Hume-Rothery rules

Last updated

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.

Contents

Substitutional solid solution rules

For substitutional solid solutions, the Hume-Rothery rules are as follows:

  1. The atomic radius of the solute and solvent atoms must differ by no more than 15%: [1]
  2. The crystal structures of solute and solvent must be similar.
  3. Complete solubility occurs when the solvent and solute have the same valency. [2] A metal is more likely to dissolve a metal of higher valency, than vice versa. [1] [3] [4]
  4. The solute and solvent should have similar electronegativity. If the electronegativity difference is too great, the metals tend to form intermetallic compounds instead of solid solutions.

Interstitial solid solution rules

For interstitial solid solutions, the Hume-Rothery Rules are:

  1. Solute atoms should have a smaller radius than 59% of the radius of solvent atoms. [5] [6]
  2. The solute and solvent should have similar electronegativity. [7]
  3. Valency factor: two elements should have the same valence. The greater the difference in valence between solute and solvent atoms, the lower the solubility.

Solid solution rules for multicomponent systems

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. In essence the Hume-Rothery rules (and Pauling's rules) are based on geometrical restraints. Likewise are the advancements being done to the Hume-Rothery rules. Where they are being considered as critical contact criterion describable with Voronoi diagrams. [8] This could ease the theoretical phase diagram generation of multicomponent systems.

For alloys containing transition metal elements there is a difficulty in interpretation of the Hume-Rothery electron concentration rule, as the values of e/a values (number of itinerant electrons per atom) for transition metals have been quite controversial for a long time, and no satisfactory solutions have yet emerged. [9] [10]

See also

Related Research Articles

<span class="mw-page-title-main">Alloy</span> Mixture or metallic solid solution composed of two or more elements

An alloy is a mixture of chemical elements of which in most cases at least one is a metallic element, although it is also sometimes used for mixtures of elements; herein only metallic alloys are described. Most alloys are metallic and show good electrical conductivity, ductility, opacity, and luster, and may have properties that differ from those of the pure elements such as increased strength or hardness. In some cases, an alloy may reduce the overall cost of the material while preserving important properties. In other cases, the mixture imparts synergistic properties such as corrosion resistance or mechanical strength.

<span class="mw-page-title-main">Metallic bonding</span> Type of chemical bond in metals

Metallic bonding is a type of chemical bonding that arises from the electrostatic attractive force between conduction electrons and positively charged metal ions. It may be described as the sharing of free electrons among a structure of positively charged ions (cations). Metallic bonding accounts for many physical properties of metals, such as strength, ductility, thermal and electrical resistivity and conductivity, opacity, and lustre.

<span class="mw-page-title-main">Solution (chemistry)</span> Homogeneous mixture of a solute and a solvent

In chemistry, a solution is defined by IUPAC as "A liquid or solid phase containing more than one substance, when for convenience one substance, which is called the solvent, is treated differently from the other substances, which are called solutes. When, as is often but not necessarily the case, the sum of the mole fractions of solutes is small compared with unity, the solution is called a dilute solution. A superscript attached to the ∞ symbol for a property of a solution denotes the property in the limit of infinite dilution." One important parameter of a solution is the concentration, which is a measure of the amount of solute in a given amount of solution or solvent. The term "aqueous solution" is used when one of the solvents is water.

<span class="mw-page-title-main">Solvation</span> Association of molecules of a solvent with molecules or ions of a solute

Solvation describes the interaction of a solvent with dissolved molecules. Both ionized and uncharged molecules interact strongly with a solvent, and the strength and nature of this interaction influence many properties of the solute, including solubility, reactivity, and color, as well as influencing the properties of the solvent such as its viscosity and density. If the attractive forces between the solvent and solute particles are greater than the attractive forces holding the solute particles together, the solvent particles pull the solute particles apart and surround them. The surrounded solute particles then move away from the solid solute and out into the solution. Ions are surrounded by a concentric shell of solvent. Solvation is the process of reorganizing solvent and solute molecules into solvation complexes and involves bond formation, hydrogen bonding, and van der Waals forces. Solvation of a solute by water is called hydration.

