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Calculation of the Hardness of a Multi-Element Equiatomic Metal Alloy

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Calculation of the Hardness of a Multi-Element Equiatomic Metal Alloy Modern Approaches on Material Science DOI: 10.32474/MAMS.2020.02.000136 ISSN: 2641-6921 Mini Review Calculation of the Hardness of a Multi-Element Equiatomic Metal Alloy Zakarian DA* and Khachatrian AV Frantzevich Institute for Problems of Materials Science NAS Ukraine, Kiev *Corresponding author: Zakarian DA, Frantzevich Institute for Problems of Materials Science NAS Ukraine, Kiev Received: December 20, 2019 Published: January 16, 2020 Abstract A phenomenological approach has been developed for the mathematical description of the hardening of high-entropy alloys (HEAs) and a quantitative assessment of their hardness. It is shown that in HEAs with a bcc lattice, the degree of hardening is always greater than in HEAs with a fcc lattice (with the same number of elements in alloys). To calculate the relative hardening of the alloy, hardnessthe type of and crystal degree lattice of hardening and its parameter of multi-element value are alloys required. (HEAS). The calculation results are consistent with experimental data. Basic parameters of HEAs are calculated from first principles. The proposed method can be considered acceptable for assessing the Keywords: Multielement alloys; energy of interaction of elements; mismatch parameter; distortion density; hardness; heas Introduction difference in the radii of the atoms present in the alloy. Basically, One of the most common characteristics that determine the the mean quadratic displacement of atoms from the equilibrium quality of metals and alloys, the possibility of their use in various position in an ideal, undistorted lattice is used as a mismatch designs and under various working conditions, is hardness. parameter [1,2]. Hardness tests are performed more often than determining other mechanical characteristics of metals: strength, elongation, etc. In [1], it was found that the normalized strength at 0 K for 8 fcc the properties of the material, measurement tasks, conditions derivatives is proportional to the mean square displacement. Thus, A specific method for determining hardness is selected based on alloys, five-element equiatomic HEA CrMnFeCoNi and its for its implementation, available equipment, etc. Hardness is a arguing that the root mean square displacement are an important technical characteristic of a material, and depends on a set of factor in predicting the yield strength of alloys at 0 K. For the same physical properties, such as: interatomic distances, coordination number, number of valence electrons, nature of the chemical that not always an increase in distortion necessarily leads to an alloys in [2], from the results of experimental studies it was found bond, brittleness, elasticity, viscosity, etc. And calculation it from improvement in physical characteristics. Those. in assessing the mechanical characteristics of a HEAs, it is necessary to take into the present stage is impossible, especially if this applies to multi- account not only the parameters of the mismatch of atomic radii, first principles without taking into account experimental data at element or high-entropy alloys (HEAs). but also the values of the interaction potential of different elements. Here it is appropriate to cite the statement of the authors of [3], It is generally accepted that one of the fundamental concepts who believe that at present there is no clear evidence that the lattice for a HEAs is that the lattice structure of a solid solution is greatly distortions in the HEAs are much higher than in conventional alloys. distorted. The displacement of atoms from their ideal positions is Another method for assessing hardening in HEAs is solid solution given as the reason for the manifestation of a number of observed hardening, where Fleischer, Lyabush and Gippen approaches are physical and mechanical properties. It is believed that the distortion used, which are mainly used for binary alloys [4]. of the crystal lattice of the HEAs creates an obstacle to the free movement of dislocations, i.e. serves as a deterrent to plastic The vast majority of works are methods that work well on some deformation. Therefore, to describe the hardening of the HEAs, the HEAs and much worse on others. The mechanism of strengthening main emphasis in the research is placed on taking into account the the HEAs is the most important feature of this class of materials and Copyright © All rights are reserved by Zakarian DA. 226 Mod App Matrl Sci . Volume 2 - Issue 3 Copyrights @ Zakarian DA, et al. electrons leads to the appearance of two additional terms in the pseudopotential of the ion associated with the overlap of s and d this issue, so far, has neither a clear explanation, nor fundamental movement of dislocations and, less commonly, on the features of waves and with the resonant interaction of d waves. We consider confirmation. The main emphasis is on creating barriers