No, the Hume-Rothery rules do not work for nano-sized particles. According to a research paper published by Japanese scientists, they find that Hume-Rothery rules did not obey their experiment with subnanometer-sized particles. In a solid solution, the atoms of an element occupy places in a crystal lattice (FCC, BCC, HCP, etc.). This element is the solvent. The atoms of one or more elements are “dissolved” in the solvent. However, in modern research, we have more advanced tools. I`ve already taken a look at the Darken-Gurry cards, which is an improvement. We also have computational tools like CALPHAD that can predict much more complex phases. The Hume-Rothery rules apply only in simple cases, and phase diagrams have already been created experimentally for all simple cases. For situations where the Hume-Rothery rules would apply, you can simply search for the answer in a database. This diagram lists the crystal structure of each element and is marked with an asterisk (*) if this crystal structure is intended (not experimentally verified).
For Hume-Rosy rules, BCC, FCC and HCP are the most important structures. For more complex crystal structures, I wrote “complex” and the Bravais lattice; For example, iodine is similar to base-centered orthorhombic molecules, but there are I2 molecules at each lattice point. If you want to know more about Bravais lattices and crystal structures, read this article. Dr. Bhadeshia at Cambridge presents a brief overview of the actual applications of Hume-Rosty rules. Nevertheless, I believe that the Hume-Rothery rules are an important first step in alloy design. Before searching the library for a particular phase diagram or starting CALPHAD for the computer to make a guess, a materials scientist can use these rules to remove alloys that “obviously” don`t work. Personally, I think the valence rule is not as important as the other Hume-Rothery rules because the crystal structure of these two elements must be identical to have good solubility in solids. Hume-Rothery rules are broken in some cases. For example, interstitial atoms are smaller than solute atoms. Thus, the solubility of interstitial atoms is limited, and the first rule invalidates.
To form a solid solution, the atomic size of the solvent and solute plays a role. If the atoms in the solute are too small compared to the atoms in the solvent, this is not a good solution. In the first Hume-Rotherys law, there is a specified experimental proportion, which gives an excellent solid solution. It`s not a solution, it`s a connection! The atoms are arranged in an ordered intermetallic arrangement. In chemistry, you`ve probably learned about chemical bonds, solutions, and mixtures. Note: If the materials do not have the exact crystal structures, they do not form good solutions. So what we can expect is a transition from one phase to another phase with a different crystal structure. A solid alternative is a solid solution in which the atoms of the solute replace or displace the solvent atoms in its lattice structure. At lattice sites where solvent atoms would typically be located, solute atoms take over from solvent atoms. Substitution-resistant solutions consist of two types of atoms. And one of these atoms will take the place of the other. In addition, the incoming atoms must have the same atomic radius, valence, and crystal structure as the solvent atoms.
As a student who needs to intuitively guess how materials behave during a test, Hume-Rothery rules are very useful. However, I don`t just blindly guess elements – I use Hume-Rothery rules and more advanced computational tools to make informed predictions about the most beneficial elements! Yet real-world experiences are the best way to collect this data. My own research focuses on adding new elements to superalloys and whether I get an alternative or an unpleasant intermetallic solution. If the atoms have a significant difference in electronegativity, they form intermetallic compounds rather than a solid solution. A difference in electronegativity usually means that atoms are attracted to each other. If the potential decrease in energy due to the organization of atoms is greater than the decrease in entropy due to the mixing of atoms, the alloy becomes intermetallic. For the substitution of solid solutions, the Hume-Rothery rules are as follows: In engineering, Hume–Rothery rules are used to predict the ability to produce alloys by mixing different solids. Before mixing metals under experimental conditions, it is better to be able to check it. To do this, we can use Hume-Rothery rules to predict the solubility of solids.
If the rules are followed, chances are it`s a good, solid solution. As long as the difference in electronegativity is small enough for entropy to “win,” atoms form a solution instead of a compound. It turns out that on the Pauling scale, this difference is about 0.3 (entropy is powerful!) What happens if the gap is large? If the gap is large, there is more chance of forming an intermetallic complex rather than developing a solid solution. For example, you can make a mixture of 3 compounds: salt, water and oil. They will end with two phases: pure oil and a solution of salt water. Since there are two phases, the end result is a mixture according to basic chemical definitions. The Hume-Rosy rules, named after William Hume-Rothery, are a set of basic rules that describe the conditions under which an element in a metal can dissolve and form a solid solution. There are two types of rules; One refers to solid alternatives and the other refers to solid interstitial solutions. The electronegativity of the solute and solution must be identical. Metals with similar valence values dissolve more efficiently.
Maximum solubility occurs when the solvent and solvent atoms have the same valence. Otherwise, the difference in electron valence can cause metal complexes to form instead of solutions. For example, in tungsten alloy steel, iron (Fe) is the solvent and tungsten (W) is the solute. In addition, iron and tungsten have an FCC structure. As a result, a solid solution was formed. Connections and solutions (and elements) consist of a single phase. Mixtures have several phases. A good mixed solution occurs when the relative percentage difference is less than 15%. And it must be less than 8% to produce completely soluble (completely dissolved) solid solutions. In a solution, the combination of 2 or more phases gives one of the original phases.
For example, a Pt-Ag alloy is formed after separate heating of solids to high temperatures. And formation is only possible if the molar ratio Ag/Pt is less than 2.5 and platinum and silver have the same crystal structure. Since platinum and silver have an FCC structure, the formation of an Ag-Pt alloy has become possible. Basically, Hume–Rothery rules are limited to binary systems that form substitutive or interstitial fixed solutions. However, this approach limits the evaluation of advanced alloys, which are typically multi-component systems. Free energy diagrams (or phase diagrams) provide in-depth knowledge of equilibrium constraints in complex systems. Essentially, Hume–Rothery rules (and Pauling rules) are based on geometric constraints. The Hume-Rothery rules are also under development. Where they are considered a critical contact criterion that can be described with Voronoi diagrams.
 This could facilitate the theoretical creation of phase diagrams of multicomponent systems.