Nanosized quasi-binary eutectic systems and their characteristicparameters

2020 ◽  
Vol 2020 (1) ◽  
pp. 17-25
Author(s):  
D. Zakarian ◽  
◽  
A. Khachatryan ◽  
Keyword(s):  
Interaction Energy ◽  
Melting Temperature ◽  
Concentration Ratio ◽  
Internal State ◽  
Eutectic Point ◽  
Energy Concentration ◽  
Binary Eutectic ◽  
Analytical Formulas ◽  
Eutectic Systems ◽  
Energy Of Interaction

A method for accounting for the influence of the outer surface on the internal state of the electron ― ion system for nanoparticles is proposed. The estimated interaction energy of the representative elements of the components (LaB6, MeB2) is part of the composite depending on the size of the nanoplate. The characteristic parameters of the eutectic of quasi-binary boride-boride systems are calculated and analytically presented. During the transition of bulk materials to nanomaterials, the melting temperature of the eutectic decreases, and the concentration ratio of the components changes. With the help of first-principle methods the scheme of calculation of energy of interaction of representative elements of components from the first principles is developed. The dependence of the interaction energy of the representative elements on the sizes of the materials is analytically obtained. It is proved that the reduction of the size of the eutectic composite leads to a significant decrease in the melting temperature at the eutectic point, as well as to a change in the concentration ratio of the components. The obtained analytical formulas allow to estimate the change of concentration and melting temperature at the eutectic point depending on the thickness of the nanocomposite. Keywords: electron-ion system energy, pseudopotential method, nanosystem, nanoplate surface energy, concentration and melting point at the eutectic point.

First principle methods for calculating the linear coefficient of thermal expansion of quasi-binary eutectic systems

2021 ◽  
Vol 2021 (3) ◽  
pp. 38-47
Author(s):  
D. A. Zakarian ◽  
◽  
A. V. Khachatrian ◽  
Keyword(s):  
Thermal Expansion ◽  
Concentration Ratio ◽  
Volume Fraction ◽  
Coefficient Of Thermal Expansion ◽  
Harmonic Approximation ◽  
Eutectic System ◽  
Linear Coefficient ◽  
Virtual Cell ◽  
Binary Eutectic ◽  
Eutectic Systems

To calculate the linear coefficient of thermal expansion (LCTE) and its temperature dependence, a combination of the method of a priori pseudopotential and quasi-harmonic approximation (author's methods) is used. After approximating the results obtained for metal-like materials (carbides, borides, silicides), the LCTE is presented in an analytical form. In the case of quasi-binary eutectic systems based on carbides, borides, silicides, to estimate the interaction energy of the elements of two components, the concept of a virtual crystal (with a virtual cell) along the line of contact of two components is introduced. A virtual cell is assigned a volume average between the volume of a unit cell of two components, taking into account their concentration ratio. The components that make up the eutectic retain their crystal structure, their LCTE can be estimated as for pure components. Without taking into account the influence of interphase interaction, the LCTE of the eutectic system is determined using the rule of mixtures based on the LCTE components, taking into account their volume fraction. Taking into account the influence of the interface on thermal expansion is estimated by the virtual cell assigned to it. To determine the LCTE of the eutectic system, a ratio is proposed that connects the LCTE components and the docking boundaries through the concentration ratio. This method more realistically describes the structure of a quasi-binary eutectic. There is a consistency between the calculated and experimental data. Keywords: electron-ion system energy, interatomic interaction potential, quasiharmonic approximation, linear coefficient of thermal expansion, eutectic temperature.

Method for constructing liquidus curves of binary eutectic systems

2015 ◽  
Vol 60 (1) ◽  
pp. 74-79 ◽  
Author(s):  
E. Yu. Moshchenskaya ◽  
V. V. Slepushkin
Keyword(s):  
Binary Eutectic ◽  
Eutectic Systems

Construction of retrograde liquidus curves of binary eutectic systems

2016 ◽  
Vol 61 (3) ◽  
pp. 339-343
Author(s):  
E. Yu. Moshchenskaya ◽  
V. V. Slepushkin
Keyword(s):  
Binary Eutectic ◽  
Eutectic Systems

Glass Transition in Binary Eutectic Systems: Best Glass-Forming Composition

2010 ◽  
Vol 114 (37) ◽  
pp. 12080-12084 ◽  
Author(s):  
Li-Min Wang ◽  
Zijing Li ◽  
Zeming Chen ◽  
Yue Zhao ◽  
Riping Liu ◽  
...  
Keyword(s):  
Glass Transition ◽  
Glass Forming ◽  
Binary Eutectic ◽  
Eutectic Systems

scholarly journals Properties and Microstructures of Sn-Bi-X Lead-Free Solders

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Fan Yang ◽  
Liang Zhang ◽  
Zhi-quan Liu ◽  
Su-juan Zhong ◽  
Jia Ma ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Rare Earth ◽  
Intermetallic Compounds ◽  
Melting Temperature ◽  
Fatigue Resistance ◽  
Low Cost ◽  
Eutectic Point ◽  
Lead Free ◽  
Melting Characteristic ◽  
Lead Free Solders

The Sn-Bi base lead-free solders are proposed as one of the most popular alloys due to the low melting temperature (eutectic point: 139°C) and low cost. However, they are not widely used because of the lower wettability, fatigue resistance, and elongation compared to traditional Sn-Pb solders. So the alloying is considered as an effective way to improve the properties of Sn-Bi solders with the addition of elements (Al, Cu, Zn, Ga, Ag, In, Sb, and rare earth) and nanoparticles. In this paper, the development of Sn-Bi lead-free solders bearing elements and nanoparticles was reviewed. The variation of wettability, melting characteristic, electromigration, mechanical properties, microstructures, intermetallic compounds reaction, and creep behaviors was analyzed systematically, which can provide a reference for investigation of Sn-Bi base solders.

The long range van der Waals forces between non-identical systems

1965 ◽  
Vol 286 (1407) ◽  
pp. 573-587 ◽  
Keyword(s):  
Perturbation Theory ◽  
Excited State ◽  
Interaction Energy ◽  
Charge Distribution ◽  
Fourth Order ◽  
Ground State ◽  
Excited Molecule ◽  
Dipole Approximation ◽  
Two Systems ◽  
Energy Of Interaction

The interaction energy between two dissimilar non-ionized molecules or atoms is calculated in fourth-order perturbation theory and dipole approximation. The interaction Hamiltonian involves the charge distribution with the complete Maxwell field and not only the Coulomb interaction between charges. At close separations between the two systems (still large compared with molecular diameters) the interaction energy is of course that corresponding to the London force. However, for separations large compared with the characteristic wavelengths associated with transitions within the molecules the London force is modified considerably. In the case of two molecules in the ground state this modification was first found by Casimir & Polder. If one of the molecules is in an excited state new effects appear at these large distances. The energy of interaction depends on the orientation of the transition moment in the excited molecule with respect to the vector displacement between the two systems. In both transverse and longitudinal orientations the potential law is considerably stronger than the R -7 of the ground state-ground state interaction. For transverse orientations there is an unmodulated R -2 energy dependence which though very weak individually could give rise to considerable effects when the excited molecule is in a macroscopic environment.

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