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Advances in Physics Volume 61, 2012 - Issue 6
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Review Articles

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Heike Emmerich Lehrstuhl für Material- und Prozesssimulation, Universität Bayreuth, D-95440, Bayreuth, GermanyCorrespondence[email protected]
,
Hartmut Löwen Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225, Düsseldorf, GermanyCorrespondence[email protected]
,
Raphael Wittkowski Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225, Düsseldorf, Germany
,
Thomas Gruhn Lehrstuhl für Material- und Prozesssimulation, Universität Bayreuth, D-95440, Bayreuth, Germany
,
Gyula I. Tóth Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, PO Box 49, H-1525, Budapest, Hungary
,
György Tegze Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, PO Box 49, H-1525, Budapest, Hungary
&
László Gránásy Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, PO Box 49, H-1525, Budapest, Hungary; BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, UKCorrespondence[email protected]
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Pages 665-743 | Received 27 Jun 2012, Accepted 18 Sep 2012, Published online: 13 Nov 2012

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P.K. Galenko & D. Jou. (2019) Rapid solidification as non-ergodic phenomenon. Physics Reports 818, pages 1-70.
Crossref
Muhammad Musaddique Ali Rafique, Stephen Niezgoda & Milan Brandt. (2019) Retracted: Development of Bulk Metallic Glass Matrix Composites (BMGMC) by Additive Manufacturing: Modelling and Simulation – A Review: Part A. Advanced Materials Research 1154, pages 1-39.
Crossref
Bo Ni, Teng Zhang, Jiaoyan Li, Xiaoyan Li & Huajian Gao. 2019. Handbook of Graphene. Handbook of Graphene 1 44 .
Ananya Renuka Balakrishna, Yet-Ming Chiang & W. Craig Carter. (2019) Phase-field model for diffusion-induced grain boundary migration: An application to battery electrodes. Physical Review Materials 3:6.
Crossref
Vili Heinonen, Keaton J. Burns & Jörn Dunkel. (2019) Quantum hydrodynamics for supersolid crystals and quasicrystals. Physical Review A 99:6.
Crossref
Simon Praetorius, Marco Salvalaglio & Axel Voigt. (2019) An efficient numerical framework for the amplitude expansion of the phase-field crystal model. Modelling and Simulation in Materials Science and Engineering 27:4, pages 044004.
Crossref
Gabriel Martine La Boissonière, Rustum Choksi, Katayun Barmak & Selim Esedoḡlu. (2019) Statistics of grain growth: Experiment versus the phase-field-crystal and Mullins models. Materialia 6, pages 100280.
Crossref
Gabriel Kocher & Nikolas Provatas. (2019) Thermodensity coupling in phase-field-crystal-type models for the study of rapid crystallization. Physical Review Materials 3:5.
Crossref
Huijun Guo, Yuhong Zhao, Yuanyang Sun, Jinzhong Tian, Hua Hou, Kewu Qi & Xiaolin Tian. (2019) Phase field crystal study of grain boundary structure and annihilation mechanism in low-angle grain boundary. Superlattices and Microstructures 129, pages 163-175.
Crossref
Marco Salvalaglio, Axel Voigt & Ken R. Elder. (2019) Closing the gap between atomic-scale lattice deformations and continuum elasticity. npj Computational Materials 5:1.
Crossref
James F. Lutsko. (2019) How crystals form: A theory of nucleation pathways. Science Advances 5:4.
Crossref
Shi Hu, Luopeng Xu & Quanyi Liu. (2019) Simulation of shear-induced nanograin deformation: the influence of temperature and grain boundary misorientation. Materials Research Express 6:7, pages 076511.
Crossref
R. Backofen, K. R. Elder & A. Voigt. (2019) Controlling Grain Boundaries by Magnetic Fields. Physical Review Letters 122:12.
Crossref
Alon Z. Shapira, Nir Gavish & Arik Yochelis. (2019) Pattern formation aspects of electrically charged tri-stable media with implications to bulk heterojunction in organic photovoltaics. EPL (Europhysics Letters) 125:3, pages 38001.
Crossref
Shuiran Peng & Hongyi Zhu. (2019) Well-posedness for modified higher-order anisotropic Cahn–Hilliard equations. Asymptotic Analysis 111:3-4, pages 201-215.
Crossref
Miguel A. Durán-Olivencia, Rishabh S. Gvalani, Serafim Kalliadasis & Grigorios A. Pavliotis. (2019) Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations. Journal of Statistical Physics 174:3, pages 579-604.
Crossref
David J. B. Lloyd. (2019) Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift--Hohenberg Equation. SIAM Journal on Applied Dynamical Systems 18:4, pages 1892-1933.
