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Philosophical Magazine B Volume 64, 1991 - Issue 6
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Original Articles

On diffusion-controlled evolution of closed solid-state thermodynamic systems at constant temperature and pressure

J. Svoboda Institute of Physical Metallurgy, Czechoslovak Academy of Sciences, Žižkova 22, CS-616 62 Brno, Czechoslovakia
&
I. Turek Institute of Physical Metallurgy, Czechoslovak Academy of Sciences, Žižkova 22, CS-616 62 Brno, Czechoslovakia
Pages 749-759 | Received 17 Jul 1990, Accepted 06 Jun 1991, Published online: 20 Aug 2006

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Daniel Larouche. (2023) Unified theory of nucleation and coarsening in the solid state. Philosophical Magazine 103:12, pages 1115-1145.
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H. Wang, C. Lai, X. Zhang, W. Kuang & F. Liu. (2015) Modeling of non-equilibrium solute diffusion upon rapid solidification: effective mobility versus kinetic energy. Materials Science and Technology 31:13, pages 1649-1657.
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E. Gamsjäger. (2008) A concise derivation of the contact conditions at a migrating sharp interface. Philosophical Magazine Letters 88:5, pages 363-369.
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J. Svoboda, I. Turek & F. D. Fischer. (2005) Application of the thermodynamic extremal principle to modeling of thermodynamic processes in material sciences. Philosophical Magazine 85:31, pages 3699-3707.
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Markus A. Hartmann, Richard Weinkamer, Peter Fratzl , JiŘÍ Svoboda & Franz Dieter Fischer. (2005) Onsager's coefficients and diffusion laws—a Monte Carlo study. Philosophical Magazine 85:12, pages 1243-1260.
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Pia Redanz & RobertM. McMeeking. (2003) Sintering of a bcc structure of spherical particles of equal and different sizes. Philosophical Magazine 83:23, pages 2693-2714.
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F. D. Fischer, J. Svoboda & P. Fratzl. (2003) A thermodynamic approach to grain growth and coarsening. Philosophical Magazine 83:9, pages 1075-1093.
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Yue Li, Zhijun Wang, Junjie Li, Jincheng Wang & Ke-gang Wang. (2023) Mean-field modelling of precipitation kinetics with a Fokker-Planck equation in the Lifshitz–Slyozov–Wagner space. Journal of Crystal Growth 618, pages 127312.
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Yue Li, Zhijun Wang, Yujian Wang, Junjie Li & Jincheng Wang. (2022) Revealing curvature and stochastic effects on grain growth: A thermodynamic perspective from extremal principle. Scripta Materialia 217, pages 114766.
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Y.S. Fan, L. Tan, X.G. Yang, D.Q. Shi, R.Z. Li, J. Huang & C. Wang. (2022) A microstructural rafting state-based constitutive model for single crystal Ni-based superalloys at elevated temperature. International Journal of Mechanical Sciences 228, pages 107484.
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R.Z. Li, B. Xie, X.G. Yang, Y.S. Fan, Y.T. Sun & D.Q. Shi. (2022) Multi-scale modelling of rafting behaviour under complex stress states for Ni3Al superalloys. International Journal of Plasticity 152, pages 103255.
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Paride Azzari, Massimo Bagnani & Raffaele Mezzenga. (2021) Liquid–liquid crystalline phase separation in biological filamentous colloids: nucleation, growth and order–order transitions of cholesteric tactoids. Soft Matter 17:27, pages 6627-6636.
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Jorge de Anda Salazar, Thomas Heuzé & Laurent Stainier. (2020) Multifield variational formulations of diffusion initial boundary value problems. Continuum Mechanics and Thermodynamics 33:2, pages 563-589.
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Ze Sheng, Manon Bonvalet Rolland, Tao Zhou, Joakim Odqvist & Peter Hedström. (2020) Langer–Schwartz–Kampmann–Wagner precipitation simulations: assessment of models and materials design application for Cu precipitation in PH stainless steels. Journal of Materials Science 56:3, pages 2650-2671.
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Klaus Hackl, Franz Dieter Fischer & Jiri Svoboda. (2019) Constraints in thermodynamic extremal principles for non-local dissipative processes. Continuum Mechanics and Thermodynamics 32:5, pages 1337-1345.
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Klaus Hackl, Franz Dieter Fischer, Gerald Andreas Zickler & Jiří Svoboda. (2020) Are Onsager's reciprocal relations necessary to apply Thermodynamic Extremal Principles?. Journal of the Mechanics and Physics of Solids 135, pages 103780.
