DOI: 10.1007/bf00251518. Toward a nonequilibrium thermodynamics of two-phase materials

Toward a nonequilibrium thermodynamics of two-phase materials

10.1007/bf00251518

Crossref journal-article

Springer Science and Business Media LLC

Archive for Rational Mechanics and Analysis (297)

Bibliography

Gurtin, M. E. (1988). Toward a nonequilibrium thermodynamics of two-phase materials. Archive for Rational Mechanics and Analysis, 100(3), 275â312.

Authors 1

Morton E. Gurtin (first)

References 29 Referenced 52

[1901] Wulff, G., Zur Frage der Geschwindigkeit des Wachsthums und der Auflösung der Krystallflächen, Zeit. Krystall. Min. 34, 449–530. / Zeit. Krystall. Min. by G. Wulff (1901)
[1960] Scriven, L. E., Dynamics of a fluid interface, Chem. Eng. Sci. 12, 98–108. (10.1016/0009-2509(60)87003-0) / Chem. Eng. Sci. by L. E. Scriven (1960)
[1960] Truesdell, C. & R. Toupin, The classical field theories. Handbuch der Physik (ed. S. Flügge), vol. III/1, Springer, Berlin Göttingen Heidelberg. / Handbuch der Physik by C. Truesdell (1960)
[1963] Coleman, B. D. & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178. (10.1007/BF01262690) / Arch. Rational Mech. Anal. by B. D. Coleman (1963)
[1963] Mullins, W. W. & R. F. Sekerka, Morphological stability of a particle growing by diffusion or heat flow, J. Appl. Phys. 234, 323–329. (10.1063/1.1702607) / J. Appl. Phys. by W. W. Mullins (1963)
[1964] Mullins, W. W. & R. F. Sekerka, Stability of a planar interface during solidification of a dilute binary alloy, J. Appl. Phys. 235, 444–451. (10.1063/1.1713333) / J. Appl. Phys. by W. W. Mullins (1964)
[1964] Chalmers, B., Principles of Solidification, Wiley, New York. / Principles of Solidification by B. Chalmers (1964)
[1965] Truesdell, C., & W. Noll, The nonlinear field theories of mechanics. Handbuch der Physik (ed. S. Flügge), vol. III/3, Springer: Berlin Heidelberg New York. / Handbuch der Physik by C. Truesdell (1965)
[1965] Voronkov, V. V., Conditions for formation of mosaic structure on a crystallization front, Sov. Phys. Solid State 6, 2378–2381. / Sov. Phys. Solid State by V. V. Voronkov (1965)
[1966] Seidensticker, R. G., Stability considerations in temperature gradient zone melting Crystal Growth (ed. H. S. Peiser), Pergamon, Oxford (1967). / Stability considerations in temperature gradient zone melting Crystal Growth by R. G. Seidensticker (1966)
[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). / Crystal Growth by L. A. Tarshis (1966)
[1968] Sekerka, R. F., Morphological stability, J. Crystal Growth 3, 4, 71–81. (10.1016/0022-0248(68)90102-4) / J. Crystal Growth by R. F. Sekerka (1968)
[1972] Chernov, A. A., Theory of the stability of face forms of crystals, Sov. Phys. Crystallog. 16, 734–753. / Sov. Phys. Crystallog. by A. A. Chernov (1972)
[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. (10.1016/0039-6028(72)90268-3) / Surface Sci. by D. W. Hoffman (1972)
