Computation of thermodynamic parameters of binary metal systems with limited solubility of components in the solid α-phase
In the region of the primary solid α-phase for systems with limited solubility thermodynamic quantities such as the partial enthalpy of dissolution Δ HαB, the activity coefficients γαB and the activities ααB in binary metal systems were calculated. The above-mentioned indicated values were determine...
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Shcherban, A.P. Datsenko, O.A. 2023-11-22T15:41:54Z 2023-11-22T15:41:54Z 2020 Computation of thermodynamic parameters of binary metal systems with limited solubility of components in the solid α-phase/ A.P. Shcherban, O.A. Datsenko // Problems of Atomic Science and Technology. — 2020. — № 1. — С. 21-26. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 65.40.Gr https://nasplib.isofts.kiev.ua/handle/123456789/194340 In the region of the primary solid α-phase for systems with limited solubility thermodynamic quantities such as the partial enthalpy of dissolution Δ HαB, the activity coefficients γαB and the activities ααB in binary metal systems were calculated. The above-mentioned indicated values were determined from the relations that connect these parameters with the equilibrium distribution coefficient k0B and known thermodynamic quantities, such as the enthalpy variation ΔHплВ and entropy variation ΔSплВ during melting of component B. The calculation of equilibrium distribution coefficients using data from experimentally constructed solidus and liquidus lines of state diagrams was performed. The values and temperature dependences of the dissolution enthalpy for such systems as Ag–Mg, Nb–Ge, Mg–Al, Mg–Ag, Al–Mg, Ni–Ga, as well as the values and dependences of the activity coefficients γαB and activities ααB of the second component on these systems were determined. В області первинної твердої α-фази для систем з обмеженою розчинністю зроблено розрахунок значень таких термодинамічних величин, як парціальна ентальпія розчинення Δ H αB, коефіцієнти активності γαB і активність ααB компонентів у бінарних металевих системах. Вище зазначені величини визначали із співвідношень, які пов'язують ці параметри з рівноважним коефіцієнтом розподілу k0B і відомими термодинамічними величинами, такими як зміна ентальпії ΔHплВ і зміна ентропії ΔSплВ при плавленні компонента В. Розрахунок рівноважних коефіцієнтів розподілу виконували з використанням даних експериментально побудованих ліній солідусу і ліквідусу діаграм стану. Визначено значення і температурні залежності ентальпії розчинення для таких систем, як Ag–Mg, Nb–Ge, Mg–Al, Mg–Ag, Al–Mg, Ni–Ga, а також значення і залежності від температури розчинення коефіцієнтів активності γαB та активність ααB другого компонента в цих системах. В области первичной твердой α-фазы для систем с ограниченной растворимостью выполнен расчет значений таких термодинамических величин, как парциальная энтальпия растворения Δ HαB, коэффициенты активности γαB и активность ααB компонентов в двойных металлических системах. Выше указанные величины определяли из соотношений, которые связывают эти параметры с равновесным коэффициентом распределения k0B и известными термодинамическими величинами, такими как изменения энтальпии ΔHплВ и энтропии ΔSплВ при плавлении компонента В. Расчет равновесных коэффициентов распределения выполняли с использованием данных экспериментально построенных линий солидуса и ликвидуса диаграмм состояния. Определены значения и зависимости от температуры энтальпии растворения для таких систем, как Ag–Mg, Nb–Ge, Mg–Al, Mg–Ag, Al–Mg, Ni–Ga, а также значения и зависимости от температуры растворения коэффициентов активности γαB и активность ααB второго компонента в этих системах. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Pure materials and the vacuum technologies Computation of thermodynamic parameters of binary metal systems with limited solubility of components in the solid α-phase Розрахунок термодинамічних параметрів бінарних металевих систем з обмеженою розчинністю компонентів у твердій α-фазі Расчет термодинамических параметров бинарных металлических систем с ограниченной растворимостью компонентов в твердой α-фазе Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Computation of thermodynamic parameters of binary metal systems with limited solubility of components in the solid α-phase |
| spellingShingle |
Computation of thermodynamic parameters of binary metal systems with limited solubility of components in the solid α-phase Shcherban, A.P. Datsenko, O.A. Pure materials and the vacuum technologies |
