Isomorphic series

We have described above the evolution of the magnetic properties of the [Cp2M (dmit)]AsFg salts upon isomorphous Mo/W substitution. Another possibility offered by this attractive series is the isomorphous substitution of the counter ion, that is PFg- vs AsF6 vs Sbl- fi. Electrocrystallization experiments conducted with [Cp2Mo(dmit)] and the three different electrolytes afforded an isomorphous series, with a smooth evolution of the unit cell parameters with the anion size [32], This cell expansion with the anion size leads to decreased intermolecular interactions between the [Cp2Mo(dmit)]+ radical cation, as clearly seen in Table 2 from the decreased Curie-Weiss temperatures and Neel temperatures (associated with the transition they all exhibit to an AF ground state). 

It can clearly be seen from the crystal data of Table 1 that the phases form two isomorphic series with a break at about 50 mol-% of selenium. The sulfur-rich species crystallize in the monoclinic y-sulfur lattice and the selenium-rich species in the monoclinic a-selenium lattice (see Fig. 1). 

Intermolecular distances in these sulfur-selenium phases are comparable to those observed for monoclinic y-sulfur and monoclinic ot-selenium The shortest distances in both isomorphic series are much shorter than the sum of the van der Waals radii of the elements. In the isomorphic series of the sulfur-rich species the shortest distanee between the molecules gets shorter with increasing selenium content of the phase but remains effectively constant in the selenium-rich series. 

Molybdo-vanadosilicates.—The simple vanado-silicates do not appear to be stable, but a number of molybdo-vanadosilicates have been obtained either by acidifying solutions which contain molybdates, vanadates and silicates, or by addition of vanadium pentoxide to the molybdo-silicates. They form heavy, yellowish-red to brownish-red crystals, which are very easily hydrolysed and are, therefore, not always reproducible. The following isomorphous series has been recognised —... 

While it is very easy, when one knows the structure of the crystal and the wavelength of the rays, to predict the diffraction pattern, it is quite another matter to deduce the crystal structure in all Its details from the observed pattern and the known wavelength. The first step is lo determine the spacing of the atomic planes from the Bragg equation, and hence the dimensions of the unit cell. Any special symmetry of the space group of the structure will be apparent from space group extinction. A Irial analysis may (hen solve the structure, or it may be necessary to measure the structure factors and try to find the phases or a Fourier synthesis. Various techniques can be used, such as the F2 series, the heavy atom, the isomorphous series, anomalous atomic scattering, expansion of the crystal and other methods. 

In glauconites, octahedral A1 ranges from 0.00 to 1.28 and Fe3+ from 0.35 to 1.77 (11 out of 82 samples have more octahedral A1 than Fe3+). Within these limits, there is a continuous isomorphous series between A1 and Fe3+. The composition of the basic unit cell of many glauconites is within the range of composition of the nontronite clays however, on the average, glauconites have more Fe2 + and Mg and less tetrahedral A1 than the average nontronite. The most variable components within the layer are the Al3+ and Fe3+ ions in the octahedral sheet. Fe3+ increases as A1 decreases. 

There is a complete isomorphous series from Si4.0Al0.o to Si3.soAl0.So. Values larger than Al0.so have been reported (Ross and Hendricks, 1945 Sawhney and Jack-son, 1958) but in these samples, the sum of the octahedral cations is excessive, usually being on the order of 2.2, and gives a positive charge to the octahedral sheet. Whether such high octahedral occupancy is real, or not, has not been satisfactorily determined. 

The analyses of dioctahedral smectites indicate that octahedral Fe and Al form a continuous isomorphous series and any subdivisions must be arbitrary. As the octahedral Al/Fe ratio increases, there is a tendency for octahedral Mg to increase (although... 

Although the octahedral sheet of chamosite is composed predominantly of Fe2+ (radius = 0.75) rather than the smaller Mg (radius = 0.65), the A1 content (x > 1.20) is sufficiently large so that the tetrahedral rotation is necessary to adjust the size differential (Radoslovich, 1963). As Mg increases relative to Fe2+, less A1 is required to afford a strain-free structure. There appears to be no reason that there cannot be a continuous isomorphous series between chamosite and serpentine. 

A first example is heptadentate 2,2,2"-tris(salicylideneimino)-triethylamine, H389 (fig. 76), which forms an isomorphous series of complexes [Ln(89)] (Bernhardt et al., 2000). A crystal field analysis based on polarized absorption and emission spectra of the trigonal... 

Urea forms an isomorphous series of crystalline non-stoichiometric inclusion compounds with n-alkanes and their derivatives (including alcohols, esters, ethers, aldehydes, ketones, carboxylic acids, amines, nitriles, thioalcohols, and thioethers), provided that their main chain contains six or more carbon atoms. 

Salts are nearly all highly hydrated, and numerous isomorphous series exist. Some examples are given in Table 10. 

An empirical set of effective ionic radii in oxides and fluorides, taking into account the electronic spin state and coordination of both the cation and anion, have been calculated (114). For six-coordinate Bk(III), the radii values are 0.096 nm, based on a six-coordinate oxide ion radius of 0.140 nm, and 0.110 nm, based on a six-coordinate fluoride ion radius of 0.119 nm. For eight-coordinate Bk(IV), the corresponding values are 0.093 and 0.107 nm, based on the same anion radii (114). Other self-consistent sets of trivalent and tetravalent lanthanide and actinide ionic radii, based on isomorphous series of oxides (145, 157) and fluorides (148, 157), have been published. Based on a crystal radius for Cf(III), the ionic radius of isoelectronic Bk(II) was calculated to be 0.114 nm (158). It is important to note, however, that meaningful comparisons of ionic radii can be made only if the values compared are calculated in like fashion from the same type of compound, both with respect to composition and crystal structure. 

One example only. There are many isomorphous series in each structural group. Each isomorphous series contains several individual minerals or species. ... 

The iodo-platinates of zinc, magnesium, etc., crystallise with 9 molecules of water, and form an isomorphous series of their own. 

Of the methods which have been applied to configurational assignment in complexes, that of less soluble diastereoisomers has probably caused more errors through uncritical application than any other. Applied to isomorphous series, it is most valuable. It is especially useful in correlating configurations between similar complexes of different metals, where, if different transitions are involved, spectroscopic methods are unreliable. 

One thing that is immediately clear from Table I is that for a given halide there is a strong tendency for the difference between the primary and the secondary bond lengths to decrease on moving from As to Sb to Bi, this being particularly well illustrated in the isomorphous series of EI3 structures. 

Tutton s main law of progression of the crystallographic properties of the salts of these isomorphous series with the atomic number of the interchangeable alkali-metal is in complete agreement with this law of atomic diameters, and the two laws may be said mutually to support each other. To go even deeper, however, the law of progression q the... 

Fig. 88. Stability of carbonates of the isomorphous series sideritc-magnesitc in rocks with excess. silica (upper temperature limits). Figures on curves indicate iron content (in mol.%) curves arc drawn through every 20% Fe.

On the basis of experimental investigations of equilibria at fluid pressure 1000 atm (Hinrichsen, 1967 Schiirmann, 1967) it is presumed that the stability fields of isomorphous series of Fe-Mg amphiboles—orthorhombic anthophyllite and monoclinic cummingtonite—overlap (Fig. 89). However, the experiments cited are not completely comparable inasmuch as cummingtonite could be synthesized only after addition of 2% CaO and equilibrium was not always attained, which we had already pointed out earlier (Mel nik, 1972b). Therefore the existence of two amphiboles of the same... 

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