The Electron Emission from Thoriated Tungsten Filaments

Electron emission from tungsten filaments containing thoria.---Ten years ago the erratic behavior of some tungsten filaments was traced to the thoria present and it was discovered that by suitable treatment the filaments, containing 1 to 2 per cent of thoria, could be activated so as to give an electron emission many thousand times that of a pure tungsten filament at the same temperature. Extensive series of experiments have led to the conclusions summarized in this paper. The increased emission is due to a layer of Th atoms absorbed on the surface of the tungsten. To form this layer, the thorium oxide which originally exists throughout the volume of the filament, must first be reduced in part, by heating for a few seconds to between 2600\ifmmode^\circ\else\textdegree\fi{} and 2800\ifmmode^\circ\else\textdegree\fi{} K; then, by heating for some time at a suitable activating temperature ${T}_{a}$ = 2000\ifmmode^\circ\else\textdegree\fi{} to 2100\ifmmode^\circ\else\textdegree\fi{} K, some of the Th atoms are brought to the surface by diffusing faster than they evaporate, the fraction of the surface covered $\ensuremath{\theta}$, increasing to a limit ${\ensuremath{\theta}}_{\ensuremath{\infty}}$ which may or may not be 1. The activity determined at a lower testing temperature ${T}_{t}={1400}^{\ensuremath{\circ}} \mathrm{to} {1500}^{\ensuremath{\circ}}$ K, increases logarithmically with $\ensuremath{\theta}$; for any filament it remains constant provided the filament is not heated above 1900\ifmmode^\circ\else\textdegree\fi{} K and the film is not allowed to be oxidized. It is evident that the rate of activation $\frac{d\ensuremath{\theta}}{\mathrm{dt}}$ depends directly on the difference between the rate of diffusion to the surface and the rate of evaporation from the surface. Rate of diffusion of Th atoms to the surface is $\mathrm{DG}$ where $G$ is the concentration gradient (atoms per ${\mathrm{cm}}^{4}$) of Th atoms near the surface, and $D$ is the coefficient of diffusion. If ${N}_{0}$ is the number of Th atoms per unit area for a saturated film, it seems probable, from the crystal structures of Th and W, that ${N}_{0}$ is only half the number of tungsten atoms in the surface; and making correction for the increased surface due to the dodecahedral structure (6 per cent), ${\mathrm{N}}_{0}$ is taken as 0.756\ifmmode\times\else\texttimes\fi{}${10}^{15}$. A mathematical analysis of the experimental results gives for the absolute value of $D$ (${\mathrm{cm}}^{2}$ per sec.): ${log}_{10}\mathrm{D}=.044\ensuremath{-}\frac{20540}{T}$, in agreement with a theoretical expression given by Dushman and Langmuir. Rate of normal evaporation of Th atoms from a partly covered tungsten surface ($\ensuremath{\theta}=.2 \mathrm{to} .8$) in atoms per ${\mathrm{cm}}^{2}$ per sec. is given by: ${log}_{10}{E}_{\mathrm{nm}}=31.43\ensuremath{-}\frac{44500}{T}$. As the surface covered decreases below.2, ${E}_{n}$ decreases but not as fast as $\ensuremath{\theta}$, while for values of $\ensuremath{\theta}$ above.8, ${E}_{n}$ increases to a value three times ${E}_{\mathrm{nm}}$. The small variation of ${E}_{n}$ with $\ensuremath{\theta}$ shows that the effect of adjacent Th atoms is small. Studies of the effect of prolonged activation of filaments indicate that the surface film is never more than one atom thick. Since the atoms do not diffuse back into the tungsten, we must suppose that when a Th atom diffusing to the surface arrives below another Th atom, one Th atom immediately evaporates. The rate of induced evaporation depends upon the diffusion and upon $\ensuremath{\theta}$, experiments showing that ${E}_{i}=DG(0.82\ensuremath{\theta}+.18{\ensuremath{\theta}}^{3})$. The rate of activation is, then, given by: $\frac{{N}_{0}d\ensuremath{\theta}}{\mathrm{dt}}=DG\ensuremath{-}{E}_{n}\ensuremath{-}{E}_{i}=DG(1\ensuremath{-}0.82\ensuremath{\theta}\ensuremath{-}.18{\ensuremath{\theta}}^{3})\ensuremath{-}{E}_{n}$. The experimental curves, however, correspond almost equally well to the simple expression: $\frac{d\ensuremath{\theta}}{\mathrm{dt}}=k({\ensuremath{\theta}}_{\ensuremath{\infty}}\ensuremath{-}\ensuremath{\theta})$, when ${\ensuremath{\theta}}_{\ensuremath{\infty}}$ is the limiting value, at which the diffusion and evaporation are balanced. Deactivation occurs when the evaporation exceeds the diffusion. The concentration gradient $G$ depends, of course, on the previous history of the filament, especially the preliminary reduction of thoria at a high temperature. The rate of reduction of thoria is given by: ${log}_{10}{p}_{r}=27.98\ensuremath{-}\frac{30160}{T}$, where ${p}_{r}$ is the number of atoms of thorium produced per sec. per ${\mathrm{cm}}^{3}$; the limiting concentration gradient (atoms per ${\mathrm{cm}}^{4}$) reached is given by: ${log}_{10}{G}_{r}=25.22\ensuremath{-}\frac{9620}{T}$, the actual concentrations of thorium in parts per million by weight varying from 1.4 to 200 for temperatures of 1800\ifmmode^\circ\else\textdegree\fi{} to 3000\ifmmode^\circ\else\textdegree\fi{} K. Various properties of thoriated filaments in a steady state are summarized in Table VIII.Energy changes for atoms of thorium, per gram atom, computed from constants in the above equations are: (1) Heat of reduction of thoria in tungsten = -138,000 cal. (absorbed); (2) Heat of evaporation of Th from tungsten = 204,000 cal.; (3) Heat of diffusion of Th through tungsten: 94,000 cal.Crystal structure of tungsten and chromium.---Both are body-centered cubic and when etched show rhombic dodecahedron faces (110). Both show pronounced cubic cleavage (100).