| title_short |
Computation of thermodynamic parameters of binary metal systems with limited solubility of components in the solid α-phase |
| title_full |
Computation of thermodynamic parameters of binary metal systems with limited solubility of components in the solid α-phase |
| title_fullStr |
Computation of thermodynamic parameters of binary metal systems with limited solubility of components in the solid α-phase |
| title_full_unstemmed |
Computation of thermodynamic parameters of binary metal systems with limited solubility of components in the solid α-phase |
| title_sort |
computation of thermodynamic parameters of binary metal systems with limited solubility of components in the solid α-phase |
| author |
Shcherban, A.P. Datsenko, O.A. |
| author_facet |
Shcherban, A.P. Datsenko, O.A. |
| topic |
Pure materials and the vacuum technologies |
| topic_facet |
Pure materials and the vacuum technologies |
| publishDate |
2020 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Розрахунок термодинамічних параметрів бінарних металевих систем з обмеженою розчинністю компонентів у твердій α-фазі Расчет термодинамических параметров бинарных металлических систем с ограниченной растворимостью компонентов в твердой α-фазе |
| description |
In the region of the primary solid α-phase for systems with limited solubility thermodynamic quantities such as the partial enthalpy of dissolution Δ HαB, the activity coefficients γαB and the activities ααB in binary metal systems were calculated. The above-mentioned indicated values were determined from the relations that connect these parameters with the equilibrium distribution coefficient k0B and known thermodynamic quantities, such as the enthalpy variation ΔHплВ and entropy variation ΔSплВ during melting of component B. The calculation of equilibrium distribution coefficients using data from experimentally constructed solidus and liquidus lines of state diagrams was performed. The values and temperature dependences of the dissolution enthalpy for such systems as Ag–Mg, Nb–Ge, Mg–Al, Mg–Ag, Al–Mg, Ni–Ga, as well as the values and dependences of the activity coefficients γαB and activities ααB of the second component on these systems were determined.
В області первинної твердої α-фази для систем з обмеженою розчинністю зроблено розрахунок значень таких термодинамічних величин, як парціальна ентальпія розчинення Δ H αB, коефіцієнти активності γαB і активність ααB компонентів у бінарних металевих системах. Вище зазначені величини визначали із співвідношень, які пов'язують ці параметри з рівноважним коефіцієнтом розподілу k0B і відомими термодинамічними величинами, такими як зміна ентальпії ΔHплВ і зміна ентропії ΔSплВ при плавленні компонента В. Розрахунок рівноважних коефіцієнтів розподілу виконували з використанням даних експериментально побудованих ліній солідусу і ліквідусу діаграм стану. Визначено значення і температурні залежності ентальпії розчинення для таких систем, як Ag–Mg, Nb–Ge, Mg–Al, Mg–Ag, Al–Mg, Ni–Ga, а також значення і залежності від температури розчинення коефіцієнтів активності γαB та активність ααB другого компонента в цих системах.
В области первичной твердой α-фазы для систем с ограниченной растворимостью выполнен расчет значений таких термодинамических величин, как парциальная энтальпия растворения Δ HαB, коэффициенты активности γαB и активность ααB компонентов в двойных металлических системах. Выше указанные величины определяли из соотношений, которые связывают эти параметры с равновесным коэффициентом распределения k0B и известными термодинамическими величинами, такими как изменения энтальпии ΔHплВ и энтропии ΔSплВ при плавлении компонента В. Расчет равновесных коэффициентов распределения выполняли с использованием данных экспериментально построенных линий солидуса и ликвидуса диаграмм состояния. Определены значения и зависимости от температуры энтальпии растворения для таких систем, как Ag–Mg, Nb–Ge, Mg–Al, Mg–Ag, Al–Mg, Ni–Ga, а также значения и зависимости от температуры растворения коэффициентов активности γαB и активность ααB второго компонента в этих системах.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/194340 |
| citation_txt |
Computation of thermodynamic parameters of binary metal systems with limited solubility of components in the solid α-phase/ A.P. Shcherban, O.A. Datsenko // Problems of Atomic Science and Technology. — 2020. — № 1. — С. 21-26. — Бібліогр.: 7 назв. — англ. |
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| fulltext |
ISSN 1562-6016. PASТ. 2020. №1(125), p. 21-26.
