Effective Work Functions of the Elements

Abstract

As a much-enriched supplement to the previous review paper entitled the “Effective work functions for ionic and electronic emissions from mono- and polycrystalline surfaces” [Prog. Surf. Sci. 83 (2008) 1–165], the present monograph summarizes a comprehensive and up-to-date database in Table 1, which includes more than ten thousands of experimental and theoretical data accumulated mainly during the last half century on the work functions (${\varphi }^{+}$, ${\varphi }^e$ and ${\varphi }^{-}$) effective for positive-ionic, electronic and negative-ionic emissions from mono- and polycrystalline surfaces of 88 kinds of chemical elements (₁H–₉₉Es), and also which includes the main experimental condition and method employed for each sample specimen (bulk or film) together with 490 footnotes. From the above database originating from 4461 references published to date in the fields of both physics and chemistry, the most probable values of ${\varphi }^{+}$, ${\varphi }^e$ and ${\varphi }^{-}$ for substantially clean surfaces are statistically estimated for about 600 surface species of mono- and polycrystals. The values recommended for ${\varphi }^e$ together with ${\varphi }^{+}$ and ${\varphi }^{-}$ in Table 2 are much more abundant in both surface species and data amount, and also they may be more reliable and convenient than those in popular handbooks and reviews consulted widely still today by great many workers, because the latter is based on less-plentiful data on ${\varphi }^e$ published generally before $\sim$1980 and also because it covers no value recommended for ${\varphi }^{+}$ and ${\varphi }^{-}$. Consequently, Table 1 may be more advantageous as the latest and most abundant database on work functions (especially ${\varphi }^e$) for quickly referring to a variety of data obtained under specified conditions. Comparison of the most probable values of ${\varphi }^e$ recommended for each surface species between this article and other literatures listed in Tables 2 and 3 indicates that consideration of the recent work function data accumulated particularly during the last $\sim$40 years is very important for correct analysis of these surface phenomena or processes concerned with either work function or its changes. On the basis of our simple model about the work function of polycrystal consisting of a number of patchy faces (1–i) having each a fractional area (F${}_i$) and a local work function (${\varphi }_i$), its values of both ${\varphi }^{+}$ and ${\varphi }^e$ are theoretically calculated and also critically compared with a plenty of experimental data. In addition, the “polycrystalline thermionic work function contrast” ($\Delta {\varphi }^{\ast }\equiv {\varphi }^{+}-{\varphi }^e$) well-known as the thermionic peculiarity inherent in every polycrystal is carefully analyzed as a function of the degree of monocrystallization (${\delta }_m$) corresponding to the largest (F${}_m$) among F${}_i$’s (Tables 4–6 and Fig. 1), thereby yielding the conclusions as follows: (1) $\Delta {\varphi }^{\ast }$ $\simeq$ const (>0) holds for the generally called “polycrystalline” surfaces (usually ${\delta }_m$ < 50%), (2) $\Delta {\varphi }^{\ast }$ ranges from $\sim$0.3 eV (Pt) to 0.7 eV (Nb) depending upon the polycrystalline surface species, (3) in the case of the “submonocrystal” (50 < ${\delta }_m$ < 100%) tentatively named here, $\Delta {\varphi }^{\ast }$ decreases parabolically down to zero as ${\delta }_m$ increases from $\sim$50% up to 100% (monocrystal), (4) $\Delta {\varphi }^{\ast }=0.0\mathrm{eV}$ applies to a clean and smooth monocrystalline surface (${\delta }_m$ $\approx$ 100%) alone, (5) regarding negative ion emission, on the other hand, our theoretical prediction of $\Delta {\varphi }^{\mathrm{\ast \ast }}\equiv {\varphi }^{-}-{\varphi }^e=0.0\mathrm{eV}$ is experimentally verified to hold for any surface species under any surface conditions (Table 7), (6) every polycrystal (usually, ${\delta }_m$ < 50%) may be concluded in general to have a unique value of ${\varphi }^e$ characteristic of its species with little dependence upon ${\delta }_m$, (7) this conclusion affords us first a sound basis for supporting theoretically the experimental fact (Table 2) that every species of polycrystal has a nearly constant value of ${\varphi }^e$ as well as ${\varphi }^{+}$ (usually within the uncertainty of $\pm$0.1 eV) depending little upon the difference in the surface components (F${}_i$ and ${\varphi }_i$) among specimens so long as ${\delta }_m$ < 50%, (8) on the contrary to polycrystal (${\delta }_m$ < 50%), any submonocrystal (50 < ${\delta }_m$ < 100%) has such an anomaly that it does not possess the unique value of work function characteristic of the surface species itself, because its ${\varphi }^e$ as well as ${\varphi }^{+}$ changes considerably depending upon ${\delta }_m$, (9) consequently, submonocrystal must be taken as another type (category) different from both poly- and monocrystals, (10) in this way, ${\delta }_m$ acts as the key factor mainly governing the work functions in the different mode between poly- and submonocrystals with ${\delta }_m$ lower and higher than the “critical point” of 50%, respectively, (11) on the contrary to ${\delta }_m$, ${\varphi }_m$ belonging to ${\delta }_m$ has a differential effect on both ${\varphi }^{+}$ and ${\varphi }^e$, but their values remain nearly constant so long as ${\delta }_m$ < 50% and, thus interestingly, (12) the complicate governance of ${\varphi }^{+}$ and ${\varphi }^e$ by both ${\delta }_m$ and ${\varphi }_m$ and also the anomaly of submonocrystal (cf. (8) above) observed first by our theoretical analysis may be considered as a new contribution to the work function studies developed to date. Together with brief comments and experimental conditions, typical data on ${\varphi }^e$ and/or ${\varphi }^{+}$ are summarized from the various aspects of (1) examination of the work function dependence upon the surface atom density of low-Miller-index monocrystals of typical metals such as Al, Ni, W and Re (Table 8), (2) demonstration of the above dependence usually called the “anisotropic work function dependence sequences” of both ${\varphi }^e$(110) > ${\varphi }^e$(100) > ${\varphi }^e$(111) and ${\varphi }^{+}$(110) > ${\varphi }^{+}$(100) > ${\varphi }^{+}$(111) for various bcc-metals (e.g., Nb, Mo, Ta and W) exactly obeying the Smoluchowski rule (Table 9), (3) substantiation of both ${\varphi }^e$(111) > ${\varphi }^e$(100) > ${\varphi }^e$(110) for a variety of fcc-metals (except Al and Pb) and ${\varphi }^{+}$(111) > ${\varphi }^{+}$(100) > ${\varphi }^{+}$(110) for Ni strictly following the above rule (Table 10), (4) verification of the quantitative relations between work function and surface energy and also melting point of the three low index planes of several metals (typically, Ni), (5) examination of the work function change ($\Delta {\varphi }^e$) due to allotropic transformation from $\alpha$ to $\beta$ or $\beta$ to $\gamma$ phase (Table 11) together with a concise outline of the Burgers orientation relationship, (6) evaluation of $\Delta {\varphi }^e$ due to liquefying (Table 12), (7) estimation of $\Delta {\varphi }^e$ due to transformation from ferro- to paramagnetic state (Table 13) in addition to a brief description of the Curie point dependence upon metastable metal film thickness above one monolayer, (8) estimation of $\Delta {\varphi }^e$ due to transition from normal to superconducting state (Table 14), (9) study of the work function dependence on the Wigner–Seitz radius and also comparison between its theoretical values (by Kohn) and experimental data (Fig. 2), (10) inspection of the annealing effect on work function for layers or films, (11) verification of the coincidence of work function values among different experimental methods, and (12) inquisition of the work function dependence upon the size of fine particles ($\sim$20–100 Å in radius) studied by theory and experiment.