Isomorphous systems alloys

Fig. 6. Effect of alloying elements on the phase diagram of titanium (a) a-stabilized system, (b) P-isomorphous system, and (c) P-eutectoid system.

FIGURE 6.32 Plane front solidification of an isomorphous binary alloy system, (a) As the... 

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. 

Our discussion of solids and alloys is mainly confined to the Ising model and to systems that are isomorphic to it. This model considers a periodic lattice of N sites of any given symmetry in which a spin variable. S j = 1 is associated with each site and interactions between sites are confined only to those between nearest neighbours. The total potential energy of interaction... 

The Ising model is isomorphic with the lattice gas and with the nearest-neighbour model for a binary alloy, enabling the solution for one to be transcribed into solutions for the others. The tlnee problems are thus essentially one and the same problem, which emphasizes the importance of the Ising model in developing our understanding not only of ferromagnets but other systems as well. 

Onsager s solution to the 2D Ising model in zero field (H= 0) is one of the most celebrated results in theoretical chemistry [105] it is the first example of critical exponents. Also, the solution for the Ising model can be mapped onto the lattice gas, binary alloy and a host of other systems that have Hamiltonians that are isomorphic to the Ising model Hamiltonian. 

Table 3.2 compares unit cell dimensions for the various allotropes and Fe-C alloys. Since the dopant species are entrained within individual unit cells, the volume of each unit cell will increase concomitantly with the concentration of carbon. Although the 5-Fe lattice is isomorphous with ferrite, the difference in volume between these allotropes corresponds to different concentrations of carbon in each solid solution. That is, 5-Fe contains an order of magnitude greater concentration of carbon than ferrite. Since a greater number of interstitial sites may be occupied by fee unit cells relative to bcc, austenite may contain an even greater concentration of C in the lattice, up to 2.1 wt%. It must be noted that the trend of increasing volume with dopant concentration is not only exhibited by the Fe-C system, but is also followed by all other interstitial alloys that we will examine later. 

Markova et al. (1967) constructed a phase diagram for the dysprosium-yttrium system utilizing thermal analyses, X-ray diffraction, metallography, hardness and electrical resistance measurements. Their starting materials were distilled yttrium and dysprosium of 99.6 to 99.7(wt )% purity. Both metals contained gaseous impurities as well as the metals Ca, Fe, Cu, Y, Gd, Dy and Ta. Alloys were prepared at approximately 10 at% intervals, arc-melted under purified helium and annealed at 850°C for 70 hr. The structure of all specimens was single phase with the hep lattice. A continuous series of solid solutions between isomorphic modifications was observed. 

Markova et al. (1964) were in the process of investigating this system when the work of Beaudry and Daane was published. Markova et al. subsequently pubhshed some photomicrographs showing single-phase structure in scandium, yttrium and alloys containing 11, 43 and 67 at% yttrium, but did not show their phase diagram for the system. They stated that their measurements showed a continuous series of solid solutions of the isomorphous modifications of the components in this system, which confirms the work of Beaudry and Daane. 

In the systems formed with A-elements - all transition metals, except for Be (in the Yb-Be system only YbBe is known to exist)-as long as the concentration of the X element does not reach a certain value, Yb maintains its divalency and correspondingly does not alloy with X, giving rise to wide liquid immiscibility ranges. Above this critical concentration, which depends on X, Yb becomes trivalent and forms compounds isomorphous with those of the neighboring lanthanides (landelli and Palenzona, 1976). This critical concentration increases regularly from left to right and down in the periodic system. 

In what follows, two important alloy systems will be briefly reviewed Ti-Al, the basis of technical a-Ii alloys and Ti-Mo, a (3-isomorphous alloy and the basis of several technical [3-Ti alloys. 

Complete solid solubility for a binary system means that atoms of one constituent can be substituted for the other over the entire range of compositions in both the solid and liquid state without introducing a different phase. Such alloys are said to be isomorphous. Hume-Rothery developed a set of criteria that must be met in order for a system to exhibit complete solid solubility ... 

Crystallization of Blends The first polymer blend was made from two polymeric mbbers in 1846, but polymer blend technology and a scientific understanding of the underlying principles controlling the compatibility (or lack of) in polymer mixtures (alloys as they have been named recently) has taken place only in the latter part of the current century. Many blends are non-crystalline but our interest in this document is focused on the kinetics of phase transformations of binary and ternary systems that receives more attention annually. Some of these systems can be very complicated, often comprised of multiple phases that m involve homopolymers, copolymers, mesophases and the like. Polymorphism and even isomorphism may occur... 

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