The atomic parameter model for the fifth and sixth transition metal quasicrystal alloys (Mc=0.5)

Abstract

The forming ability of quasicrystal phase has a relationship with the atomic bond factors based on differences in atom size and electron factors. Usually, those factors or their combination are used to describe the forming ability, stability of alloys, etc. In this paper, the quasicrystal alloy forming abilities for the fifth and sixth transition metals (Y, Zr, Nb, Mo, Ru, Rh, Pd and La, Hf, Ta, W, Re, Os, Ir, Pt) based alloys have been studied by the size factor and the atomic parametric function. It has been found that an ellipse curve can be used to separate the quasicrystal formed area from the informed area in the size factor and atomic parameters functional graph. The ellipse curve can be defined by an equation (x−m) 2 /c 2 +( y−n) 2 /d 2 =1. The overall reliabilities for the model are up to 97.4% and 95.5% for the fifth and the sixth transition metals based quasicrystal alloys, respectively. Also, the ellipse parameters m, n, c and d can be paraphrased by some appropriate parameters for each host metal.quasicrystal, transition metal, atomic parametric model, ellipse model Quasicrystal (QC) is a new class of solid material with new crystallographic properties and special structure. Since the first discovery of an icosahedral structure of Al-Mn alloy by Shechtman et al. [1] in 1984 two decades have passed. Much effort, including experimental, theoretical, empirical and semi-empirical methods, has been made to understand the formation mechanism and the physical properties of this new material. This has encouraged the discovery of many quasicrystals including TM-based (TM=transition metal) quasicrystals.Athanasiou and Jeevan have analyzed the effect of atomic size in the formation of quasicrystal. Athanasiou et al. [2] considered that the formation of quasicrystal phases depends upon the atomic radius ratio of the constituents. Jeevan et al. [3] proposed a classification of quasicrystals on the basis of atomic size to recognize the dominant role in forming the quasicrystal phases. They pointed out that the atomic size is the dominant parameter for the formation of quasicrystal alloys rather than composition.Dong et al. [4] , Qing et al. [5] , and Tsai [6] have analyzed the effect of valence electron concentration in the formation of quasicrystal. Dong et al. [4] and Qiang et al. [5] have analyzed the formation of the Al-Cu-Fe-Cr quasicrystal alloys system with the valence electron concentration, and have discussed that quasicrystal is a constant valence electron concentration phase. Tsai [6] has verified the availability of the Hume-Rothery rules [7] for the sta-

Prediction of Glass Forming Ranges in Ti–Ni–Zr, Ti–Cu–Zr and Ti–Cu–Hf Systems Based on Miedema and Atomic Parameter Models

“…can be defined by specific parameters of the constituent elements. 21,22) m and n are the coordinates of the center point of the ellipse. From the theoretical criterion for amorphous formation, we speculate that m and n depend on the bond parameter function of the equivalent constituent elements and the amorphous formation enthalpy of the system, respectively.…”

“…where X p is the Pauling electronegativity, the bond parameters z/r k and z/r cov are the ratios of atomic valence to atomic kernel radius and of atomic valence to covalent radius, respectively. 21) Atomic kernel radius r k is the ionic radius, omitting valence electrons, and covalent radius r cov is one half of the distance between the nuclei of two covalently bonded atoms of the same element in a molecule. For a ternary metallic glass A 100¹b¹c B b C c , A represents the host element, B and C represent the constituent elements, and b and c are the atomic percentages of constituent elements B and C, respectively.…”

“…To determine the bond parameter function, we assumed that elements B and C make up element D and that the parameters z/r k , z/r cov and X p of element D can be obtained by linear weighting, i.e. 21)…”

Glass Forming Ability of Zr–(Ni, Cu) Based Ternary Metallic Glasses Based on Bond Parameter Function and Formation Enthalpy Model

“…In this work, the bond parameter functions of the ternary metallic glasses were calculated using a linear weighted method. 21) The relevant parameter values are shown in Table 1. Formation enthalpy is another crucial parameter to evaluate GFA.…”