Isomorphism and Solid Solutions

For atomic clusters of sufficiently small size, the melting conditions can be met even at ambient temperature this size can be estimated by purely thermodynamic method. Let us imagine a solid with the molar volume (in cm ) to be fragmented into n = Vjn/D particles of cubic shape with the edge D. The total surface of these particles will be 

According to Eq. 6.27 the minimum size of crystal grains in elemental solids of the A1-A4 types vary from 2.4 to 46.4 nm with the average ofl7 9nm the calculations for all elements are presented in Table S6.5. 

Indeed, a sharp decrease of the melting enthalpy after a shock-wave treatment has been shown experimentally [72], a thermodynamic interpretation of these results can be found in [64], Depression of melting temperatures and enthalpies in organic crystals has been reported [73-76] and different models of these dependences are available [77, 78]. A simple empirical rule has been established the enthalpy of the defect formation is nearly proportional to the melting temperature, viz. in alkali halides AHi T = 2 10 (for AHi in kJ/mol and r in K) it was also shown that dTmldP=kVo, where V is the molar volume andA =5.7 10 K mol/J [79]. 

In 1819Mitscherlich discovered that certain substances of different composition give similar crystal forms, named this phenomenon isomorphism and concluded (correctly, as we know today) that it reflects similarity of the atomic structure. 

10-15 % it is easier to substitute a smaller atom for a larger one than the other 

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In our discussions of the internal structure of crystals, we have shown that each atom (or molecule) has a precise location in a repeating structure. If this structure is disrupted in some way the crystal is said to have imperfections. There are a number of different kinds of imperfections that can occur. If a foreign atom (or molecule in a molecular crystal) is present in the crystal lattice, this is known as a chemical imperfection. The foreign atom can be present at a lattice site having substituted for an atom in the structure as we saw in our brief discussion of isomorphism and solid solutions. This is called a substitutional impurity. The foreign atom can also be present in the crystal by fitting between the atoms in the lattice. This is called a interstitial impurity. Both of these types of impurities can cause the atoms in the crystal to be slightly displaced since the impurity atoms do not really fit in the perfect lattice structure. The displacement of the atoms causes a strain in the crystal. 

Bixbyite, found only in Utah, about 35 miles southwest of Simpson, is described by Penfield and Foote2) as forming shiny black cubic crystals with a trace of octahedral cleavage. The composition assigned it by them was Fe++Mn+40A, with a little isomorphous replacement of Fe++ by Mg++ and Mn++ and of Mn+i by Ti+i. It was shown by Zachariasen that the X-ray data exclude this formulation, and indicate instead that the mineral is a solid solution of Mn20A and Fe20A. We shall reach a similar conclusion. 

Isomorphism. Like TiC and ZrC, HfC forms solid solutions with oxygen and nitrogen, which have a wide range of composition. HfC forms solid solutions with the other monocarbides of Group IV and V, particularly NbC.b l... 

Isomorphism. TaC forms solid solutions with the carbides of Group IV and the other monocarbides of Group V and with the mononitrides of these two groups. 

Being isomorphous, PbSe and PbTe form solid solutions in the whole range of compositions. Cathodic electrodeposition of the PbSe Tei-x ternary (0 < x < 1)... 

Zinc, Cu and Ni have similar ionic radii and electron configurations (Table 5.6). Due to the similarity of the ionic radii of these three metals with Fe and Mg, Zn, Cu and Ni are capable of isomorphous substitution of Fe2+ and Mg2+ in the layer silicates. Due to differences in the electronegativity, however, isomorphous substitution of Cu2+ in silicates may be limited by the greater Pauling electronegativity of Cu2+ (2.0), whereas Zn2+ (1.6) and Ni2+ (1.8) are relatively more readily substituted for Fe2+ (1.8) or Mg2+ (1.3) (McBride, 1981). The three metals also readily coprecipitate with and form solid solutions in iron oxides (Lindsay, 1979 Table 5.7). 

But many computations of phase-formation based on the application of pseudo-potential, quantum-mechanical techniques, statistic-thermodynamic theories are carried out now only for comparatively small number of systems, for instance [1-3], A lot of papers dedicated to the phenomenon of isomorphic replacement, arrangement of an adequate model of solids, energy theories of solid solutions, for instance [4-7], But for the majority of actual systems many problems of theoretical and prognostic assessment of phase-formation, solubility and stable phase formation are still unsolved. 