<span class="mw-page-title-main">Solubility</span> Capacity of a substance to dissolve in a homogeneous way

In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution.

<span class="mw-page-title-main">Hydride</span> Molecule with a hydrogen bound to a more electropositive element or group

In chemistry, a hydride is formally the anion of hydrogen (H), a hydrogen ion with two electrons. In modern usage, this is typically only used for ionic bonds, but it is sometimes (and more frequently in the past) been applied to all compounds containing covalently bound H atoms. In this broad and potentially archaic sense, water (H2O) is a hydride of oxygen, ammonia is a hydride of nitrogen, etc. In covalent compounds, it implies hydrogen is attached to a less electronegative element. In such cases, the H centre has nucleophilic character, which contrasts with the protic character of acids. The hydride anion is very rarely observed.

<span class="mw-page-title-main">Intermetallic</span> Type of metallic alloy

An intermetallic is a type of metallic alloy that forms an ordered solid-state compound between two or more metallic elements. Intermetallics are generally hard and brittle, with good high-temperature mechanical properties. They can be classified as stoichiometric or nonstoichiometic intermetallic compounds.

William Hume-Rothery OBE FRS was an English metallurgist and materials scientist who studied the constitution of alloys.

<span class="mw-page-title-main">Cottrell atmosphere</span> Concept in materials science

In materials science, the concept of the Cottrell atmosphere was introduced by A. H. Cottrell and B. A. Bilby in 1949 to explain how dislocations are pinned in some metals by boron, carbon, or nitrogen interstitials.

Hardening is a metallurgical metalworking process used to increase the hardness of a metal. The hardness of a metal is directly proportional to the uniaxial yield stress at the location of the imposed strain. A harder metal will have a higher resistance to plastic deformation than a less hard metal.

A solid solution, a term popularly used for metals, is a homogeneous mixture of two compounds in solid state and having a single crystal structure. Many examples can be found in metallurgy, geology, and solid-state chemistry. The word "solution" is used to describe the intimate mixing of components at the atomic level and distinguishes these homogeneous materials from physical mixtures of components. Two terms are mainly associated with solid solutions – solvents and solutes, depending on the relative abundance of the atomic species.

In metallurgy, solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element to the crystalline lattice of another element, forming a solid solution. The local nonuniformity in the lattice due to the alloying element makes plastic deformation more difficult by impeding dislocation motion through stress fields. In contrast, alloying beyond the solubility limit can form a second phase, leading to strengthening via other mechanisms.

In chemistry, a Zintl phase is a product of a reaction between a group 1 or group 2 and main group metal or metalloid. It is characterized by intermediate metallic/ionic bonding. Zintl phases are a subgroup of brittle, high-melting intermetallic compounds that are diamagnetic or exhibit temperature-independent paramagnetism and are poor conductors or semiconductors.

This glossary of chemistry terms is a list of terms and definitions relevant to chemistry, including chemical laws, diagrams and formulae, laboratory tools, glassware, and equipment. Chemistry is a physical science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions; it features an extensive vocabulary and a significant amount of jargon.

<span class="mw-page-title-main">Chemical compound</span> Substance composed of multiple chemically bonded elements

A chemical compound is a chemical substance composed of many identical molecules containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element is therefore not a compound. A compound can be transformed into a different substance by a chemical reaction, which may involve interactions with other substances. In this process, bonds between atoms may be broken and/or new bonds formed.

The Rigid-Band Model is one of the models used to describe the behavior of metal alloys. In some cases the model is even used for non-metal alloys such as Si alloys. According to the RBM the shape of the constant energy surfaces and curve of density of states of the alloy are the same as those of the solvent metal under the following conditions:

  1. The excess charge of the solute atoms localizes around them.
  2. The mean free path of the electrons is much greater than the lattice spacing of the alloy.
  3. The electron states of interest in the pure solvent are all in one energy band, which is greatly separated in energy from the other bands.