to the the interaction of dissimilar atoms with each other. Undoubtedly, the case when the system consists of different metal atoms with N the asymmetric environment of each of the atoms in the crystal concentrations Cc(1∑ = forming an alloy of the substitution type. iii=1 of a disordered alloy leads to the fact that the equilibrium state The pseudopotential of the alloy is determined according to of the alloy is accompanied by the appearance of distortions of its V() q= ∑ Cvii () q the conditions of its additive nature i where vi(q) is the crystal lattice. These distortions depend only on the composition pseudopotential of the i-th ion. of the alloy; they do not arise and do not disappear during the thermomechanical treatment. In this paper, we propose a “hybrid” Note that in high-entropy alloys, quantum-mechanical calculations are carried out in the same way as for pure metals, but with an average pseudopotential of the form [1]. The energy of the method - a combination of first-principle methods, the use of approach to assess the hardness of a HEAs with a bcc and fcc single- electron-ion system is calculated using the perturbation theory in experimental data (relating to pure metals) and a phenomenological phase structure. pseudopotential up to second order inclusive. In order to evaluate the hardening of multi-element alloys by theoretical methods, it Calculation of Basic Parameters of a HEAs is necessary to study the mechanical behavior of an increasingly To calculate the basic parameters of a HEAs, an a priori complicated sequence of alloys related in composition. Using an a pseudopotential is used [5].When studying the properties of priori pseudopotential [5], for pure metals and alloys with an fcc transition metals using the pseudopotential method, the state of and bcc structure, the type of crystal structure, lattice parameters, d electrons is taken into account, which occupy an intermediate position between highly localized internal states and free electrons HEAs are determined from the minimum energy. The calculated and elastic moduli for the family of equiatomic nickel CrMnFeCoNi in the crystal. The interaction of d electrons with conduction data are consistent with experimental data [6,7] (Figure 1) Table 1. Figure 1: Lattice parameter of multi-element alloys with bcc and fcc lattices and their experimental values (2, 7, 9). R2 is the coefficient of determination Table 1: The calculated (Eс) and experimental (Eex) values of the elastic moduli of Ni based alloys (in GPa). Material CrMnFeCoNi CrFeCoNi FeCoNi CrCoNi CoNi FeNi Ni Eс 203,78 218,97 164,79 227,85 215,24 168,72 202,54 Eex [2] 201,6 215,04 162,0 226,2 216,7 166,16 199,12 As for the mean square displacement, paired interatomic alloys consisting of two types of atoms. To determine the distances potentials are used to determine it. If we calculate the pair between atoms of the same type, calculations are carried out as for interactions for any two atoms in the alloy (i.e., surrounded by random types of atoms), then the result will be the same for all pairs of any new element on the characteristics of the selected element pure metals. Theoretically, it is possible to evaluate the influence of atoms, because the interatomic distance is determined using the in the alloy. To assess the mechanical characteristics of the HEAs, average lattice parameter. Therefore, to determine the interatomic averaged basic parameters are used, such as the lattice parameter, distance of different types of atoms, we carry out calculations for atomic radius, and root mean square displacement [8]. Citation: Zakarian DA, Khachatrian AV. Mod App Matrl Sci 2(3)- 2020. MAMS.MS.ID.000136. DOI: 10.32474/MAMS.2020.02.000136 227 Calculation of the Hardness of a Multi-Element Equiatomic Metal Alloy Mod App Matrl Sci . Volume 2 - Issue 3 Copyrights @ Zakarian DA, et al. = ∑ Modeling the Structure and Properties of HEAs, where H0 CHii is the average alloy hardness, estimated Hi is the hardness of a Calculation Results and Discussion single crystal consisting of the i-th element included in the alloy), according to the rule of the mixture ( We model the structure of a HEA with n elements. Depending c is the material constant, which is proportional to the number of on the type of crystal lattice, for a complete description of the elements included in the alloy. As for distortion, it is possible to use structure of the HEAs, it is necessary to take into account: different versions of its representation [6]. Based on the results of a. The number of unit cells where pair interactions are realized, successful option is to present the distortion in the form ∆=rr − r both between the same type and the different type elements. a computational experiment, the most unambiguous, therefore,max min (rmax and rmin b. The number of unit cells, which takes into account the are the maximum and minimum atomic radii of the diversity of the population of atoms (taking into account the unit cell volume 3 (а is the lattice parameter), we obtain: concentration ratio).
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