In surface precipitation cations (or anions) which adsorb to the surface of a mineral may form at high surface coverage a precipitate of the cation (anion) with the constituent ions of the mineral. Fig. 6.9 shows schematically the surface precipitation of a cation M2+ to hydrous ferric oxide. This model, suggested by Farley et al. (1985), allows for a continuum between surface complex formation and bulk solution precipitation of the sorbing ion, i.e., as the cation is complexed at the surface, a new hydroxide surface is formed. In the model cations at the solid (oxide) water interface are treated as surface species, while those not in contact with the solution phase are treated as solid species forming a solid solution (see Appendix 6.2). The formation of a solid solution implies isomorphic substitution. At low sorbate cation concentrations, surface complexation is the dominant mechanism. As the sorbate concentration increases, the surface complex concentration and the mole fraction of the surface precipitate both increase until the surface sites become saturated. Surface precipitation then becomes the dominant "sorption" (= metal ion incorporation) mechanism. As bulk solution precipitation is approached, the mol fraction of the surface precipitate becomes large. 

The solids occurring in nature are seldom pure solid phases. Isomorphous replacement by a foreign constituent in the crystalline lattice is an important factor by which the activity of the solid phase may be decreased. If the solids are homogeneous, that is, contain no concentration gradient, one speaks of homogeneous solid solutions. The thermodynamics of solid solution formation has been discussed by Vaslow and Boyd (1952) for solid solutions formed by AgCI(s) and AgBr(s). 

The phenomena of surface precipitation and isomorphic substitutions described above and in Chapters 3.5, 6.5 and 6.6 are hampered because equilibrium is seldom established. The initial surface reaction, e.g., the surface complex formation on the surface of an oxide or carbonate fulfills many criteria of a reversible equilibrium. If we form on the outer layer of the solid phase a coprecipitate (isomorphic substitutions) we may still ideally have a metastable equilibrium. The extent of incipient adsorption, e.g., of HPOjj on FeOOH(s) or of Cd2+ on caicite is certainly dependent on the surface charge of the sorbing solid, and thus on pH of the solution etc. even the kinetics of the reaction will be influenced by the surface charge but the final solid solution, if it were in equilibrium, would not depend on the surface charge and the solution variables which influence the adsorption process i.e., the extent of isomorphic substitution for the ideal solid solution is given by the equilibrium that describes the formation of the solid solution (and not by the rates by which these compositions are formed). Many surface phenomena that are encountered in laboratory studies and in field observations are characterized by partial, or metastable equilibrium or by non-equilibrium relations. Reversibility of the apparent equilibrium or congruence in dissolution or precipitation can often not be assumed. 

Almost all the crystalline materials discussed earlier involve only one molecular species. The ramifications for chemical reactions are thereby limited to intramolecular and homomolecular intermolecular reactions. Clearly the scope of solid-state chemistry would be vastly increased if it were possible to incorporate any desired foreign molecule into the crystal of a given substance. Unfortunately, the mutual solubilities of most pairs of molecules in the solid are severely limited (6), and few well-defined solid solutions or mixed crystals have been studied. Such one-phase systems are characterized by a variable composition and by a more or less random occupation of the crystallographic sites by the two components, and are generally based on the crystal structure of one component (or of both, if they are isomorphous). 

The particular combinations of ions and molecules that will form precipitates in a given solution can be predicted from equilibrium thermodynamics. However, this often gives a misleading picture because there are kinetic limitations or there is inhibition, particularly in soil solutions. There may also be isomorphous substitution of one cation for another in the precipitate, resulting in a solid solution with a different solubility to the pure compound. 

How can we be sure that the U +(Q2-) complex in a mixed metal oxide is present as the UO octahedron This can be done by studying solid solution series between tungstates (tellurates, etc.) and uranates which are isomorphous and whose crystal structure is known. Illustrative examples are solid solution series with ordered perovskite structure A2BWi aUa 06 and A2BTei-a Ua 06 91). Here A and B are alkahne-earth ions. The hexavalent ions occupy octahedral positions as can be shown by infrared and Raman analysis 92, 93). Usually no accurate determinations of the crystallographic anion parameters are available, because this can only be done by neutron diffraction [see however Ref. (P4)]. Vibrational spectroscopy is then a simple tool to determine the site symmetry of the uranate complex in the lattice, if these groups do not have oxygen ions in common. In the perovskite structure this requirement is fulfilled. 

The existence of these isostructural compounds suggests that solid solutions could be formed between two end members via isomorphous substitution for Fe " by other cations. The likelihood of substitution depends on the similarity of the ionic radii and the valency of the cations (Goldschmidt, 1937). m " is the most suitable cationic species and a radius about 18% higher or lower than that of high-spin Fe " in sixfold coordination can be tolerated. Isomorphous replacement of Fe in Fe oxides by a number of cations has been observed in nature and, more frequently, in the laboratory. As far as is known, however, almost all these solid solutions have broad miscibility gaps, possibly induced by development of structural strain as substitution rises. 

The other single phase region is the liquid L. In addition to the two phase a+0 region, there are two other two phase regions L + a and L + 0. Just as in the isomorphous diagram the solidus and liquidus lines are connected by tie-lines of constant temperature. In a like manner, the a + 0 region is also considered to possess tie-lines joining the two solid-solution or solvus curves. 

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