Solid solutions, defect ordered

The Mossbauer effect, although not a substitute for other analytical methods such as x-ray diffraction, can be used to obtain several kinds of structural information about solids. In favorable cases, it is possible to obtain rather detailed information about the electronic configuration of atoms and the local symmetry of their sites by measuring the isomer shift and quadrupole splitting. If more than one valence state of a given atom is present, a semiquantitative determination of the amount of each kind is possible. In solid solutions, the amount of local or long range order can be estimated, and in certain defect structures the relation between the active atoms and the defects can be studied. 

Trivial examples of metastability are solid solutions. Because these are inherently defect systems, they cannot be thermodynamically stable at low temperatures. Most of our high Tc superconductors need to be regarded as solid solutions which are then necessarily metastable phases. We could dismiss this as an irrelevant observation on the basis that solid solutions are merely required in order to adjust the carrier concentration to appropriate levels. However, we seem unable to generally make stable high Tc superconductors. One could even suggest that there is a correlation between Tc and metastability the higher the Tc, the more unstable. 

The second type of impurity, substitution of a lattice atom with an impurity atom, allows us to enter the world of alloys and intermetallics. Let us diverge slightly for a moment to discuss how control of substitutional impurities can lead to some useful materials, and then we will conclude our description of point defects. An alloy, by definition, is a metallic solid or liquid formed from an intimate combination of two or more elements. By intimate combination, we mean either a liquid or solid solution. In the instance where the solid is crystalline, some of the impurity atoms, usually defined as the minority constituent, occupy sites in the lattice that would normally be occupied by the majority constituent. Alloys need not be crystalline, however. If a liquid alloy is quenched rapidly enough, an amorphous metal can result. The solid material is still an alloy, since the elements are in intimate combination, but there is no crystalline order and hence no substitutional impurities. To aid in our description of substitutional impurities, we will limit the current description to crystalline alloys, but keep in mind that amorphous alloys exist as well. 

The existence of tridymite as a distinct phase of pure crystalline silica has been questioned (42,58—63). According to this view, the only true crystalline phases of pure silica at atmospheric pressure are quartz and a highly ordered three-layer cristobalite having a transition temperature variously estimated from 806 250°C to about 1050°C (50,60). Tridymites are considered to be defect structures in which two-layer sequences predominate. The stability of tridymite as found in natural samples and in fired silica bricks has been attributed to the presence of foreign ions. This view is, however, disputed by those who cite evidence of the formation of tridymite from very pure silicon and water and of the conversion of tridymite M, but not tridymite S, to cristobalite below 1470°C (47). It has been suggested that the phase relations of silica are determined by the purity of the system (42), and that tridymite is not a true form of pure silica but rather a solid solution of mineralizer and silica (63). However, the assumption of the existence of tridymite phases is well established in the technical literature pertinent to practical work. 

The NaCl structure is also found in compounds like TiO, VO and NbO, possessing a high percentage of cation and anion vacancies. Ternary oxides of the type MggMn 08 crystallize in this structure with of the cation sites vacant. Solid solutions such as Li,j )Mg Cl (0 x 1) crystallize in the rocksalt structure stoichiometric MgCl may indeed be considered as having a defect rocksalt structure with 50% of ordered cation vacancies. 

Within certain composition limits, every possible composition can attain a unique, fully ordered structure, without defects arising from solid solution effects and with no biphasic coexistence ranges between successive structures. 

We wish to determine under isothermal and isobaric conditions the concentration of defects as a function of the solid solution composition (e.g NB in alloy (A, B)). Consider a vacancy, the formation Gibbs energy of which is now a function of NB. In ideal (A, B) solutions, we may safely assume that the local composition in the vicinity of the vacancy does not differ much from Ns and /VA in the undisturbed bulk. Therefore, we may write the vacancy formation Gibbs energy Gy(NE) (see Eqn. (2.50)) as a series expansion G%(NE) = Gv(0) + A Gv Ab+ higher order terms, so that AGv = Gv(Nb = l)-Gv(AfB = 0). It is still true (as was shown in Section 2.3) that the vacancy chemical potential /Uy in the homogeneous equilibrium alloy is zero. Thus, we have (see Eqn. (2.57))... 

These elements of disorder will not lead to a shift of a sharp peak. Shifts occur only if defects order in such a way as to modify all unit cells of the crystal in the same way (Figure 4). This effect is frequently encountered in solid solutions (Abd Hamid et al., 2003 Langford and Louer, 1996 Valtchev and Bozhilov, 2004), in which atoms of different sizes occupy the same lattice positions. In many cases there are linear... 

There has been one unexpected though perhaps not too surprising result While a solid solution range for an ordered compound may be achieved by randomly dissolving defect atoms into an otherwise ordered lattice, these random defect atoms may themselves order and break the compound into a multitude of new true phases (microphases) separated by two-phase regions. 

In order to decide whether the nonstoichiometric phases contain interstitial anions, or vacant cation sites, we compared the pycnometric density with the calculated density for each type of defect. The experimental values agree with the last type of defects, and these solid solutions are represented using Rees s notation by... 

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