Binding energy of atoms

Figure 9.15 Kinetic current density (squares) at 0.8 V for O2 reduction on supported Pt monolayers in a 0.1 M HCIO4 solution, and the calculated activation energy barriers for O2 dissociation (filled circles) and OH formation (open circles) on PtML/Au(lll), Pt(lll), PtML/ Pd(lll), and PtML/lT(lll). as a function of the calculated binding energy of atomic oxygen (BEo). The current density data for Pt(lll) were obtained fiom [Maikovic et al., 1999] and ate included for comparison. Key 1, Pt]y[L/Ru(0001) 2, Pb /bllll) 3, PtML/Rh(lH)i 4, Ptim,/ Au(lll) 5, Pt(lll) 6, PtML/Pd(lll). Surface coverage is ML O2 in O2 dissociation and ML each for O and H in OH formation. (Reproduced with permission fiom Zhang et al. [2005a].)...

In Fig. 1 there is presented the first-order shell correction of the total binding energy of atoms, cations, and anions from beryllium to calcium. As expected, the oscillating part of the energy displays minima for the atoms... 

Figure 1. The first-order shell correction SiE of the total binding energy of atoms (squares), cations (circles) and airions (triangles) from beryllium to calcium, as a function of the atomic number Z.

An attempt has also been made to derive the binding energy of atoms in clusters from a measurement of the critical energy deficit of cluster ions. For n+ cluster ions of m atom size, from consideration of Born-Haber energy cycle, the critical ion energy deficit can be easily shown to be given by100... 

One final key feature of photoelectron diffraction which is not shared by LEED or SEXAFS is the ability to exploit so-called chemical shifts in photoelectron binding energies of atoms of the same element in different structural and electronic environments to obtain chemical state specificity in the local structural information. 

But now it has been shown [cf. equation (30) above] that the binding energies of atoms are closely related to the electrostatic potential created at the nucleus by the electronic charge cloud. If we assume the unperturbed charge cloud to be that of a neutral atom (Z-1, Z— 1), then its interaction with the nucleus is increased by a factor Z/Z— 1 on adding a proton and this strongly suggests that one should form the quantity (Z,Z—1)-(Z/Z— l)i (Z—1,Z— 1). One obtains from the 1/Z expansion... 

Figure 3 The binding energy of atomic hydrogen at the 3-fold fee site on the Pd-Re surfaces as a function of the d-band center relative to the Fermi energy. (Adapted from Ref. [43].)...

Figure 4 The binding energy of atomic hydrogen at the most favorable sites on Pd-Re alloyed surfaces (a) ReML/Pd(lll), (b) PdssRegeML/PdCl 11), (c) PdeeRessMo/PdClH), (d) Pd(lll), (e) PdML/Re(0001), (f) Pd66Re33ML/Re(0001), (g) Pd33Re66ML/Re(0001), and (h) ReML/Re(0001)- (Adapted from Ref. [43].)...

Similar expressions are valid also for the concentration of vacancies in the boundary layer. The binding energy of atoms in coinciding boundary sites is somewhat lower on the average than in the LRC volume. Therefore the vacancies concentration in coincident sites is higher than in the LRC body. If one accounts for the fact that on the boundaries the concentration of nonthermal partial vacancies is high, then we may state that the diffusion of atoms by the vacancy mechanism on the boundaries is considerably higher than in LRC. 

Mass defect B) - Defined by fi = Zm( H) + Nm - m, where Z is the atomic number, m( H) is the mass of the hydrogen atom, N is the neutron number, m is the rest mass of the neutron, and is the mass of the atom in question. Thus Bc can be equated to the binding energy of the nucleus if the binding energy of atomic electrons is neglected. [1]... 

Figure 7.4 (A) Polarization curves for O2 reduction on platinum monolayers (PIml) on Ru(OOOI), lr(111), Rh(111), Au(111), and Pd(111) surfaces in 02-saturated 0.1 M HCIO4 solution on a disk electrode. The rotation rate is 1600 rpm, and the sweep rate is 20 mV s (50 mV s for R(111)) y= current density, RHE = reversible hydrogen electrode. (Reprinted with permission from Ref. 6) (B) kinetic currents (yi< square symbols) at 0.8 V for O2 reduction on the platinum monolayers supported on different single-crystal surfaces in 02-saturated 0.1 M HCIO4 solution and calculated binding energies of atomic oxygen (BEO filled circles) as functions of calculated d-band center (fd cp relative to the Fermi level) of the respective clean Pt monolayers. Labels (1) PtMi/Ru(0001),(2) RMi/lrOU). (3) PtMi/Rh(111),(4) PtMi/Au(111), (5) Pt(111), (6) PtML/Pd(111). Reprinted with permission from Ref. 22.

An important practical development in practical ah initio quantum chemistry and electrochemistry in recent years has been the application of the density-functional theory (DFT) methods for the calculation of properties of large ensembles of atoms [82-84]. This is because the classical Hartree-Fock methods are extremely time consuming when large systems are involved. DFT calculations can compute binding energies of atoms and molecules with an accuracy 10-20 kj mol , which is a reasonable first approximation. In DFT calculations, the energy of the quantum chemical system is calculated directly from a single function, the electronic density. 

Fig. 4 Kinetic currents (Jk square symbols) at 0.8 V for O2 reduction on the platinum monolayers supported on different single-crystal surfaces in a 0.1 M HCIO4 solution and calculated binding energies of atomic oxygen (BEq filled circles) as functions of calculated d-band center (Cd-ep) relative to the Fermi level of the respective clean platinum monolayersLabels. 1 PIml/ Ru(0001), 2 PtML/Ir(l 11), 3...

FIGURE 4.2 XPS spectra of a 2.4 nm thick film of PFOM on the air bearing surface of a slider. Cls spectrum (a), and Ols spectrum (b). The arrows indicate the binding energies of atoms with different chemical environments. 

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