The DOI matches its Crossref record; 31 of the 31 references it cites were found in a registry or an index.
Phase-field models in materials science
Abstract
The phase-field method is reviewed against its historical and theoretical background. Starting from Van der Waals considerations on the structure of interfaces in materials the concept of the phase-field method is developed along historical lines. Basic relations are summarized in a comprehensive way. Special emphasis is given to the multi-phase-field method with extension to elastic interactions and fluid flow which allows one to treat multi-grain multi-phase structures in multicomponent materials. Examples are collected demonstrating the applicability of the different variants of the phase-field method in different fields of materials science.
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Cites
Free Energy of a Nonuniform System. I. Interfacial Free Energy
Cahn, J. W., & Hilliard, J. E. (1958) · The Journal of Chemical Physics · doi:10.1063/1.1744102 · Cited by 10,437
Reciprocal Relations in Irreversible Processes. I.
Onsager, L. (1931) · Physical Review · doi:10.1103/physrev.37.405 · Cited by 6,660
Reciprocal Relations in Irreversible Processes. II.
Onsager, L. (1931) · Physical Review · doi:10.1103/physrev.38.2265 · Cited by 5,367
Fundamentals of Solidification
Kurz, W., & Fisher, D. J. (2012) · ASM International eBooks · doi:10.31399/asm.tb.pdub.t53420429 · Cited by 3,287
Phase-Field Models for Microstructure Evolution
Chen, L.-Q. (2002) · Annual Review of Materials Research · doi:10.1146/annurev.matsci.32.112001.132041 · Cited by 2,989
Free Energy of a Nonuniform System. III. Nucleation in a Two-Component Incompressible Fluid
Cahn, J. W., & Hilliard, J. E. (1959) · The Journal of Chemical Physics · doi:10.1063/1.1730447 · Cited by 2,013
Morphological Stability of a Particle Growing by Diffusion or Heat Flow
Mullins, W. W., & Sekerka, R. F. (1963) · Journal of Applied Physics · doi:10.1063/1.1702607 · Cited by 2,004
Fundamentals of Solidification: Fourth Revised Edition
Kurz, W., & Fisher, D. J. (1998) · Retrospective Collection · doi:10.4028/www.scientific.net/rc.35 · Cited by 1,955
Theory of structural transformations in solids
Newnham, R. (1984) · Materials Research Bulletin · doi:10.1016/0025-5408(84)90018-7 · Cited by 1,944
Theory of structural transformations in solids
Khachaturi︠a︡n, A. G. (1983) · Cited by 1,811
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Materials discovery and design using machine learning
Liu, Y., Zhao, T., Ju, W., & Shi, S. (2017) · Journal of Materiomics · doi:10.1016/j.jmat.2017.08.002 · Cited by 1,276
Engineering grain boundaries at the 2D limit for the hydrogen evolution reaction
He, Y., Tang, P., Hu, Z., He, Q., Zhu, C., Wang, L., Zeng, Q., Golani, P., Gao, G., Fu, W., et al. (2020) · Nature Communications · doi:10.1038/s41467-019-13631-2 · Cited by 267
Microstructure modelling for metallic additive manufacturing: a review
Tan, J. H. K., Sing, S. L., & Yeong, W. Y. (2020) · Virtual and Physical Prototyping · doi:10.1080/17452759.2019.1677345 · Cited by 266
Metadata
- Authors
- Steinbach, I.
- Venue
- Modelling and Simulation in Materials Science and Engineering
- Publisher
- IOP Publishing
- Published
- 2009-07-30
- Volume
- 17
- Issue
- 7
- Pages
- 073001
- ISSN
- 0965-0393 (ISSN-L)
- 1361-651X
- OpenAlex
- W2107436920
- Cited by
- 1,310
- References
- 31
- FWCI
- 18.50
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
