Solid solutions terminal

The points R have to be on a straight line terminating in the composition of the methanol hydroquinone clathrate (A) in equilibrium with a-hydroquinone at 25°C. The point B roughly corresponds to the composition of the clathrate obtained by Palin and Powell24 when crystallizing hydroquinone from methanol points between A and B form a continuous range of solid solutions in equilibrium with liquid phases whose compositions lie on the curve CE. It is found that the equilibrium clathrate has a composition corresponding to y — 0.474 at 25°C. 

Because of the interest in its use in elevated-temperature molten salt electrolyte batteries, one of the first binary alloy systems studied in detail was the lithium-aluminium system. As shown in Fig. 1, the potential-composition behavior shows a long plateau between the lithium-saturated terminal solid solution and the intermediate P phase "LiAl", and a shorter one between the composition limits of the P and y phases, as well as composition-dependent values in the single-phase regions [35], This is as expected for a binary system with complete equilibrium. The potential of the first plateau varies linearly with temperature, as shown in Fig. 2. 

In addition to this work on the / phase, both the thermodynamic and kinetic properties of the terminal solid-solution region, which extends to about 9 atom% lithium at 423 °C, were also investigated in detail [36]. 

When two metals A and B are melted together and the liquid mixture is then slowly cooled, different equilibrium phases appear as a function of composition and temperature. These equilibrium phases are summarized in a condensed phase diagram. The solid region of a binary phase diagram usually contains one or more intermediate phases, in addition to terminal solid solutions. In solid solutions, the solute atoms may occupy random substitution positions in the host lattice, preserving the crystal structure of the host. Interstitial soHd solutions also exist wherein the significantly smaller atoms occupy interstitial sites... 

Several experimental parameters have been used to describe the conformation of a polymer adsorbed at the solid-solution interface these include the thickness of the adsorbed layer (photon correlation spectroscopy(J ) (p.c.s.), small angle neutron scattering (2) (s.a.n.s.), ellipsometry (3) and force-distance measurements between adsorbed layers (A), and the surface bound fraction (e.s.r. (5), n.m.r. ( 6), calorimetry (7) and i.r. (8)). However, it is very difficult to describe the adsorbed layer with a single parameter and ideally the segment density profile of the adsorbed chain is required. Recently s.a.n.s. (9) has been used to obtain segment density profiles for polyethylene oxide (PEO) and partially hydrolysed polyvinyl alcohol adsorbed on polystyrene latex. For PEO, two types of system were examined one where the chains were terminally-anchored and the other where the polymer was physically adsorbed from solution. The profiles for these two... 

Figure 1.1 (a) Chemical potential diagrams for systems forming a complete range of solid solutions. The tangent shows at its terminal points, X, Y the chemical potentials of the elements x and y which are in equilibrium with the solid solution of composition M (b) Potentials for the system A-B, which forms the two stable compounds the stoichiometric A2B and the non-stoichiometric AB2. The graph shows that there are many pairs of potentials A, B in equilibrium with A2B and only one pair for a particular composition of AB2 AB is metastable with respect to decomposition to A2B and AB2... 

The mathematical treatment can be further simplified in one particular case, that corresponding to Figure 4.10(a). As we saw in the previous section, in some binary systems the two terminal solid solution phases have very different physical properties and the solid solubility may be neglected for simplicity. If we assume no solid solubility (i.e. as =a =1) and in addition neglect the effect of the heat capacity difference between the solid and liquid components, eqs. (4.29) and (4.30) can be transformed to two equations describing the two liquidus branches ... 

In the general case a complex behaviour may be expected for the extension of the terminal solid solutions which, for a pair of metals Mb M2, also depends on the stoichiometry and stability of the M (or, respectively, M2) richest phase. However a certain regularity of the dependence of the mutual solid solubility on the position of the metals involved in the Periodic Table may be observed. This can be related to the so-called Hume-Rothery rules (1931) ... 

In Fig. 2.19, on the contrary, we observe that intermediate solid phases with a variable composition are formed (non-stoichiometric phases). In the diagrams shown here we see therefore examples both of terminal and intermediate phases. (For instance, the Hf-Ru diagram shows the terminal solid solutions of Ru in a and (3Hf and of Hf in Ru and the intermediate compound containing about 50 at.% Ru). These phases are characterized by homogeneity ranges (solid solubility ranges), which, in the case of the terminal phases, include the pure components and which, generally, have a variable temperature-dependent extension. 

The situation in the solid state is generally more complex. Several examples of binary systems were seen in which, in the solid state, a number of phases (intermediate and terminal) are formed. See for instance Figs 2.18-2.21. Both stoichiometric phases (compounds) and variable composition phases (solid solutions) may be considered and, as for their structures, both fully ordered or more or less completely disordered phases. This variety of types is characteristic for the solid alloys. After a few comments on liquid alloys, particular attention will therefore be dedicated in the following paragraphs to the description and classification of solid intermetallic phases. 

Figure 6.10. A generic binary phase diagram is shown for an A-B system in which two compounds, AB and ABm, are formed. Different parts of the liquidus line are indicated. 1 is the line of primary crystallization of the terminal solid-solution based on the component A (which, on cooling, will be followed by the peritectic formation of AB ) 2 is the line of primary crystallization of the compound AB (to be followed by the eutectic crystallization of AB + ABm) 3 and 4 are lines of primary crystallization of ABm (to be followed, respectively, by the crystallization of the eutectic AB + ABm or of the eutectic AB, + B-based solid solution).