COMPUTATION OF THERMODYNAMIC PARAMETERS OF BINARY
METAL SYSTEMS WITH LIMITED SOLUBILITY OF COMPONENTS
IN THE SOLID α-PHASE
A.P. Shcherban, O.A. Datsenko
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
E-mail: shcherban@kipt.kharkov.ua
In the region of the primary solid α-phase for systems with limited solubility thermodynamic quantities such as
the partial enthalpy of dissolution
BH , the activity coefficients В
and the activities
Ba in binary metal systems
were calculated. The above mentioned indicated values were determined from the relations that connect these
parameters with the equilibrium distribution coefficient k0B and known thermodynamic quantities, such as the
enthalpy variation mВH and entropy variation mВS during melting of component B. The calculation of
equilibrium distribution coefficients using data from experimentally constructed solidus and liquidus lines of state
diagrams was performed. The values and temperature dependences of the dissolution enthalpy for such systems as
Ag-Mg, Nb-Ge, Mg-Al, Mg-Ag, Al-Mg, Ni-Ga, as well as the values and dependences of the activity coefficients
В and activities
Ba of the second component on these systems were determined.
PACS: 65.40.Gr
INTRODUCTION
The formation of solid solutions occupies an
important place in the thermodynamics of a solid state.
Both in nature and in technology, one constantly has to
deal with solutions, and not with pure components.
Pure substances are only a limiting state that is never
really achieved. In physicochemical analysis, an
important aspect is the establishment of a relationship
between the composition and properties of compound
systems. For a quantitative calculation of the formation
of solid solutions and alloys, an approach of interest is
the one in which the equilibrium temperatures between
the liquid and solid phases, as well as the temperatures
of phase equilibria in the solid state, are chosen as the
main property.
In the formation of solid solutions one of the main
thermodynamic parameters is the partial enthalpy of
dissolution of the element
BH dissolved in the α-
phase of the primary solid solution. Other important
thermodynamic quantities are the activity coefficients
В and the activity
Ba of the soluble component in the
solid state. Reference data on the value of
thermodynamic values of dissolution are very limited,
and for most metal systems they are completely absent.
It is of practical interest to determine the value of these
thermodynamic quantities for systems with limited
solubility of the components in the base.
One of the necessary parameters for calculating the
thermodynamic quantities during the formation of solid
solutions of binary metallic systems is the equilibrium
distribution coefficient k0B. The value of k0B was
determined from the phase equilibria of the binary state
diagrams (SD) as the ratio of the concentration of the
second component in the solid and liquid phases
xSB/xLB. The main types of phase equilibria are
presented in [1].
In this work the calculation method for determining
the values of the above parameters in binary metal
systems with limited solubility of the second component
in the base was studied. The calculations for binary
metal systems such as Ag-Mg, Nb-Ge, Mg-Al, Mg-Ag,
Al-Mg, Ni-Ga were performed.
FORMULATION OF THE PROBLEM
The method for determining the thermodynamic
quantities:
BH ,
В and
Ba of the dissolved
element for binary metal systems with low solubility of
the second component in the solid α-phase was
developed by the authors of this work [2]. The values
and temperature dependences of the dissolution
enthalpy
BH of the sparingly soluble component, as
well as the activity
Ba and activity coefficients
В of
the second component in the saturated α-phase for such
systems as Cd-Na, Cd-Tl, Te-Ga, Te-As, Te-Cu were
determined by the proposed method.
The determination of thermodynamic quantities for
systems with limited solubility is based on the method
described in [2]. The difference from systems with low
solubility takes place in the determination of the
equilibrium distribution coefficients k0B necessary for
calculations depending on the dissolution temperature.
For systems with low solubility, the procedure for
determining k0B requires additional calculations [3-5].
Since experimentally constructed lines of solidus and
liquidus of SD are known for systems with limited
solubility, their analysis allows one to directly
determine the values k0B.
The aim of this work is to determine the values of
such thermodynamic parameters as the partial
dissolution enthalpy
BH , activity coefficient
B , and
activity
Ba of the second component in binary metal
systems with limited solubility of the components in a
solid state.
mailto:shcherban@kipt.kharkov.ua
CALCULATION METHOD
The distribution coefficients k0B were determined
from the pairs of temperatures and concentrations TS(i),
xSB(i) and TL(j), xLB(j) taken from the corresponding state
diagrams in the range from the melting temperature ТМА
of the main component to the maximum solution
temperature close to the eutectic temperature
Tmax ~ TEA. Using the pairs of temperature values (°С)
and the corresponding concentrations (at.%) of the
maximum solubility of the second component in the
solid and liquid phase taken from the state diagrams, the
distribution coefficient k0B was determined (see Table):
LBSBB xxk /0 . (1)
It should be noted a slight increase in the distribution
coefficient k0B for all systems in the selected range of
temperatures and concentrations of the second
component. The maximum variation k0, about 2.1 times,
was observed for Mg-Ag and Nb-Ge systems.
