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Research Papers

Thermal Fluctuations as a Computational Microscope for Studying Crystalline Interfaces: A Mechanistic Perspective

[+] Author and Article Information
Dengke Chen

Department of Mechanical Engineering,
University of Houston,
Houston, TX 77204

Yashashree Kulkarni

Department of Mechanical Engineering,
University of Houston,
Houston, TX 77204
e-mail: ykulkarni@uh.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 5, 2017; final manuscript received September 8, 2017; published online September 22, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(12), 121001 (Sep 22, 2017) (6 pages) Paper No: JAM-17-1485; doi: 10.1115/1.4037885 History: Received September 05, 2017; Revised September 08, 2017

Interfaces such as grain boundaries are ubiquitous in crystalline materials and have provided a fertile area of research over decades. Their importance stems from the numerous critical phenomena associated with them, such as grain boundary sliding, migration, and interaction with other defects, that govern the mechanical properties of materials. Although these crystalline interfaces exhibit small out-of-plane fluctuations, statistical thermodynamics of membranes has been effectively used to extract relevant physical quantities such as the interface free energy, grain boundary stiffness, and interfacial mobility. In this perspective, we advance the viewpoint that thermal fluctuations of crystalline interfaces can serve as a computational microscope for gaining insights into the thermodynamic and kinetic properties of grain boundaries and present a rich source of future study.

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Figures

Grahic Jump Location
Fig. 1

Atomistic configuration of a fluctuating coherent twin boundary in a face-centered cubic metal obtained from molecular dynamics. The colors represent the distance of the atoms above (red) and below (blue) the initial flat configuration. The fluctuations have been exaggerated for illustration. The simulations were performed in LAMMPS [17] using the embedded-atom method (EAM) interatomic potential developed by Mishin et al. [18] for Cu and visualized in OVITO [19]. Reproduced from Chen and Kulkarni [20].

Grahic Jump Location
Fig. 2

Schematic of a bicrystal representing the flat interface by dotted lines and the fluctuating interface at finite temperature by solid lines

Grahic Jump Location
Fig. 3

Power spectra of the thermal fluctuations of two interfaces as a function of wave number k obtained by molecular dynamics simulations. The red points represent Σ3(111) twin boundary with a slope of −1 (shown by a solid line). The blue points represent Σ5(310) high angle grain boundary with a slope of −2 (shown by a solid line). The simulations were performed in LAMMPS [17] using the EAM interatomic potential developed by Mishin et al. [18] for Cu and by Ackland et al. [23] for Ni.

Grahic Jump Location
Fig. 4

A schematic of a grain boundary fluctuating from the equilibrium position (indicated by the solid red line) to new positions (indicated by the dashed red lines). The random walk of the mean grain boundary positions (indicated by the dashed lines) deviating from its equilibrium position (indicated by the solid blue line) can be considered as a Brownian motion in the migration direction.

Grahic Jump Location
Fig. 5

Temporal evolution of the variance 〈h¯2〉 for the Σ17(410) grain boundary in Ni at 1200 K. The dots represent simulation data, while the solid red line shows the linear fit of the form 〈h¯2〉=Dt. Computing D from this plot yields the mobility. The simulations were performed in LAMMPS [17] using the EAM interatomic potential developed by Baskes and co-workers [24,25].

Grahic Jump Location
Fig. 6

Distribution of the average interface position h¯(t) with respect to the initial position (h¯(0)=0) at different time intervals obtained from molecular dynamics. The results are for the case of a Σ17(410) grain boundary in Ni at 1200 K. The Gaussian form f=Be−αh¯2 is fitted to the data and shown by solid lines, where B and α are measures of the height and width of the distribution, respectively. The simulations were performed in LAMMPS [17] using the EAM interatomic potential developed by Baskes and co-workers [24,25].

Grahic Jump Location
Fig. 7

Fluctuation spectra as a function of wave number k for Σ3(111) twin boundary (in red) and Σ5(210) high-angle grain boundary (in blue) obtained from molecular dynamics. The high angle grain boundary shows suppressed fluctuations due to neighboring grain boundaries thus deviating from the linear dependence with −2 slope (shown by blue dashed line) at long wavelengths. In contrast, the twin boundary shows enhanced fluctuations due to neighboring twin boundaries thus deviating from the linear dependence with −1 slope (shown by red dashed line) at long wavelengths. The simulations were performed in LAMMPS [17] using the EAM interatomic potential for Cu developed by Mishin et al. [18].

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