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COLLOQUIUM ON THE BUILD-UP OF PETROLOGICAL PHASE DIAGRAMS
ST. MARGHERITA LIGURE, FEBRUARY 27TH – MARCH 1ST 2013
Convenors
Giulio Ottonello & Daniele Castelli
CONTENTS
THEORY (February 28th – morning 8:30 – 13:00)
Pascal Richet (Institut de Physique du Globe, Paris)
Basic features of the physical chemistry of silicate melts: effect of temperature, pressure and
chemical composition
Even since the formation of the Earth, the transport and thermodynamic properties of silicate melts
have played a major role in geological activity. Not only is the present stratification of the planet a
direct consequence of this role, but the chemical differences observed from the lower mantle to the
crust illustrate the very strong dependence of the physical properties of silicate melts on
temperature, pressure and composition. The main features of these variations will thus be presented,
and related to the relevant structural features of these liquids.
James Connolly (EidgenössischeTechnische Hochshule, Zurich)
Phase diagrams: what, how and, maybe, why.
The first part of this lecture will provide a brief review of the principles and nomenclature of phase
diagrams (Hillert, 1986). The second part will describe a simple method for computing phase
diagrams (Connolly, 2009). If time allows, the final part of the lecture will illustrate how phase
equilibrium calculations can be used in geophysical inversions for planetary structure, composition
and temperature (Khan et al., 2006).
Donato Belmonte (Dipartimento di Scienze della Terra, dell’Ambiente e della Vita, Università di
Genova)
Effects of thermo-physical parameterization on phase diagrams topology at high pressure and
temperature: insights from ab-initio calculations
The calculation of Gibbs free energy of solid and liquid phases at high pressure and temperature is a
quite complicated task since physical unsoundness may arise due to choice of the equation-of-state
formalism (Belmonte et al., 2012). A robust parameterization of thermophysical properties (e.g.
thermal expansion and compressibility) at those conditions is thus crucial to obtain a reliable
representation of phase diagrams topology. Ab initio methods provide an alternative and selfconsistent way to check the confidence of the thermodynamic dataset adopted for a phase diagram
calculation (Ottonello et al., 2010). Some examples in the CAS and MAS ternary systems will be
presented and discussed, along with some possible petrological and geophysical implications.
Pascal Richet (Institut de Physique du Globe, Paris)
The glass transition
A melt eventually transforms to a glass if crystallization is by-passed upon cooling. This transition
from a liquid to a solid is accompanied by marked changes in second-order thermodynamic
properties. To account for these changes, it is useful to assume that properties of liquids are made of
two largely independent contributions related to changes in either vibrational excitations or in the
structure of the material. These features will be described and some of their geochemical
consequences discussed. In particular, attention will be paid to the consequences of the glass
transition on the entropy of glasses and, more generally, of disordered solids.
CALCULUS (February 28th – afternoon 15:00 – 18:00)
Marco Attene & Luca Chiarabini (Istituto di Matematica Applicata e Tecnologie Informatiche –
CNR, Genova)
Models and tools for liquidus hypersurfaces in high dimensions
The liquidus of a multi-component system is a hypersurface and, as such, can be represented
piecewise-linearly through a simplicial complex. We describe an operational pipeline that exploits
computational geometry to efficiently derive such a complex. Although some existing algorithms
that extract the liquidus are generalizable to any number d of pure components, none of them
provides evidence of functionality for d > 3. We have verified that extending state-of-the-art
algorithms to general dimensions is not as easy as expected due to the size of the data involved, to
numerical issues and to the lack of suitable data structures to treat large, arbitrary-dimensional
simplicial complexes. Thus, we describe an effective implementation that works for any d and a
case study for d = 4.