[1973] Sekerka, R. F., Morphological stability, Crystal Growth: an Introduction, North Holland, Amsterdam. / Crystal Growth: an Introduction by R. F. Sekerka (1973)
[1974] Cahn, J. W. & D. W. Hoffman, A vector thermodynamics for anisotropic surfaces — 2. curved and faceted surfaces, Act. Metall. 22, 1205–1214. (10.1016/0001-6160(74)90134-5) / Act. Metall. by J. W. Cahn (1974)
[1974] Delves, R. T., Theory of interface instability, Crystal Growth (ed. B. R. Pamplin), Pergamon, Oxford. / Crystal Growth by R. T. Delves (1974)
[1975] Gurtin, M. E. & A. I. Murdoch, A continuum theory of elastic material surfaces, Arch. Rational Mech. Anal. 57, 291–323. (10.1007/BF00261375) / Arch. Rational Mech. Anal. by M. E. Gurtin (1975)
[1975] Moeckel, G. P., Thermodynamics of an interface, Arch. Rational Mech. Anal. 57, 255–280. (10.1007/BF00280158) / Arch. Rational Mech. Anal. by G. P. Moeckel (1975)
[1976] Murdoch, A. I., A thermodynamic theory of elastic material interfaces, Q. J. Mech. Appl. Math. 29, 245–275. (10.1093/qjmam/29.3.245) / Q. J. Mech. Appl. Math. by A. I. Murdoch (1976)
[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.
[1978] Taylor, J. E., Crystalline variational problems, Bull. Am. Math. Soc. 84, 568–588. (10.1090/S0002-9904-1978-14499-1) / Bull. Am. Math. Soc. by J. E. Taylor (1978)
[1979] Fernandez-Diaz, J. & W. O. Williams, A generalized Stefan condition, Zeit. Angew. Math. Phys. 30, 749–755. (10.1007/BF01590684) / Zeit. Angew. Math. Phys. by J. Fernandez-Diaz (1979)
[1979] Wollkind, D. J., A deterministic continuum mechanical approach to morphological stability of the solid-liquid interface, Preparation of Properties of Solid State Materials, (ed. C. R. Wilcox), Dekker, New York. / Preparation of Properties of Solid State Materials by D. J. Wollkind (1979)
[1980] Langer, J. S., Instabilities and pattern formation in crystal growth, Rev. Mod. Phys. 52, 1–27. (10.1103/RevModPhys.52.1) / Rev. Mod. Phys. by J. S. Langer (1980)
[1983] Rogers, J. C. W., The Stefan problem with surface tension, Free Boundary Problems: Theory and Applications, (eds. A. Fasano, M. Primicerio), Pitman Boston. / Free Boundary Problems: Theory and Applications by J. C. W. Rogers (1983)
[1984] Sekerka, R. F., Morphological instabilities during phase transformations, Phase Transformations and Material Instabilities in Solids, (ed. M. E. Gurtin), Academic Press, New York. / Phase Transformations and Material Instabilities in Solids by R. F. Sekerka (1984)
[1985] Dunn, J. E. & J. Serrin, On the thermomechanics of interstitial working, Arch. Rational Mech. Anal. 88, 95–133. (10.1016/0025-326X(83)90602-1) / Arch. Rational Mech. Anal. by J. E. Dunn (1985)
[1986] Gurtin, M. E., On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96, 199–241. (10.1007/BF00251907) / Arch. Rational Mech. Anal. by M. E. Gurtin (1986)

