Unitary ion level

Figure 3-8 shows the unitary level of the surface ion of a semiconductor of single element Simple calculation gives the unitary ion level of the surface ion (5e of semiconductor germanium to be a. = -6.8 eV. 

Fig. 3-9. Ion levels at the surface and in the interior of a semiconductor of single element ag.= energy level of ion S ag.gQ= ion level of semiconductor aj. = unitary ion level in semiconductor interior, = unitary atom level in semiconductor interior.

It thus follows that the A ion level oa-cab) in the interior of crystalline compoimd AB is located midway between the unitary ion level a]. at lattice sites and the unitary ion level a. at interstitial sites as shown in Fig. 3-12. 

In the case in which ionic equilibrium is established between the surface and the interior, the surface ion level, qa,-, equals the interior ion level, aA.cAB>. Consequently, the unitary ion levels at the lattice and interstitial sites bend either upward or downward forming a space char ge layer in a region adjacent to the surface as shown in Fig. 3—13. When the surface A ion level, Oa+, is lower than tire interior A ion level, aA (AB A ions move from the interior to the... 

Fig. 3-1. Ionic dissociation of a gaseous molecule XY and X ion level in molecule XY t = energy, unitary X ion level (unitary chemical potential) Dxt = ionic dissociation energy of XY.

The unitary energy level of surface metal ions... 

Instead of the real potential, we may use the unitary electrochemical potential, pj,., to represent the unitary energy level of the surface metal ion as shown in Eqn. 3-8 ... 

The metal ion level at the surface is equal to the metal ion level in the metal interior, if ionic equilibrium is established between the surface and the interior of the metal phase. However, the imitary metal ion level, a, at the surface differs in general from the unitary metal ion level, aj, in the interior of the solid. The metal ion in the interior is located at a lattice site or at an interstitial site ... 

Since the concentration of kink sites ( k 10 to 10 in the molar fraction) on the metal surface is much greater than the concentration of vacant lattice sites (xy = 10 to lO in the molar fraction) in the interior, the metal ion level of a metal phase is close to the unitary level of surface metal ions a . as shown in Eqn. 3-12 and in Fig. 3-6 ... 

In Eqns. 3-15 and 3-16, Og. and aj. are the unitary levels of the ion at the surface kink site and at the interior lattice site Ug and Ug are the unitary levels of the atom at the surface kink sit and at the interior lattice site Cy and ey are the levels of the valence band edge at the surface and in the interior, respectively. The ion levels of Ug. and ag. are dependent on the hole level but the atom levels of ttg and agj are constant and characteristic of individual semiconductors. 

Since the concentration of surface kink sites is much greater ihan the concentration of lattice vacancies ( k/ v) 1, it follows from Eqn. 3-17 that the ion level cisnsc) of a semiconductor is close to the unitary level ag. of the siirface ion as shown in Eqn. 3-18 and in Fig. 3-9 ... 

Fig. 3-12. Lattice defects and ion levels of ionic compound AB (a) ionnation of a pair of ion vacancy and interstitial ion, (b) A ion levels in ionic crystals. Va = A ion vacancy A] = intoatitial A ion Oa. = A ion level = unitary A ion level at lattice sites ...

Since acetic acid is a weak add with its unitary proton level (HAc/Ac") lower than the unitary addic proton level (H30 /H20), the proton moves from the unitary occupied acidic proton level to the unitary vacant proton level of acetic acid, thereby reducing the concentration of H3O" ions toward the acetic acid. Contrastively, in strong adds such as hydrochloric add whose unitary proton level (HC1/C1 ) is higher than the unitary addic proton level, the proton moves from the occupied proton level of hydrochloric acid to the vacant level of acidic proton ( H30 /H20 ), thereby increasing the concentration of H3O ions. 

