Diffusive molecular dynamics and its application to nanoindentation and sintering

Ju Li, Sanket Sarkar, William T. Cox, Thomas J. Lenosky, Erik Bitzek, and Yunzhi Wang

Phys. Rev. B 84, 054103 – Published 4 August 2011

Abstract

The interplay between diffusional and displacive atomic movements is a key to understanding deformation mechanisms and microstructure evolution in solids. The ability to handle the diffusional time scale and the structural complexity in these problems poses a general challenge to atomistic modeling. We present here an approach called diffusive molecular dynamics (DMD), which can capture the diffusional time scale while maintaining atomic resolution, by coarse-graining over atomic vibrations and evolving a smooth site-probability representation. The model is applied to nanoindentation and sintering, where intimate coupling between diffusional creep, displacive dislocation nucleation, and grain rotation are observed.

Received 12 April 2011

DOI:https://doi.org/10.1103/PhysRevB.84.054103

Authors & Affiliations

Ju Li^1,4,*, Sanket Sarkar², William T. Cox^2,4, Thomas J. Lenosky¹, Erik Bitzek^1,3, and Yunzhi Wang^2,4,†

¹Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
²Department of Materials Science and Engineering, The Ohio State University, Columbus, Ohio 43210, USA
³Department Werkstoffwissenschaften, Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
⁴State Key Laboratory for Mechanical Behavior of Materials and Frontier Institute of Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China

^*liju@seas.upenn.edu
^†wang.363@osu.edu

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Vol. 84, Iss. 5 — 1 August 2011

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Images

Figure 1
Benchmarking VG/DMD with Mishin EAM potential (Ref. 10) for Cu. Calculations were performed with $(1 - c) = 10^{- 20}$ on occupied sites of a perfect crystal. (a) Helmholtz free energy per atom $F_{DMD} / atom$ (red solid line), in comparison with analytical free energy $e_{0} + N^{- 1} \sum_{k = 1}^{3 N} k_{B} T \ln (ℏ ω_{k} / k_{B} T)$ based on harmonic phonon theory (blue dash-dotted line), with phonon frequencies ${ω_{k}}$ extracted from $T \approx 0$ MD simulations. (b) Lattice parameter $a_{0}$ from DMD calculation (red solid line), in comparison with direct MD simulations (black dashed line). (c) Root mean square displacement $(〈 | x_{i} - X_{i} |^{2} {〉)}^{1 / 2}$ per atom, based on DMD calculation ( $= {[3 {(2 α)}^{- 1}]}^{1 / 2}$ , red solid line), full-spectrum harmonic phonon theory ( $= {[N^{- 1} \sum_{k = 1}^{3 N} k_{B} T {(m ω_{k}^{2})}^{- 1}]}^{1 / 2}$ , blue dash-dotted line), and direct MD simulations (black dashed line).Reuse & Permissions
Figure 2
(a) Vacancy concentration of the initially vacant site over time at several temperatures. Lines show the analytic solution and mean vacancy jump period $b^{2} / D_{V}$ . (b) Vacancy concentration along the $[111]$ direction for different reduced times at $900 K$ . Solid lines show the analytic solutions.Reuse & Permissions
Figure 3
(a) Indenter accommodation by pure diffusional creep in the form of a surface vacancy disk at $\tilde{t} = 1000$ for the slower indentation rate. The black to white color scale represents the value of $c$ with black signifying fully occupied sites. Atomic sites having $c ⩽ 0.01$ are not shown. (b) Dislocation structures viewed by centrosymmetry parameter (Ref. 21) along $[11 \bar{2}]$ direction. Dislocation nucleation occurs at $\tilde{t} = 1010$ . In the inset, shown is a typical dislocation loop grown after homogeneous nucleation. (c) Load-displacement curve for slower and faster rate indentation showing reduced dislocation nucleation load, due to surface vacancy disk/terrace created by prior diffusion.Reuse & Permissions
Figure 4
(a) Initial configuration with $c = 0.9999$ for black sites, $c = 0.0001$ for white sites. (b) Final configuration after compressing to theoretical density over a reduced time of $\tilde{t} = 13.30$ . Atomic sites with $c ⩽ 0.01$ are not shown. A movie of this simulation is included in the supplementary online material (Ref. 25). (c) Time evolution of $F_{DMD}$ per site referenced to the bulk free energy $F_{DMD}^{bulk}$ per site for a perfect crystal. In the inset, distribution of site-wise chemical potential is shown for the initial and final configurations.Reuse & Permissions
Figure 5
Time evolution of the microstructure at (a) $\tilde{t} = 0$ , (b) $\tilde{t} = 1.33$ , (c) $\tilde{t} = 4.00$ , (d) $\tilde{t} = 6.64$ , (e) $\tilde{t} = 9.30$ , (f) $\tilde{t} = 12.72$ , and (g) $\tilde{t} = 13.30$ . Atomic sites with $c ⩽ 0.01$ are not shown. The significance of the arrows is discussed in the text.Reuse & Permissions

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