Dates

Type	When
Created	20 years, 11 months ago (Sept. 15, 2004, 10:08 p.m.)
Deposited	6 years, 4 months ago (April 3, 2019, 7:56 a.m.)
Indexed	3 weeks, 1 day ago (Aug. 2, 2025, 12:57 a.m.)
Issued	36 years, 11 months ago (Sept. 1, 1988)
Published	36 years, 11 months ago (Sept. 1, 1988)
Published Print	36 years, 11 months ago (Sept. 1, 1988)

Funders 0

None

BibTeX

@article{Gurtin_1988, title={Toward a nonequilibrium thermodynamics of two-phase materials}, volume={100}, ISSN={1432-0673}, url={http://dx.doi.org/10.1007/bf00251518}, DOI={10.1007/bf00251518}, number={3}, journal={Archive for Rational Mechanics and Analysis}, publisher={Springer Science and Business Media LLC}, author={Gurtin, Morton E.}, year={1988}, month=sep, pages={275–312} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        2
      ]
    ],
    "date-time": "2025-08-02T04:57:40Z",
    "timestamp": 1754110660923
  },
  "reference-count": 29,
  "publisher": "Springer Science and Business Media LLC",
  "issue": "3",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1988,
            9,
            1
          ]
        ],
        "date-time": "1988-09-01T00:00:00Z",
        "timestamp": 589075200000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "http://www.springer.com/tdm"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1988,
        9
      ]
    ]
  },
  "DOI": "10.1007/bf00251518",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2004,
        9,
        16
      ]
    ],
    "date-time": "2004-09-16T02:08:47Z",
    "timestamp": 1095300527000
  },
  "page": "275-312",
  "source": "Crossref",
  "is-referenced-by-count": 52,
  "title": "Toward a nonequilibrium thermodynamics of two-phase materials",
  "prefix": "10.1007",
  "volume": "100",
  "author": [
    {
      "given": "Morton E.",
      "family": "Gurtin",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "297",
  "reference": [
    {
      "key": "BF00251518_CR1",
      "first-page": "449",
      "volume": "34",
      "author": "G. Wulff",
      "year": "1901",
      "unstructured": "[1901] Wulff, G., Zur Frage der Geschwindigkeit des Wachsthums und der Aufl\u00f6sung der Krystallfl\u00e4chen, Zeit. Krystall. Min. 34, 449\u2013530.",
      "journal-title": "Zeit. Krystall. Min."
    },
    {
      "key": "BF00251518_CR2",
      "doi-asserted-by": "crossref",
      "first-page": "98",
      "DOI": "10.1016/0009-2509(60)87003-0",
      "volume": "12",
      "author": "L. E. Scriven",
      "year": "1960",
      "unstructured": "[1960] Scriven, L. E., Dynamics of a fluid interface, Chem. Eng. Sci. 12, 98\u2013108.",
      "journal-title": "Chem. Eng. Sci."
    },
    {
      "key": "BF00251518_CR3",
      "volume-title": "Handbuch der Physik",
      "author": "C. Truesdell",
      "year": "1960",
      "unstructured": "[1960] Truesdell, C. & R. Toupin, The classical field theories. Handbuch der Physik (ed. S. Fl\u00fcgge), vol. III/1, Springer, Berlin G\u00f6ttingen Heidelberg."
    },
    {
      "key": "BF00251518_CR4",
      "doi-asserted-by": "crossref",
      "first-page": "167",
      "DOI": "10.1007/BF01262690",
      "volume": "13",
      "author": "B. D. Coleman",
      "year": "1963",
      "unstructured": "[1963] Coleman, B. D. & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167\u2013178.",
      "journal-title": "Arch. Rational Mech. Anal."
    },
    {
      "key": "BF00251518_CR5",
      "doi-asserted-by": "crossref",
      "first-page": "323",
      "DOI": "10.1063/1.1702607",
      "volume": "234",
      "author": "W. W. Mullins",
      "year": "1963",
      "unstructured": "[1963] Mullins, W. W. & R. F. Sekerka, Morphological stability of a particle growing by diffusion or heat flow, J. Appl. Phys. 234, 323\u2013329.",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "BF00251518_CR6",
      "doi-asserted-by": "crossref",
      "first-page": "444",
      "DOI": "10.1063/1.1713333",
      "volume": "235",
      "author": "W. W. Mullins",
      "year": "1964",
      "unstructured": "[1964] Mullins, W. W. & R. F. Sekerka, Stability of a planar interface during solidification of a dilute binary alloy, J. Appl. Phys. 235, 444\u2013451.",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "BF00251518_CR7",
      "volume-title": "Principles of Solidification",
      "author": "B. Chalmers",
      "year": "1964",
      "unstructured": "[1964] Chalmers, B., Principles of Solidification, Wiley, New York."
    },
    {
      "key": "BF00251518_CR8",
      "volume-title": "Handbuch der Physik",
      "author": "C. Truesdell",
      "year": "1965",
