Work function thermionic

Another potential, mentioned in the next section, is the thermionic work function, where ei gives the work necessary to remove an electron from the highest populated level in a metal to a point outside. We can write... 

B. Volta Potentials, Surface Potential Differences, and the Thermionic Work Function... 

While field ion microscopy has provided an effective means to visualize surface atoms and adsorbates, field emission is the preferred technique for measurement of the energetic properties of the surface. The effect of an applied field on the rate of electron emission was described by Fowler and Nordheim [65] and is shown schematically in Fig. Vlll 5. In the absence of a field, a barrier corresponding to the thermionic work function, prevents electrons from escaping from the Fermi level. An applied field, reduces this barrier to 4> - F, where the potential V decreases linearly with distance according to V = xF. Quantum-mechanical tunneling is now possible through this finite barrier, and the solufion for an electron in a finite potential box gives... 

We see that the negative logarithm of field emission current varies as the Y. power of the thermionic work function x and inversely as the applied field. A more rigorous derivation leads to the same type of dependence on field and work function and is given by the Fowler-... 

Many theories of adsorption, following Langmuir, have assumed that the rate of adsorption is proportional to (1 — 0), i.e., to the fraction of the surface which is bare or not yet covered. Langmuir first proved the (1 — 0) law by measuring experimentally how the thermionic work function

changed with time as thorium reached the surface of a tungsten filament at a constant rate (10). He then assumed that tp decreased linearly with 0 and thus deduced that dd/di was proportional to (1 — 0). But this assumption has been shown to be incorrect for such cases as Cs on W, Ba on W, SrO on W, and other systems. Hence it follows that the (1 — 0) law is not valid. The experiments described above for N2 on W not only show that dQ/dt is not proportional to (1 — 0), but they show by a direct experiment that dd/dt for a constant arrival rate is independent of 0 between 0 = 0 and 1.0. 

The work function, W, is defined as the work required to remove an electron out of a metal material from the top of the energy distribution. The work function is related to the potential function , known as the thermionic work function, by... 

Fiq. XXIX-6.—Occupied energy levels for the free electron model of a metal, at the absolute zero, illustrating the relation between Wa, W%, and the thermionic work function or latent heat of vaporization of electrons. 

Lennard-Jones and Goodwin2 have, however, shown that the adsorbed atoms can be activated by collisions with the free electrons in the underlying metal there is no reason to expect a simple connexion between activation and the thermionic work function. 

In studies on electron diffraction, however,-yet another potential is considered, called the mean inner potential . The metal may be considered as a potential box, the distance of the uppermost level below the potential just outside the metal, V, the electrostatic potential already referred to, being equal to x> the thermionic work function. The lowest level (at low temperatures) is, according to the new statistics, a distance below the upper equal to [/1], where... 

Both of these quantities contain an arbitrary constant, the zero from which the potentials are measured, but differences of either the electrostatic potential or of the electrochemical potential, between two phases, are definite. The thermionic work function, x, the work required to extract electrons from the highest energy level within the phase, to a state of rest just outside the phase, is also definite and the relation between the three definite quantities fa, V, and x is given by (3.1), where is the electrochemical potential of electrons very widely separated from all other charges. The internal electric potential , and other expressions relating to the electrical part of the potential inside a phase containing dense matter, are undefined, and so are the differences of these quantities between two phases of different composition. This indefiniteness arises from the impossibility of separating the electrostatic part of the forces between particles, from the chemical, or more complex interactions between electrons and atomic nuclei, when both types of force are present. 

Thermionic work function contact potential. Representing two different metals a and jS, initially separate and each at zero electrostatic potential, by the diagram in Fig. 48 a, in which the ordinates are the energy levels of electrons, we see that the energy level of the electrons in oc is higher than that in / by the difference between the thermionic work functions, On connecting the two metals, as in Fig. 48 6, the... 

Table XVI gives recent values of the thermionic work functions for several clean metals and also (for discussion later) the accepted values of the standard electrode potential of the metal in contact with an activity molar aqueous solution of one of its salts, where the concentration is such that the activity coefficient multiplied by the molarity is unity.

Thermionic work functions, and standard electrode potentials on the... 

Langmuir,2 in considering the importance of contact potentials for electrolytic cells, pointed out in 1916 that there is a general parallelism between the thermionic work function and the standard electrode potentials. This is shown in Table XVI, where the last column gives the difference between the electrode potential, on the normal hydrogen scale, and the work function. This difference varies much less than the values of either the work function, or the electrode potentials, separately. 

As electrons are extracted from, or returned to, the metal in these types of electrodes, the thermionic work function of the electrode material is of importance to the single potential difference between the metal and the solution. But this does not provide a means of estimating the magnitude of the work of extraction of electrons, since as was pointed out by Butler, Hugh, and Hey,1... 

Readers of Gurney s paper in 1931 have sometimes considered, from the frequent appearance of the thermionic work function in this paper, that the values of over-potential should, on the theory that the block lies at (9), depend on g. This does not appear to be justified although electrons have to be extracted from the metal, they do also in a reversible electrode, and in either case the x 8 cancel out, as described at the end of 4, through a second contact potential elsewhere in the circuit. A glance at the figures for overpotential on p. 324 shows no correlation with x> from Table XVI. 1 Z. phyrikal. Chem., 113, 213 (1924). 

The electronic work function, or thermionic work function, generally exprassed in volts, is a measure of the amount of energy required to remove an electron from the metal — is, therefore, the free energy change, in electron-volts, accompanying the return of the z electrons to the metal. 

The average energy required to remove an electron from the interior of a metal to a state of rest in a vacuum outside is the thermionic work function w,... 

TABLE 5.7. Thermionic Work Functions of Several Metals... 

The electron flux leaving the surface increases with increasing temperature and decreasing work function. Thermionic emission is the method used most frequently to produce electron beams. Table 5.7 gives the thermionic work function of several materials. Barium and its compounds (oxide and silicate) and cesium are used most frequently as cold cathodes, since large electron currents may be obtained from their surfaces even at low temperatures because of their work functions. 

Energy contours of metal-semiconductor contacts, (a) Electron loss by semiconductor, in the presence of surface states (b) electron gain by semiconductor, in the absence of surface states, n-type material.

[Pg.314]

The energy required to transfer an equivalent of electrons from one metal to another is evidently given by the difference between their thermionic work functions. Thus, if (p is the thermionic work function of metal 1 and ( that of metal 2, the energy required to transfer eleetrons from I to 2 per equivalent is... 

The greater the thermionic work function of a metal, the greater is the affinity for electrons. Thus electrons tend to move from one metal to another in the direction in which energy is liberated. This tendency is balanced by the setting up of a potential difference at the junction. When a current flows across a metal junction, the energy required to carry the electrons over the potential difference is provided by the energy liberated in the transfer of electrons from the one metal to... 

It should be noted that the thermionic work function is really an energy change and not a reversible work quantity and is not therefore a precise measure of the affinity of a metal for electrons. When an electric current flows across a junction the difference between the energy liberated in the transfer of electrons and the electric work done in passing through the potential difference appears as heat liberated at the junction. This heat is a relatively small quantity, and the junction potential difference can be taken as approximately equal to the difference between the thermionic work functions of the metals. 

Moreover, when a charged particle (ion or electron) is transferred from the vacuum to the interior of the phase, work has to be done (or is gained) and this work is in principle accessible to measurement for instance in the form of the thermionic work function of metals ... 

---