The Richardson-Dushman equation relates the current density of a thermionic emission to the work function (W) and temperature (T) of the emitting material:
js = A T2 exp(-W/kT)
js is the current density of the emission
A is Richardson's constant. A = 4*πmek2/h3 ~ 1202 mA/mm2K2, 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.
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, js may be entered directly.
|Material||W (eV)||A*b (A cm-2 K-2
(b is material correction factor)
|Ba on W||1.56||1.5|
|Cs on W||1.36||3.2|
|Th on W||2.63||3.0|
|BaO + SrO||0.95||~10-2|