Work function electronic

The electronic work function in a solid is defined as the difference between the electrochemical potential d of the electrons in the solid and the electrostatic potential -qVe of the electrons in the vacuum near the surface of the solid  

Statistical thermodynamics make it possible to demonstrate that the Fermi energy Ep is equal to the partial derivative of the free enthalpy G  

Using [4.12] and [4.13], we arrive at the conclusion that the Fermi energy is equal to the electronic electrochemical potential. 

Under such conditions, the work function is the amount of energy required by an electron trapped in the solid, and whose energy is equal to the Fermi energy, in order to reach the vacuum with a zero velocity. 

The Fermi level is the highest energy level occupied by electrons at 0°K temperature the work function, as we have defined it above, therefore represents the lowest amount of energy that has to be supplied so that one of the solid s electrons is extracted without gaining kinetic energy. 

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Cesium was first produced ia the metallic state by electrolysis of a molten mixture of cesium and barium cyanides (2). Subsequentiy the more common thermochemical—reduction techniques were developed (3,4). There were essentially no iadustrial uses for cesium until 1926, when it was used for a few years as a getter and as an effective agent ia reduciag the electron work function on coated tungsten filaments ia radio tubes. Development of photoelectric cells a few years later resulted ia a small but steady consumption of cesium and other appHcations for cesium ia photosensing elements followed. 

Austritts arbeit, /. (of electrons) work function. geschwindigkeit, /. velocity of exit or discharge rate of escape, -dffnung, /. outlet, exit discharge opening steam port (of a... 

For a metal/solution interface, the pcz is as informative as the electron work function is for a metal/vacuum interface.6,15 It is a property of the nature of the metal and of its surface structure (see later discussion) it is sensitive to the presence of impurities. Its value can be used to check the cleanliness and perfection of a metal surface. Its position determines the potential ranges of ionic and nonionic adsorption, and the region where double-layer effects are possible in electrode kinetics.8,10,16... 

Owing to the rapid development of the field from an experimental point of view, and the persistence of discussions on some of the aspects outlined above, a chapter on the pzc that includes a discussion of the relation between the electrochemical and the ultrahigh vacuum (UHV) situation in reference to the conditions at the pzc seems timely. This review of the literature will not be exhaustive but selective, taking into account the compilations already existing. In any case, the objective is to evaluate the existing data in order to recommend the most reliable. Finally, the data on pzc will be discussed in comparison with electron work function values. The role and significance of work functions in electrochemistry were discussed by Trasatti6 in 1976. 

As a metal comes in contact with a liquid polar phase (a solvent), the situation can be depicted as in Fig. 2. The electron work function will be modified by A4 so that... 

According to Fig. 2, as M comes in contact with S,3 4 the electron distribution at the metal surface (giving the surface potential XM) will be perturbed X ) The same is the case for the surface orientation of solvent molecules (Xs + SXS). In addition, a potential drop has to be taken into account at the free surface of the liquid layer toward the air (xs). On the whole, the variation of the electron work function (if no charge separation takes place as assumed at the pzc of a polarizable electrode) will measure the extent of perturbation at the surfaces of the two phases, i.e.,... 

Equation (17) shows the relationship between electrode potentials and electronic energy. The electrode potential is measured by the electron work function of the metal, modified by the contact with the solution (solvent). This establishes a straightforward link, not only conceptually but also experimentally, between electrochemical and UHV situations.6,32 In many cases, electrochemical interfaces are synthesized in UHV conditions55-58 by adding the various components separately, with the aim possibly of disentangling the different contributions. While the situation can be qualitatively reproduced, it has been shown above that there may be quantitative differences that are due to the actual stmctural details. 

It has been consistently found that small amounts of Pb in Sn + Pb alloys cause an appreciable decrease in the electron work function of Sn, which is in good agreement with data for liquid Sn + Pb alloys.816-818 The surface activity of Pb has been found to increase as the temperature decreases.817,818... 

It was shown in Section I that the potential of zero charge is related to the electron work function of the electrode metal by Eq. (27) ... 

Figure 16. Plot of the potential of zero charge, Eamo, vs. the electron work function of several low-index and stepped surfaces of Au. E a0 and measured on the same...

Figure 17. Plot of the potential of zero charge, EaJi, vs. the electron work function, . The point is the most probable value. Data for E0wq from Ref. 140 for Au (111) from Ref. 25 for Pt (111) from Ref. 867.

The potential of zero charge measures, on a relative scale, the electron work function of a metal in an electrochemical configuration, i.e., immersed in a solution rather than in a vacuum. Converted to an absolute value (UHV scale) and compared with the classic electron work function of the given metal, the difference between the two quantities tells us what occurs from the local structural point of view as the metal comes in contact with the solution. 

Experiments at present are concentrated on sd-metals and Pt-group metals. The sp-metals, on which theories of the double layer have been based, are somewhat disregarded. In some cases the most recent results date back more than 10 years. It would be welcome if double-layer studies could be repeated for some sp-metals, with samples prepared using actual surface procedures. For instance, in the case of Pb, the existing data manifest a discrepancy between the crystalline system and the crystal face sequence of other cases (e.g., Sn and Zn) the determination of EgaQ is still doubtful. For most of sp-metals, there are no recent data on the electron work function. 