Giulio Ottonello (Dipartimento di Scienze della Terra, dell’Ambiente e della Vita, Università di
Genova)
Energies and interactions in NKCMAS silicate liquids: first principles and thermodynamic
assessments
Reproducing the correct topology of a phase diagram at liquidus involves an accurate
parameterization of energies and interactions of the liquid components in mixture. Concerning the
energy of pure melt component one must know the entropy (S°), the enthalpy of formation from the
elements at stable state H°f, the isochoric heat capacity (CP), the thermal expansion (), the bulk
modulus and its thermal and baric derivatives (K°, dK/dT, dK/dP). The complex nature of the
translational and rotational partition function (Qtrans, Qrot) in the liquid (Ottonello et al., 2010) suggest
the adoption of fictive states deprived of the two contributions and opportunely scaled to standard
state on the basis of the observed thermodynamic properties of the pure solids at their 1 bar melting
point. Interactions among components at the liquid state are of various kind. The “chemical”
interaction may be reproduced through polymer chemistry by “counting” the number of contacts
among quasi-species and applying the principle of equal reactivity of co-condensing units. The
“strain” energy is more tricky and, until now still poorly resolved, due to the fact that the acidity of
the petrological systems (and the ensuing extension of the interacting structons) is highly variable.
Finally, recent investigations delineate a complex role of the reaction field on the energy of -bonding
orbitals in the network, which further complicate an already complex picture (Gatti et al., 2012).
Daniele Giordano (Dipartimento di Scienze della Terra, Università di Torino)
Parameterization of the viscosity of simplified silicate melts systems and the multicomponent
magmas
The accurate prediction of silicate melt viscosity as a function of state variables and composition for
anhydrous and volatile-bearing melts is of paramount importance for modeling and understanding
magmatic and volcanic processes as well as for industrial and material science purposes. Viscosity
measurements can also be translated into configurational entropies of the investigated systems via
the Adam-Gibbs theory, therefore, modeling silicate melt viscosity is also of great important to
estimate thermodynamic quantities. Due to the experimental complexity to obtain a critical number
of data, the implementation of models able to calculate silicate liquid viscosity of both simplified
and multicomponent natural systems remained for long time an undeveloped task. This trend has
been changed in the last decades when, thanks to the improved technological performances of
instrumental devices, new data and, with that, the implementation of new numerical strategies for
calculating silicate melt viscosities have been provided. Here I present and discuss some of the main
findings obtained by using recent numerical strategies.
EXPERIMENTS VS MODELING (March 1st – morning)
Patrizia Fumagalli (Dipartimento di Scienze della Terra “Ardito Desio”, Università di Milano)
Experimental simulation of subsolidus processes: the rules of the game
Experimental strategies for simulating subsolidus processes will be presented. 1. The preparation
and choice of the starting materials; 2. Controlling the redox conditions in both just solids, and
fluids-bearing experiments; 3. The approach of equilibrium: bracketing vs. synthesis experiments,
working with solid solutions and constraining continuous reactions. 3. Some examples from high
pressure experiments in mafic and ultramafic systems.
Manuele Faccenda (Dipartimento di Geoscienze, Università di Padova)
Numerical modeling of metamorphic and igneous processes in geodynamics: the role of phase
diagrams.
The dynamic of Earth’s geological processes is characterized by several metamorphic and igneous
reactions occurring at spreading centers, intra-oceanic settings and subduction zones. As those
reactions are linked to geodynamical processes taking place at geological timescales and depths
such that they are not directly observables, numerical modeling offers a unique tool to explore their
interactions. We will discuss the techniques to implement experimental and thermodynamic (e.g.,
PERPLE_X) phase diagrams in numerical codes leading to the modeling of important metamorphic
and igneous processes like slab/mantle wedge hydration and dehydration, crust and mantle melting,
oceanic crust eclogitization and other major mantle phase transitions, deep subduction and
exhumation of continental crust.
Bernardo Cesare (Dipartimento di Geoscienze, Università di Padova)
Modeling of C-O-H fluids in graphitic rocks.
Graphite is a common, often overlooked, accessory mineral in metamorphic rocks, especially
metapelites. The presence of graphite imposes the fluid to be described in (at least) the C-O-H
system, and implies that aH2O < 1. As a consequence of the presence of graphite, metamorphic
dehydration reactions move to lower T, whereas H2O-present melting reactions move to higher T.
We will consider the modelling of graphitic systems first by observing C-O-H fluid speciation as a
function of P, T and a fluid compositional variable (XO or fO2). Then we will observe and compare
the behavior of metapelites in the graphitic and non-graphitic situations.
