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Acta Metall Sin  2018, Vol. 54 Issue (2): 278-292    DOI: 10.11900/0412.1961.2017.00336
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Phase Field Crystal Model and Its Application for Microstructure Evolution of Materials
Yingjun GAO1,2(), Yujiang LU2, Lingyi KONG2, Qianqian DENG1,2, Lilin HUANG2,3, Zhirong LUO2,3
1 Guangxi Key Laboratory for the Relativistic Astrophysics and Guangxi College and University Key Laboratory of Novel Energy Materials, Guangxi University, Nanning 530004, China
2 School of Physical Science and Technology, Guangxi University, Nanning 530004, China
3 Institute of Physics Science and Engineering Technology, Yulin Normal University, Yulin 537000, China
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With the rapid development of computer technology, the roles of computer numerical simulation technology in materials are more and more prominent. Computer numerical simulation technology, real experimental observation and theoretical model analysis are the same important and are known as three great scientific research methods since the 20th century. In this paper, several important computational numerical simulation methods are briefly compared, firstly, in the spatial characteristic resolution scale and the characteristic time scale, for example, for molecular dynamics (MD), traditional phase field (TPF), and phase field crystal (PFC) method. For simulation of microstructure evolution in nano-scale, the PFC method is of the advantage on the characteristic time scale. Then, the PFC model, and its physical and mathematical basises for establishment, as well as the special feature of the method, are introduced. Next, the development of the PFC models are presented, including the PFC model of binary and multi-element alloys, of gas-liquid-solid three systems, of two-mode and multimode systems, as well as the key technology and the main procedure of the numerical calculation of the dynamic equation solution. After that, combining with the research works of the authors' group in the microstructure evolution of materials, several examples of important aspects of application of the PFC model are presented, including the nanostructure of defects of materials, dendritic growth and heterogenous epitxial growth, premelting under deformation at high temperature and dynamic recovery, extension and bifurcation of cracks on nanoscale, matalllic glass transition, defect structures of graphene, voids formation of electromigration in metal interconnects, microstructure in multiferroic composite matrials, and the formation of the structure of the metal foams. Finally, a summary is given and the development direction and future emphasis application and new fields of the PFC model are pointed out.

Key words:  phase field crystal      numerical simulation      microstructure evolution      defect      void-crack     
Received:  14 August 2017     
Fund: Supported by National Natural Science Foundation of China (Nos.51161003 and 51561031) and Guangxi Natural Science Foundation (No.2012GXNSFDA053001)

Cite this article: 

Yingjun GAO, Yujiang LU, Lingyi KONG, Qianqian DENG, Lilin HUANG, Zhirong LUO. Phase Field Crystal Model and Its Application for Microstructure Evolution of Materials. Acta Metall Sin, 2018, 54(2): 278-292.

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Fig.1  The main numerical methods for microstructures corresponding to different length scales
Method tc (AV) / s tc (AD) / s Lc Strain rate Ref.
MD 10-12 - nm 104~106 [14,16,17]
TPF - 10-6 μm 10-6~10-2 [2,15]
PFC - 10-6 nm 10-6~10-2 [2,15,17,18]
Exp. - 10-6 nm 10-6~10-2 [15,17]
Table 1  The comparison of several methods in characteristic time scale and spatial resolution scale[2,14~18]
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