The values of k0B obtained above were used to
determine the partial dissolution enthalpy
BH from
the relation obtained in [6] and transformed to the form
(2)
mВmВ0B lnH STHkRT B
, (2)
where
BH is the partial enthalpy of dissolution of
component B in the α-phase at temperature T; k0B is the
equilibrium distribution coefficient; mВH melting
enthalpy of component B; R is the universal gas
constant; mВS is the melting entropy of component B.
The conclusion of the desired expression (2) is made
under the assumption that the primary solid α-phase
behaves as a regular solution, and the liquid phase,
which is in equilibrium with the solid phase above the
eutectic temperature, behaves as an ideal solution.
When the value
BH is known, it is possible to
determine the activity coefficient
B from expression
(3), which is included in the expression of the chemical
potential of the component for a real solution,
characterizing the deviation of the system from ideal
behavior [6]:
BB HRT ln , (3)
where
В the activity coefficient of component B in
the saturated α-phase at temperature T;
BH , R are the
same quantities as in (2).
From the thus determined values of the activity
coefficients
В , the activity
Ba of component B in the
α-phase was also calculated depending on the saturation
concentration, using the following expression.
Вxa BB , (4)
where
Ba is the activity of component B in the
saturated α-phase, %;
В is activity coefficient;
Bx is
component B concentration on the solidus line, at.%.
RESULTS AND DISCUSSION
For the studied systems Ag-Mg, Nb-Ge, Ni-Ga, Mg-
Ag, Al-Mg, Mg-Al, the temperature dependences of the
values
BH , calculated by formula (2) were shown in
Fig. 1.
Reference data of the enthalpy mВH and melting
entropy mВS of the dissolved component for
calculations were taken from [7].
An analysis of the results obtained on the dissolution
enthalpy shows that in the systems under study a change
in the partial enthalpies with a change in the dissolution
temperature was observed. With decreasing temperature
of the solution, a decrease in the partial enthalpies of
dissolution of the second component was observed.
From the general regularity of the positive values of the
partial dissolution enthalpies for the studied systems, the
distinctive feature was shown by the Nb-Ge and Ni-Ga
systems, which were characterized by a negative value
BH . A negative value
BH indicates the
exothermic dissolution of germanium in niobium and
gallium in nickel, in contrast to other systems in which
the dissolution of the second component occurs with
heat absorption.
Fig. 2 shows the graphical dependences of activity
coefficients
В as a function of the reciprocal
temperature for the systems studied. The obtained data
of the dependence of activity coefficients
В on
temperature show that in the systems under study, a
decrease in the value of activity coefficients is observed
with a decrease in the dissolution temperature.
An insignificant (1.22.1 times) temperature
dependence of the activity coefficients was observed for
the systems under study in a given range of
temperatures and concentrations of the second
component and a slight concavity of the dependence
curves
В = f (1/T).
Fig. 1. The temperature dependence of the dissolution enthalpy of the second component in the base for systems:
Ag-Mg, Nb-Ge, Ni-Ga, Mg-Ag, Al-Mg, Mg-Al
If the activity coefficients of the second component
in the solid phase is known, it is possible to determine
the activity
Ba of component B itself, depending on the
concentration of maximum solubility. Activity was
determined using expression (4).
The calculated values of the obtained
thermodynamic quantities of the second component in
the systems under study for three values of temperatures
and concentrations were showed in the Table.
The temperatures and the corresponding
concentrations of the second component are selected for
three arbitrary values on the SD.
An analysis of the values for the activities of the
second component shows that with a decrease in the
temperature of the solution there is an increase in the
activities of the second component in the process of its
dissolution for all studied systems.
The Mg-Ag system was characterized by a minimum
change in activity of 1.9 times, and the Nb-Ge system
by a maximum of 3.7 times.