Crossref
Shi Hu & Song Wang. (2019) The influences of crystal orientation and crack interaction on the initiation of growth and propagation mode of microcrack: A phase-field-crystal study. Physica B: Condensed Matter 552, pages 104-109.
Crossref
Ilya Starodumov, Vladimir Ankudinov & Peter Galenko. (2019) Crystal structures predicted by the PFC method with atomic density fluctuations. Materials Today: Proceedings 11, pages 118-123.
Crossref
P Subramanian, A J Archer, E Knobloch & A M Rucklidge. (2018) Spatially localized quasicrystalline structures. New Journal of Physics 20:12, pages 122002.
Crossref
Audun Skaugen, Luiza Angheluta & Jorge Viñals. (2018) Separation of Elastic and Plastic Timescales in a Phase Field Crystal Model. Physical Review Letters 121:25.
Crossref
Jiaoyan Li, Bo Ni, Teng Zhang & Huajian Gao. (2018) Phase field crystal modeling of grain boundary structures and growth in polycrystalline graphene. Journal of the Mechanics and Physics of Solids 120, pages 36-48.
Crossref
Lukas Ophaus, Svetlana V. Gurevich & Uwe Thiele. (2018) Resting and traveling localized states in an active phase-field-crystal model. Physical Review E 98:2.
Crossref
James F. Lutsko & Julien Lam. (2018) Classical density functional theory, unconstrained crystallization, and polymorphic behavior. Physical Review E 98:1.
Crossref
Jin-Xing Shi, Keiichiro Ohmura, Masatoshi Shimoda & Xiao-Wen Lei. (2018) A consistent methodology for optimal shape design of graphene sheets to maximize their fundamental frequencies considering topological defects. Journal of the Mechanics and Physics of Solids 116, pages 117-134.
Crossref
Raymond Aschheim, Laurenţiu Bubuianu, Fang Fang, Klee Irwin, Vyacheslav Ruchin & Sergiu I. Vacaru. (2018) Starobinsky inflation and dark energy and dark matter effects from quasicrystal like spacetime structures. Annals of Physics 394, pages 120-138.
Crossref
Marco Salvalaglio, Rainer Backofen, K. R. Elder & Axel Voigt. (2018) Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model. Physical Review Materials 2:5.
Crossref
Simon Praetorius, Axel Voigt, Raphael Wittkowski & Hartmut Löwen. (2018) Active crystals on a sphere. Physical Review E 97:5.
Crossref
Zi-Le Wang, Zhirong Liu & Zhi-Feng Huang. (2018) Angle-adjustable density field formulation for the modeling of crystalline microstructure. Physical Review B 97:18.
Crossref
J Em-Udom & N Pisutha-Arnond. (2018) Investigation on Viscoelastic-Creep Behavior of the Phase-Field Crystal Method. IOP Conference Series: Materials Science and Engineering 361, pages 012009.
Crossref
J Em-Udom & N Pisutha-Arnond. (2018) Pressure-Controlled Dynamic Equation for the Phase-Field Crystal Method. IOP Conference Series: Materials Science and Engineering 361, pages 012006.
Crossref
Zhi Chen, Zhaoyang Wang, Xinrui Gu, Yufei Chen, Limei Hao, Jos de Wit & Kexin Jin. (2018) Phase-field crystal simulation facet and branch crystal growth. Applied Physics A 124:5.
Crossref
Ananya Renuka Balakrishna & W. Craig Carter. (2018) Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys. Physical Review E 97:4.
Crossref
Paul Jreidini, Gabriel Kocher & Nikolas Provatas. (2018) Classical nucleation theory in the phase-field crystal model. Physical Review E 97:4.
Crossref
Zi-Le Wang, Zhi-Feng Huang & Zhirong Liu. (2018) Elastic constants of stressed and unstressed materials in the phase-field crystal model. Physical Review B 97:14.
Crossref
Gabriel Martine La Boissonière & Rustum Choksi. (2018) Atom based grain extraction and measurement of geometric properties. Modelling and Simulation in Materials Science and Engineering 26:3, pages 035001.
Crossref
Jincheng Lei & Zishun Liu. (2018) The structural and mechanical properties of graphene aerogels based on Schwarz-surface-like graphene models. Carbon 130, pages 741-748.
Crossref
Mohsen Asle Zaeem & Ebrahim Asadi. 2018. Integrated Computational Materials Engineering (ICME) for Metals. Integrated Computational Materials Engineering (ICME) for Metals 49 70 .
Niloufar Faghihi, Simiso Mkhonta, Ken R. Elder & Martin Grant. (2018) Magnetic islands modelled by a phase-field-crystal approach. The European Physical Journal B 91:3.
