Solid solution approach

This type of defect equilibrium treatment has been used extensively to model the defect chemistry and non-stoichiometry of inorganic substances and has the great advantage that it easily takes several simultaneous defect equilibria into account [22], On the other hand, the way the mass action laws are normally used they are focused on partial thermodynamic properties and not on the integral Gibbs energy. The latter is often preferred in other types of thermodynamic analyses. In such cases the following solid solution approach is an alternative. 

For thermochemical uses, an expression for the integral Gibbs energy of formation of the compound ABC can be derived by integration of eq. (9.104), but in order to show clearly some of the main implications of the model a more detailed analysis starting from the partition function is preferred [23]. 

It can be shown that the partition function in this case can be expressed as 

The configurational entropy term, given by the degeneracy, gc, is included in AfG but not in AfGc. Let us assume the existence of two compounds with different formal oxidation states for the B atom, ABO3 and ABO2.5. The two compounds have the same (perovskite-type) structure and the non-stoichiometric phase 

5is seen as a solution of these two end members. Often only one of the limiting compounds is physically realizable. 

---

In a landmark synthesis, Trimeris-Roche manufactured the 36-residue fusion inhibitor Enfuvirtide (T-20 or Fuzeon) (Figure 18.5A) on a multi-ton scale by using a hybrid solid-solution approach [46, 47]. For this purpose, the peptide was divided... 

Application of EQ3/6 to many important problems will depend critically on the ability to model compositional variation in clays and zeolites. Thermodynamic data for 2 1 clays, and to a lesser extent zeolites, are not sufficiently abundant or of high enough quality to construct definitive solid solution models for these phases. Nevertheless, incorporation of reasonable models into EQ3/6 is a prerequisite to assessing the sensitivity of the geochemical modeling results to different solid solution approaches and for testing predictions against experimental and field observations. 

Made a study of the oxalates of licrylliiim in the same manner as the previous work, (KJ04, 10) on the sulphate and concludes that an acid oxalate does not exist and the oxalates of Iwryllium alone are the mono and trihydrates. Further that all of the so-called basic oxalates are in reality solid solutions approaching the hydroxide in composition. Give a list and general discussion of basic beryllium comjxmnds and state their belief that no definite basic compounds claimed to have been formed in presence of water have any real exist-... 

Since the work of Coble in 1961, the MgO-doped AI2O3 system has represented one of the most celebrated examples of the effectiveness of the solid solution approach to microstructure control. Whereas the dramatic effect of MgO on the sintered microstructure of AI2O3 was easily reproduced (see Fig. 11.43), understanding the mechanism by which MgO acts proved to be more difficult despite numerous investigations. One of the main obstacles in the earlier work has been the use of powders containing impurities that have tended to mask the true effect of MgO. However, as described in a thorough review by Bennison and Harmer (81), the dopant role in this system is now fairly well understood, at least at a phenomenological level. 

The example clearly demonstrates the main advantages of solution chemistry over the solid-phase approach ... 

From a general point of view, the tautomeric studies can be divided into 12 areas (Figure 20) depending on the migrating entity (proton or other groups, alkyl, acyl, metals. ..), the physical state of the study (solid, solution or gas phase) and the thermodynamic (equilibrium constants) or the kinetic (isomerization rates) approach. 

Questions of the analytic control of maintenance of the bivalent metals cations to their joint presence in materials of diverse fixing always were actual. A simultaneous presence in their composition of two cations with like descriptions makes analysis by sufficiently complicated process. Determination of composition still more complicates, if analyzed object is a solid solution, in which side by side with pair of cations (for example, Mg " -Co ", Mn -Co, Zn -Co ) attends diphosphate anion. Their analysis demands for individual approach to working of methods using to each concrete cations pair. 

Aluminium and magnesium melt at just over 900 K. Room temperature is 0.3 T and 100°C is 0.4 T, . Substantial diffusion can take place in these alloys if they are used for long periods at temperatures approaching 80-100°C. Several processes can occur to reduce the yield strength loss of solutes from supersaturated solid solution, overageing of precipitates and recrystallisation of cold-worked microstructures. 