      "unstructured": "[1965] Truesdell, C., & W. Noll, The nonlinear field theories of mechanics. Handbuch der Physik (ed. S. Fl\u00fcgge), vol. III/3, Springer: Berlin Heidelberg New York."
    },
    {
      "key": "BF00251518_CR9",
      "first-page": "2378",
      "volume": "6",
      "author": "V. V. Voronkov",
      "year": "1965",
      "unstructured": "[1965] Voronkov, V. V., Conditions for formation of mosaic structure on a crystallization front, Sov. Phys. Solid State 6, 2378\u20132381.",
      "journal-title": "Sov. Phys. Solid State"
    },
    {
      "key": "BF00251518_CR10",
      "volume-title": "Stability considerations in temperature gradient zone melting Crystal Growth",
      "author": "R. G. Seidensticker",
      "year": "1966",
      "unstructured": "[1966] Seidensticker, R. G., Stability considerations in temperature gradient zone melting Crystal Growth (ed. H. S. Peiser), Pergamon, Oxford (1967)."
    },
    {
      "key": "BF00251518_CR11",
      "volume-title": "Crystal Growth",
      "author": "L. A. Tarshis",
      "year": "1966",
      "unstructured": "[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)."
    },
    {
      "issue": "4",
      "key": "BF00251518_CR12",
      "doi-asserted-by": "crossref",
      "first-page": "71",
      "DOI": "10.1016/0022-0248(68)90102-4",
      "volume": "3",
      "author": "R. F. Sekerka",
      "year": "1968",
      "unstructured": "[1968] Sekerka, R. F., Morphological stability, J. Crystal Growth 3, 4, 71\u201381.",
      "journal-title": "J. Crystal Growth"
    },
    {
      "key": "BF00251518_CR13",
      "first-page": "734",
      "volume": "16",
      "author": "A. A. Chernov",
      "year": "1972",
      "unstructured": "[1972] Chernov, A. A., Theory of the stability of face forms of crystals, Sov. Phys. Crystallog. 16, 734\u2013753.",
      "journal-title": "Sov. Phys. Crystallog."
    },
    {
      "key": "BF00251518_CR14",
      "doi-asserted-by": "crossref",
      "first-page": "368",
      "DOI": "10.1016/0039-6028(72)90268-3",
      "volume": "31",
      "author": "D. W. Hoffman",
      "year": "1972",
      "unstructured": "[1972] Hoffman, D. W. & J. W. Cahn, A vector thermodynamics for anisotropic surfaces \u2014 1. Fundamentals and applications to plane surface junctions, Surface Sci. 31, 368\u2013388.",
      "journal-title": "Surface Sci."
    },
    {
      "key": "BF00251518_CR15",
      "volume-title": "Crystal Growth: an Introduction",
      "author": "R. F. Sekerka",
      "year": "1973",
      "unstructured": "[1973] Sekerka, R. F., Morphological stability, Crystal Growth: an Introduction, North Holland, Amsterdam."
    },
    {
      "key": "BF00251518_CR16",
      "doi-asserted-by": "crossref",
      "first-page": "1205",
      "DOI": "10.1016/0001-6160(74)90134-5",
      "volume": "22",
      "author": "J. W. Cahn",
      "year": "1974",
      "unstructured": "[1974] Cahn, J. W. & D. W. Hoffman, A vector thermodynamics for anisotropic surfaces \u2014 2. curved and faceted surfaces, Act. Metall. 22, 1205\u20131214.",
      "journal-title": "Act. Metall."
    },
    {
      "key": "BF00251518_CR17",
      "volume-title": "Crystal Growth",
      "author": "R. T. Delves",
      "year": "1974",
      "unstructured": "[1974] Delves, R. T., Theory of interface instability, Crystal Growth (ed. B. R. Pamplin), Pergamon, Oxford."
    },
    {
      "key": "BF00251518_CR18",
      "doi-asserted-by": "crossref",
      "first-page": "291",
      "DOI": "10.1007/BF00261375",
      "volume": "57",
      "author": "M. E. Gurtin",
      "year": "1975",
      "unstructured": "[1975] Gurtin, M. E. & A. I. Murdoch, A continuum theory of elastic material surfaces, Arch. Rational Mech. Anal. 57, 291\u2013323.",
      "journal-title": "Arch. Rational Mech. Anal."
    },
    {
      "key": "BF00251518_CR19",
      "doi-asserted-by": "crossref",
      "first-page": "255",
      "DOI": "10.1007/BF00280158",
      "volume": "57",
      "author": "G. P. Moeckel",
      "year": "1975",
      "unstructured": "[1975] Moeckel, G. P., Thermodynamics of an interface, Arch. Rational Mech. Anal. 57, 255\u2013280.",
      "journal-title": "Arch. Rational Mech. Anal."
    },
    {
      "key": "BF00251518_CR20",
      "doi-asserted-by": "crossref",
      "first-page": "245",
      "DOI": "10.1093/qjmam/29.3.245",
      "volume": "29",
      "author": "A. I. Murdoch",
      "year": "1976",
      "unstructured": "[1976] Murdoch, A. I., A thermodynamic theory of elastic material interfaces, Q. J. Mech. Appl. Math. 29, 245\u2013275.",
