Binary isomorphous alloys

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. 

A binary alloy of two components A and B with nearest-neighbour interactions respectively, is also isomorphic with the Ising model. This is easily seen on associating spin up with atom A and spin down with atom B. There are no vacant sites, and the occupation numbers of the site are defined by... 

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. 

In pure titanium, the crystal structure is dose-packed hexagonal (a) up to 882°C and body-centered cubic (p) to the melting point. The addition of alloying dements alters the a—p transformation temperature. Elements that raise the transformation temperature are called a-stabilizers those that depress the transformation temperature, p-stabilizers the latter are divided into p-isomorphous and p-eutectoid types. The p-isomorphous elements have limited a-solubility and increasing additions of these dements progressively depresses the transformation temperature. The p-eutectoid elements have restricted p-solubility and form intermetallic compounds by eutectoid decomposition of the p-phase. The binary phase diagram illustrating these three types of alloy... 

Zhu] Zhu, Y.T., Devletian, J.H., Precise Determination of Isomorphous and Eutectoid Transformation Temperatures in Binary and Ternary Zr Alloys , J. Mater. Sci., 26(22), 6128-6122 (1991) (Experimental, Phase Relations, Thermodyn., 13)... 

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

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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