Solid-phase chemistry is an efficient synthetic tool that, compared with solution-phase chemistry, simplifies the work-up of the reaction, allows the process to be driven to completion by using excess of reagents, and can be automatized [2a]. In recent years, many studies have been devoted to developing both surface-mediated and resin-supported synthesis. Today the solid-phase approach is not limited to peptides and oligonucleotides but is also used to synthesize molecules of lower molecular weight. 

The most important nanomaterial synthesis methods include nanolithography techniques, template-directed syntheses, vapor-phase methods, vapor-liquid-solid (VLS) methods, solution-liquid-solid (SLS) approaches, sol-gel processes, micelle, vapor deposition, solvothermal methods, and pyrolysis methods [1, 2]. For many of these procedures, the control of size and shape, the flexibility in the materials that can be synthesized, and the potential for scaling up, are the main limitations. In general, the understanding of the growth mechanism of any as-... 

These authors constructed Pourbaix diagrams for the MnTe, ZnTe, Cdi , Mn i Te, and Cdi cZn cTe systems and argued that the related analysis is an effective approach to determine conditions for selective etching, chemical polishing, passivation, and self-metallization of ZnTe, MnTe, and their solid solutions. 

Crystalline materials are commonly associated with purity, but recent demands lead to almost suprapure materials, and it is common to ask for an impurity profile. Crystallization epitomizes purification at the molecular level and the technology exploits the ability of a crystal surface to reject molecules that it does not recognize (Davey, 1994). This is essentially a supramolecular process. Two types of approaches are possible, viz. the use of eutectic and solid solutions. In the eutectic approach there is efficient rejection, whereas in solid solutions molecular level discrimination is difficult. 

This problem illustrates the solution approach to a one-dimensional, nonsteady-state, diffusional problem, as demonstrated in the simulation examples, DRY and ENZDYN. The system is represented in Fig. 4.2. Water diffuses through a porous solid, to the surface, where it evaporates into the atmosphere. It is required to determine the water concentration profile in the solid, under drying conditions. The quantity of water is limited and, therefore, the solid will eventually dry out and the drying rate will reduce to zero. 

With regard to the solution approach, it is imperative that the solvent used be of the highest possible purity. Solution headspace is applicable to a much wider range of samples than the solid approach. When working with... 

Characterization of cerium-zirconium solid solutions prepared by the microwave-assisted approach. Wuji Huaxue Xuebao, 25, 812-817. 

Merriman and colleagues have reported the cydization of N-acyl-l,2-diaryl-l,2-ethanediamine derivatives, obtained by way of a solid-phase approach, to 4,5-diaryl-imidazolines by treatment with trimethylsilyl polyphosphate (TMS-PP) in dichloro-methane solution (Scheme 6.204) [367]. The best results were obtained by micro-... 

For this solid-phase approach, conventional iPrOCH2-functionalized polystyrene resin (Merrifield linker) was employed. After attachment of the requisite substrate, the resin was pre-swollen in a solution of barium(II) hydroxide in N,N-dimethyl-formamide within an appropriate sealed microwave vial. The vial was heated in the microwave cavity for 5 x 2 min cycles (overall 10 min) with the reaction mixture being allowed to cool to room temperature in between irradiation cycles (Scheme 7.50), leading to comparatively modest isolated yields of hydantoins. 

Bulk Ag-Al alloys, containing up to 12 a/o Al, were electrodeposited from melt containing benzene as a co-solvent. Examination by x-ray diffraction (XRD) indicated that the low-Al deposits were single-phase fee Ag solid solutions whereas those approaching 12 a/o were two-phase, fee Ag and hep i>-Ag2Al. The composition at which ti-Ag2Al first nucleates was not determined. The maximum solubility of aluminum in fee silver is about 20.4 a/o at 450 °C [20] and is reduced to about 7 a/o at room temperature. One would expect the lattice parameter of the fee phase to decrease only slightly when aluminum alloys substitutionally with silver because the... 

Equations (4.7) and (4.8) may be solved numerically or graphically. The latter approach is illustrated in Figure 4.2 by using the Gibbs energy curves for the liquid and solid solutions of the binary system Si-Ge as an example. The chemical potentials of the two components of the solutions are given by eqs. (3.79) and (3.80) as... 

---