Module knock_on 

Knock-on (displacement) threshold report for an electron beam.

Pure kinematics on resolved input; it needs no transport. For a beam electron of kinetic energy E hitting a free target atom of mass M at rest head on, conservation of energy and momentum gives the largest energy the atom can take (relativistic, electron rest energy mc²):

T_max = 2 E (E + 2 m c²) / (M c²)

This follows from conservation of energy and momentum for a head-on elastic collision with a heavy atom at rest (electron momentum p²c² = E (E + 2 m c²), recoil T = 2 p²c² / (M c²)); it is the form used in electron-irradiation damage work, for example F. Seitz and J. S. Koehler, Solid State Physics 2, 305 (1956) (not opened for this change; the derivation above stands on its own). It treats the atom as free and at rest and the recoil as non-relativistic (T_max << Mc²), so lattice binding, thermal motion and the crystal direction are ignored: E_d is the threshold displacement energy of the input, a damage-accounting convention, not a measured property of one direction.

An atom can be displaced when T_max >= E_d. Setting T_max = E_d and solving the quadratic in E gives the threshold beam energy:

E_th = -m c² + sqrt((m c²)² + E_d M c² / 2)

evaluated as (E_d M c² / 2) / (m c² + sqrt(...)) so that it does not cancel for small E_d / Mc².

The report says nothing about a displacement cross section or a dpa: it is a threshold test only. An element with no E_d in the input is reported with e_d_ev = None (printed “not set”); no default is invented here.

M is the atomic weight of the element (relative atomic mass) times the atomic mass unit; the electron mass difference of the atom is neglected.

Structs

KnockOnElement

The knock-on result for one element of a layer.

KnockOnLayer

The knock-on result for every element of one layer.

Functions

atom_rest_energy_ev

Rest energy M c², eV, of an atom of atomic_weight (relative atomic mass, i.e. g/mol).

electron_rest_energy_ev

Electron rest energy m c², eV.

layer_report

Knock-on report of layer layer, made of material, for a beam of beam_ev. E_d is read from the material; an element without one is reported as not set.

t_max_ev

Largest energy, eV, an electron of kinetic energy beam_ev can transfer to a free atom at rest of rest energy atom_rest_ev (see the module docs).

threshold_beam_energy_ev

Beam energy, eV, at which T_max equals e_d_ev (see the module docs).