Notice that the structures presented in this paragraph are unary structures, that is one species only is present in all its atomic positions. In the prototypes listed (and in the chemically unary isostructural substances) this species is represented by a pure element. In a number of cases, however, more than one atomic species may be equally distributed in the various atomic positions. If each atomic site has the same probability of being occupied in a certain percentage by atoms X and Y and all the sites are compositionally equivalent, the unary prototype is still a valid structural reference. In this case, from a chemical point of view, the structure will correspond to a two-component phase. Notice that there can be many binary (or more complex) solid solution phases having for instance the Cu-type or the W-type structures. Such phases are formed in several metallic alloy systems either as terminal or intermediate phases. 

The C-terminal steroid-modified heptapeptides, corresponding to the C-terminus of Hedgehog proteins, were synthesized in a combined solid-/solution-phase approach. The strategy was based on a dipeptide. 

Identification of unknown crystal structures and determination of phase fields by X-rays can be problematical if the characteristic patterns of the various phases are quite similar, for example in some b.c.c. A2-based ordered phases in noble-metal-based alloys. However, in many cases the characteristic patterns of the phases can be quite different and, even if the exact structure is not known, phase fields can still be well established. Exact determination of phase boundaries is possible using lattice-parameter determination and this is a well-established method for identifying solvus lines for terminal solid solutions. The technique simply requires that the lattice parameter of the phase is measured as a function of composition across the phase boimdary. The lattice parameter varies across the single-phase field but in the two-phase field becomes constant. Figure 4.12 shows such a phase-boundary determination for the HfC(i i) phase where results at various temperatures were used to define the phase boundary as a fimction of temperature (Rudy 1969). As can be seen, the position of is defined exactly and the method can be used to identify phase fields across the whole composition range. 

CALPHAD calculations were made for a number of binary systems including Au-Si, (Hf,Ti,Zr)-Be and Ni-Ti (Saunders and MiodoAvnik 1983) and a series of ternaries Hf-Ti-Be, Hf-Zr-Be and Hf-Ti-Be (Saunders et al. 1985). Figure 11.6 shows such a calculation for Ni-Ti. The results were encouraging in that they predicted with reasonable accuracy the limit to glass formation when the terminal solid solutions were considered. However, there was limited success when taking into account compoimd phases. To this end the approach was extended to include the kinetics of transformation more explicitly. Remarkably good results were then obtained for a wide variety of binary and ternary system and these are reported in Section 11.3.4. 

The early work of Schwarz and Johnson (1983) used a prediction of the underlying thermodynamics of the Au-La system to explain the relative stability of the liquid/amorphous phase in their elemental layered composites (Fig. 11.7). However, they utilised the method proposed by Miedema (1976) for thermodynamic stability of the liquid/amorphous phase. There are clear limitations to the Miedema approach firstly it is not guaranteed to produce the correct phase diagram and therefore phase competition is at best only approximated, and secondly, the thermodynamics of the terminal solid solutions are chosen quite arbitrarily. 

The Cu-Zn system (see Figure 2.7) displays a number of intermediate solid solutions that arise due to limited solubility between the two elements. For example, at low wt% Zn, which incidently is the composition of alloys known as brass, the relatively pure copper a phase is able to accommodate small amounts of Zn as an impurity in the crystal structure. This is known as a terminal solid phase, and the solubility limit where intermediate solid solutions (such as a + /S) begin to occur is called the solvus line. Some of the three-phase transformations that are found in this diagram include a peritectic (5 - - L -> e) and a eutectoid (5 -> y - - e). Remember that these three-phase transformations are defined for equilibrium coohng processes, not heating or nonequihbrium conditions. 

The variation of Hm, TSm, and Gm with composition for a system with limited solubility. The arrows indicate the solubility limits of the terminal solid solutions. 

Polythermal projections of the liquidus discussed in section 4.3.2. do not provide information on the compositions of solid phases if solid solutions or non-stoichiometric compounds are formed at equilibrium. For providing this information, the method of isothermal section is particularly useful. The following figure represents a simple ternary eutectic system with terminal solid solutions formed. 

Microstructurally, alloys are composed of alloy constituents that include alloy phases and, in some cases, unalloyed metals. Crystalline alloy phases can be subdivided into intermetallic phases, metal-nonmetal compounds such as borides or carbides see Borides Solid-state Chemistry Carbides Transition Metal Solid-state Chemistry), and terminal or complete solid solutions. 

The extent and type of solid solution formation depends on several parameters. If both component elements are isostructural and, in addition, similar in size, valence electron concentration, and electronegativity, a series of complete substitutional solid solutions may form across the diagram, as for V-Cr, Ni-Cu, Cu-Au, and Sb-Bi otherwise, limited terminal solid solutions form which are substitutional for elements with a solute-solvent size difference less than 15%, but may be interstitial for element pairs with size ratios of more than 20%, for example, for Fe(C) or Pb(Au) (here, the bracketed element is the solute). 

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