Skip to main content
Log in

Thermodynamic driving forces and anisotropic interface motion

  • Math and Material
  • Overview
  • Published:
JOM Aims and scope Submit manuscript

Abstract

The objective of much research is to make mathematical models for various types of crystal-surface motions and to prove theorems, develop new methods of computation, and apply the results to problems in materials science. Surface curvature affects phase equilibria and drivingforces for phase change and surface motion, whether the surfaces have isotropic or anisotropic surface free energy. Weighted mean curvature reveals how the free energy of curved surfaces acts as a thermodynamic driving force and, thus, how it interacts with bulk free energies. The relations are valid for anisotropic surfaces even when faceted, although faceting often affects kinetics. The mechanisms for surface motion that are considered are attachment/detachment kinetics, diffusion of atoms over surfaces, and, perhaps, diffusion within the bulk phases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Jean E. Taylor, “Anisotropic Interface Motion,” Modern Methods for Modeling Microstructure Evolution in Material (TMS/SIAM, 1996).

    Google Scholar 

  2. Jean E. Taylor, John W. Cahn, and Carol A. Handwerker, “Geometric Models of Crystal Growth,” Acta Metall. Mater., 40 (1992), pp. 1443–1474.

    CAS  Google Scholar 

  3. John W. Cahn and Jean E. Taylor, “Surface Motion by Surface Diffusion,” Acta Metall. Mater., 42 (1994), pp. 1045–1063.

    CAS  Google Scholar 

  4. John W. Cahn and Jean E. Taylor, “ThermodynamiC Driving Forces and Equilibrium in Multicomponent Systems with Anisotropic Surfaces,” Modern Methods for Modeling Microstructure Evolution in Materials (TMS/SIAM 1996, to appear).

    Google Scholar 

  5. M. Jeannette Kelly, “Edge Energy-Minimizing Surfaces and Crystal Shape,” Modern Methods for Modeling Microstructure Evolution in Material (TMS/SIAM, 1996).

    Google Scholar 

  6. Francis Larch and John W. Cahn, ″The Interactions of Composition and Stress in Crystalline Solids, Acta Met., 33 (1985), pp. 331–367; reprinted in Francis Larch and John W. Cahn, “The Interactions of Composition and Stress in Crystalline Solids Journal of Research of NBS, 89 (1984), pp. 467–500.

    Google Scholar 

  7. W. Craig Carter et al., “Shape Evolution by Surface Diffusion and Surface Attachment Limited Kinetics on Completely Faceted Surfaces,” Acta Metal. Mater., 43 (1995), pp. 4309–4323.

    CAS  Google Scholar 

  8. Jean E. Taylor, “Mean Curvature and Weighted Mear. Curvature,” Acta Metall. Mater., 40 (1992), pp. 1475–1485.

    CAS  Google Scholar 

  9. J. Willard Gibbs, The Collected Works of J.W. Gibbs, vol. 1 (New York: Longmans, Green and Co., 1928).

    Google Scholar 

  10. Pedro Martins Girao, “Convergence of a Crystalline Algorithm for the Motion of a Simple Closed Convex Curve by Weighted Curvature,” SIAM J. Numer.Anal., 32 (3) (1995), pp. 886–899.

    Google Scholar 

  11. Jean E. Taylor, “Motion of Curves by Crystalline Curvature, Including Triple Junctions and Boundary Points,” Differential Geometry Proceedings of Symposia in Pure Math., 51 (part 1) (1993), pp. 417–438.

    Google Scholar 

  12. Jean E. Taylor, “Motion by Crystalline Curvature, in Computing Optimal Geometries,” Selected Lectures in Milthematics, ed. J.E. Taylor (Providence, RI: American Mathematical Society, 1991), pp. 63–65 (plus video).

    Google Scholar 

  13. S. Angenent and M. Gurtin, “Multiphase Thermomechanics with Interracial Structure. 2. Evolution of an Isothermal Interface,” Arch Rat. Mech. Anal, 108 (1989), pp. 323–391.

    Google Scholar 

  14. Fred Almgren and Jean E. Taylor, “Flat Flow is Motion by Crystalline Curvature for Curves with Crystalline Energies,” J. Differential Geometry, 42 (1995), pp. 1–22.

    Article  Google Scholar 

  15. Andrew Roosen, “Simulation of Two-Dimensional Facetted Crystal Growth in a Single Diffusion Field,” Computational Crystal Growers Workshop, Selected Lectures in Mathematics, ed. J.E. Taylor (Providence, RI: American Mathematical Society, 1992) (includes video).

    Google Scholar 

  16. Fred Almgren, Jean Taylor, and Lihe Wang, “Curvature Driven Flows: A Variational Approach, SIAM Journal of Control and Optimization, 31 (1993), pp. 386–437.

    Google Scholar 

  17. Andrew R. Roosen and Jean E. Taylor, “Modeling Crystal Growth in a Diffusion Field Using Fully Faceted Interfaces,” J. Computational Physics, 114 (1994), pp. 113–128.

    CAS  Google Scholar 

  18. Jean E. Taylor, “Geometric Crystal Growth in 3D via Faceted Interfaces,” Computational Crystal Growers Workshop, Selected Lectures in Mathematics, ed. J.E. Taylor (Providence, RI: American Mathematical Society, 1992), pp. 111–113 (plus video 20:25-26:00).

    Google Scholar 

  19. David Caraballo, Princeton University Mathematics Department thesis (1996).

    Google Scholar 

  20. Nung-Kwan Yip, Princeton University Mathematics Department thesis (1996).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Taylor, J.E. Thermodynamic driving forces and anisotropic interface motion. JOM 48, 19–22 (1996). https://doi.org/10.1007/BF03223260

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03223260

Keywords

Navigation