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Alloys
Published in Alan Cottrell, An Introduction to Metallurgy, 2019
The Hume-Rothery rules show the broad pattern of alloy behaviour. From the free electron standpoint, we expect the alkali metals and the copper group to be good solvents for other metals. However, alkali metal atoms are large and electropositive, so that only rarely is there good solubility in an alkali metal (e.g. complete miscibility in K-Rb, K-Cs, Rb-Cs systems; extensive solubility of Mg in Li).
High Entropy Alloys
Published in T.S. Srivatsan, Manoj Gupta, High Entropy Alloys, 2020
Rohit R. Shahi, Rajesh K. Mishra
From the classical Hume–Rothery rules, the formation of a solid-solution phase in conventional alloys is governed by atomic size difference, the structure of alloying elements, and the difference in electronegativity [17]. In addition to these parameters, enthalpy of mixing and entropy of mixing are the two prominent phase formation parameters for HEAs. Zhang and co-workers [18] and Guo and co-workers [19] studied the effect of these parameters on the phase formation for HEAs. They reported that the formation of a solid-solution phase in HEAs is governed mainly by three factors: these are enthalpy of mixing (∆Hmix), entropy of mixing (∆Smix), and atomic size difference (δ) [18,19]. It has been reported that the formation of simple solid-solution phases (i.e., face-centered cubic (fcc), body-centered cubic (BCC), or their mixture, including both ordered/disordered cases) will occur when the enthalpy of mixing, entropy of mixing, and atomic size difference satisfy simultaneously −22 ≤ ∆Hmix ≤ 7 kJ/mol, 11 ≤ ∆Smix ≤ 19.5 J/K.mol and δ ≤ 8.5 conditions [19]. It has also been reported that the large ∆Hmix leads to phase separation and large negative ∆Hmix favors the formation of intermetallic phases (such as µ, σ, Laves phase, etc.) [20–22]. Moreover, atomic size difference should be small enough, because large atomic size difference favors the formation of amorphous phase [19]. Apart from these thermodynamic parameters, Yang and co-workers proposed that the formation of simple solid-solution phase in multicomponent HEAs can be effectively predicted by the Ω parameter, where Ω represents the effect of entropy relative to that of enthalpy [23]. They concluded that when the value of Ω ≥ 1.1 and δ ≤ 6.6%, the formation of a simple solid-solution phase will occur. The parameters Ω and δ are defined as follows [23]: Ω=TmΔSmix|ΔHmix|δ=∑i=1nCi(1−ri/r¯)2
Symbols, Terminology, and Nomenclature
Published in W. M. Haynes, David R. Lide, Thomas J. Bruno, CRC Handbook of Chemistry and Physics, 2016
W. M. Haynes, David R. Lide, Thomas J. Bruno
Homopolymer - A polymer derived from one species of (real, implicit, or hypothetical) monomer. [8] Hooke's law - The statement that the ratio of stress to strain is a constant in a totally elastic medium. Horse power - A non-SI unit of energy, equal to approximately 746 W. Hubble constant - The ratio of the recessional velocity of an extragalactic object to the distance of that object. Its value is about 2 × 10-18 s-1. Huckel theory - A simple approximation for calculating the energy of conjugated molecules in which only the resonance integrals between neighboring bonds are considered. Also called CNDO method (complete neglect of differential overlap). Hume-Rothery rules - A set of empirical rules for predicting the occurrence of solid solutions in metallic systems. The rules involve size, crystal structure, and electronegativity. Hund's rules - A series of rules for predicting the sequence of energy states in atoms and molecules. One of the important results is that when two electrons exist in different orbitals, the state with their spins parallel (triplet state) lies at lower energy than the state with antiparallel spins (singlet). Hydrazines - Hydrazine (diazane), H2NNH2, and its hydrocarbyl derivatives. When one or more substituents are acyl groups, the compound is a hydrazide. [5] Hydrocarbon - A compound containing only carbon and hydrogen. [5] Hydrolysis - A reaction occurring in water in which a chemical bond is cleaved and a new bond formed with the oxygen atom of water. Hyperfine structure - Splitting of energy levels and spectral lines into several closely spaced components as a result of interaction of nuclear spin angular momentum with other angular momenta in the atom or molecule. Hysteresis* - An irreversible response of a system (parameter A) as a function of an external force (parameter F), usually symmetric with respect to the origin of the A vs. F graph after the initial application of the force. A common example is magnetic induction vs. magnetic field strength in a ferromagnet. Ideal gas law - The equation of state pV = RT, which defines an ideal gas, where p is pressure, V molar volume, T temperature, and R the molar gas constant. Ideal solution - A solution in which solvent-solvent and solventsolute interactions are identical, so that properties such as volume and enthalpy are exactly additive. Ideal solutions follow Raoult's law, which states that the vapor pressure pi of component i is pi = xipi*, where xi is the mole fraction of component i and pi* the vapor pressure of the pure substance i. Ignition temperature* - The lowest temperature at which combustion of a material will occur spontaneously under specified conditions. Sometimes called autoignition temperature, kindling point. [10] Imides - Diacyl derivatives of ammonia or primary amines, especially those cyclic compounds derived from diacids. Also used for salts having the anion RN2-. [5] Impedance (Z) - The complex representation of potential difference divided by the complex representation of current. In terms of reactance X and resistance R, the impedance is given by Z = R + iX. [1] Index of refraction (n)* - For a non-absorbing medium, the ratio of the velocity of electromagnetic radiation in vacuo to the phase velocity of radiation of a specified frequency in the medium. [1]
High-entropy alloys fabricated via powder metallurgy. A critical review
Published in Powder Metallurgy, 2019
J. M. Torralba, P. Alvaredo, Andrea García-Junceda
The formation of one single phase is a desired objective when producing HEAs. In a conventional alloy, where we could have one main component and some minor alloying elements, the prediction of possible solid solutions are governed by the Hume-Rothery rules. In HEAs, where we have a much more complex situation in terms of alloying elements, the enthalpy and entropy of mixing play the most relevant role. There are a couple of deep investigations [179–181] that have studied these key parameters on the phase formation, and they have proposed different empirical rules: the formation of solid solutions or intermetallics depends on the enthalpy of mixing (ΔHmix), the entropy of mixing (ΔSmix) and the atomic size (δ). There are some specific conditions related to the limits of these parameters that promote the formation of simple phases or intermetallics. In Figure 7 the different regions are mapped according to these limits: ΔHmix cannot be too large in value because large positive ΔHmix leads to phase separation and large negative ΔHmix typically generates intermetallic phases. δ has to be small enough since large δ leads to excess strain energy and destabilises simple structures.