This is a preview of subscription content, log in via an institution to check access.
References
[1951] Herring, C., Surface tension as a motivation for sintering, The Physics of Powder Metallurgy (ed. W. E. Kingston) McGraw-Hill, New York.
[1958] Frank, F. C., On the kinematic theory of crystal growth and dissolution processes, Growth and Perfection of Crystals (eds. R. H. Doremus, B. W. Roberts, D. Turnbull) John Wiley, New York.
[1960] Scriven, L. E., Dynamics of a fluid interface, Chem. Eng. Sci. 12, 98–108.
[1961] Ericksen, J. L., Conservation laws for liquid crystals, Trans. Soc. Rheol. 5, 23–34.
[1963] Chernov, A. A., Crystal growth forms and thsir kinetic stability [in Russian], Kristallografiya 8, 87–93. English Transl. Sov. Phys. Crystall. 8, 63–67 (1963).
[1963] Chernov, A. A., Application of the method of characteristics to the theory of the growth forms of crystals [in Russian], Kristallografiya 8, 499–505. English Transl. Sov. Phys. Crystall. 8, 401–405 (1964).
[1963] Coleman, B. D., & V. J. Mizel, Thermodynamics and departures from Fourier's law of heat conduction, Arch. Rational Mech. Anal. 13, 245–261.
[1963] Coleman, B. D., & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178.
[1963] Mullins, W. W., & R. F. Sekerka, Morphological stability of a particle growing by diffusion or heat flow, J. Appl. Phys. 34, 323–329.
[1964] Mullins, W. W., & R. F. Sekerka, Stability of a planar interface during solid-ification of a dilute binary alloy, J. Appl. Phys. 35, 444–451.
[1964] Voronkov, V. V., Conditions for formation of mosaic structure on a crystallization front [in Russian], Fizika Tverdogo Tela 6, 2984–2988. English Transl. Sov. Phys. Solid State 6, 2378–2381 (1965).
[1965] Truesdell, C., & W. Noll, The non-linear field theories of mechanics, Hand-buch der Physik, vol. III/3 (ed. S. Flügge), Springer-Verlag, Berlin.
[1966] Seidensticker, R. G., Stability considerations in temperature gradient zone melting, Crystal Growth (ed. H. S. Peiser), Pergamon, Oxford (1967).
[1966] Tarshis, L. A., & W. A. Tiller, The effect of interface-attachment kinetics on the morphological stability of a planar interface during solidification, Crystal Growth (ed. H. S. Peiser), Pergamon, Oxford (1967).
[1968] Sekerka, R. F., Morphological stability, J. Crystal Growth 3, 4, 71–81.
[1971] Chernov, A. A., Theory of the stability of face forms of crystals [in Russian], Kristallografiya 16, 842–863. English Transl. Sov. Phys. Crystall. 16, 734–753 (1972).
[1972] Chernov, A. A., Theory of the stability of face forms of crystals, Sov. Phys. Crystallog. 16, 734–753.
[1972] Hoffman, D. W., & J. W. Cahn, A vector thermodynamics for anisotropic surfaces—1. Fundamentals and applications to plane surface junctions, Surface Sci. 31, 368–388.
[1973] Sekerka, R. F., Morphological stability, Crystal Growth: an Introduction, North-Holland, Amsterdam.
[1974] Cahn, J. W., & D. W. Hoffman, A vector thermodynamics for anisotropic surfaces—2. curved and faceted surfaces, Act. Metall. 22, 1205–1214.
[1974] Chernov, A. A., Stability of faceted shapes, J. Crystal Growth 24/25, 11–31.
[1974] Delves, R. T., Theory of interface instability, Crystal Growth (ed. B. R. Pamplin), Pergamon, Oxford.
[1975] Gurtin, M. E., & A. I. Murdoch, A continuum theory of elastic material surfaces, Arch. Rational Mech. Anal. 57, 291–323.
[1975] Moeckel, G. P., Thermodynamics of an interface, Arch. Rational Mech. Anal. 57, 255–280.
[1976] Murdoch, A. I., A thermodynamic theory of elastic material interfaces, Q. J. Mech. Appl. Math. 29, 245–275.
[1978] Brakke, K. A., The Motion of a Surface by its Mean Curvature, Princeton University Press.
[1978] Murdoch, A. I., Direct notation for surfaces with application to the thermodynamics of elastic material surfaces of second grade, Res. Rept. ES 78–134, Dept. Eng. Sci., U. Cincinnati.
[1979] Allen, S. M., & J. W. Cahn, A macroscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Act. Metall. 27, 1085–1095.
[1979] Fernandez-Diaz, J., & W. O. Williams, A generalized Stefan condition, Zeit. Angew. Math. Phys. 30, 749–755.
[1980] Langer, J. S., Instabilities and pattern formation in crystal growth, Rev. Mod. Phys. 52, 1–27.
[1984] Sekerka, R. F., Morphological instabilities during phase transformations, Phase Transformations and Material Instabilities in Solids (ed. M. E. Gurtin), Academic Press, New York.
[1985] Alexander, J. I. D., & W. C. Johnson, Thermomechanical equilibrium in solid-fluid systems with curved interfaces, J. Appl. Phys. 58, 816–824.
[1986] Gage, M., & R. S. Hamilton, The heat equation shrinking convex plane curves, J. Diff. Geom. 23, 69–96.
[1986g] Gurtin, M. E., On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96, 199–241.
[1986] Johnson, W. C., & J. I. D. Alexander, Interfacial conditions for thermomechanical equilibrium in two-phase crystals, J. Appl. Phys. 58, 816–824.
[1987] Grayson, M. A., The heat equation shrinks embedded plane curves to round points, J. Diff. Geom. 26, 285–314.
[1987] Leo, P. H., The effect of elastic fields on the morphological stability of a precipitate grown from solid solution, Ph. D. Thesis, Dept. Metall. Eng. Mat. Sci., Carnegie-Mellon U., Pittsburgh, PA.
[1988g] Gurtin, M. E., Toward a nonequilibrium thermodynamics of two phase materials, Arch. Rational Mech. Anal., 100, 275–312.
[1988a] Angenent, S., & M. E. Gurtin, Multiphase thermomechanics with interfacial structure. 2. Evolution of an isothermal interface. Forthcoming.
[1988s] Gurtin, M. E., & A. Struthers. Forthcoming.
[1988] Fonseca, I., Interfacial energy and the Maxwell rule, Arch. Rational Mech. Anal. Forthcoming.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gurtin, M.E. Multiphase thermomechanics with interfacial structure 1. Heat conduction and the capillary balance law. Arch. Rational Mech. Anal. 104, 195–221 (1988). https://doi.org/10.1007/BF00281354
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00281354