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Hume-Rothery rules, named after William Hume-Rothery, are a set of basic rules that describe the conditions under which an element could dissolve in a metal, forming a solid solution. There are two sets of rules; one refers to substitutional solid solutions, and the other refers to interstitial solid solutions.
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)
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.
A solubility equilibrium exists when a chemical compound in the solid state is in chemical equilibrium with a solution containing the compound. This type of equilibrium is an example of dynamic equilibrium in that some individual molecules migrate between the solid and solution phases such that the rates of dissolution and precipitation are equal to one another.
The following chart shows the solubility of various ionic compounds in water at 1 atm pressure and room temperature (approx. 25 °C, 298.15 K). "Soluble" means the ionic compound doesn't precipitate, while "slightly soluble" and "insoluble" mean that a solid will precipitate; "slightly soluble" compounds like calcium sulfate may require heat to precipitate.
Electron microscopy of antisites (a, Mo substitutes for S) and vacancies (b, missing S atoms) in a monolayer of molybdenum disulfide.Scale bar: 1 nm. [1]A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids.
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 ...