Therefore the absolute potential of a single electrode is its electron work function (Fig. S), which may be expressed in the form... 

Conductor-insulator and conductor-vacuum interfaces lack a continuous exchange of free charges, and there is no electrochemical equilibrium. For this reason the work that is performed in transferring charged particles from one phase to the other is not zero. The total work, X, which must be performed by the external forces in transferring (extracting) an electron from a metal (M) into vacuum (0) is called the electron work function (or simply the work function). The work function for all metals is always positive, since otherwise the electrons would leave the conductor spontaneously. 

The work function of charged particles found for a particular conductor depends not only on its bulk properties (its chemical nature), which govern parameter but also on the state of its surface layer, which influences the parameter (a) xhis has the particular effect that for different single-crystal faces of any given metal, the electron work functions have different values. This experimental fact is one of the pieces of evidence for the existence of surface potentials. The work function also depends on the adsorption of foreign species, since this influences the value of... 

Several methods exist for measuring the electron work functions of metals. In all these methods one determines the level of an external stimulus (light, heat, etc.) required to extract electrons from the metal. 

We thus reach the important conclusion that a metal s electron work function in solutions is independent of the nature of the metal when determined at the same value of electrode potential (i.e., it has identical values for all electrodes). 

Electron work functions of metals in solution can be determined by measurements of the current of electron photoemission into the solution. In an electrochemical system involving a given electrode, the photoemission current ( depends not only on the light s frequency v (or quantum energy hv) but also on the potential E. According to the quantum-mechanical theory of photoemission, this dependence is given by... 

The Volta potential between two metals is related directly to the electron work functions of these metals. Taking into account that for two metals in contact at equilibrium we have = p, and that = 1, we obtain from Eq. (9.2) ... 

Equation (9.2) can be used to calculate the metal s surface potential. The value of the electron work function X can be determined experimentally. The chemical potential of the electrons in the metal can be calculated approximately from equations based on the models in modem theories of metals. The accuracy of such calculations is not very high. The surface potential of mercury determined in this way is roughly -F2.2V. 

The values of electron work function (see Section 9.2.1) have been adduced most often when correlating electrocatalytic activities of given metals. They are situated between 3 and 5 eV. Two points were considered when selecting the electron work function as the parameter of comparison (1) it characterizes the energy of the electrons as basic, independent components of aU electrochemical reactions, and (2) it is closely related to many other parameters of metals. 

It was demonstrated, however, in 1947 by John O M. Bockris that between the exchange current densities of the hydrogen reaction at different metals and the values of the electron work function (into vacuum), a definite correfation does exist. Many workers have confirmed this correlation. An example of this correlation is shown as a plot of log f vs. X° in Fig. 28.2. 

FIGURE 28.2 Relation between the exchange current densities of hydrogen evolution and ionization at different metals and the electron work functions. 

Unlike the values of values of electron work function always refer to the work of electron transfer from the metal to its own point of reference. Hence, in this case, the relation established between these two parameters by Eq. (29.1) is disturbed. The condition for electronic equilibrium between two phases is that of equal electrochemical potentials jl of the electrons in them [Eq. (2.5)]. In Eig. 29.1 the energies of the valence-band bottoms (or negative values of the Fermi energies) are plotted downward relative to this common level, in the direction of decreasing energies, while the values of the electron work functions are plotted upward. The difference in energy fevels of the valence-band bottoms (i.e., the difference in chemical potentials of the... 

Constant A in Eqs. (29.5) and (29.6) is about 4.4 eV when the standard hydrogen electrode is used as the reference electrode. This value has been determined from experimental values for the electron work function of mercury in vacuum, which is 4.48 eV, and for the Volta potential, between the solution and a mercury electrode polarized to = 0 V (SHE), which is -0.07 V (the work of electron transfer is 0.07 eV). The sum of these two values, according to Eq. (9.8), corresponds to the solution s electron work function at this potential (i.e., to the value of constant A with an inverted sign). 

When photons are absorbed in a metal, the ensemble of electrons are excited and some of the electrons are promoted to higher energy levels. The excited state is preserved in the metal for only a short time, and the system returns rapidly to its original state. When the photon energy hv is higher than the metal s electron work function, in the solution at a given potential, individual excited electrons... 

The basic law of electron photoemission in solntions which links the photoemission current with the light s frequency and with electrode potential is described by Eq. (9.6) (the law of five halves). This eqnation mnst be defined somewhat more closely. As in the case of electrochemical reactions (see Section 14.2), not the fnll electrode potential E as shown in Eq. (9.6) is affecting the metal s electron work function in the solution bnt only a part E - / ) of this potential which is associated with the potential difference between the electrode and a point in the solntion jnst outside the electrode. Hence the basic law of electron photoemission into solntions should more correctly be written as... 

When semicondnctors are irradiated with photons of high energy, electron photoemission is possible, as in the case of metals. When the photon energy is lower than the electron work function in the solution, under given conditions, but is still higher than the semiconductor s bandgap W, ... 

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