The Thermionic Work Function of Tungsten

Abstract

Measurements of the Thermionic Work Function of Pure Tungsten have been made by two methods for the same segment of a uniformly heated filament simultaneously. The filament, of diameter 0.0755 mm. and with three finer tungsten leads welded to it 3.85 cm. apart, was kept stretched, by means of a molybdenum spring, between two molybdenum plates used to apply an electric field and to receive the space current, the ends of the filament being surrounded by guard boxes to limit the emission to the section of the filament between the potential leads. All parts were sealed inside a tube and so thoroughly out-gassed by alternately baking the tube and heating the metal parts that the residual pressure during the measurements was only about ${10}^{\ensuremath{-}7}$ mm., as measured with an ionization manometer. (1) In the calorimetric method, the equivalent voltage of the work function was computed from the relation $\ensuremath{\phi}=\frac{2EI(\frac{\ensuremath{\Delta}E}{i})}{(E\ensuremath{-}\frac{\mathrm{IdE}}{\mathrm{dI}})}$, where $E$ is the voltage across the segment and $I$ the current through it, and $\ensuremath{\Delta}E$ is the voltage change when the space current $i$ flows from the filament, $I$ being kept constant. Since $\ensuremath{\Delta}E$ was only from ${10}^{\ensuremath{-}3}$ to ${10}^{\ensuremath{-}4}$ times $E$, special precautions had to be taken to measure it with sufficient accuracy and to keep $I$ sufficiently constant. Observations from 2070\ifmmode^\circ\else\textdegree\fi{} K. to 2300\ifmmode^\circ\else\textdegree\fi{} K. show an apparent increase for $\ensuremath{\phi}$ of about 2 per cent. in this range, considerably greater than is to be expected theoretically. At 2270\ifmmode^\circ\else\textdegree\fi{} K., when correction is made for the asymmetry of the electric shielding (- 2.24 per cent.) and for the radiation from the plates heated by the space current (+ 4.12 per cent.), $\ensuremath{\phi}$ comes out 4.91 \ifmmode\pm\else\textpm\fi{}.05 volts. (2) In the temperature variation method, assuming Richardson's equation $log i=\mathrm{const}.+\frac{1}{2} log T\ensuremath{-}\frac{\ensuremath{\phi}e}{\mathrm{kT}}$, measurements of the emission in the range 1930\ifmmode^\circ\else\textdegree\fi{} to 2300\ifmmode^\circ\else\textdegree\fi{} K. give for $\ensuremath{\phi}$ the values 4.87 or 4.78 volts according as the temperature scale of Langmuir or that of Worthing and Forsythe is adopted. The latter scale is probably more reliable but gives a value of $\ensuremath{\phi}$ 2.7 per cent. less than the value obtained calorimetrically, a difference believed to be greater than the probable error of the measurements.Suggested Modification of the Theory of Conduction of Electricity in Metals.---The thermal energy of conduction electrons is supposed to be $\frac{3}{2kT}$ by the classical theory upon which the above computations of $\ensuremath{\phi}$ are based. If, however, the energy is taken to be practically zero then the same data lead to 4.52 and 4.48 volts for the values of $\ensuremath{\phi}$ by the two methods and the agreement is within the probable error of the measurements.