A new front-tracking method to model anisotropic grain and phase boundary motion in rocks

Microstructures of rocks play an important role in determining rheological properties and help to reveal the processes that lead to their formation. Some of these processes change the microstructure significantly and may thus have the opposite effect in obliterating any fabrics indicative of the previous history of the rocks. One of these processes is grain boundary migration (GBM). During static recrystallisation, GBM may produce a foam texture that completely overprints a pre-existing grain boundary network and GBM actively influences the rheology of a rock, via its influence on grain size and lattice defect concentration. In this paper we present a new front-tracking method to simulate GBM. Generally, any movement of boundaries is driven by the minimisation of the internal free energy of a system. The new method moves boundaries along the energy gradient towards a lower total energy state of the system. The calculation of the energy gradient is not necessarily limited to (an)isotropic boundary energies but may also include metamorphism, melting, reaction energies, surface energies and elastic stresses, etc. Two examples are included in this paper where we simulate grain growth with isotropic boundary energy functions and grain growth with isotropic and anisotropic boundary energy functions in a system with a melt present.

[1]  R. Heilbronner,et al.  Dynamic recrystallization of quartz: correlation between natural and experimental conditions , 2002, Geological Society, London, Special Publications.

[2]  P. Bentley,et al.  Evolving 3D Microstructures Using a Genetic Algorithm , 2004 .

[3]  D. Weaire,et al.  Soap, cells and statistics – random patterns in two dimensions , 1984 .

[4]  A. Provost,et al.  Wetting Angles, Equilibrium Melt Geometry, and the Permeability Threshold of Partially Molten Crustal Protoliths , 1997 .

[5]  M. Jessell,et al.  Dominance of microstructural processes and their effect on microstructural development: insights from numerical modelling of dynamic recrystallization , 2002, Geological Society, London, Special Publications.

[6]  G. Hirth,et al.  The brittle‐plastic transition in experimentally deformed quartz aggregates , 1994 .

[7]  M. Jessell,et al.  Modeling of anisotropic grain growth in minerals , 2001 .

[8]  Charles A. Williams,et al.  Reassessment of pore shapes in microstructurally equilibrated rocks, with implications for permeability of the upper mantle , 2003 .

[9]  U. Faul,et al.  Effects of Crystalline Anisotropy on Fluid Distribution in Ultramafic Partial Melts , 1992 .

[10]  M. Jessell,et al.  The numerical simulation of microstructure , 2002, Geological Society, London, Special Publications.

[11]  D. McKenzie,et al.  The Generation and Compaction of Partially Molten Rock , 1984 .

[12]  E. Watson,et al.  Grain growth control of isotope exchange between rocks and fluids , 2005 .

[13]  P. Bons,et al.  Syndeformational grain growth: microstructures and kinetics , 1992 .

[14]  Glazier,et al.  Soap froth revisited: Dynamic scaling in the two-dimensional froth. , 1989, Physical review letters.

[15]  Paul F. Williams,et al.  An Outline of Structural Geology , 1976 .

[16]  S. Bauer,et al.  Simple shear experiments on calcite rocks: rheology and microfabric , 1987 .

[17]  J. H. Kruhl.  Crystallographic control on the development of foam textures in quartz, plagioclase and analogue material , 2001 .

[18]  C. Dafermos.  Polygonal approximations of solutions of the initial value problem for a conservation law , 1972 .

[19]  Norman H. Sleep,et al.  Tapping of melt by veins and dikes , 1988 .

[20]  J. D. Bresser,et al.  Deformation Mechanisms, Rheology and Tectonics: Current Status and Future Perspectives , 2003 .

[21]  Nikolaus von Bargen,et al.  Permeabilities, interfacial areas and curvatures of partially molten systems: Results of numerical computations of equilibrium microstructures , 1986 .

[22]  G. Gottstein,et al.  Recrystallization and grain growth : proceedings of the first joint international conference, August 27-31, 2001, RWTH Aachen, Germany , 2001 .

[23]  H. Koyi,et al.  Tectonic Modeling : A Volume in Honor of Hans Ramberg , 2001 .

[24]  J. D. Bresser.  On the mechanism of dislocation creep of calcite at high temperature: Inferences from experimentally measured pressure sensitivity and strain rate sensitivity of flow stress , 2002 .

[25]  M. Jessell,et al.  The preservation potential of microstructures during static grain growth , 2003 .

[26]  J. A. Tyburczy,et al.  Mechanical and thermodynamic constraints on fluid distribution in partial melts , 1979 .

[27]  W. E. Stephens,et al.  Granite: From Segregation of Melt to Emplacement Fabrics , 1997 .

[28]  M. Rabinowicz,et al.  Compaction in a mantle mush with high melt concentrations and the generation of magma chambers , 2001 .

[29]  Greg Hirth,et al.  Experimental constraints on the dynamics of the partially molten upper mantle: Deformation in the diffusion creep regime , 1995 .

[30]  J. Kermode,et al.  Computer simulation of a two-dimensional soap froth II. Analysis of results , 1984 .

[31]  G. Hirth,et al.  Dislocation creep regimes in quartz aggregates , 1992 .

[32]  James A. Glazier,et al.  Dynamics of two-dimensional soap froths. , 1987 .

[33]  M. Holness,et al.  Quartz recrystallization and fluid flow during contact metamorphism: a cathodoluminescence study , 2001 .

[34]  Paul D. Bons,et al.  Elle: the numerical simulation of metamorphic and deformation microstructures , 2001 .

[35]  H. C. Heard,et al.  Mineral and rock deformation : laboratory studies : the Paterson volume , 1986 .

[36]  M. Jessell,et al.  Numerical simulation of disequilibrium structures in solid- melt systems during grain-growth , 2004 .

[37]  Daniel Calvete,et al.  A nonlinear model study on the long-term behavior of shore face–connected sand ridges , 2003 .

[38]  David J. Stevenson,et al.  Magma ascent by porous flow , 1986 .