Bragg additivity

Code: lindhard/src/ion/stopping/bragg.rs (bragg_cross_section_per_atom, CompoundCorrection).

Model

The stopping cross section of a compound or mixture, per average atom, is the atom-fraction-weighted sum of the element cross sections (Bragg and Kleeman 1905):

\[ S_\mathrm{compound} = f \sum_j x_j S_j, \qquad -\frac{dE}{dx} = N f \sum_j x_j S_j, \]

with \( x_j \) the atom fractions, \( S_j \) the element cross sections from the chosen model (or a user table for that pair), \( N \) the total atom density and \( f \) a per-compound correction factor.

Selecting it

Always on: every layer’s electronic loss goes through the Bragg sum, which for a pure element is just that element’s cross section. summary.json lists it under physics.models as bragg-additivity. The CLI applies no correction (\( f = 1 \)). The library hook CompoundCorrection (a constant or energy-dependent factor, finite and non-negative) is there for chemical or phase corrections, such as cores-and-bonds schemes, supplied by the caller from a cited source.

Assumptions

• Each atom stops the ion independently of its chemical environment.

Validity

Wherever the element models apply. Bragg additivity ignores the chemical and physical state of the target, and no correction for it is applied unless one is supplied.

Verification status

The sum and the rejection of invalid correction factors are unit-tested.

References

• W. H. Bragg and R. Kleeman, Phil. Mag. 10, 318 (1905).