Great question! You’re already off to a strong start with the Matsunami-Yamamura modified Sigmund formula—this is the go-to model for single-element targets. But composites introduce multi-component interactions that single-element models don’t account for, so we need to adapt this framework. Here are the most practical approaches:

1. Rule of Mixtures (ROM) #

This is the simplest and most widely used approximation, assuming the composite’s sputtering yield is a weighted average of its individual components' yields, weighted by atomic fraction:
$$Y_{comp}(E) = \sum_{i=1}^{n} f_i Y_i(E)$$
Where:

• $f_i$ = atomic fraction of the $i$-th component in the composite
• $Y_i(E)$ = sputtering yield of the $i$-th pure element, calculated using the Matsunami-Yamamura formula you referenced

This works best for mechanically mixed composites with no strong inter-component bonding (e.g., simple powder blends).

2. Modified Rule of Mixtures (for Interacting Components) #

If your composite has chemical bonding or significant atomic interactions (like alloys or compounds), you’ll need to add interaction correction factors:
$$Y_{comp}(E) = \sum_{i=1}^{n} f_i Y_i(E) \cdot \beta_{ij}$$
Here, $\beta_{ij}$ is a correction term for interactions between component $i$ and $j$. These factors are usually determined experimentally or via molecular dynamics simulations, as they vary widely by material system.

3. Extended Sigmund Model for Composites #

You can directly extend the original Sigmund formula by using average composite properties instead of single-element values:

• Average atomic number: $\bar{Z} = \sum_{i=1}^{n} f_i Z_i$
• Average atomic mass: $\bar{M} = \sum_{i=1}^{n} f_i M_i$
• Average surface binding energy: $\bar{U_0} = \sum_{i=1}^{n} f_i U_{0i}$

Plug these into your existing formula:
$$Y_{comp}(E)=\frac{3.56}{\bar{U_0}} \frac{\bar{Z} Z_p}{\sqrt{\bar{Z}^{2/3} + Z_p^{2/3}}} \frac{M_p}{\bar{M}+M_p} \alpha(\bar{M}/M_p) S_n(E/E_{tp})$$

And to fill in the missing $\alpha(x)$ correction coefficient you mentioned—here’s the complete form from Matsunami & Yamamura’s 1988 work:
$$\alpha(x) = \begin{cases}
1 + 0.18x^{0.5} + 0.008x^{1.5} & x \leq 1 \
1 + 0.18x^{-0.5} + 0.008x^{-1.5} & x > 1
\end{cases}$$
Where $x = M_t/M_p$ (for composites, this becomes $\bar{M}/M_p$).

4. System-Specific Empirical Models #

For common composite types (e.g., ceramic-reinforced metal matrix composites), researchers have developed empirical formulas calibrated to experimental data. These offer higher precision for their target systems but lack universal applicability. For example, models for SiC-Al composites might include terms for the reinforcement phase’s volume fraction and particle size.

Key Notes #

• All these models work best for ion energies between 100 eV and 100 keV—typical for focused ion beam (FIB) milling with Ga⁺, Ar⁺, or similar ions.
• For highly heterogeneous composites (e.g., with distinct phase separation), the rule of mixtures will have larger errors. In these cases, combine model calculations with experimental measurements or molecular dynamics simulations to refine results.

内容的提问来源于stack exchange，提问作者Pxx