Research Papers

Simulations of Anisotropic Grain Growth Involving Two-Phase Nanocrystalline/Amorphous Systems Using Q-State Monte Carlo

[+] Author and Article Information
J. B. Allen

Information Technology Laboratory,
U.S. Army Engineer Research
and Development Center,
3909 Halls Ferry Road,
Vicksburg, MS 39180
e-mail: jeffrey.b.allen@erdc.dren.mil

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received January 31, 2014; final manuscript received March 24, 2014; published online April 30, 2014. Assoc. Editor: Irene Beyerlein.

J. Eng. Mater. Technol 136(3), 031004 (Apr 30, 2014) (7 pages) Paper No: MATS-14-1025; doi: 10.1115/1.4027323 History: Received January 31, 2014; Revised March 24, 2014

The present work incorporates an implementation of the two dimensional, Q-state Monte Carlo method to evaluate anisotropic grain growth in two-phase nanocrystalline/amorphous systems. Specifically, anisotropic grain boundaries are simulated via the use of surface energies and binding energies; the former attributable to the variation in grain orientation and assigned through a mapping process involving Wulff plots. The secondary, amorphous phase is randomly assigned to the lattice in accordance with a specified initial volume fraction. Among other findings, the results reveal that the grain boundary surface energy, as governed by the shape of the Wulff plot, plays a critical role in the resulting microstructure. Additionally, it was found that the addition of a secondary amorphous phase to an existing anisotropic grain boundary system evolves into primary grain microstructures characteristic of single phase isotropic systems.

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Fig. 1

Illustrations of the two events simulated in this study: reorientation and site exchange. Gray and white regions signify the two different phases while the numbered hexagonal elements signify grain orientation.

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Fig. 2

Hexagonal grain elements and orientation angle (ϕ)

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Fig. 3

Elliptical (n = 2) Wulff plot with surface energy characterization

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Fig. 4

Lattice independent results, showing the convergence of average grain area for a resolution of N = 500 (isothermal; isotropic; Q = 60; t = 1000 MCS)

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Fig. 5

The slope of a straight fit through a plot of log R versus log (t) by least squares fitting provides an estimate for the inverse grain growth exponent (1/r). As shown, to a good approximation, the slope (0.49) is in agreement with the power-law prediction (isothermal; isotropic; Q = 60; t = 100 MCS; N = 500).

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Fig. 6

Contours of isotropic grain growth evolution (Q = 60; t = 500 MCS). The secondary amorphous phase migrates toward grain boundaries and the “pinning” effect resulting in smaller grains with increasing second phase addition. (a) Single phase (J1A = J1B = 1.6); (b) dual phase (J1A = J2A = 1.6, J1AB = J2AB = 0.1; %B = 5); (c) dual phase (J1A = J2A = 1.6, J1AB = J2AB = 0.1; %B = 10); and (d) dual phase (J1A = J2A = 1.6, J1AB = J2AB = 0.1; %B = 15).

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Fig. 7

Contours of anisotropic grain growth evolution (Q = 60; t = 500 MCS). Like the isotropic system, the second phase continues to migrate to the grain boundaries. It is also observed that with increased secondary phase, the grains tend to become more isotropic in shape. (a) Single phase (J1A = 1.6, J2A = 0.8, t = 1 × 10−6); (b) dual phase (J1A = 1.6, J2A = 0.8, J1AB = J2AB = 0.1; %B = 5; t = 1.0 × 10−6); (c) dual phase (J1A = 1.6, J2A = 0.8, J1AB = J2AB = 0.1; %B = 10; t = 1.0 × 10−6); and (d) dual phase (J1A = 1.6, J2A = 0.8, J1AB = J2AB = 0.1; %B = 15; t = 1.0 × 10−6).

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Fig. 8

Average grain area versus time (MCS) for isotropic single and dual phase grain growth shows the effect of pinning: the higher the fraction of secondary (B) phase the smaller the average grain size (J1A = J2A = 1.6 kT; J1AB = J2AB = 0.1 kT).

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Fig. 9

Average grain area versus MCS for anisotropic single and dual phase grain growth (J1A = 1.6 kT, J2A = 0.8 kT; J1AB = J2AB = 0.1 kT)

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Fig. 10

Average grain area versus % concentration of secondary phase (B) for isotropic and anisotropic cases. Results show the “pinning threshold” corresponding to the minimum allowable secondary phase concentration for fully constrained grain growth. The inset plot shows that a characteristic power-law curve for secondary concentrations less than the “pinning threshold.”

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Fig. 11

Plot of average AR versus time (MCS). The addition of a secondary amorphous phase to high aspect ratio/anisotropic grain systems evolves into grains characteristic of isotropic systems.




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