Alkali halide crystals, /-potential

Early applications of pseudopotentials in cluster models [62,63], which dealt with impurities in alkali halide crystals, used Hartree-Fock (HF) based model potentials [64] and complete-cation norm-conserving pseudopotentials [65]. A similar technique was found valuable to describe bulk properties of alkaline-earth oxides [66-68]. A general procedure for calculating embedded clusters under the assumption of a frozen environment and orthogonality requirements for the wave function of the cluster and the environment was also discussed... 

The next phase for the theorists in connection with this work lies in predictions of helium atom scattering intensities associated with surface phonon creation and annihilation for each variety of vibrational motion. In trying to understand why certain vibrational modes in these similar materials appear so much more prominently in some salts than others, one is always led back to the guiding principle that the vibrational motion has to perturb the surface electronic structure so that the static atom-surface potential is modulated by the vibration. Although the polarizabilities of the ions may contribute far less to the overall binding energies of alkali halide crystals than the Coulombic forces do, they seem to play a critical role in the vibrational dynamics of these materials. 

The F-center is the most fundamental color center defect in the alkali halide lattice. Although it is not laser-active, the optical properties of the F-center are important in understanding the laser physics of other color center lasers. The fundamental absorption band of the F-center, called the F band, corresponds to a transition fi om the Is-like ground state to the 2p-like first excited state of the square-well potential. The F-band transition is very strong, and dominates the optical spectrum of the alkali-halide crystal. In fact, the term F-center comes fi om the German word Farbe, meaning color, and refers to the strong color imparted to the otherwise transparent alkali-halide crystals. 

Tasker [15] calculated the surface energies and surface stresses for a group of alkali halide crystals using empirical potentials similar to... 

Figure 21 Potential energy diagram of the ground and the first excited electronic states of [Ag(CN)32 (eclipsed configuration) as plotted from extended Huckel calculations. The excimer [Ag(CN)32 corresponds to the potential minimum of the excited state. The optical transitions shown are (a) excimer emission, (b) solid state excitation and (c) dilute solution absorption. (Reproduced with permission from Omary MA and Patterson HH (1998) Luminescent homoatomic exciplexes in dicyanoargentate 0) ions doped in alkali halide crystals 1. Exciplex tuning by site-selective excitation. Journal of the American Chemical Society 120 7606-7706.

Both methods for estimating x-potenlials have been applied by Verwey. Straightforward model considerations have been applied to the case of alkali halide crystals K The results appear to be rather uncertain even with respect to the sign of the x-poten-tial. Only in the case of LiF and perhaps LiCl are the crystals in all probability more positive than the surrounding vacuum and the potential drop is of the order of msngjai-tude of 1 volt. 

As we have seen, several atomic properties are important when considering the energies associated with crystal formation. Ionization potentials and heats of sublimation for the metals, electron affinities, and dissociation energies for the nonmetals, and heats of formation of alkali halides are shown in Tables 7.1 and 7.2. 

For the unit-point-charge crystal, the absolute value of the electrostatic energy is equal to the potential at the nuclear position. This potential will be equal for both ions in the alkali halide structure, as their positions are equivalent that is,... 

Dipolar ions like CN and OH can be incorporated into solids like NaCl and KCl. Several small dopant ions like Cu and Li ions get stabilized in off-centre positions (slightly away from the lattice positions) in host lattices like KCl, giving rise to dipoles. These dipoles, which are present in the field of the crystal potential, are both polarizable and orientable in an external field, hence the name paraelectric impurities. Molecular ions like SJ, SeJ, Nf and O J can also be incorporated into alkali halides. Their optical spectra and relaxation behaviour are of diagnostic value in studying the host lattices. These impurities are characterized by an electric dipole vector and an elastic dipole tensor. The dipole moments and the orientation direction of a variety of paraelectric impurities have been studied in recent years. The reorientation movements may be classical or involve quantum-mechanical tunnelling. 

