Solid solutions isomorphous crystals

A necessary and sufficient condition for the formation of substitutional solid solutions of organic molecules is similarity of shape and size of the component molecules, For the formation of a continuous series of solid solutions the crystal structures of the pure components must be isomorphous Due to the rather irregular shape of organic molecules the principle of close packing leads to structures of low symmetry so that the latter requirement is not often fulfilled. Several diacetylenes which were found to form mixed crystals are given in Table 5. A large number of... 

Isomorphous substances often crystallize together from a mixed solution to form solid solutions, single crystals containing both substances. In a solid solution the different ions (such as Mn++ and Ca+ +) are arranged at random in the positions occupied by one kind of ion alone in a pure substance. For example, solid solu tions of chrome alum, KCr(S04)2 12HoO, and ordinary alum, KA1(S04) 12H20,... 

If atoms of another nature with similar atomic radii fall into the valleys V and the deeper ones V (Fig. 1), then crystals may grow, solid solutions being crystallized under certain conditions. It will be a case of isomorphism. 

Solid solution. Mixed crystals formed when isomorphous substances crystallize together out of a solution. Supersaturation. The departure from solution saturation usually caused by cooling of the mixture and/... 

For example, if we dope a semiconductor with an impurity by diffusion, there will be a higher concentration of dopant atoms near the surface, but we do not consider this a separate phase unless we exceed the solid solubility with the concentration of dopant atoms causing them to form a precipitate. The precipitate would be considered a second phase. Similarly, if we solidify a solid solution (isomorphous) system, the resulting polycrystalline alloy is considered a single phase because all of the grains have the same crystal structure, even though the first-to-freeze grains may have a different composition than the last-to-freeze. On the other hand, a liquid or gas may have the same composition as a solid, but clearly have different structures and therefore must be considered as separate phases. 

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. TiC is isomorphous with TiN and TiO. Thus oxygen and nitrogen as impurities, or as deliberate addition, can substitute for carbon to form binary and ternary solid solutions over a wide range of homogeneity. These solutions may be considered as Ti(C,N,0) mixed crystals. TiC forms solid solutions with the other monocarbides of Group IV and V. It is the host lattice for WC.li" ... 

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). 

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. 

Now that we can determine overall compositions on a ternary diagram, we can retnm to the issue of representing temperature in the diagram. As mentioned earlier, the temperature axis is perpendicular to the compositional, triangular plane, as shown in Figure 2.16 for the case of three components that form a solid solution, a. Recall that in order to form solid solutions, the components must generally have the same crystal structure. Such substances are said to be isomorphous. 

From the preceding sections it is clear that isomorphism of monomeric units in synthetic copolymeric systems is a quite general phenomenon. We wish to recall here that the requirements for the isomorphous substitution in the macromolecular field are similar to those holding for solid solutions in ionic or metallic crystals however, the degree of... 

For these experiments it was important to establish that solid solutions were formed, and that the crystals had structures that were isomorphous with that of pure UP. The crystals were shown to be single by examination with a polarizing microscope, and to have lattice constants within 0.1% of pure UP by X-ray diffractometry. The presence of a single melting endotherm upon differential scanning calorimetry showed that the DUP molecules had not segregated into a separate phase. Certain spectroscopic similarities between DUP and UP sites also indicate that the DUP is included within the crystal lattice of UP. 

Theory of the solubility of two isomorphous salts.— This assimilation into a solid solution of mixed crystals formed by two isomorphous salts leads to a complete theory of the phenomena which are produced when two isomorphous salts are brought into the presence of water. 

One of the ions of a precipitate can be replaced by a foreign ion of the same charge, provided the ions do not differ in size by more than about 5% and provided the two salts crystallize in the same system. Thus silver chloride and silver bromide form a complete series of solid solutions by isomorphous replacement of bromide by chloride. 

Isomorphism Similarity of crystal shape, unit cell dimensions, and structure between substances of similar chemical composition. Generally only the identity of one atom in the chemical formula is changed. Ideally, the substances are so closely similar that they may form a continuous series of solid solutions. 

The isomorphous CugO and Ag20 are of unusual structure. The metal atoms have two collinear bonds and the oxygens four tetrahedral bonds in a cubic structure similar to that of cristobalite. The low co-ordination, 4 2, is indicative of covalence. The structure represented in Fig. 270 is not the complete picture. An identical framework, in which the structure shown is moved forward so that the oxygens marked A take up the positions B, interpenetrates it without cross-connection by M—O bonds. The interpenetrating structure is unique in crystal chemistry. Both oxides form solid solutions with the metal. 

In Figure 5 the phase diagram of the system (6) and the 3-pentyl homologue (7) is given. Three distinct ranges can be detected A and C represent solid solutions of the two monomers in the triclinic centrosymmetric structures of pure (6) and (7), respectively, but range B clearly indicates the formation of a new phase. The cell constants of a crystal of 50(6) 50(7) composition, as well as the stereochemistry of the topochemical products, indicated that indeed this phase is isomorphous to enantiomeric and racemic (2) (Table 1), thus confirming the validity of the model. 

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