APPLICATIONS (March 1st)
Gaetano Ortolano (Dipartimento di Scienze Biologiche, Geologiche e Ambientali, Università di
Catania)
Thermodynamic modeling of metapelite system assisted by multivariate statistical image analysis of
X-Ray Map.
Thermodynamic modeling of metamorphic rocks via phase diagram computation (e.g. PERPLE_X;
THERMOCALC) has affirmed as a routinely performed method for unraveling the P-T evolution of
metamorphic complexes. Nevertheless, due to the difficulty in defining the real reacting equilibrium
volume, the system parameters cannot be always unequivocally fixed. The topic of this lecture is to
provide some examples of thermodynamic modeling of metapelite rock systems using PERPLE_X
software package assisted by multispectral statistical image analysis of X-ray maps via GIS
(Geographic Information System) based tools. This in order to minimize the operator subjectivity
related to the identification of composition and relative percentages of effective equilibrium
assemblages.
Paolo Papale (Istituto Nazionale di Geofisica e Vulcanologia, Pisa)
Thermodynamic modeling of the compositional dependent H2O-CO2 (and C-O-S-H) saturation
surface in silicate melts.
The lecture focuses on the thermodynamic principles subtending multicomponent equilibrium, and
their applications to silicate melts and magmatic volatiles. Different modeling systems are
illustrated and discussed in terms of their intrinsic limitations as they result from the employed
model equations. The potential and current limits in the development of a general internally
consistent thermodynamic model of silicate melts plus volatiles are also discussed.
Chiara Groppo (Dipartimento di Scienze della Terra, Università di Torino)
Phase equilibria modelling of melt-bearing metapelites
In addition to a review of petrogenetic grids in the KFMASH system, this lecture aims at discuss
both theoretical and practical issues of forward, (i.e. the protolith is known) and reverse (i.e. the
protolith is unknown) modelling of melt-bearing metapelite systems. The pseudosection approach
will be used to address the following topics: i) excess H2O vs. fixed H2O: the influence of H2O
amounts on the position of solidi; ii) modelling melt loss and its consequences on mineral
assemblages; iii) reconstruction of retrograde evolution: methods to evaluate H2O contents; iv)
reconstruction of prograde evolution: melt-reintegration methods.
Gisella Rebay (Dipartimento di Geoscienze, Università di Pavia)
Modeling equilibrium assemblages in metabasic rocks.
Examples of modeling of natural HP metabasic rocks will be presented. The role of fluid in the
preservation of assemblages and of oxidation state will be discussed. Comparison of predictions vs.
observations will be shown.
James Connolly (EidgenössischeTechnische Hochshule, Zurich)
VERTEX Tutorial (*)
(*) Details on the tutorial
Participants should bring their laptop. No special memory requirements are needed because virtual memory may be
used.
A bunch of memory sticks will be available on site to install PERPLEX without the web but of course the program may
be more efficiently installed at home following the instructions:
WINDOWS: http://www.perplex.ethz.ch/perplex/ibm_and_mac_archives/README_WIN_USERS.txt
OSX: http://www.perplex.ethz.ch/perplex/ibm_and_mac_archives/README_MAC_USERS.txt
LINUX: http://www.perplex.ethz.ch/perplex/ibm_and_mac_archives/README_LINUX_USERS.txt
UNIX: http://www.perplex.ethz.ch/perplex/ibm_and_mac_archives/README_UNIX_USERS.txt
If participants do not have Matlab installed on their laptop and would like to be able to make 3-d color plots of mineral
and/or system properties then a free program for that purpose is at
http://petrol.natur.cuni.cz/~ondro/pywerami:home
Perple_X generates postscript graphical output, usually this can be viewed and edited in Corel or Adobe Illustrator.
Ghostview is a free alternative for viewing, but recent versions of Ghostview have font compatibility issues that can be
resolved by changing the “default font” in perplex_plot_option.dat. An alternative to changing the default font is to
copy an old version of Ghostview, for WINDOWS users a compatible version is at:
http://www.perplex.ethz.ch/perplex/ibm_and_mac_archives/Windows/ghostview/
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