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Manon Bonvalet-Rolland, Thomas Philippe & John Ågren. (2019) Kinetic theory of nucleation in multicomponent systems: An application of the thermodynamic extremum principle. Acta Materialia 171, pages 1-7.
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Anders Salwén. 2019. TMS 2019 148th Annual Meeting & Exhibition Supplemental Proceedings. TMS 2019 148th Annual Meeting & Exhibition Supplemental Proceedings 1019 1025 .
J. Svoboda & F.D. Fischer. (2018) Influence of accounting for translational motion of grains on grain growth kinetics and size distribution. Scripta Materialia 146, pages 255-259.
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P. Remmert, W. Heinrich, B. Wunder, L. Morales, R. Wirth, D. Rhede & R. Abart. (2017) Synthesis of monticellite–forsterite and merwinite–forsterite symplectites in the CaO–MgO–SiO2 model system: influence of temperature and water content on microstructure evolution. Contributions to Mineralogy and Petrology 173:1.
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K. G. Wang & Gabriel Q. Wang. (2017) Phase coarsening in multicomponent systems. Physical Review E 95:2.
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J. Svoboda, P. Fratzl, G.A. Zickler & F.D. Fischer. (2016) A new treatment of transient grain growth. Acta Materialia 115, pages 442-447.
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Markus Schmuck & Serafim Kalliadasis. (2016) General framework for adsorption processes on dynamic interfaces. Journal of Physics A: Mathematical and Theoretical 49:12, pages 125502.
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G. Stechauner & E. Kozeschnik. (2015) Thermo-kinetic modeling of Cu precipitation in α-Fe. Acta Materialia 100, pages 135-146.
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Haifeng Wang, P.K. Galenko, Xiao Zhang, Wangwang Kuang, Feng Liu & D.M. Herlach. (2015) Phase-field modeling of an abrupt disappearance of solute drag in rapid solidification. Acta Materialia 90, pages 282-291.
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Haifeng Wang, Wangwang Kuang, Xiao Zhang & Feng Liu. (2014) A hyperbolic phase-field model for rapid solidification of a binary alloy. Journal of Materials Science 50:3, pages 1277-1286.
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Haifeng Wang, Feng Liu & D. M. Herlach. (2014) Kinetics of triple-junctions in eutectic solidification: a sharp interface model. Journal of Materials Science 50:1, pages 176-188.
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Haifeng Wang, Feng Liu & D. M. Herlach. (2013) Modeling the growth kinetics of a multi-component stoichiometric compound. Journal of Materials Science 49:4, pages 1537-1543.
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Haifeng Wang, Feng Liu, G.J. Ehlen & D.M. Herlach. (2013) Application of the maximal entropy production principle to rapid solidification: A multi-phase-field model. Acta Materialia 61:7, pages 2617-2627.
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Klaus Hackl & Jörg Renner. (2013) High-temperature deformation and recrystallization: A variational analysis and its application to olivine aggregates. Journal of Geophysical Research: Solid Earth 118:3, pages 943-967.
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Haifeng Wang, Feng Liu, Haimin Zhai & Kang Wang. (2012) Application of the maximal entropy production principle to rapid solidification: A sharp interface model. Acta Materialia 60:4, pages 1444-1454.
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Christian M. Ulrich, Adham Hashibon, Jiřı´ Svoboda, Christian Elsässer, Dirk Helm & Hermann Riedel. (2011) Diffusion kinetics in aluminium–gold bond contacts from first-principles density functional calculations. Acta Materialia 59:20, pages 7634-7644.
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Gary Purdy, John Ågren, Annika Borgenstam, Yves Bréchet, Masato Enomoto, Tadashi Furuhara, Ernst Gamsjager, Mohamed Gouné, Mats Hillert, Christopher Hutchinson, Matthias Militzer & Hatem Zurob. (2011) ALEMI: A Ten-Year History of Discussions of Alloying-Element Interactions with Migrating Interfaces. Metallurgical and Materials Transactions A 42:12, pages 3703-3718.
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J. Svoboda, E. Gamsjäger, F.D. Fischer, Y. Liu & E. Kozeschnik. (2011) Diffusion processes in a migrating interface: The thick-interface model. Acta Materialia 59:12, pages 4775-4786.
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Klaus Hackl & Franz Dieter Fischer. (2007) On the relation between the principle of maximum dissipation and inelastic evolution given by dissipation potentials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464:2089, pages 117-132.
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F. D. Fischer & J. Svoboda. (2007) A Note on the Principle of Maximum Dissipation Rate. Journal of Applied Mechanics 74:5, pages 923-926.
