Equilibrium solute segregation to matrix-${\theta }^{\prime }$ precipitate interfaces in Al-Cu alloys from first principles

Particular combinations of solute atoms segregated to the interface of the Al and ${\theta }^{\prime }\text{−}{\mathrm{Al}}_2\mathrm{Cu}$ in Al-Cu alloys can help stabilize ${\theta }^{\prime }$ precipitates at high temperatures. Stabilization of such precipitates is determined by a combination of thermodynamics (including driving forces for coarsening and transformation and solute segregation tendencies) and kinetic effects (including solute diffusion and interfacial mobility in the presence of interfacial solute segregation). For some alloys such as recent Al-Cu-based alloys, multiple solutes segregate in significant quantities to interfaces, and solute-solute interactions at the interface are important, with multiple types of solutes competing for similar interfacial sites. To treat this situation, we develop and apply a statistical mechanics approach to calculate the temperature-dependent equilibrium solute atoms distribution near the coherent and semicoherent interfaces between the Al matrix and the ${\theta }^{\prime }\text{−}{\mathrm{Al}}_2\mathrm{Cu}$ precipitates. The developed approach is applied to the investigation of Si, Mn, and Zr segregation at the interface, as particular combinations of these elements affect the thermal stability of the ${\theta }^{\prime }$ precipitates. We demonstrate that because Si and Mn atoms segregate on the same semicoherent interface, the presence of Si reduces the concentration of Mn solutes at the interface. Si atoms preferably occupy the first layer of the interface and compete with Mn atoms for one type of particular sites in the layer. Mn atoms preferably occupy the second layer of the semicoherent interface, and the Mn-Mn interaction plays an important role in their distribution. Zr atoms mostly segregate on one of the two nonequivalent sites of the second layer of the coherent interface. Due to symmetry properties of the coherent interface, the calculations show that the segregation Zr of atoms to this interface will likely lead to the formation of ${\mathrm{L}1}_2$ ordered ${\mathrm{Al}}_3\mathrm{Zr}$ layer.

Figure 1

Supercell used to model (a) coherent and (b) semicoherent interfaces, respectively, after Biswas et al. [21]. The semicoherent substitute atoms interactions are shown by arrows in the cross section (d). Here the same notation ${\mathrm{v}}_1$ is used for two different interaction. However, these two interaction easily can be distinguished, since, in the text, ${\mathrm{v}}_1$ is always followed by lattice site type (either 1 or 3).

Figure 2

Interfacial solute compositions in alloy (precipitate)${}_x{\left({\mathrm{matrix}}_{100-y-z}{\mathrm{Si}}_y{\mathrm{Mn}}_z\right)}_{1-x}$, where $y=0.15$ at. % and $z=0.15$ at. %, corresponding to the content for an Al 206 alloy. (a) Calculated local Si atom concentration (at. %) obtained with incorporated interaction [Fig. 1 and Table 4] presented with linear $y$-axis scale. (b) Calculated local Si atom concentration with linear $y$-axis scale, obtained by neglecting the interaction between substitution atoms; (c) the same with logarithmic $y$-axis scale. [(d)–(f)] Similar results for Mn substitute with interacting solute atoms (d) and with noninteracting [(f) and (e)], respectively.

Figure 3

Equilibrium Si [(a)–(c)] and Mn [(d)–(f)] atoms distribution at semicoherent interface in alloy (precipitate)${}_x{\left({\mathrm{matrix}}_{100-y-z}{\mathrm{Si}}_y{\mathrm{Mn}}_z\right)}_{1-x}$, where $x=7$%, $z=0.11$%, and [(a) and (d)] $y=0.8$%, [(b) and (e)] 0.1%, and [(c) and (f)] 0.01%.

Figure 4

Equilibrium Zr solute atom distribution: (a) linear $y$-axis scale obtained by incorporating interactions between Zr atoms; (b) linear $y$-axis scale, calculated with no interaction between Zr atom; and (c) the same as (b), but logarithmic $y$-axis scale.

Figure 5

The derivative of free energy change $\text{F}$ due to Zr atoms segregation with precipitates surface area $A_{\mathrm{Zr}}$ at different temperatures.