Compensation effects in thermionic electron emission

Abstract

It could be demonstrated that, as in the case of thermionic ion emission [Pederson and Vanselow, Surface Sci. 135 (1983) 553; Vanselow and Pederson, Surface Sci. 140 (1984) 123], thermionic electron emission can be described by j = ∗j exp(φ/k ∗T) exp(− φ/kT) , where j is the current density, ∗ j and ∗ T are the isokinetic coordinates ( ∗ T  isokinetic tempera-ture), and φ is the work function. This description is subject to the usual assumptions as to the nature of work function and reflection coefficient. Using the experimentally determined (apparent) Richardson constant, A a, and work function, φ a, one obtains ln A a = 2.69 − 2.5 ln ∗T + α k dφ dT + φ a k ∗T . The latter is of the form of the classical compensation equation, which means that if the work function of a crystal face with given orientation { hkl} is altered by adsorption or by an external electric field, or if, for a given metal, clean crystal faces with different surface structures (different work functions) are considered. In A a versus φ a plots should yield straight lines. Using appropriate experimental ( A a, φ a) pairs, this dependence could indeed be verified for all above mentioned cases. The slope of such a plot allows the calculation of the corresponding isokinetic temperature, ∗ T. Using the maximum energy barrier height, φ a,max, for each homologous series, the corresponding entropy change, Δ ∗S − exp = φ a,max / ∗T , can be calculated and compared with the theoretical Sackur-Tetrode entropy, Δ ∗S − theor ( for p = ∗p = 1 dyn/cm 2, T = ∗T and G = 2) . It was found t in general, Δ ∗S − exp < Δ ∗S − theor , which may indicate an influence of the temperature dependence of the work function. However, in most cases the deviations are only about 4% and, therefore, lie within the limits of error. The entropy values are of the order of 40 eu. As to be expected, the isokinetic temperature increases with increasing φ a,max.