Lattice vibrations ionic compounds

The interpretation of the lattice vibrations for scheeUte type molybdates or tungstates with relatively light cations, Ca or Sr, has indicated that the lowest translational vibrations are produced by Mo—Mo or W—W motions respectively, while those at higher frequency are from cation-cation motions 98). This has not been found, however, in the case of the barium or lead compounds. The librational frequencies have been found to decrease hnearly with the ionic radius of the cation for AMO4 type compounds, where A = Ca, Sr, Ba, or Pb and M =Mo or W 98). 

The vibrational spectra of inorganic molecular crystals of binary compounds of the type AB and AB2, as well as ionic crystals of complex anions and cations, have been studied recently under pressures up to 70 Kbar (217—219). By this technique it is possible to differentiate between internal and lattice vibrations (220) since lattice modes have a greater dependence on pressure. 

Given this description of the forces, there is no difficulty in carrying out the calculation of the full vibration spectrum for an ionic solid in the manner described in Chapter 9. At least for the compounds we have considered here the structures are sufficiently simple that the complications which arose in calculating the spectra for the mixed tetrahedral solids are not present. The elastic con.stants describe the low-frequency lattice vibrations and there is no reason to expect the description at high frequencies to be cither worse or better. (Some discussion of the vibration spectra of ionic crystals is given, for example, by Wallis, 1965 a number of properties related to anharmonicily are described by Cowley, 1971.)... 

The ionic insulators discussed in some detail in the previous section have closed shell electronic configurations similar to the noble gases and electronic distributions which are localized around the electronic core. The principal interactions are Coulombic, although their polarizabilities appear to influence greatly the response of the electronic distribution to surface lattice vibrations. For other materials, particularly metals and some layered compounds, the conduction and valence electrons are best thought of as somewhat delocalized if not entirely free. These electrons are what the helium atoms scatter from, and their states of motion are significantly modulated by the vibrations of the atomic cores. Thus, for these materials HAS is very... 

Earlier, when we were looking at molecular solids (see section 1.5.1), we saw the mixture of Debyean and Einsteinian terms in the partition function of the same solid with degrees of vibration of the lattice and degrees of vibration within the molecule. We will now make broader use of this concept, which was developed by Bom and Blackman, on the subject of ionic compounds. 

To begin with, we can accept the hypothesis that a point defect does not affect the lattice s fundamental vibration frequency, and therefore the term v in relation [3.51] does not depend on the species involved in the quasi-chemical reaction. For ionic compounds, we sometimes choose one anionic vibration frequency and one cationic frequency. Certain authors, such as Mott [MOT 38], opt instead for a half frequency for the defect. We will now examine a few examples, with the vibration frequency being kept constant and unique. 

Ionic compounds do not conduct electricity when in the solid state. This is because the ions are fixed in the lattice and can only vibrate around a fixed point. When molten, an ionic compound conducts electricity because the ions are mobile. 

In molecular crystals or in crystals composed of complex ions it is necessary to take into account intramolecular vibrations in addition to the vibrations of the molecules with respect to each other. If both modes are approximately independent, the former can be treated using the Einstein model. In the case of covalent molecules specifically, it is necessary to pay attention to internal rotations. The behaviour is especially complicated in the case of the compounds discussed in Section 2.2.6. The pure lattice vibrations are also more complex than has been described so far . In addition to (transverse and longitudinal) acoustical phonons, i.e. vibrations by which the constituents are moved coherently in the same direction without charge separation, there are so-called optical phonons. The name is based on the fact that the latter lattice vibrations are — in polar compounds — now associated with a change in the dipole moment and, hence, with optical effects. The inset to Fig. 3.1 illustrates a real phonon spectrum for a very simple ionic crystal. A detailed treatment of the lattice dynamics lies outside the scope of this book. The formal treatment of phonons (cf. e(k), D(e)) is very similar to that of crystal electrons. (Observe the similarity of the vibration equation to the Schrodinger equation.) However, they obey Bose rather than Fermi statistics (cf. page 119). 

Like infrared spectrometry, Raman spectrometry is a method of determining modes of molecular motion, especially the vibrations, and their use in analysis is based on the specificity of these vibrations. The methods are predominantly applicable to die qualitative and quantitative analysis of covalently bonded molecules rather than to ionic structures. Nevertheless, they can give information about the lattice structure of ionic molecules in the crystalline state and about the internal covalent structure of complex ions and the ligand structure of coordination compounds both in the solid state and in solution. 

Access to the low-wavenumber regions of the vibrational Raman spectra of minerals and solids of geological relevance have yielded information on crystal lattice symmetries and on the effect of ionic impurities. Databases of geological materials now rival those of organic compounds and affiliations to solid-state physics, crystal engineering and to substrate characterization for thin-film devices are numerous. 

Generally, the difference between LO and TO vibrations of a compound material can reveal its ionicity. The difference between Vto and Vlo of cBN decreases slowly with pressure while both Vto and Vlo increase with pressure, indicating that the cBN lattice becomes hard and tight under high pressure (143,144). The decrease in the Vto - Vlo difference with pressure indicates that the ionicity of cBN decreases with pressure as observed for other III-V compounds (144). 

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