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J. Svoboda & F.D. Fischer. (2007) A new approach to modelling of non-steady grain growth. Acta Materialia 55:13, pages 4467-4474.
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Gerhard Inden. (2007) Diffusion and Phase Transformations in Multi-Component Systems. Defect and Diffusion Forum 263, pages 11-20.
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J. Svoboda, F.D. Fischer & P. Fratzl. (2006) Diffusion and creep in multi-component alloys with non-ideal sources and sinks for vacancies. Acta Materialia 54:11, pages 3043-3053.
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M. Hillert & J. Ågren. (2006) Extremum principles for irreversible processes. Acta Materialia 54:8, pages 2063-2066.
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Peter Fratzl, Franz Dieter Fischer & Jiri Svoboda. (2005) Energy Dissipation and Stability of Propagating Surfaces. Physical Review Letters 95:19.
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J. Svoboda. 2005. Moving Interfaces in Crystalline Solids. Moving Interfaces in Crystalline Solids 117 168 .
T. Roubíček. 2005. Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials. Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials 269 304 .
E. Kozeschnik, J. Svoboda & F.D. Fischer. (2004) Modified evolution equations for the precipitation kinetics of complex phases in multi-component systems. Calphad 28:4, pages 379-382.
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J. Svoboda, F.D. Fischer, P. Fratzl & E. Kozeschnik. (2004) Modelling of kinetics in multi-component multi-phase systems with spherical precipitates. Materials Science and Engineering: A 385:1-2, pages 166-174.
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J.S. Chen, V. Kotta, H. Lu, D. Wang, D. Moldovan & D. Wolf. (2004) A variational formulation and a double-grid method for meso-scale modeling of stressed grain growth in polycrystalline materials. Computer Methods in Applied Mechanics and Engineering 193:12-14, pages 1277-1303.
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J Svoboda, E Gamsjäger, F.D Fischer & P Fratzl. (2004) Application of the thermodynamic extremal principle to the diffusional phase transformations. Acta Materialia 52:4, pages 959-967.
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F.D. Fischer, F. Appel & H. Clemens. (2003) A thermodynamical model for the nucleation of mechanical twins in TiAl. Acta Materialia 51:5, pages 1249-1260.
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Alexander Mielke & Tomás Roubícek. (2003) A Rate-Independent Model for Inelastic Behavior of Shape-Memory Alloys. Multiscale Modeling & Simulation 1:4, pages 571-597.
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J Svoboda, F.D Fischer, P Fratzl & A Kroupa. (2002) Diffusion in multi-component systems with no or dense sources and sinks for vacancies. Acta Materialia 50:6, pages 1369-1381.
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S.M. Schlögl, J. Svoboda & E. Van der Giessen. (2001) Evolution of the methane pressure in a standard 2.25Cr–1Mo steel during hydrogen attack. Acta Materialia 49:12, pages 2227-2238.
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F. Parhami, R.M. McMeeking, A.C.F. Cocks & Z. Suo. (1999) A model for the sintering and coarsening of rows of spherical particles. Mechanics of Materials 31:1, pages 43-61.
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J. Svoboda & P. Lukáš. (1998) Model of creep in 〈001〉-oriented superalloy single crystals. Acta Materialia 46:10, pages 3421-3431.
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J. Svoboda & P. Lukás̆. (1996) Modelling of kinetics of directional coarsening in Ni-superalloys. Acta Materialia 44:6, pages 2557-2565.
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Yang Wei & Suo Zhigang. (1996) Global view of microstructural evolution: Energetics, kinetics and dynamical systems. Acta Mechanica Sinica 12:2, pages 144-157.
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B. Sun, Z. Suo & A.C.F. Cocks. (1996) A global analysis of structural evolution in a row of grains. Journal of the Mechanics and Physics of Solids 44:4, pages 559-581.
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Weiqing Wang, Z. Suo & T.-H. Hao. (1996) A simulation of electromigration-induced transgranular slits. Journal of Applied Physics 79:5, pages 2394-2403.
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J. Svoboda & H. Riedel. (1995) Quasi-equilibrium sintering for coupled grain-boundary and surface diffusion. Acta Metallurgica et Materialia 43:2, pages 499-506.
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J. Svoboda & H. Riedel. (1995) New solutions describing the formation of interparticle necks in solid-state sintering. Acta Metallurgica et Materialia 43:1, pages 1-10.
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J. Svoboda. (1993) Cooperation of diffusive processes at cavity nucleation in high temperature creep. Acta Metallurgica et Materialia 41:12, pages 3495-3503.
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