Fig. 2. The values of the activity coefficient of the second component in the solid α-phase depending on the inverse
temperature for systems Ag-Mg, Nb-Ge, Mg-Al, Mg-Ag, Al-Mg, Ni-Ga
The values of thermodynamic quantities of the studied systems for the selected temperatures and concentrations
System T, °C xs, at.% k0 Н, J/mol γ Activity, %
Ag-Mg
904 7.6 0.65 1825 1.21 9.13
825 18.1 0.75 985 1.11 20.17
788 23.5 0.80 671 1.08 25.22
Nb-Ge
2341 1.3 0.20 -10190 0,63 0,79
2220.1 3.1 0.26 -13270 0,53 1,63
2011 7.6 0.41 -18190 0,38 2,91
Mg-Al
602 2.7 0.29 9739 3.82 10.32
525.7 6.7 0.33 8852 3.80 25.35
475.2 9.8 0.37 8238 3.77 36.89
Mg-Ag
579 0.8 0.09 5959 2.32 1.86
521 2 0.15 2684 1.50 3.01
493 3 0.19 1082 1.19 3.56
Al-Mg
601.6 3.3 0.29 9583 3.74 12.35
550.9 7.2 0.34 8375 3.40 24.50
498.3 12 0.40 7312 3.13 37.60
Ni-Ga
1402 3.6 0.37 -11370 0.44 1.57
1347 7.5 0.44 -13320 0.37 2.79
1290.6 12.4 0.53 -15050 0.31 3.89
CONCLUSIONS
The values and temperature dependences of the
dissolution enthalpy
BH of the sparingly soluble
second component were determined for the Ag-Mg, Nb-
Ge, Mg-Al, Mg-Ag, Al-Mg, and Ni-Ga systems.
The Nb-Ge and Ni-Ga systems were characterized
by a negative value
BH , which indicated the
exothermic process of dissolution of germanium in
niobium and gallium in nickel. In Ag-Mg, Mg-Al, Mg-
Ag, Al-Mg systems, the dissolution of the second
component occurs with heat absorption.
The obtained data of the dependence of activity
coefficients
В on temperatures show that in the studied
systems with a decrease in the dissolution temperature
there is a not significant decrease of 1.22.1 times the
value of the activity coefficients for the studied systems.
For the systems under study, the activity
Ba of the
components in the saturated solid phase was determined
depending on temperature and concentration. An
increase in dissolution activities of the second
component is observed with a decrease in temperature
in a given range of temperatures and concentrations.
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Article received 04.10.2019
РАСЧЕТ ТЕРМОДИНАМИЧЕСКИХ ПАРАМЕТРОВ БИНАРНЫХ МЕТАЛЛИЧЕСКИХ
СИСТЕМ С ОГРАНИЧЕННОЙ РАСТВОРИМОСТЬЮ КОМПОНЕНТОВ
В ТВЕРДОЙ α- ФАЗЕ
А.П. Щербань, О.А. Даценко
В области первичной твердой α-фазы для систем с ограниченной растворимостью выполнен расчет
значений таких термодинамических величин, как парциальная энтальпия растворения
BH , коэффициенты
активности
В и активность
Ba компонентов в двойных металлических системах. Выше указанные
величины определяли из соотношений, которые связывают эти параметры с равновесным коэффициентом
распределения k0B и известными термодинамическими величинами, такими как изменения энтальпии
плВH и энтропии плВS при плавлении компонента В. Расчет равновесных коэффициентов распределения
выполняли с использованием данных экспериментально построенных линий солидуса и ликвидуса
диаграмм состояния. Определены значения и зависимости от температуры энтальпии растворения для таких
систем, как Ag–Mg, Nb–Ge, Mg–Al, Mg–Ag, Al–Mg, Ni–Ga, а также значения и зависимости от температуры
растворения коэффициентов активности
В и активность
Ba второго компонента в этих системах.
РОЗРАХУНОК ТЕРМОДИНАМІЧНИХ ПАРАМЕТРІВ БІНАРНИХ МЕТАЛЕВИХ СИСТЕМ
З ОБМЕЖЕНОЮ РОЗЧИННІСТЮ КОМПОНЕНТІВ У ТВЕРДІЙ α-ФАЗІ
О.П. Щербань, О.А. Даценко
В області первинної твердої α-фази для систем з обмеженою розчинністю зроблено розрахунок значень
таких термодинамічних величин, як парціальна ентальпія розчинення
BH , коефіцієнти активності В
і
активність
Ba компонентів у бінарних металевих системах. Вище зазначені величини визначали із
співвідношень, які пов'язують ці параметри з рівноважним коефіцієнтом розподілу k0B і відомими
термодинамічними величинами, такими як зміна ентальпії
плВH і зміна ентропії плВS при плавленні
компонента В. Розрахунок рівноважних коефіцієнтів розподілу виконували з використанням даних
експериментально побудованих ліній солідусу і ліквідусу діаграм стану. Визначено значення і температурні
залежності ентальпії розчинення для таких систем, як Ag–Mg, Nb–Ge, Mg–Al, Mg–Ag, Al–Mg, Ni–Ga, а
також значення і залежності від температури розчинення коефіцієнтів активності
В та активність
Ba
другого компонента в цих системах.
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