Contributions to Mineralogy and Petrology

, Volume 166, Issue 6, pp 1709–1723 | Cite as

Phase-field study of grain boundary tracking behavior in crack-seal microstructures

  • Kumar AnkitEmail author
  • Britta Nestler
  • Michael Selzer
  • Mathias Reichardt
Original Paper


In order to address the growth of crystals in veins, a multiphase-field model is used to capture the dynamics of crystals precipitating from a super-saturated solution. To gain a detailed understanding of the polycrystal growth phenomena in veins, we investigate the influence of various boundary conditions on crystal growth. In particular, we analyze the formation of vein microstructures resulting from the free growth of crystals as well as crack-sealing processes. We define the crystal symmetry by considering the anisotropy in surface energy to simulate crystals with flat facets and sharp corners. The resulting growth competition of crystals with different orientations is studied to deduce a consistent orientation selection rule in the free-growth regime. Using crack-sealing simulations, we correlate the grain boundary tracking behavior depending on the relative rate of crack opening, opening trajectory, initial grain size, and wall roughness. Further, we illustrate how these parameters induce the microstructural transition between blocky (crystals growing anisotropically) to fibrous morphology (isotropic) and formation of grain boundaries. The phase-field simulations of crystals in the free-growth regime (in 2D and 3D) indicate that the growth or consumption of a crystal is dependent on the orientation difference with neighboring crystals. The crack-sealing simulation results (in 2D and 3D) reveal that crystals grow isotropically and grain boundaries track the opening trajectory if the wall roughness is high, opening increments are small, and crystals touch the wall before the next crack increment starts. Further, we find that within the complete crack-seal regime, anisotropy in surface energy results in the formation of curved/oscillating grain boundaries (instead of straight) when the crack-opening velocity is increased and wall roughness is not sufficiently high. Additionally, the overall capability of phase-field method to simulate large-scale polycrystal growth in veins (in 3D) is demonstrated enumerating the main advantages of adopting the novel approach.


Phase-field method Crystal growth Anisotropic surface energy Veins 



Drs. Abhik Choudhury (Ecole Polytechnique, Palaiseau, France) and Frank Wendler (Institute of Applied Geosciences, Karlsruhe Institute of Technology) are thanked for many insightful discussions. KA and BN acknowledge the financial support by Graduate school 1483 of German Research Foundation and by the project CCMSE of the European Union (EFRE) together with the state Baden-Wuerttemberg. KA also thanks former co-workers Drs. Denis Pilipenko and Michael Fleck (Materials and Process Simulations, University of Bayreuth) for preliminary discussions concerning the model and Center for Computing and Communication at RWTH Aachen University (HPC Cluster) for computational resources.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Kumar Ankit
    • 1
    Email author
  • Britta Nestler
    • 1
  • Michael Selzer
    • 1
  • Mathias Reichardt
    • 1
  1. 1.IAM-ZBSKarlsruhe Institute of Technology (KIT)KarlsruheGermany

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