Metallurgy at the nanoscale: domain walls in nanoalloys

Abstract

In binary alloys, domain walls play a central role not only on the phase transitions but also on their physical properties and were at the heart of the 70's metallurgy research. Whereas it can be predicted, with simple physics arguments, that such domain walls cannot exist at the nanometer scale due to the typical lengths of the statistical fluctuations of the order parameter, here we show, with both experimental and numerical approaches how orientational domain walls are formed in CuAu nanoparticles binary model systems. We demonstrate that the formation of domains in larger NPs is driven by elastic strain relaxation which is not needed in smaller NPs where surface effects dominate. Finally, we show how the multivariants NPs tend to form an isotropic material through a continuous model of elasticity.

Figures (14)

• Figure 1: (a) HR-STEM image of a Cu$_{50}$Au$_{50}$ NP (mean size of 8 nm) oriented along the [001] axis (top) and its global diffraction pattern (bottom) corresponding to a L1$_{2}$ phase. The numerical diffraction pattern of the areas corresponding to the NP core (blue) and sides (red and green) are presented in the right panel. Note that in the diffraction scheme, the rectangles have been slightly oversized to illustrate the tetragonality. (b) Examples of Cu$_{50}$Au$_{50}$ NPs presenting multi-domain walls. (c) Schematic representations of the with mono-(left) and multi-variants (right) L1$_{0}$ NPs where some slice views are presented. Au atoms are in yellow and Cu atoms are in brown.
• Figure 2: (a) HR-STEM image revealing the presence of a large NP with wall domains and smaller NPs of the monodomain type. (b) HR-STEM image of a Cu$_{50}$Au$_{50}$ NP (mean size of 3 nm) oriented along the [001] axis (top) and its FFT (bottom) corresponding to a L1$_{0}$ phase.
• Figure 3: Top: Equilibrium configurations of Cu-Au NPs after performing MC simulations and their local diffraction patterns. Global and cross-section views of a characteristic equilibrium configuration are presented for a NP containing (a) 6266 atoms where multivariant domains are identified and (b) 1289 atoms where monovariant domain is observed. Au atoms are in yellow and Cu atoms are in brown. Bottom: HRSTEM simulations images of the corresponding configurations imaged along the [001] zone axis for the 6266 atoms NP and [100] zone axis for the 1289 atoms NP. Diffraction patterns are given in inset.
• Figure 4: Internal stress distribution in Cu-Au NPs of different sizes. $\sigma_{xx}$, $\sigma_{yy}$, $\sigma_{zz}$ and $\sigma_{yz}$ components are plotted for 3 nm diameter NPs in panel (a) and for 6 nm diameter NPs in panel (b) for L1$_{0}$ structure and after MC relaxation.
• Figure 5: The patterns of the elastic stiffness tensor for (a), (b) and (c) corresponding to the L1$_{0}$ structures with different orientations (the $\mathbf{c}$ axis is in red) and (d) the cubic system. Only the non-zero components are indicated and equal components are connected. (e) Evolution of the $c/a$ ratio of the CuAu NP during MC simulations under heating and cooling.