Crossref
Nan Wang, Gabriel Kocher & Nikolas Provatas. (2018) A phase-field-crystal alloy model for late-stage solidification studies involving the interaction of solid, liquid and gas phases. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376:2113, pages 20170212.
Crossref
P. K. Galenko, I. G. Nizovtseva, K. Reuther & M. Rettenmayr. (2018) Kinetic transition in the order–disorder transformation at a solid/liquid interface. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376:2113, pages 20170207.
Crossref
Nirand Pisutha-Arnond. (2018) Fourier-spectral-method implementation of deformation in the phase-field crystal model. MATEC Web of Conferences 192, pages 01028.
Crossref
S. Alireza Etesami & Ebrahim Asadi. (2018) Molecular dynamics for near melting temperatures simulations of metals using modified embedded-atom method. Journal of Physics and Chemistry of Solids 112, pages 61-72.
Crossref
E. López-Quiroga. (2018) Reduced order methods for the solution of solidification Phase-Field models ⁎ ⁎This work has been funded by the RCUK National Centre for the Sustainable Energy Use in Food Chains (CSEF) (EPSRC grant no. EP/K011820/1).. IFAC-PapersOnLine 51:2, pages 637-642.
Crossref
Stephen DeWitt & Katsuyo Thornton. 2018. Computational Materials System Design. Computational Materials System Design 67 87 .
Xiaodong Wang, Hongxi Zhang, Wen Zhou & Jie Ouyang. (2017) A 3D phase-field model for simulating the crystal growth of semi-crystalline polymers. International Journal of Heat and Mass Transfer 115, pages 194-205.
Crossref
Eli Alster, David Montiel, Katsuyo Thornton & Peter W. Voorhees. (2017) Simulating complex crystal structures using the phase-field crystal model. Physical Review Materials 1:6.
Crossref
J. Zhang, Z. Chen, C. Cheng & Y. X. Wang. (2017) A phase field crystal model simulation of morphology evolution and misfit dislocation generation in nanoheteroepitaxy. Modern Physics Letters B 31:30, pages 1750283.
Crossref
Raphael Wittkowski, Joakim Stenhammar & Michael E Cates. (2017) Nonequilibrium dynamics of mixtures of active and passive colloidal particles. New Journal of Physics 19:10, pages 105003.
Crossref
Susanta Ghosh. (2017) A novel technique to obtain analytical direct correlation functions for use in classical density functional theory. Computational Materials Science 138, pages 384-391.
Crossref
Marcelo M Amaral, Raymond Aschheim, Laurenţiu Bubuianu, Klee Irwin, Sergiu I Vacaru & Daniel Woolridge. (2017) Anamorphic quasiperiodic universes in modified and Einstein gravity with loop quantum gravity corrections. Classical and Quantum Gravity 34:18, pages 185002.
Crossref
Nan Wang, Nathan Smith & Nikolas Provatas. (2017) Investigating gas-phase defect formation in late-stage solidification using a novel phase-field crystal alloy model. Physical Review Materials 1:4.
Crossref
Marco Salvalaglio, Rainer Backofen, Axel Voigt & Ken R. Elder. (2017) Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model. Physical Review E 96:2.
Crossref
Julia Kundin & Muhammad Ajmal Choudhary. (2017) Application of the anisotropic phase-field crystal model to investigate the lattice systems of different anisotropic parameters and orientations. Modelling and Simulation in Materials Science and Engineering 25:5, pages 055004.
Crossref
V.W.L. Chan, N. Pisutha-Arnond & K. Thornton. (2017) Thermodynamic relationships for homogeneous crystalline and liquid phases in the phase-field crystal model. Computational Materials Science 135, pages 205-213.
Crossref
Akinori Yamanaka, Kevin McReynolds & Peter W. Voorhees. (2017) Phase field crystal simulation of grain boundary motion, grain rotation and dislocation reactions in a BCC bicrystal. Acta Materialia 133, pages 160-171.
Crossref
Claas Hüter, Jörg Neugebauer, Guillaume Boussinot, Bob Svendsen, Ulrich Prahl & Robert Spatschek. (2015) Modelling of grain boundary dynamics using amplitude equations. Continuum Mechanics and Thermodynamics 29:4, pages 895-911.
Crossref
Doaa Taha, S. K. Mkhonta, K. R. Elder & Zhi-Feng Huang. (2017) Grain Boundary Structures and Collective Dynamics of Inversion Domains in Binary Two-Dimensional Materials. Physical Review Letters 118:25.
