Modeling compositional changes in binary solid solutions under ion bombardment: Application to the ${\mathrm{Ar}}^{+}$ bombardment of MgAl alloys

A model is presented which describes the steady state composition-depth profile developing in the surface adjacent region of a binary solid solution under continuous ion bombardment as a function of the bulk alloying content and the type and kinetic energy of the incident ions. To this end, the combined processes of preferential sputtering and bombardment-enhanced Gibbsian segregation are considered, while accounting for the depth and concentration dependence of the vacancy-enhanced diffusion coefficient in the solid. The model was applied to ${\mathrm{Ar}}^{+}$ bombardment of Mg-based MgAl alloys for various bulk Al contents $(2.63–7.31\mathrm{at.}\%)$ and various incident ${\mathrm{Ar}}^{+}$ ion energies $(0.1–3\mathrm{keV})$. Very good agreement was obtained between the calculated, steady state Al concentration-depth profiles and the “as-measured” ones as determined experimentally by Auger electron spectroscopy, angle-resolved x-ray photoelectron spectroscopy, and ion scattering spectroscopy.

Figure 1

Optimized values for (a) the fit parameter $\alpha$ and (b) the fit parameter $\beta$ both as a function of the incident ${\mathrm{Ar}}^{+}$ ion energy $E_{{\mathrm{Ar}}^{+}}$ and (c) the fit parameter $\chi$ as a function of the Al bulk concentration $C_{\mathrm{Al}}^{\infty }$ each for continuous ${\mathrm{Ar}}^{+}$ bombardment of MgAl alloys of various compositions.

Figure 2

Experimental $⟨C_{\mathrm{Al}}^{\exp }⟩$ (solid markers) and calculated $⟨C_{\mathrm{Al}}^{\mathrm{cal}}⟩$ (open markers) Al concentrations as a function of the incident ion energy $E_{{\mathrm{Ar}}^{+}}$ (AES) and the escape depth ${\lambda }_{\mathrm{Mg}}^{\mathrm{eff},\mathrm{Mg}\mathrm{Al}}\cos \theta$ (for the different techniques, with ISS pertaining to zero escape depth, see Sec. 4A) as determined for the steady state of ${\mathrm{Ar}}^{+}$ bombardment of MgAl alloys with an Al content of $2.63\mathrm{at.}\%$ [(a) and (b)], $5.78\mathrm{at.}\%$ [(c) and (d)], and $7.31\mathrm{at.}\%$ [(e) and (f)]. The experimental Al concentrations, as determined using AES for the KLL and LVV peaks, are plotted as a function of $E_{{\mathrm{Ar}}^{+}}$ for the respective alloy compositions in (a), (c), and (e). The “as-measured” Al concentrations, as determined using AES, AR-XPS, and ISS, are presented as a function of the escape depth for $E_{{\mathrm{Ar}}^{+}}=1\mathrm{keV}$ for the respective alloy compositions in (b), (d), and (f).

Figure 3

Calculated steady state Al concentration-depth profile for the Mg $7.31\mathrm{at.}\%$ Al alloy under continuous ${\mathrm{Ar}}^{+}$ bombardment for various incident ion energies $E_{{\mathrm{Ar}}^{+}}$. Note that the composition of the first atom layer at the alloy surface is independent of $E_{{\mathrm{Ar}}^{+}}$, since it is only determined by the preferential sputtering [see Eq. (5b), Sec. 2].

Figure 4

Calculated steady state vacancy concentration-depth profile for the Mg $2.63\mathrm{at.}\%$ Al alloy under continuous ${\mathrm{Ar}}^{+}$ bombardment for various incident ion energies $E_{{\mathrm{Ar}}^{+}}$.

Figure 5

The depth where the vacancy concentration has fallen to a value below 5% of its maximum concentration value $z_v^{\max }$ as determined from the vacancy concentration-depth profiles determined by fitting to the experimental concentration values (엯) and as determined by Monte Carlo simulations using the SRIM software (Ref. 34) (▵), both as a function of the incident ${\mathrm{Ar}}^{+}$ ion energy $E_{{\mathrm{Ar}}^{+}}$ for the Mg $5.78\mathrm{at.}\%$ Al alloy.