

Building upon the award-winning second edition, this comprehensive textbook provides a fundamental understanding of the formative processes of igneous and metamorphic rocks. Encouraging a deeper comprehension of the subject by explaining the petrologic principles, and assuming knowledge of only introductory college-level courses in physics, chemistry, and calculus, it lucidly outlines mathematical derivations fully and at an elementary level, making this the ideal resource for intermediate and advanced courses in igneous and metamorphic petrology. With over 500 illustrations, many in color, this revised edition contains valuable new material and strengthened pedagogy, including boxed mathematical derivations allowing for a more accessible explanation of concepts, and more qualitative end-of-chapter questions to encourage discussion. With a new introductory chapter outlining the “bigger picture,” this fully updated resource will guide students to an even greater mastery of petrology.

Principles of Igneous and Metamorphic Petrology

http://www.perplex.ethz.ch/papers/epsl_kerrick_2001.pdf

Metamorphic devolatilization of subducted oceanic metabasalts: implications for seismicity, arc magmatism and volatile recycling

We formulate an algorithm for the calculation of stable phase relations of a system with constrained bulk composition as a function of its environmental variables. The basis of this algorithm is the approximate representation of the free energy composition surfaces of solution phases by inscribed polyhedra. This representation leads to discretization of high variance phase fields into a continuous mesh of smaller polygonal fields within which the composition and physical properties of the phases are uniquely determined. The resulting phase diagram sections are useful for understanding the phase relations of complex metamorphic systems and for applications in which it is necessary to establish the variations in rock properties such as density, seismic velocities and volatile-content through a metamorphic cycle. The algorithm has been implemented within a computer program that is general with respect to both the choice of variables and the number of components and phases possible in a system, and is independent of the structure of the equations of state used to describe the phases of the system.

D. R. Waldbaum

Papers

Mixing properties of sanidine crystalline solutions: III. Calculations based on two-phase data

Mixing properties of sanidine crystalline solutions: IV. Phase diagrams from equations of state

Mixing properties of sanidine crystalline solutions: I. Calculations based on ion-exchange data

Authigenic albite from Rhodes