The Richardson-Dushman equation relates the current density of a thermionic emission to the work function (W) and temperature (T) of the emitting material:

j_{s} = A T^{2} exp(-W/kT)

where

j_{s} is the current density of the emission
(mA/mm^{2})

A is Richardson's constant. A =
4*πmek^{2}/h^{3} ~ 1202
mA/mm^{2}K^{2}, where m is the mass of electron, e is
elementary charge, and h is Plank's constant. In practice, A may be
multiplied by a correction factor that depends on the material (see
Table I below).
Note that A varies from about 32 to 160 A cm^{-2} K^{-2}
for pure (polycrystalline) metals and over a much greater range
for oxide and composite surfaces.[1]

T is temperature (K)

W is the work
function of the cathode material (J or eV)

k is the Boltzmann constant (1.3806488E-23 J K-1 or 8.6173324E-5 eV K-1) [*]

In Cathode Emissions in CPO, A is treated as an empirical constant. In fact, j_{s}
may be entered directly.

Material | W (eV) | A*b (A cm^{-2} K^{-2}(b is material correction factor) |
---|---|---|

Molybdenum | 4.15 | 55 |

Nickel | 4.61 | 30 |

Tantalum | 4.12 | 60 |

Tungsten | 4.54 | 60 |

Barium | 2.11 | 60 |

Cesium | 1.81 | 160 |

Iriduim | 5.40 | 170 |

Platinum | 5.32 | 32 |

Rhenium | 4.85 | 100 |

Thorium | 3.38 | 70 |

Ba on W | 1.56 | 1.5 |

Cs on W | 1.36 | 3.2 |

Th on W | 2.63 | 3.0 |

Thoria | 2.54 | 3.0 |

BaO + SrO | 0.95 | ~10^{-2} |

Cs-oxide | 0.75 | ~10^{-2} |

TaC | 3.14 | 0.3 |

LaB_{6} | 2.70 | 29 |

theoretical: | 120.2 (b=1) |

## References

- [1] Bernhard Wolf. Handbook of ion sources. CRC Press, 1995. ISBN 0849325021, 9780849325021. p.27,11 [*]
- [2] C. J. Smithells, Metals Reference Book, Vol III, Butterworths, London, 1967, 737ff.
- [3] Wikipedia:Thermionic Emission [*]
- [4] CODATA2010 http://physics.nist.gov/cuu/index.html