Theoretical evaluation of the effective work functions for positive-ionic and electronic emissions from polycrystalline metal surfaces

Effective work functions (phi(+) and phi(e)) for positive-ionic and electronic emissions from polycrystalline metals of Nb, Mo, Ta, Wand Ir are calculated according to our theoretical model by using those published data on both fractional surface area (F(i)) and local work function (phi(i)) of each metal surface composed of several patchy faces (1, 2,..., i). Comparison between the theoretical values thus obtained and those experimental data published to date yields the conclusions as follows. (1) With a slight error of less than similar to 0.1 eV, the value of we calculated with each of the metals is in fair or good agreement with that determined by experiment. (2) Such agreement is found also with phi(+) for W. (3) In a typical case of W, where the degree of monocrystallization (delta(m)) corresponding to the largest among the values of F(i) is less than similar to 0.5, the thermionic contrast (Delta phi* equivalent to phi(+) - phi(e)) is found again to be nearly equal to both theoretical and experimental values reported previously. (4) Each of the five metals shows that Delta phi* at delta(m) = 0.68 - 0.95 is smaller than Delta phi* at delta(m) < 0.5. (5) This result strongly supports our theoretical prediction that Delta phi* decreases gradually to zero as delta(m) increases beyond similar to 0.5 up to similar to 1. (6) Particularly, such a surface which has delta(m) >= 0.96 exhibits Delta phi* approximate to 0, apparently equivalent to the so-called monocrystalline surface (delta(m) = 1)''. These results lead to the conclusion that our theoretical model is valid for evaluating the effective work functions probably with a slight error of less than similar to 0.1 eV, irrespective of both the surface species and the range of delta(m). In addition, our simple model makes it possible to analyze the mechanism of change in phi(+) and phi(e) according to the change in surface characters of both phi(i) and F(i). (C) 2008 Elsevier B.V. All rights reserved.