lindhard/ion/stopping/
bragg.rs

1//! Bragg additivity for compounds and mixtures.
2//!
3//! W. H. Bragg and R. Kleeman, Phil. Mag. 10, 318 (1905): the stopping cross
4//! section of a compound is the atom-fraction-weighted sum of the element
5//! cross sections,
6//!
7//! `S_compound (per average atom) = Σ_j x_j S_j`,
8//!
9//! so `-dE/dx = N Σ_j x_j S_j · f`, with `N` the total atom density and `f` a
10//! per-compound correction factor ([`CompoundCorrection`]; default 1) as a hook
11//! for chemical/phase corrections (e.g. cores-and-bonds) supplied by the caller
12//! from a cited source.
13
14use super::{ElectronicStopping, Ion, StoppingError};
15use crate::material::Material;
16
17/// Per-compound correction factor applied to the Bragg sum.
18pub trait CompoundCorrection {
19    /// Multiplicative factor at the given ion energy. Must be finite and
20    /// non-negative (zero is allowed); [`bragg_cross_section_per_atom`] rejects
21    /// anything else with [`StoppingError::InvalidParameter`].
22    fn factor(&self, material: &Material, ion: &Ion, energy_ev: f64) -> f64;
23}
24
25/// No correction: factor exactly 1.
26#[derive(Debug, Clone, Copy, Default)]
27pub struct NoCorrection;
28
29impl CompoundCorrection for NoCorrection {
30    fn factor(&self, _: &Material, _: &Ion, _: f64) -> f64 {
31        1.0
32    }
33}
34
35/// An energy-independent constant factor.
36#[derive(Debug, Clone, Copy)]
37pub struct ConstantCorrection(pub f64);
38
39impl CompoundCorrection for ConstantCorrection {
40    fn factor(&self, _: &Material, _: &Ion, _: f64) -> f64 {
41        self.0
42    }
43}
44
45/// Stopping cross section per average atom of `material`, J m²
46/// (`f · Σ_j x_j S_j`).
47pub fn bragg_cross_section_per_atom(
48    model: &dyn ElectronicStopping,
49    correction: &dyn CompoundCorrection,
50    ion: &Ion,
51    material: &Material,
52    energy_ev: f64,
53) -> Result<f64, StoppingError> {
54    let mut sum = 0.0;
55    for c in material.components() {
56        sum += c.atom_fraction() * model.stopping(ion, c.z(), energy_ev)?;
57    }
58    let factor = correction.factor(material, ion, energy_ev);
59    if !(factor.is_finite() && factor >= 0.0) {
60        return Err(StoppingError::InvalidParameter {
61            name: "compound_correction",
62            value: factor,
63        });
64    }
65    Ok(factor * sum)
66}
67
68/// Linear stopping power `-dE/dx`, J/m: `N` times
69/// [`bragg_cross_section_per_atom`].
70pub fn bragg_stopping_power(
71    model: &dyn ElectronicStopping,
72    correction: &dyn CompoundCorrection,
73    ion: &Ion,
74    material: &Material,
75    energy_ev: f64,
76) -> Result<f64, StoppingError> {
77    Ok(material.atom_number_density()
78        * bragg_cross_section_per_atom(model, correction, ion, material, energy_ev)?)
79}
80
81#[cfg(test)]
82mod tests {
83    use super::super::lindhard_scharff::LindhardScharff;
84    use super::*;
85
86    #[test]
87    fn single_element_equals_element_stopping_exactly() {
88        let m = LindhardScharff::new();
89        let ion = Ion::new(15).unwrap();
90        let si = Material::from_atom_fractions(&[(14, 1.0)], None).unwrap();
91        let want = m.stopping(&ion, 14, 3.0e4).unwrap();
92        let got = bragg_cross_section_per_atom(&m, &NoCorrection, &ion, &si, 3.0e4).unwrap();
93        assert_eq!(got.to_bits(), want.to_bits());
94    }
95
96    #[test]
97    fn sio2_is_hand_weighted_sum() {
98        let m = LindhardScharff::new();
99        let ion = Ion::new(5).unwrap();
100        let sio2 = Material::from_atom_fractions(&[(14, 1.0), (8, 2.0)], Some(2200.0)).unwrap();
101        let e = 2.0e4;
102        let (s_si, s_o) = (
103            m.stopping(&ion, 14, e).unwrap(),
104            m.stopping(&ion, 8, e).unwrap(),
105        );
106        let hand = (s_si + 2.0 * s_o) / 3.0;
107        let got = bragg_cross_section_per_atom(&m, &NoCorrection, &ion, &sio2, e).unwrap();
108        assert!((got / hand - 1.0).abs() < 1e-14);
109        let p = bragg_stopping_power(&m, &NoCorrection, &ion, &sio2, e).unwrap();
110        assert!((p / (sio2.atom_number_density() * hand) - 1.0).abs() < 1e-14);
111    }
112
113    #[test]
114    fn correction_hook_scales() {
115        let m = LindhardScharff::new();
116        let ion = Ion::new(5).unwrap();
117        let sio2 = Material::from_atom_fractions(&[(14, 1.0), (8, 2.0)], Some(2200.0)).unwrap();
118        let a = bragg_cross_section_per_atom(&m, &NoCorrection, &ion, &sio2, 1e4).unwrap();
119        let b =
120            bragg_cross_section_per_atom(&m, &ConstantCorrection(0.9), &ion, &sio2, 1e4).unwrap();
121        assert!((b / a - 0.9).abs() < 1e-14);
122    }
123
124    #[test]
125    fn rejects_bad_compound_correction() {
126        let m = LindhardScharff::new();
127        let ion = Ion::new(5).unwrap();
128        let sio2 = Material::from_atom_fractions(&[(14, 1.0), (8, 2.0)], Some(2200.0)).unwrap();
129        for bad in [-1.0, f64::NAN, f64::INFINITY] {
130            let r = bragg_cross_section_per_atom(&m, &ConstantCorrection(bad), &ion, &sio2, 1e4);
131            assert!(matches!(
132                r,
133                Err(StoppingError::InvalidParameter {
134                    name: "compound_correction",
135                    ..
136                })
137            ));
138            let r = bragg_stopping_power(&m, &ConstantCorrection(bad), &ion, &sio2, 1e4);
139            assert!(r.is_err());
140        }
141        let z = bragg_cross_section_per_atom(&m, &ConstantCorrection(0.0), &ion, &sio2, 1e4);
142        assert_eq!(z.unwrap(), 0.0);
143    }
144
145    #[test]
146    fn bad_element_correction_propagates_through_bragg() {
147        let m = LindhardScharff::new().with_correction(8, -1.0);
148        let ion = Ion::new(5).unwrap();
149        let sio2 = Material::from_atom_fractions(&[(14, 1.0), (8, 2.0)], Some(2200.0)).unwrap();
150        assert!(matches!(
151            bragg_cross_section_per_atom(&m, &NoCorrection, &ion, &sio2, 1e4),
152            Err(StoppingError::InvalidParameter { .. })
153        ));
154    }
155}
lindhard/ion/stopping/bragg.rs

lindhard/ion/stopping/
bragg.rs
