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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.
Substitutional solute in lattice. Depending on the size of the alloying element, a substitutional solid solution or an interstitial solid solution can form. [2] In both cases, atoms are visualised as rigid spheres where the overall crystal structure is essentially unchanged.
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)
Notice the strain in the lattice that the solute atoms cause. The interstitial solute could be carbon in iron for example. The carbon atoms in the interstitial sites of the lattice creates a stress field that impedes dislocation movement. This is a schematic illustrating how the lattice is strained by the addition of substitutional solute.
Interstitial atoms (blue) occupy some of the spaces within a lattice of larger atoms (red) In materials science, an interstitial defect is a type of point crystallographic defect where an atom of the same or of a different type, occupies an interstitial site in the crystal structure.
Example on bottom where albite (Na Al Si 3 O 8) changes to anorthite (Ca Al 2 Si 2 O 8), Al 3+replaces Si 4+ and Ca 2+ for Na +. Coupled substitution is the geological process by which two elements simultaneous substitute into a crystal in order to maintain overall electrical neutrality and keep the charge constant. [1]
This strengthening mechanism is related to solid-solution strengthening and has been observed in a variety of fcc and bcc substitutional and interstitial alloys, metalloids like silicon, and ordered intermetallics within specific ranges of temperature and strain rate. [1]
Homogeneous and heterogeneous solid solutions of metals, and interstitial compounds such as carbides and nitrides are excluded under this definition. However, interstitial intermetallic compounds are included, as are alloys of intermetallic compounds with a metal.