Concentration profile across a representative high angle grain boundary in the Pd–Au 50% alloy of 10 nm grain size after alloying. The gradient color scale in the inset indicates deviations from the global concentration. Blue denotes Au depletion of 10%, red denotes Au enrichment of 10%. In this context, the local concentration is defined as the average occupancy of a lattice site with an Au atom in the statistical semi-grandcanonical ensemble. Evidently, the GBs are depleted in Au. The thickness of the depletion zone is on the order of 2 nm. Snapshots were generated using OVITO. 40
(a)-(d) Stress-strain behavior and plastic crystal slip strain of nc Pd–Au 50% for various testing conditions and two different grain sizes, where (a) and (c) show the 5 nm case and (b) and (d) show the data for the 10 nm grain size. The crystal slip strain is measured for the structures under the applied load. Evidently, the stress-strain behavior sensibly depends on the straining conditions. The crystal slip strain of the deformed structures is independent of the straining conditions. (e) Stress-strain behavior for the case of an alternating MC swap fraction (the swap fraction is changed at constant time intervals as indicated by the vertical black lines) for the 10 nm grain size. In dashed grey, the reference data are shown, where the swap fraction was not changed during straining (same data as in b)). Altering the balance between MD straining and local relaxation changes the deformation properties at all straining stages. After a short time, the system reaches a steady-state deformation regime, independent of the straining history. (f) Stress-strain behavior during straining with an altered number of MD steps between two successive MC steps (ΔMD). Reference data (dashed, grey) are shown which correspond to the cases of an identical time interval for one full MC step obtained by a change in the swap fraction (same data as in (b)).
Microstructure and the stress-strain behavior of nc Pd–Au 50% with a grain size of 10 nm, where (a) no MC is carried out during straining and (b) local relaxation is carried out during straining with the highest frequency. In the snapshots, the gradient color scheme is according to the displacement from the initial atomic positions. The structures are rescaled to the initial size and the imposed deformation does therefore not contribute to a local displacement. Grain boundary and stacking fault atoms are highlighted in white and black, respectively. The arrows indicate the state of the snapshot on the stress-strain curve, where three snapshots under tensile load (at a total strain of 2, 3.2 and 4%, respectively) and one snapshot under zero external load (after unloading from a total strain of 4%) are shown. It becomes evident, that pure MD straining results in a plastic deformation, which is reversible under unloading. This is not observed for the case, where local relaxation is carried out. Analysis and visualization were carried out, using OVITO. 40
Total irreversible strain measured after unloading as a function of the total strain for various testing conditions and the two studied grain sizes. Evidently, for the case of pure MD simulations, the microstructures can be deformed to a total strain of more than 4% without any irreversible plastic strain.
Contribution of crystal slip to the irreversible strain for various testing conditions and the two studied grain sizes. The contribution by dislocation processes to the irreversible plastic strain decreases as local relaxation is accounted for.
Snapshots and stress-strain behavior of nc Pd–Au 50% with a microstructure, where several GBs were initially aligned and which are known to deform by stress coupled GB motion. 52 The case of conventional MD (noMC) is compared with straining, where local relaxation is accounted for by the MC algorithm with a swap fraction of 1.0 and a ΔMC of 10. Color coding for the microstructures is such, that white atoms belong to the grain interior, black atoms to the GB and gray atoms are neighboring a stacking or twinning fault (according to Common Neighbor Analysis 38 ). The gradient color scheme shows the local atomic concentration as the average site occupancy during the MC trial exchanges. Local relaxation reduces the stress for the onset of normal GB motion. From the snapshots it can be furthermore seen that local relaxation mobilizes the concentration gradient in the GBs. Visualization was carried out using OVITO. 40
Tensile testing conditions and the according labels. Swap fraction denotes the fraction of atoms in the system which is treated during one step by the MC algorithm. ΔMD is the number of MD steps, carried out between two successive (partial) MC steps (see text).
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