Hume Rothery solubility rules

The likelihood of forming a substitutional solid solution between two metals will depend on a variety of chemical and physical properties, which are discussed in Chapter 6 (see the Hume-Rothery solubility rules in Section 6.1.4). Broadly speaking, substitutional solid solution in metallic systems is more likely when ... 

Hume-Rothery s Rules of Solid Solubility (metallurgy) (1) Complete miscibility can occur only if the unit cells of the two components are essenhally alike. (2) If the diameters of... 

The effect of relative atomic size on alloy structures was discussed on p. 134. It also influences the extent of terminal solid solubility in metallic alloys as expressed in the Hume-Rothery 15% rule " and its extension by Darken and Gurry to also take account of the effect of electronegativity difference in limiting solid solubility. The Hume-Rothery rule has now come to be stated that if the sizes of the solute and solvent atoms differ by less than 15%, extended terminal solid solutions may form, whereas if they differ by more, it is very unlikely that extended solid solutions will form. The rule is only permissive for the formation of extended solid solutions at radii differing by less than 15%, since other factors such as, for example, large electronegativity difference may still prevent their forming. 

Just as the saturated solubility of sugar in water is limited, so the solid solubility of element B in metal A may also be limited, or may even be so low as to be negligible, as for example with lead in iron or carbon in aluminium. There is extensive interstitial solid solubility only when the solvent metal is a transition element and when the diameter of the solute atoms is < 0 6 of the diameter of the solvent atom. The Hume-Rothery rules state that there is extensive substitutional solid solubility of B in >1 only if ... 

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) ... 

Person 2 Do Cu and Ni satisfy the third and fourth Hume-Rothery rules for complete solid solubility ... 

Apart from a few general rules, the alloying behaviour of metals is rather empirical. The classical rules of Hume-Rothery [220] explain this behaviour reasonably well. Such factors as size, electronegativity, valency, electron concentration, free energy, formation of intermediate phases and isomorphism are found to influence the alloying tendency of metals. However, size and electronegativity are the two most important factors, and they profoundly influence the solubility of the solute atoms and greatly affect the crystal structures of the alloys. 

Solid-fluid phase diagrams of binary hard sphere mixtures have been studied quite extensively using MC simulations. Kranendonk and Frenkel [202-205] and Kofke [206] have studied the solid-fluid equilibrium for binary hard sphere mixtures for the case of substitutionally disordered solid solutions. Several interesting features emerge from these studies. Azeotropy and solid-solid immiscibility appear very quickly in the phase diagram as the size ratio is changed from unity. This is primarily a consequence of the nonideality in the solid phase. Another aspect of these results concerns the empirical Hume-Rothery rule, developed in the context of metal alloy phase equilibrium, that mixtures of spherical molecules with diameter ratios below about 0.85 should exhibit only limited solubility in the solid phase [207]. The simulation results for hard sphere tend to be consistent with this rule. However, it should be noted that the Hume-Rothery rule was formulated in terms of the ratio of nearest neighbor distances in the pure metals rather than hard sphere diameters. Thus, this observation should be interpreted as an indication that molecular size effects are important in metal alloy equilibria rather than as a quantitative confirmation of the Hume-Rothery rule. 

The factors determining the particular structure adopted hy an intermetallic compound or, indeed, whether such a compound exists at all as a single-phase material, have been the subject of much discussion for a considerable period of time. The Hume-Rothery rules for electron compound formation will he very familiar and are related physically to the size of the Fermi sphere in the appropriate Brillouin zone. For example, electron compounds are expected for valence electron concentrations of , fj and l for the bcc, y-brass and cph structures, respectively. The interplay of other factors such as the atomic size, solubility and crystal structure of the components on the formation of intermetallic compounds has been considered in considerable detail by many workers, including Yao (1962), who suggested that transition metal binary systems could be classified into groups according to an excess energy dE expressed as... 

HUME-ROTHERY RULES FOR COMPLETE SOLID SOLUBILITY... 

Finally, from x = 0.98 until x = 1.0, a solution of copper in the zinc matrix is observed. The regions of homogeneous solutions are examples of Hume-Rothery s third rule. The higher valent atom (zinc) is more soluble in the lower valent solvent (copper) then vice versa. 

Find the Hume-Rothery criterion (15% rule) of mutual solubility of elementary metals and discuss it in terms of the Johnson interstitial electron model. 

In order to form a stable substitutional solid solution of appreciable solubility, the following Hume-Rothery rules, must be satisfied. Though these requirements are... 

As a more stringent application of the Hume-Rothery rules that govern the alloying of metals, if the difference in radii is less than 8%, the metals will be soluble throughout the full range of compositions. This is the case for nickel and copper, whose radii are 1.49 and 1.45 A, respectively. Hence, there are over 20 different alloys that are used in industry based on the mutual solubility of copper and nickel in... 

In two-component systems, the Gibbs phase rule allows one degree of freedom, usually in the form of a temperature vs. composition line. If there is little or no excess heat of mixing and the components are highly compatible, i.e., nearly same atomic radius and electronegativity, same crystal structure, and same valence (Hume-Rothery rules), the system can have complete solid and liquid solubility over the entire range of composition. Such systems are said to be isomorphous. However, even isomorphic systems do not solidify... 

The limit of solubility of B in A, to form a substitutional solution, is governed - particularly with metal alloys - by the empirical rules devised by Hume and Rothery. According to these rules, there are four factors which determine the degree of solubility of a substance B in a substance A ... 

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