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Fundamentally, the Hume-Rothery rules are restricted to binary systems that form either substitutional or interstitial solid solutions. However, this approach limits assessing advanced alloys which are commonly multicomponent systems. Free energy diagrams (or phase diagrams) offer in-depth knowledge of equilibrium restraints in complex systems.
The rationale of crystal geometry to atom solubility prediction is summarized in the Hume-Rothery rules and Pauling's rules. Substitutional solid solution strengthening occurs when the solute atom is large enough that it can replace solvent atoms in their lattice positions. Some alloying elements are only soluble in small amounts, whereas some ...
The propensity for any two substances to form a solid solution is a complicated matter involving the chemical, crystallographic, and quantum properties of the substances in question. Substitutional solid solutions, in accordance with the Hume-Rothery rules, may form if the solute and solvent have: Similar atomic radii (15% or less difference)
Then there is the Hume-Rothery rule, which states that two metals that differ by more than 15% in their atomic radius will not form substitutional solid solutions. This rule can only be used reliably (90 % success) to predict poor solubility; it cannot predict good solubility.
The solubility of a specific solute in a specific solvent is generally expressed as the concentration of a saturated solution of the two. [1] Any of the several ways of expressing concentration of solutions can be used, such as the mass, volume, or amount in moles of the solute for a specific mass, volume, or mole amount of the solvent or of the solution.
The diffusion coefficient can also be expressed in terms of enthalpy of migration and entropy of migration of a vacancy, which are the same as for the migration of a substitutional atom: D v = 1 6 α 2 z v exp Δ S m R exp − Δ H m R T {\displaystyle D_{v}={\frac {1}{6}}\alpha ^{2}zv\exp {\frac {\Delta S_{m}}{R}}\exp {\frac {-\Delta H ...
(However, PE only dissolves at temperatures well above 100 °C.) Poly(styrene) has a solubility parameter of 9.1 cal 1/2 cm −3/2, and thus ethyl acetate is likely to be a good solvent. Nylon 6,6 has a solubility parameter of 13.7 cal 1/2 cm −3/2, and ethanol is likely to be the best solvent of those tabulated. However, the latter is polar ...
Ornstein-Zernike equation with the assumption of spherical symmetry. ρ is the liquid density, r is the separating distance, h(r) is the total correlation function, c(r) is the direct correlation function. h(r) and c(r) are the solutions to the MOZ equations. In order to solve for h(r) and c(r), another equation must be introduced.