In aquatic chemistry, the unitary proton level of the proton dissociation reaction is expressed by the logarithm of the reciprocal of the proton dissociation constant i.e. p = - log K here, a higher level of proton dissociation corresponds with a lower pK. When the pKy of the adsorbed protons is lower than the pH of the solution, the protons in the adsorbed hydronium ions desorb, leave acidic vacant proton levels in adsorbed water molecules, and form hydrated protons in the aqueous solution. Fig. 9-22 shows the occupied and vacant proton levels for the acidic and basic dissociations of adsorbed hydronium ions and of adsorbed water molecules on the interface of semiconductor electrodes. 

Fig. 9-22. Unitary proton levels of hydrated and adsorbed hydronium ions (acidic proton) and of hydrated and adsorbed water molecules (basic proton) the left side is the occupied proton level (the real potential of acidic protons), and the right side is the vacant proton level. Hi/HjO) = unitary occupied proton level of adsorbed hydronium ions (acidic proton level) H20.d = unitary vacant proton level of adsorbed hydronium ions (acidic proton level) and unitary occupied proton level of adsorbed water molecules (basic proton level) OH = unitary vacant proton level of adsorbed water molecules (basic proton level) (pHi, ) = hydrated proton level at iso-electric point pR...

Assuming that an isolated gaseous ion X is at the reference zero energy level as shown in Fig. 3-1, we define the occupied energy level of X ion (the unitary X ion donor level, molecule XY by the negative ionic dissociation... 

Fig. 3-Z Energy of ionic dissociation of gaseous HCl molecules and proton levels h-= proton level fiH.ojci.D)= unitary occupied proton level (donor level) in gaseous HC(L molecules Xj4.,n-, = unitary vacant proton level (acceptor level) of gaseous Cl ions.

Figure 3—4 shows the eneigy level of surface silver ions on metallic silver, we estimate the unitary level of surface silver ions to be = - Fa = —5.84 eV referred to the standard gaseous silver ion at the outer potential of the metal phase. 

Fig. 3-6. Ions on the surface and in the interior of solids 0=occupied or vacant lattice site - surface kink site (S> = surface adsorption site = surface lattice vacancy, (f) = step plane = terrace ai = unitary level of occupied or vacant lattice site ions a = unitary level of surface kink site ions.

The unitary level of the surface ion referred to the standard gaseous ion S sTD) at the outer potential of the semiconductor is represented by the unitary real potential, Ug. (= - 7s). This unitary real potential is equivalent to the sum of the standard free enthalpy AG of sublimation of the semiconductor, the ionization energy Is of the gaseous atom S, and the electron energy sy at the upper edge level of the valence band as shown in Eqn. 3-14 ... 

Fig. 3-8. Energy for formation of the standard gaseous ions, S(Vnj), from the surface atoms of a semiconductor of single element S dGnbi = standard free enthalpy of the surface atom sublimation h = ionization energy of gaseous atoms aj. = unitary level of the surface ion = - (dGsM + /s) = unitary level of the surface atom referred to the standard gaseous ions and elections.

The ion energy level Oa. , ) consists of the unitaiy term (the unitary... 

In the same way as the acidic proton level, the unitary proton acceptor level H (OH-,A) of OH" ion is equal to the unitary proton donor level cih.chjo.d) of H2O molecule ... 

It is interesting to point out the similarity between the proton level diagram of aqueous solutions and the electron level diagram of semiconductors as shown in Fig. 3-20. The ionic dissodation energy (1.03 eV) of water molecule H2O to form an ion pair of H30 -0H is the energy gap between the imitary acidic proton level and the unitary basic proton level this may correspond to the band gap of semiconductors. The concentration product, of the addic... 

An electron spin can relax by coupling with a neighboring electron spin. Therefore, when a paramagnetic metal ion interacts with a second paramagnetic metal ion, the electron relaxation rates of the two metal ions may be dramatically affected. If Si and S2 are the two spins coupled by a scalar interaction, new spin levels will be established due to the interaction, with total S varying in unitary steps from Si — S2I to Si + S2. The energies of these spin levels are given by )... 

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