Stoichiometry variations

Finally, the total preexponential factor includes the stoichimetry deviation represented by c°(, or c° so an extrapolated Arrhenius plot will show an intercept which is very sensitive to composition. Experimental data will be hard to reproduce both because of stoichiometry variations and because of the slow approach to thermal equilibrium. 

Gross stoichiometry variations in these modular systems are often acconunodated by the formation of other series members or the incorporation of planar faults, often equivalent to isolated lamellae of other series members, into the structure. However, many individual phases also show composition variation which is sometimes accommodated by random populations of point defects and in other phases by ordering and the generation of new structures. In both cases composition flexibility is important in influencing the physical and chemical properties of these materials. In particular this effect has been well studied in the cuprate superconductors, where changes in composition have repercussions for the superconducting transition temperature, r, of the phase. 

The simplest argument that TmS is trivalent, TmSe intermediate valent and TmTe divalent under normal conditions comes from comparing the lattice constants of the lanthanide sulfides, selenides and tcllurides as shown in fig. 58 (after Bucher et al. 1975). The lanthanide contraction is the cause for the general trend in the curves and the standard divalent Sm, Eu and Yb ions with their larger ionic radius are the obvious deviations. TmTe lies on the divalent curve, TmS on the trivalent one and TmSe is intermediate and by linear interpolation between a hypothetical divalent and trivalent TmSe one obtains a valency of 2.75. The figure also shows that SmS, in this case by pressure or trivalent rare earth doping, can be intermediate valent, TmSe, in this case by stoichiometry variation, can become trivalent and TmTe, in this case by pressure, oxidation and stoichiometry variation, can become intermediate valent. 

It also becomes clear that in TmSe a change of the lattice constant in either direction, which can be achieved by pressure, stoichiometry variation or alloying, will move more or less electrons in or out of the 4f band. One can also say that the 4f band gets moved through the Fermi level. Thus it is no surprise that the Hall effect and the thermopower change sign when the Fermi level crosses the middle of the 4f band. The same effect occurs in SniS, where, however, it has been observed with various amounts of alloying (Jayaraman 1979). 

The interesting case is that one has within the TmSe system a trivalent reference compound and can investigate the evolution of intermediate valence without using external parameters like pressure or temperature. In the stoichiometry variation of Tm tSe it is essential that the stoichiometry is chemically controlled, the materials are never handled in air and all physical investigations are made on the same single crystal of the desired composition. Some physical properties of a series of compositions are compiled in table 3. 

When ceria is used as a membrane, significant stoichiometry variations may be induced over the membrane. As the unit cell volume of ceria depends on the oxygen content (cf. Section 12.2.2.3) this results in a strain profile across the membrane, which leads to mechanical stresses. The strain associated with stoichiometry changes may, as discussed in Section 12.2.2.3, be of the order of 1-2%. Typical rupture strain levels in ceramics are of the order of 0.1%. This means that these lattice strains can result in mechanical... 

Experimentally we titrate the neutral component into or out of the sample in this manner for a certain time At, then switch off the current, await homogenization and repeat the procedure. Measiurement of the volt e in the currentless homogeneous state (i.e. EMF E) allows determination of the stoichiometry variation and the associated activity. The time behaviour of the voltage during relaxation yields — diffusion controlled kinetics assumed — the chemical diflFusion coefficients if the boundary conditions (and naturally the initial condition) are known [574,615]. 

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