Ion crystallization

Many complex ions, such as NH4+, N(CH3)4+, PtCle", Cr(H20)3+++, etc., are roughly spherical in shape, so that they may be treated as a first approximation as spherical. Crystal radii can then be derived for them from measured inter-atomic distances although, in general, on account of the lack of complete spherical symmetry radii obtained for a given ion from crystals with different structures may show some variation. Moreover, our treatment of the relative stabilities of different structures may also be applied to complex ion crystals thus the compounds K2SnCle, Ni(NH3)3Cl2 and [N(CH3)4]2PtCl3, for example, have the fluorite structure, with the monatomic ions replaced by complex ions and, as shown in Table XVII, their radius ratios fulfil the fluorite requirement. Doubtless in many cases, however, the crystal structure is determined by the shapes of the complex ions. 

Metal ion Crystal ionic radius A Complexation constant... 

R. Herny, Electron Processes in Ion Crystals, A.F. Ioffe (ed.). Foreign Literature Publ., Moscow, 1950... 

Details of the calculation of Madelung constants for all of the common types of crystals are beyond the scope of this book. When the arrangement of ions differs from that present in NaCl, the number of ions surrounding the ion chosen as a starting point and the distances between them may be difficult to determine. They will most certainly be much more difficult to represent as a simple factor of the basic distance between a cation and an anion. Therefore, each arrangement of ions (crystal type) will have a different value for the Madelung constant. The values for several common types of crystals are shown in Table 7.3. 

Another factor that affects trends in the stability constants of complexes formed by a series of metal ions is the crystal field stabilization energy. As was shown in Chapter 17, the aqua complexes for +2 ions of first-row transition metals reflect this effect by giving higher heats of hydration than would be expected on the basis of sizes and charges of the ions. Crystal field stabilization, as discussed in Section 17.4, would also lead to increased stability for complexes containing ligands other than water. It is a pervasive factor in the stability of many types of complexes. Because ligands that form tt bonds... 

Cogel method by impregnating Ti02-Si02 cogel with TEAOH solution in the presence of some amount of aluminium ions. Crystallization at 408 K while tumbling the autoclave (60 rpm). Zeolite yields —29% Si/Al — 300. Requires lesser amount of TEA+ ions than classical prehydrolysis method... 

Quite a few complexes with the bidentate pentasulfido ligand are also known. The first reported was the homoleptic and optically active complex [Pt(85)3] (15) (53, 64, 65, 68, 69, 176). Brick-red (NH4)2[Pt(85)3] 2H20 is formed from the reaction of K2[PtCl6] with aqueous (NH4)28 solution. Addition of concentrated HCl results in the separation of maroon (NH4)2[Pt8i7] 2H20 (54). The [Pt(85)3] ion crystallizes from the solution as a racemate, which can be resolved by forming diastereoisomers. Upon crystallization, [Pt8,7] undergoes a second-order asymmetric transformation, so that the solid contains an excess of the (—) enantiomer (54). 

For the crystal composed of ions, the equality given in Eq. (9.33) is no longer valid, because the two ionic charge distributions, which partly shield the nuclear charges, are different. For the free-ion crystal, the values of the potential at the nuclear positions in NaF, evaluated according to Section 9.3.2, are... 

The structure of and possible cation location in these materials is fairly well known (2, 8, 4, )> and their ion-exchange behavior toward a multitude of pairs of ions, mostly including sodium, has been measured and interpreted in terms of basic properties of ions, crystal structures, and pore dimensions. The major part of these studies is with alkali- and alkaline-earth cations, alkylammonium ions, rare-earth cations, and silver and thallium ions (1). In contrast, the ion adsorption of transition metals in faujasite has received little attention. 

There are two major theories of bonding in d-metal complexes. Crystal field theory was devised to explain the colors of solids, particularly ruby, which owes its color to Cr3+ ions. Crystal field theory is simple to apply and enables us to make useful predictions with very little labor. However, it does not account for all the properties of complexes. A more sophisticated approach, ligand field theory, is based on molecular orbital theory. 

Let s consider the solubility equilibrium in a saturated solution of calcium fluoride in contact with an excess of solid calcium fluoride. Like most sparingly soluble ionic solutes, calcium fluoride is a strong electrolyte in water and exists in the aqueous phase as dissociated hydrated ions, Ca2+(aq) and F (aq). At equilibrium, the ion concentrations remain constant because the rate at which solid CaF2 dissolves to give Ca2+(aq) and F aq) exactly equals the rate at which the ions crystallize to form solid CaF2 ... 

A saturated solution of calcium fluoride in contact with solid CaF2 contains constant equilibrium concentrations of Ca2+ aq) and F (aq) because at equilibrium the ions crystallize at the same rate as the solid dissolves. 

Another vital type of ligand is a heavy-metal atom or ion. Crystals of protein/ heavy-metal complexes, often called heavy-atom derivatives, are usually needed in order to solve the phase problem mentioned in Chapter 2 (Section VI.F). I will show in Chapter 6 that, for the purpose of obtaining phases, it is crucial that heavy-atom derivatives possess the same unit-cell dimensions and symmetry, and the same protein conformation, as crystals of the pure protein, which in discussions of derivatives are called native crystals. So in most structure projects, the crystallographer must produce both native and derivative crystals under the same or very similar circumstances. 

Molecular mechanics is a simple technique for scanning the potential energy surface of a molecule, molecular ion, crystal lattice, or solvate. The model is based on chemical and physical principles. The resulting functions are parameterized on the basis of experimental data. That is, the potential energy surface is computed not by thorough theoretical expressions but by using functions whose parameters are derived empiri-... 

Evaluation of A Energy separations between resolved 3d orbital energy levels correspond to visible and near-infrared radiation. Measurements of absorption spectra of transition metal compounds and minerals are used to obtain A and to evaluate the CFSE of the ions. Crystal field splittings may also be estimated from plots of thermodynamic data for the first-series transition metal compounds. The magnitude of A depends on ... 

Chapter 5 summarizes the crystal field spectra of transition metal ions in common rock-forming minerals and important structure-types that may occur in the Earth s interior. Peak positions and crystal field parameters for the cations in several mineral groups are tabulated. The spectra of ferromagnesian silicates are described in detail and correlated with the symmetries and distortions of the Fe2+ coordination environments in the crystal structures. Estimates are made of the CFSE s provided by each coordination site accommodating the Fe2+ ions. Crystal field splitting parameters and stabilization energies for each of the transition metal ions, which are derived from visible to near-infrared spectra of oxides and silicates, are also tabulated. The CFSE data are used in later chapters to explain the crystal chemistry, thermodynamic properties and geochemical distributions of the first-series transition elements. 

Figure 7. Models of magnetic anisotropy (a) N6el model and (b) single-ion crystal-field...

Molecular mechanics is a simple technique for scanning the potential energy surface of a molecule, molecular ion, crystal lattice or solvate. The model is based on a set of functions which may or may not be based on chemical and physical principles. These functions are parameterized based on experimental data. That is, the potential energy surface is not computed by fundamental theoretical expressions but by using functions whose parameters are derived empirically by reproducing experimentally observed data. Molecular mechanics then is, similar to a neural network, completely dependent on the facts that it has been taught. The quality of results to be obtained depends on the choice of the experimental data used for the parameterization. Clearly, the choice of potential energy functions is also of some importance. The most common model used is loosely derived from... 

---