References
- M. Glicksman, and K. Ankit, Detection of capillary mediated energy fields on a grain boundary groove: Solid-liquid interface perturbations, Metals 7(12) (2017), pp. 547–567. doi: 10.3390/met7120547
- M. Glicksman and K. Ankit, Measuring solid-liquid interfacial energy fields: Diffusion limited patterns, J. Mat. Sci. 53(17) (2018), pp. 1–24.
- M. Glicksman, Mechanism of dendritic branching, Metall. Mater. Trans. A 43A (2012), pp. 391–404. doi: 10.1007/s11661-011-0984-5
- M. Glicksman, Capillary-mediated interface perturbations: Deterministic pattern formation, J. Cryst. Growth 450 (2016), pp. 119–139. doi: 10.1016/j.jcrysgro.2016.03.031
- H. Le Châteliér, Sur un énoncé général des lois des équilibres chimiques, Compt. Rend. l'Acad. Sci. 99 (1884), p. 786.
- F. Braun, Löslichkeit fester Körper und die den Vorgang begleitenden Volumund Energieänderungen, Z. Phys. Chem. 1 (1887), p. 269.
- G. Bolling and W. Tiller, Growth from the melt: Part 1. the influence of surface intersections in pure metals, J. Appl. Phys. 31 (1960), p. 1345. doi: 10.1063/1.1735840
- S. Li, X. Li, J. Lowengrub, and M. Glicksman, A deterministic mechanism for side-branching in dendritic growth, FDMP 4(1) (2008), pp. 27–41.
- G. Nash and M. Glicksman, A general method for determining solid-liquid interfacial free energies, Phil. Mag. 24 (1971), p. 577. doi: 10.1080/14786437108217031
- D. Jones, The measurement of solid-liquid interfacial energies from the shapes of grain-boundary grooves, Phil. Mag. 27 (1973), p. 569. doi: 10.1080/14786437308219232
- R. Weinstock, Calculus of Variations, Dover Publications, Inc., New York, 1974.
- M.E. Glicksman, Principles of Solidification, Springer, New York, 2011. 287–289.
- R. Schaefer, M. Glicksman, and J. Ayers, High-confidence measurement of solid-liquid surface energy in a pure material, Phil. Mag. 32 (1975), pp. 725–743. doi: 10.1080/14786437508221616
- S. Hardy, A grain boundary groove measurement of the surface tension between ice and water, Phil. Mag. 35 (1977), p. 471. doi: 10.1080/14786437708237066
- B. Bayender, N. Marasli, E. Cadirli, H. Sisman, and M. Gündüz, Solid-liquid surface energy of pivalic acid, J. Cryst. Growth 194 (1998), pp. 119–124. doi: 10.1016/S0022-0248(98)00533-8
- B. Bayender, N. Marasli, E. Cadirli, and M. Gündüz, Solid-liquid interfacial energy of camphene, Mat. Sci. and Engr. A 270 (1999), pp. 343–348. doi: 10.1016/S0921-5093(99)00162-8
- N. Noel, H. Jamgotchian, and B. Billia, Influence of grain boundaries and natural convection on microstructure formation in cellular directional solidification of dilute succinonirile alloys in a cylinder, J. Cryst. Growth 187 (1998), pp. 516–526. doi: 10.1016/S0022-0248(97)00882-8
- K. Keslioglu and N. Marasli, Experimental determination of solid-liquid interfacial energy for zinc solid solution in equilibrium with the zinc-aluminum eutectic liquid, Met. Mat. Trans. A 35 (2004), pp. 3665–3672. doi: 10.1007/s11661-004-0272-8
- R. Rogers and B. Ackerson, The measurement of solid-liquid interfacial energy in colloidal suspensions using grain boundary grooves, Phil. Mag. 91 (2011), pp. 682–729. doi: 10.1080/14786435.2010.527306
- M.E. Glicksman, Principles of Solidification, Springer, New York, 2011, 199–210.
- W. Moore, Physical Chemistry, 2nd Ed, Prentice-Hall, Inc., Englewood Cliffs (NJ), 1955.
- M. Gurtin, Thermomechanics of Evolving Phase Boundaries in the Plane, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1993.
- D.W. Hoffman and J.W. Cahn, A vector thermodynamics for anisotropic surfaces: I. fundamentals and application to plane surface junctions, Surf. Sci. 31 (1972), pp. 368–388. doi: 10.1016/0039-6028(72)90268-3
- J. Cahn and D. Hoffman, A vector thermodynamics for anisotropic surfaces, Acta Metall. 22 (1974), pp. 1205–1214. doi: 10.1016/0001-6160(74)90134-5
- A.A. Wheeler and G. McFadden, A xi-vector formulation of anisotropic phase-field models: 3-d asymptotics, Eur. J. Appl. Maths 7 (1995), pp. 367–381. doi: 10.1017/S0956792500002424
- A. Gray, E. Abbena, and S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed., Chapman & Hall/CRC, Boca Raton (FL), 2006.
- L. Kells, Calculus, 7th ed., Prentice-Hall, Inc., New York, 1946.
- G. Ehrlich and K. Stolt, Surface diffusion, Ann. Rev. Phys. Chem. 31 (1980), pp. 603–637. doi: 10.1146/annurev.pc.31.100180.003131
- H. Carslaw and J. Jaeger, Conduction of Heat in Solids, 2nd ed., Oxford Science Publications, Clarendon Press, Oxford, 1959.
- J. Jackson, Classical Electrodynamics, 3rd ed., John Wiley & Sons, Inc., New York, NY, 1999.
- L. Wang, Z. Wang, X. Lin, M. Wang, and W. Huang, The effect of interfacial energy anisotropy on planar interface instability in a succinonitrile alloy under a small temperature gradient, Chin. Phys. B 21(6) (2012), p. 066801.
- L. Wang, X. Lin, Z. Wang, and W. Huang, Orientation dependent morphological stability of a grain boundary groove, Chin. Phys. B 23(12) (2014), p. 124702.