DFG-Research Unit Proposal "Nanoscale Processes and Geomaterials Properties" - Project No. 3



1.0 Application for a Research Grant 1.1 Applicants 1.2 Title 1.3 Short Title 1.4 Research Fields 1.5 Expected total duration 1.6 Duration 1.7 Requested starting date 1.8 Summary

The kinetics of polymorphic phase transformations of selected mineral systems (calcite -> aragonite, quartz -> coesite) is investigated with combined experimental and theoretical methods. On the basis of the determined relevant solid-state nucleation mechanism at the atomic scale, we use a scaling law to derive a set of critical nano-scale control parameter such as the grain-boundary energy for solid-state nucleation from experimental observation. For this purpose, we conduct kinetic high-pressure experiments in the diamond anvil cell. These experiments are done under visual control and allow a precise determination of the respective kinetic phase boundaries in dependence of temperature. The obtained kinetic phase boundaries at the laboratory time scale are then extrapolated to the natural time scale under subduction zone conditions. They may then be used to derive, e.g., critical isotherms for thermo-mechanical modelling of coupled metamorphic and deformation processes during lithosphere subduction.

2. State of research and previous work

2.1 Current state of research

Kinetics of polymorphic phase transformations - general statements

As a consequence of geodynamic or tectonic processes, minerals and mineral assemblies may become energetically unfavourable due to changes in external physical and/or chemical conditions. Such perturbation driven phase transformations and mineral reactions proceed to establish a new equilibrium state that tends to minimize the system free energy. The path along which the system develops towards equilibrium is controlled by reaction kinetics, i.e., by several relaxation processes driving the system back to (local) equilibrium. If one aims at unravelling the reaction kinetics, information engraved in rock microstructures and textures is the key. A rock sample, however, shows only the time-integrated result of the various kinetic processes, acting sequentially or in parallel at different time scales. Only if the mechanisms of the underlying phase transformation and mineral reactions are completely understood, it is possible to infer the reaction kinetics from "post-mortem" rock microstructures. The experimental and theoretical basis for the thermodynamic treatment of phase equilibria has been well established for more than a decade now (Holland and Powell 1985, 1989, 1998, Berman 1988, Spear 1993, Connolly & Petrini 2002) and research activities on macroscopic equilibrium thermodynamic properties of systems of geological interest have somewhat saturated. In contrast, after the pioneering work of Lasaga and Kirkpatrick (1981) and Rubie and Thompson (1985), the kinetic treatment of mineral reactions and phase transformations became increasingly an active and rapidly developing field. The monograph on "Kinetic Theory in the Earth Sciences" (Lasaga 1998) gives an account of the advances made till 1998.
Since then, great progress in high-pressure experimentation and analytical methods made it possible to determine kinetic properties in more detail; a number of studies, e.g., have been performed to establish rate laws for individual polymorphic mineral reactions (Mosenfelder & Bohlen 1997; Rubie 1998; Mosenfelder et al. 2001; Hacker et al. 2005).

Nucleation and growth processes

Polymorphic mineral reactions and phase transformations start with a nucleation stage, followed by the growth stage after a stable nucleus has been formed. A nucleus forms by local fluctuations of the chemical composition and/or the atomic structure. The positive free energy associated with the formation of new interfaces and the strain energy associated with deformation due to finite reaction volume act against the formation of a stable nucleus. The contribution of interphase boundary energy to the specific free energy of a nucleus or grain decreases with increasing size, and a nucleus becomes stable after it has reached a critical size (Christian 1975). In the case of isochemical transformations, the interphase grainboundary energy and the mechanical coupling between the newly growing and the parent phase control reaction kinetics and microstructure evolution (Riedel and Karato 1996). In contrast, phase transformations and mineral reactions with changes in chemical composition require long-range mass transfer across the phase boundary ("reaction-diffusion" systems). If the mass transfer is the rate limiting process, microstructures with a high degree of spatial organization such as reaction bands or corona structures may develop (Joesten 1977, Ortoleva 1994). The various ways in which mass transfer, the formation of new interfaces and reaction induced strain may be coupled give rise to a rich inventory of microstructures observed in natural rocks.

Sluggish kinetics and metastability

One particular problem regards the influence of a possible metastable hindrance / delay during mineral phase transformations. Metastability is likely to cause complex behaviour because of possibly existing strong non-linearities in the transition mechanism far from equilibrium, beyond the validity of linear Onsager relations. A commonly held view amongst petrologists - neglecting metastability - is, that metamorphic reactions occur close to equilibrium, an assumption which enables P-T paths to be constructed on the basis of observed mineral assemblages together with phase equilibria data (Spear 1989, Peacock 2000). Due to sluggish kinetics, however, reactions may occur progressively and continuously along a P-T-t path under disequilibrium conditions, at a rate which is mainly dependent on temperature. For this type of process, textures of partial reaction can, in principle, be combined with experimental kinetic data to derive quantitative information about the P-T-t path and in particular about rates of heating or cooling. An alternative disequilibrium model was suggested on both observations of partial reaction in metamorphic rocks and the results of experimental studies. According to this model, mineral assemblages persist metastably outside of their stability fields on long time scales in the absence of deformation, primarily because of large nucleation barriers. Reaction to a lower-energy mineral assemblage (possibly also metastable), if it occurs, takes place rapidly under pronounced disequilibrium conditions. This type of behaviour can be documented for solid-solid and hydration reactions, during high-pressure metamorphism for example, but may also apply in the case of dehydration reactions and melting reactions which involve several reactant and/or product phases (Rubie 1998). Since both responsible relaxation mechanisms, nucleation and growth, show a largely different dependence on pressure and temperature at metamorphic overstepping, rock microstructures are not only dependent on the P-T-path itself, but are, in addition, dependent on the time scale of the system change, i.e., the rate of the process: Slow metamorphic overstepping yields largely different microstructures than those microstructures resulting from processes with fast overstepping (typically for laboratory experiments).

