Abstract
The article considers basic expansion of thermodynamics and thermodynamic interaction coefficients of the first, second and third orders of low-concentrated binary alloys. The values of interaction coefficients of the first and second orders in 37 such systems were estimated according to experimental thermodynamic data on the concentration dependence of excess chemical potential of an impurity in liquid alloys of binary systems. Estimates were obtained by the numerical differentiation method. This method is based on Newton first interpolation formula. Calculation formulas for the corresponding estimates are given. A simple theory is proposed that relates the thermodynamic interaction coefficient of the second order with the first-order one in the liquid alloy of certain system. The theory is based on the lattice model of a solution and the principles of statistical mechanics. The FCC lattice is adopted as a model lattice. The model of pair interaction between metal atoms in the alloy was used. The radius of this interaction corresponds to radius of the nearest atomic shell. Using the proposed theory, thermodynamic interaction coefficients of the second-order for all 37 systems considered in this work, as well as the values of the third order interaction coefficients for 23 systems out of 37 mentioned above, were calculated. For these 23 systems, theoretical estimates of the second-order interaction coefficients are in agreement with experimental ones both by sign and by order of magnitude. This circumstance can be considered as evidence of applicability of the numerical differentiation method for estimation of thermodynamic interaction coefficients of the first and second orders in liquid binary alloys. The accuracy of estimating the values of the third derivative by numerical differentiation is insufficient. That makes it impossible to compare the calculated values of the interaction coefficients of the third order with the experimental ones, obtained by this method. It can be assumed that the theoretical calculations just give an idea of the magnitudes’ order of these coefficients.
Highlights
The values of interaction coefficients of the first and second orders in 37 such systems were estimated according to experimental thermodynamic data on the concentration dependence of excess chemical potential of an impurity in liquid alloys of binary systems
This method is based on Newton first interpolation formula
Using the proposed theory, thermodynamic interaction coefficients of the second-order for all 37 systems considered in this work, as well as the values of the third order interaction coefficients for 23 systems out of 37 mentioned above, were calculated
Summary
Вологодский государственный университет (160000, Россия, Вологда, ул. Ленина,). Рассмотрены основное разложение термодинамики малоконцентрированных бинарных сплавов и термодинамические параметры взаимодействия первого, второго и третьего порядков в этих сплавах. По экспериментальным термодинамическим данным о концентрационной зависимости избыточного химического потенциала примеси в жидких сплавах бинарных систем оценены значения параметров взаимодействия первого и второго порядков в 37 таких системах. Это обстоятельство может рассматриваться как свидетельство в пользу применимости, в принципе, метода численного дифференцирования для оценки значений термодинамических параметров взаимодействия первого и второго порядков в жидких бинарных сплавах. Одной из основных целей настоящей работы является оценка значений параметров взаимодействия первого и второго порядков по экспериментальным данным в жидких бинарных сплавах. Оценки термодинамических параметров взаимодействия методом численного дифференцирования, сделанные по формулам (2) и (4) на основании экспериментальных данных [20] о концентрационной зависимости избыточного химического потенциала примеси в жидких бинарных сплавах, приведены в табл.
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