Crossref
Sai Tang, Jincheng Wang, Junjie Li, Zhijun Wang, Yaolin Guo, Can Guo & Yaohe Zhou. (2017) Phase-field-crystal investigation of the morphology of a steady-state dendrite tip on the atomic scale. Physical Review E 95:6.
Crossref
Bálint Korbuly, Tamás Pusztai, Hervé Henry, Mathis Plapp, Markus Apel & László Gránásy. (2017) Grain coarsening in two-dimensional phase-field models with an orientation field. Physical Review E 95:5.
Crossref
Frigyes Podmaniczky, Gyula I. Tóth, György Tegze & László Gránásy. (2017) Hydrodynamic theory of freezing: Nucleation and polycrystalline growth. Physical Review E 95:5.
Crossref
Rosa Maria Mininni, Alain Miranville & Silvia Romanelli. (2017) Higher-order Cahn–Hilliard equations with dynamic boundary conditions. Journal of Mathematical Analysis and Applications 449:2, pages 1321-1339.
Crossref
Shi Hu, Wen Xi, Zheng Chen, Song Wang & Ting-Hui Zhang. (2017) Coupled motion of grain boundaries and the influence of microcracks: A phase-field-crystal study. Computational Materials Science 132, pages 125-131.
Crossref
V Ankudinov & P K Galenko. (2017) The diagram of phase-field crystal structures: an influence of model parameters in a two-mode approximation. IOP Conference Series: Materials Science and Engineering 192, pages 012019.
Crossref
P. Vignal, N. Collier, L. Dalcin, D.L. Brown & V.M. Calo. (2017) An energy-stable time-integrator for phase-field models. Computer Methods in Applied Mechanics and Engineering 316, pages 1179-1214.
Crossref
T. Yang, Y. Gao, D. Wang, R.P. Shi, Z. Chen, J.F. Nie, J. Li & Y. Wang. (2017) Non-conservative dynamics of lattice sites near a migrating interface in a diffusional phase transformation. Acta Materialia 127, pages 481-490.
Crossref
Laurence Cherfils, Alain Miranville & Shuiran Peng. (2017) Higher-order anisotropic models in phase separation. Advances in Nonlinear Analysis 8:1, pages 278-302.
Crossref
Lei Wang, Nan Wang & Nikolas Provatas. (2017) Liquid channel segregation and morphology and their relation with hot cracking susceptibility during columnar growth in binary alloys. Acta Materialia 126, pages 302-312.
Crossref
Caroline Desgranges & Jerome Delhommelle. (2017) Ginzburg-Landau free energy for molecular fluids: Determination and coarse-graining. Chemical Physics Letters 669, pages 218-223.
Crossref
Ahmad Nourian-Avval & Ebrahim Asadi. (2017) On the quantification of phase-field crystals model for computational simulations of solidification in metals. Computational Materials Science 128, pages 294-301.
Crossref
Ebrahim Asadi & Mohsen Asle Zaeem. (2017) Quantitative phase-field crystal modeling of solid-liquid interfaces for FCC metals. Computational Materials Science 127, pages 236-243.
Crossref
Alain Miranville. (2017) The Cahn–Hilliard equation and some of its variants. AIMS Mathematics 2:3, pages 479-544.
Crossref
Jin-Xing SHI, Keiichiro OHMURA & Masatoshi SHIMODA. (2017) Structural optimization method of carbon nanomaterials by introducing defects. Transactions of the JSME (in Japanese) 83:853, pages 17-00077-17-00077.
Crossref
Laurence Cherfils, Alain Miranville & Shuiran Peng. (2017) HIGHER-ORDER MODELS IN PHASE SEPARATION. Journal of Applied Analysis & Computation 7:1, pages 39-56.
Crossref
Miguel González-Pinto, Yuri Martínez-Ratón & Enrique Velasco. (2017) Dynamical properties of heterogeneous nucleation of parallel hard squares. Soft Matter 13:48, pages 9246-9258.
Crossref
Frigyes Podmaniczky, Gyula I. Tóth, György Tegze, Tamás Pusztai & László Gránásy. (2017) Phase-field crystal modeling of heteroepitaxy and exotic modes of crystal nucleation. Journal of Crystal Growth 457, pages 24-31.
Crossref
Bálint Korbuly, Tamás Pusztai, Gyula I. Tóth, Hervé Henry, Mathis Plapp & László Gránásy. (2017) Orientation-field models for polycrystalline solidification: Grain coarsening and complex growth forms. Journal of Crystal Growth 457, pages 32-37.
Crossref
Hartmut Löwen. 2017. Variational Methods in Molecular Modeling. Variational Methods in Molecular Modeling 255 284 .

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