      "journal-title": "Q. J. Mech. Appl. Math."
    },
    {
      "key": "BF00251518_CR21",
      "unstructured": "[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."
    },
    {
      "key": "BF00251518_CR22",
      "doi-asserted-by": "crossref",
      "first-page": "568",
      "DOI": "10.1090/S0002-9904-1978-14499-1",
      "volume": "84",
      "author": "J. E. Taylor",
      "year": "1978",
      "unstructured": "[1978] Taylor, J. E., Crystalline variational problems, Bull. Am. Math. Soc. 84, 568\u2013588.",
      "journal-title": "Bull. Am. Math. Soc."
    },
    {
      "key": "BF00251518_CR23",
      "doi-asserted-by": "crossref",
      "first-page": "749",
      "DOI": "10.1007/BF01590684",
      "volume": "30",
      "author": "J. Fernandez-Diaz",
      "year": "1979",
      "unstructured": "[1979] Fernandez-Diaz, J. & W. O. Williams, A generalized Stefan condition, Zeit. Angew. Math. Phys. 30, 749\u2013755.",
      "journal-title": "Zeit. Angew. Math. Phys."
    },
    {
      "key": "BF00251518_CR24",
      "volume-title": "Preparation of Properties of Solid State Materials",
      "author": "D. J. Wollkind",
      "year": "1979",
      "unstructured": "[1979] Wollkind, D. J., A deterministic continuum mechanical approach to morphological stability of the solid-liquid interface, Preparation of Properties of Solid State Materials, (ed. C. R. Wilcox), Dekker, New York."
    },
    {
      "key": "BF00251518_CR25",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1103/RevModPhys.52.1",
      "volume": "52",
      "author": "J. S. Langer",
      "year": "1980",
      "unstructured": "[1980] Langer, J. S., Instabilities and pattern formation in crystal growth, Rev. Mod. Phys. 52, 1\u201327.",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "BF00251518_CR26",
      "volume-title": "Free Boundary Problems: Theory and Applications",
      "author": "J. C. W. Rogers",
      "year": "1983",
      "unstructured": "[1983] Rogers, J. C. W., The Stefan problem with surface tension, Free Boundary Problems: Theory and Applications, (eds. A. Fasano, M. Primicerio), Pitman Boston."
    },
    {
      "key": "BF00251518_CR27",
      "volume-title": "Phase Transformations and Material Instabilities in Solids",
      "author": "R. F. Sekerka",
      "year": "1984",
      "unstructured": "[1984] Sekerka, R. F., Morphological instabilities during phase transformations, Phase Transformations and Material Instabilities in Solids, (ed. M. E. Gurtin), Academic Press, New York."
    },
    {
      "key": "BF00251518_CR28",
      "doi-asserted-by": "publisher",
      "first-page": "95",
      "DOI": "10.1016/0025-326X(83)90602-1",
      "volume": "88",
      "author": "J. E. Dunn",
      "year": "1985",
      "unstructured": "[1985] Dunn, J. E. & J. Serrin, On the thermomechanics of interstitial working, Arch. Rational Mech. Anal. 88, 95\u2013133.",
      "journal-title": "Arch. Rational Mech. Anal."
    },
    {
      "key": "BF00251518_CR29",
      "doi-asserted-by": "crossref",
      "first-page": "199",
      "DOI": "10.1007/BF00251907",
      "volume": "96",
      "author": "M. E. Gurtin",
      "year": "1986",
      "unstructured": "[1986] Gurtin, M. E., On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96, 199\u2013241.",
      "journal-title": "Arch. Rational Mech. Anal."
    }
  ],
  "container-title": "Archive for Rational Mechanics and Analysis",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF00251518.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/article/10.1007/BF00251518/fulltext.html",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF00251518",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    },
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF00251518.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2019,
        4,
        3
      ]
    ],
    "date-time": "2019-04-03T11:56:06Z",
    "timestamp": 1554292566000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "http://link.springer.com/10.1007/BF00251518"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1988,
        9
      ]
    ]
  },
  "references-count": 29,
  "journal-issue": {
    "issue": "3",
    "published-print": {
      "date-parts": [
        [
          1988,
          9
        ]
      ]
    }
  },
  "alternative-id": [
    "BF00251518"
  ],
  "URL": "http://dx.doi.org/10.1007/BF00251518",
  "relation": {},
  "ISSN": [
    "0003-9527",
    "1432-0673"
  ],
  "subject": [],
  "container-title-short": "Arch. Rational Mech. Anal.",
  "published": {
    "date-parts": [
      [
        1988,
        9
      ]
    ]
  }
}