Key role of nucleation processes

In a solid polycrystal, there exist in general - in addition to homogeneous nucleation - three different types of (heterogeneous) grain-boundary nucleated reactions: new phase nucleation either on grain boundary surface, grain edges, or grain corners. The relative importance of each of these processes to the total nucleation rate is hereby controlled by their respective interface energies (Cahn 1956, Christian 1975). Nucleation rates in the solid state are particularly difficult to determine. One way to estimate a grain-boundary nucleation rate is to count the number of product phase grains under the electron microscope, see Figure 1 (Hacker et al. 2005). The counted number must be divided by the sample volume to yield the nucleation rate per unit volume. The result is usually a very large number, in the case of calcite to aragonite transition, the so calculated number is of the order of > 10^7 nuclei m-2 s-1.

This formalism invokes a great uncertainty, since the selected measurements at the submicron TEM scale are extrapolated to mesoscopic resp. macroscopic nucleation rates over more than 6 orders in magnitude, without suitable statistical averaging. The obtained results are therefore likely prone to large errors.



2.2 Previous work of the proponents

Michael Riedel

The research of MR has been focused on the kinetics of mineral phase transformations and its feedback into the rheology of subducting slabs. After the study of the kinetics of the pressure-induced B1-B2 phase transformation in the diamond-anvil cell, he investigated within a general theoretical framework the microstructural development during nucleation and growth (Riedel and Karato 1996, 1997). The found scaling properties were then used to model the creep properties of subducting slabs with respect to their geodynamic behaviour in the transition zone and the possible mechanisms of deep-focus earthquakes (Karato et al. 2001, Riedel 2006). In the context of the suggested research, MR will provide expertise in the kinetics of high-pressure phase transformations and its coupling to continuum mechanics.

Roland Oberhänsli

The research of RO concerns the metamorphic evolution, especially of mafic and acidic highpressure rocks (Oberhänsli et al., 1985, Franz et al., 2001) Recently the focus of this research changed towards low-grade high-pressure metamorphism of peltic metasediments (Oberhänsli et al., 1995). In these lithologies combined studies of crystallisation and deformation coupled with thermodynamic analyses led to the devellopement of a method using local equilibria (Oberhänsli et al., 2002; Romer et al., 2003; Rimmelé et al., 2005). Our studies showed that K-bearing phases that formed in equilibrium with the HP index mineral in metapelites are well suited for age determination of the metamorphic peak conditions (Oberhänsli et al., 1998). Now we try to date petrologically well constrained local equilibria by 39 Ar/40 Ar lased ablation methods in Potsdam.

3. Goals and working programme

3.1 Scientific objectives

Instead of attempting to estimate nucleation rates directly at the TEM level (Mosenfelder et al. 2001, Hacker et al. 2005), one can use the information stored in the microstructure that develops with kinetic overstepping p to derive the nucleation controlling parameter. In a sense, this is a way to avoid the difficult problem of statistical averaging of counted nucleation events at the TEM sub-micron scale to the mesoscopic scale - instead, the experiment does the needed thermodynamic average.
This proposed research project aims at this approach: Knowing the relevant mechanism of nucleation at the atomic scale, we use additional macroscopic measurements / investigations of the phase transformation kinetics (kinetic phase boundary resp. metastable pressure overshoot p vs. temperature T) in combination with a scaling law for the kinetic phase boundary of isochemical uni-variant phase transitions under natural conditions (Riedel and Karato 1997) to infer inversely the respective nucleation rate.
For this purpose, we study the transition kinetics of selected mineral systems (e.g. calcite -> aragonite, quartz -> coesite) under in-situ conditions in a diamond-anvil cell. The amount of metastable overshoot p(T), measured as a function of temperature T, contains nonlinearly enciphered both nucleation rate and growth rate of the transformation process. Because growth rates are comparatively easy to determine by various methods (e.g. digital image processing) with sufficient accuracy, we may utilise the information stored in p(T) for the inverse determination of the unknown nucleation rate as a function of temperature T. This experimental strategy relies on TEM (or double-beam SEM) observations only for identifying the correct type of solid-solid nucleation. This is, however, a crucial step of the method, since the detailed form of the scaling relationship to be used is dependent on the special geometry of nucleation sites (Riedel 2006). Knowing the type, we will mainly use "macroscopic" experiments to infer the nucleation rate at the atomic scale (in a statistical averaged sense).
Once both nucleation and growth rates are known, the overall transformation kinetics at arbitrary time scales (i.e., as well at the laboratory time scale as at the geological time scale) follows from an appropriate statistical combination of nucleation and growth, in dependence of the dominating solid-solid nucleation mechanism (Cahn 1956, Christian 1975).

Specific questions to be addressed within the project