Variables 2 and Zj are charges of ions i and j Ay is the Pauling factor defined as Ay = (1 + zjnx + z-Jn i, where nK and nj represent the numbers of electrons in the outermost shell of ions i and j, respectively Cy = (3/2) aiajEiEj/(Ei + Ej) and dy = (9/4e2)Cy(a, 1/Ar1 + atjE/Nj), where a denotes the polarizability of ions, N is the number of the total electrons of an ion, and E is the first ionization potential, evaluated from the Equation Ef = Nle2h2I Tr2mai for ion i, where h and m are the Planck constant and the mass of the ion, respectively. Values of p, b, and cr are estimated from isothermal compressibilities and thermal expansion coefficients of 17 rock-salt-type crystals of alkali halides by Fumi and Tosi (15). 

These processes give rise to the electronic absorption bands of lowest energy observed in the pure undamaged single crystals which occur at 7.68 eV for MgO and 6.8 eV for CaO (142). Defects within the crystal structure are associated with optical absorption bands at reduced energies [for example, the anion vacancy band in the alkali halides (143)] because of the lower Madelung potential. The energy is still absorbed by the processes described in Eqs. (27) and (28), but the exciton is now bound to a defect and is equivalent to an excited electronic state of the defect. 

The simplest examples of this type of defect are provided by the alkali halides, studied extensively by Pohl and his colleagues (2). Sodium chloride heated in sodium vapour assimilates sodium atoms, which occupy normal cation sites as TSIa+ ions, while the extra electrons are trapped in the neighbourhood of the newly-created vacant anion sites. Vacant anion sites act as centres of effective positive charge in the crystal and produce a Coulomb-like potential field capable of binding electrons. This will be discussed in more detail in 2.2. It is difficult... 

There is a long history of calculations of adsorption potentials for simple gases adsorbed on the exposed low index Miller planes of ionic crystals, especially alkali halides (see the review [26] and references therein). The total interaction potential energy between an adsorbed molecule and the surface of a solid is generally expressed as a sum of dispersion, repulsion, induction, and electrostatic contributions (see, e.g.. Ref. [27]) ... 

Expressions for the force constant, i.r. absorption frequency, Debye temperature, cohesive energy, and atomization energy of alkali-metal halide crystals have been obtained. Gaussian and modified Gaussian interatomic functions were used as a basis the potential parameters were evaluated, using molecular force constants and interatomic distances. A linear dependence between spectroscopically determined values of crystal ionicity and crystal parameters (e.g. interatomic distances, atomic vibrations) has been observed. Such a correlation permits quantitative prediction of coefficients of thermal expansion and amplitude of thermal vibrations of the atoms. The temperature dependence (295—773 K) of the atomic vibrations for NaF, NaCl, KCl, and KBr has been determined, and molecular dynamics calculations have been performed on Lil and NaCl. Empirical values for free ion polarizabilities of alkali-metal, alkaline-earth-metal, and halide ions have been obtained from static crystal polarizabilities the results for the cations are in agreement with recent experimental and theoretical work. 

There are several methods for determining ionic radii from physical characteristics of atoms and crystals. Thus, Fumi and Tosi [209] derived ionic radii (similar to the bonded ones) for alkali halides, using the Born model of crystal lattice energy with experimental interatomic distances, compressibilities and polarizabilities. Rossein-sky [210] calculated ionic radii from ionization potentials and electron affinities of atoms, his results were close to Pauling s. Important conclusions can also be drawn from the behaviour of solids under pressure. Considering metal as an assembly of cations immersed into electron gas, its compressibility at extremely high pressures... 

The location of ion cores near singular surfaces of inert gas crystals and simple ionic crystals such as the alkali halides and simple oxides (eg. MgO) has been the subject of considerable theoretical work over a long period of time. The prime reason for the theoretical interest in these materials is that many of the bulk properties can reasonably well be described using pair potentials. For the alkali halides calculations have been made of the ion positions, electronic dipoles and surface energies for some of the most closely packed surfaces, (111) and (100). A comprehensive and critical review of earlier work in this area has been given by Benson and Yun(l). 

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