Dynamic strain aging (DSA) for materials science is an instability in plastic flow of materials, associated with interaction between moving dislocations and diffusing solutes. Although sometimes dynamic strain aging is used interchangeably with the Portevin–Le Chatelier effect (or serrated yielding), dynamic strain aging refers specifically to the microscopic mechanism that induces the Portevin–Le Chatelier effect. 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.

<span class="mw-page-title-main">Bismuth–indium</span>

The elements bismuth and indium have relatively low melting points when compared to other metals, and their alloy bismuth–indium (Bi–In) is classified as a fusible alloy. It has a melting point lower than the eutectic point of the tin–lead alloy. The most common application of the Bi-In alloy is as a low temperature solder, which can also contain, besides bismuth and indium, lead, cadmium, and tin.

<span class="mw-page-title-main">High-entropy alloy</span> Alloys with high proportions of several metals

High-entropy alloys (HEAs) are alloys that are formed by mixing equal or relatively large proportions of (usually) five or more elements. Prior to the synthesis of these substances, typical metal alloys comprised one or two major components with smaller amounts of other elements. For example, additional elements can be added to iron to improve its properties, thereby creating an iron-based alloy, but typically in fairly low proportions, such as the proportions of carbon, manganese, and others in various steels. Hence, high-entropy alloys are a novel class of materials. The term "high-entropy alloys" was coined by Taiwanese scientist Jien-Wei Yeh because the entropy increase of mixing is substantially higher when there is a larger number of elements in the mix, and their proportions are more nearly equal. Some alternative names, such as multi-component alloys, compositionally complex alloys and multi-principal-element alloys are also suggested by other researchers.

Miedema's model is a semi-empirical approach for estimating the heat of formation of solid or liquid metal alloys and compounds in the framework of thermodynamic calculations for metals and minerals. It was developed by the Dutch scientist Andries Rinse Miedema while working at Philips Natuurkundig Laboratorium. It may provide or confirm basic enthalpy data needed for the calculation of phase diagrams of metals, via CALPHAD or ab initio quantum chemistry methods. For a binary system composed by elements A and B, a generic Miedema Formula could be cast as where terms Phi and nwS are explained and reported below. For a binary system the physical picture could be simplified by considering a relatively simpler function of the difference of these three physical parameters resulting in a more complex form

References

  1. 1 2 Callister, William D.; Rethwisch, David G. (January 2018). Materials Science and Engineering: An Introduction (10th ed.). Wiley. p. 992. ISBN   978-1-119-40549-8.
  2. Foundations of Materials Science and Engineering, 4th ed., W. Smith and J. Hashemi, pp.139-140 (2006).
  3. Goodman, D. A.; Bennett, L. H.; Watson, R. E. (January 1983). "Valency effects and relative solubilities in transition metal alloys". Scripta Metallurgica. 17 (1): 91–96. doi:10.1016/0036-9748(83)90077-7.
  4. Bhadeshia, K. D. H. "Solid Solutions: The Hume-Rothery Rules". PT (Phase Transformations) Group Home. University of Cambridge. Retrieved 16 August 2024.
  5. "The Structure of Metals - PPT video online download".
  6. "Introduction the properties and behavior of metals (And alloys) depend on their: Structure Processing history and Composition Engr PPT video online download".
  7. "Hume-Rothery Rules". Van Nostrand's Scientific Encyclopedia. John Wiley & Sons, Inc. 2002.
  8. Wang, Zhijun; Huang, Yunhao; Liu, C. T.; Li, Junjie; Wang, Jincheng (4 Apr 2019), "Atomic packing and size effect on the Hume-Rothery rule", Intermetallics, 109: 139–144, doi:10.1016/j.intermet.2019.04.001, S2CID   141214774
  9. Gao, Michael C (2016). High-Entropy Alloys: Fundamentals and Applications.
  10. Mizutani, Uichiro; Sato, Hirokazu (January 2017). "The Physics of the Hume-Rothery Electron Concentration Rule". Crystals. 7 (1): 9. doi: 10.3390/cryst7010009 . ISSN   2073-4352.

Further reading