Metal ions lattices

The description of metal bonding by interstitial electrons was given in 1972. In the interstitial electron model, atoms in metals shed some of their valence electrons, which occupy interstitial holes in the metal ion lattice. Not all of the valence electrons are in the interstices. The more electrons that are removed from the atoms, the more electronegative the cations become and the less they tend to donate further electrons to the interstices. Thus some valence electrons stay behind on the metal ions. How many depends on the atom. 

The common structural element in the crystal lattice of fluoroaluminates is the hexafluoroaluminate octahedron, AIF. The differing stmctural features of the fluoroaluminates confer distinct physical properties to the species as compared to aluminum trifluoride. For example, in A1F. all corners are shared and the crystal becomes a giant molecule of very high melting point (13). In KAIF, all four equatorial atoms of each octahedron are shared and a layer lattice results. When the ratio of fluorine to aluminum is 6, as in cryoHte, Na AlF, the AIFp ions are separate and bound in position by the balancing metal ions. Fluorine atoms may be shared between octahedrons. When opposite corners of each octahedron are shared with a corner of each neighboring octahedron, an infinite chain is formed as, for example, in TI AIF [33897-68-6]. More complex relations exist in chioUte, wherein one-third of the hexafluoroaluminate octahedra share four corners each and two-thirds share only two corners (14). 

Ideal lattice with octahedra of oxygen ions sharing corners = metal ion... 

Fig. 2. Structures for the solid (a) fee Cco, (b) fee MCco, (c) fee M2C60 (d) fee MsCeo, (e) hypothetical bee Ceo, (0 bet M4C60, and two structures for MeCeo (g) bee MeCeo for (M= K, Rb, Cs), and (h) fee MeCeo which is appropriate for M = Na, using the notation of Ref [42]. The notation fee, bee, and bet refer, respectively, to face centered cubic, body centered cubic, and body centered tetragonal structures. The large spheres denote Ceo molecules and the small spheres denote alkali metal ions. For fee M3C60, which has four Ceo molecules per cubic unit cell, the M atoms can either be on octahedral or tetrahedral symmetry sites. Undoped solid Ceo also exhibits the fee crystal structure, but in this case all tetrahedral and octahedral sites are unoccupied. For (g) bcc MeCeo all the M atoms are on distorted tetrahedral sites. For (f) bet M4Ceo, the dopant is also found on distorted tetrahedral sites. For (c) pertaining to small alkali metal ions such as Na, only the tetrahedral sites are occupied. For (h) we see that four Na ions can occupy an octahedral site of this fee lattice.

In an ionizing solvent, the metal ion initially goes into solution but may then undergo a secondary reaction, combining with other ions present in the environment to form an insoluble molecular species such as rust or aluminum oxide. In high-temperature oxidation, the metal ion becomes part of the lattice of the oxide formed. 

There are two basic questions which can be decided only by experiments. First, we must know whether the metal or the oxygen is present in excess, and second, we must know how the excess component is incorporated in the oxide lattice. In connection with the latter question we have to remember that a non-stoichiometric crystal remains electrically neutral (except in narrow regions near the surfaces), so that if the excess component is present in the crystal as ions, lattice defects with charges of opposite sign must necessarily be present also (see Figs. 1.77 and 1.78). The most important defect structures will be discussed in this section. 

Before considering the principles of this method, it is useful to distinguish between anodic protection and cathodic protection (when the latter is produced by an external e.m.f.). Both these techniques, which may be used to reduce the corrosion of metals in contact with electrolytes, depend upon the electrochemical mechanisms that result from changing the potential of a metal. The appropriate potential-pH diagram for the Fe-H20 system (Section 1.4) indicates the magnitude and direction of the changes in the potential of iron immersed in water (pH about 7) necessary to make it either passive or immune in the former case the stability of the metal depends on the formation of a protective film of metal oxide (passivation), whereas in the latter the metal itself is thermodynamically stable and egress of metal ions from the lattice into the solution is thus prevented. 

Consider the cathodic reduction of a hydrated metal ion M (aq.) to a lattice metal atom at the interface M/M (aq.) by a simple one-step reaction... 

Reaction overpotential. Both overpotentials mentioned above are normally of higher importance than the reaction overpotential. It may happen sometimes, however, that other phenomena, which occur in the electrolyte or during electrode processes, such as adsorption and desorption, are the speed-limiting factors. Crystallization overpotential. This exists as a result of the inhibited intercalation of metal ions into their lattice. This process is of fundamental importance when secondary batteries are charged, especially during metal deposition on the negative side. 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

In Fig. 8-13 are plotted lattice energies for MCI2 species. The metal ions are high-spin and lie in octahedral sites in the lattice. The double-hump form of the curve is obviously similar to that for the hydration energies we have just discussed. The reasons for the observed trend in lattice energy are virtually identical to those described for hydration energies. In one system, a metal(ii) ion is octahedrally coordinated by six water molecules within a liquid medium in the other, a metal(ii) ion is octahedrally coordinated by six chlorine atoms within a solid lattice. 

The dominant features which control the stoichiometry of transition-metal complexes relate to the relative sizes of the metal ions and the ligands, rather than the niceties of electronic configuration. You will recall that the structures of simple ionic solids may be predicted with reasonable accuracy on the basis of radius-ratio rules in which the relative ionic sizes of the cations and anions in the lattice determine the structure adopted. Similar effects are important in determining coordination numbers in transition-metal compounds. In short, it is possible to pack more small ligands than large ligands about a metal ion of a given size. 

Various other interactions have been considered as the driving force for spin-state transitions such as the Jahn-Teller coupling between the d electrons and a local distortion [73], the coupling between the metal ion and an intramolecular distortion [74, 75, 76] or the coupling between the d electrons and the lattice strain [77, 78]. At present, based on the available experimental evidence, the contribution of these interactions cannot be definitely assessed. Moreover, all these models are mathematically rather ambitious and do not show the intuitively simple structure inherent in the effect of a variation of molecular volume considered here. Their discussion has to be deferred to a more specialized study. 

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