Abstract
As a result of research using the boiling point method, the partial pressure of magnesium above Mg–Sn alloys was determined, represented by the temperature-concentration dependence. The decomposition of dimagnesium stannide into its constituent metals has been preliminarily established. The pressure of magnesium above the intermetallic compound (pD) corresponds to the equation: ln pD [Pa] = 26.695–21,250 × T−1. The decomposition temperature of Mg2Sn at atmospheric pressure corresponds to the value (1401 ± 131 K), which, within the limits of determination errors, coincides with the boiling point of the melt (1494 ± 105 K). The thermodynamic activities of magnesium and tin were determined, based on which the partial and integral mixing functions—entropy and enthalpy—were calculated and presented in tabular form. Based on the partial values of the vapor pressure of magnesium and tin, the boundaries of the vapor–liquid equilibrium fields at atmospheric pressure (101.3 kPa) and in a vacuum (0.7 kPa) were calculated. A complete phase diagram was constructed, including the boundaries of the liquid–vapor phase transition at the specified pressures. A pressure drop in the system below 0.7 kPa may be accompanied by the crystallization of dimagnesium stannide from the melt. The boiling point of magnesium at atmospheric pressure is 1100 °C, in a vacuum − 695 °C, tin –2609 °C and 1791 °C, respectively. The areas of coexistence of liquid and vapor are large in terms of temperature. The boiling point of the melt in a vacuum (821 °C), corresponding to dimagnesium stannide, exceeds the melting point of the compound (770.5 °C) by ⁓50 °C. The composition of the equilibrium vapor phase is represented by magnesium in virtually the entire range of component concentrations. Thus, at a content of 0.1 wt. % Mg (1 × 10–3 at. %) in the melt, the vapor phase will contain 99.73–99.76 wt. % magnesium, with the remainder being tin. That is, the separation of magnesium by distillation in a vacuum does not present any technological difficulties.
Keywords: Magnesium, Tin, Dimagnesium stannide, Entropy, Enthalpy
Subject terms: Chemistry, Energy science and technology, Materials science, Physics
Introduction
Magnesium and its alloys are widely used in various industries1–6. In recent years, researchers have focused on the production of biodegradable magnesium alloys used in orthopedics: magnesium alloys with zinc, alloyed with calcium, silver, and tin to improve the anti-corrosion properties of the alloy, as well as binary alloys of these metals, which have a minimal negative impact on the human body.
Along with the expansion of the range of magnesium-based alloys, problems have arisen with the processing of the wide variety of waste and secondary raw materials based on it. However, to date, no rational technology has been developed to process the biodegradable secondary raw materials and defective products. One promising method to process them may be vacuum distillation, with magnesium being transferred to the vapor phase and impurities being concentrated in the still bottom. The possibility of distillation separation of the system into its components can be assessed if the liquid–vapor phase transition boundaries are available on the phase diagram, in particular, for the magnesium–tin system. Data on the boundaries for the Mg–Sn system are not available in known sources of information. In this regard, it became necessary to construct these boundaries based on experimental thermodynamic studies based on the saturated vapor pressure values of the components that make up the system.
Magnesium and tin form alloys with unlimited solubility in the liquid state and the presence of a congruent melting compound Mg2Sn at 778°C7,8.
A number of papers9–20 are devoted to the study of the thermodynamic properties of magnesium–tin system melts.
In studies9,10, using the method of electromotive forces of concentration chains, the thermodynamic functions of the system at temperatures of 650 °C and 800 °C were determined over the entire range of liquid alloy concentrations, and large negative deviations from ideal behavior were found. In paper11, the saturated vapor pressure of magnesium, the thermodynamic functions of liquid alloys, and the liquidus lines of the phase diagram were determined using the isopyestic method at 990 and 1290 K. The authors of12,13 determined the thermodynamic functions, thermal stability, and other physical properties of the Mg2Sn compound. In the study14, the partial pressure of saturated magnesium vapor for alloys containing 10–60 at. % Sn was determined using the boiling point method at temperatures of 1154—1385 K (881–1112 °C). The authors15 presented the isotherm of magnesium activity at 1350 K (1077 °C) in alloys with tin, indicating a significant negative deviation of the Mg–Sn liquid system from Raoult’s law.
In papers16,17, the results of previous studies of the thermodynamic properties and state diagram of Mg–Sn are analyzed, and the most reliable data are entered into a double system model using a modified quasi-chemical model. The obtained results showed very good agreement with the published experimental data.
In study18, based on the results of studies of the curvature of the liquidus in the approximation of the ideal associated solution model with the use of compound dissociation schemes, calculations of the activities of the components were performed. The presented dependencies of the isotherms of magnesium activities in alloys with tin have a negative deviation from ideality and are close to those obtained in previous studies.
Excess thermodynamic functions and activity coefficients, based on which the saturated vapor pressure can be determined for magnesium–tin alloy components at a temperature of 1073 K (800 °C), are given in publications19,20.
Other studies have investigated the physical properties and structure of magnesium alloys containing tin21–23, as well as the effect of alloying additives on them24. No other information on the thermodynamic properties of the Mg–Sn system has been found in available sources.
Thus, despite a significant number of thermodynamic studies, there is no information on the phase transition boundaries between melt and vapor.
The aim of this paper is to construct the phase transition boundaries between melt and vapor in the magnesium–tin system and to interpret the results for technological needs.
Materials
Alloys, the compositions of which are given in Table 1, were prepared to conduct experiments to determine the saturated vapor pressure of the components. Tin (99.99% wt.%; GOST 860–75, Novosibirsk, Russia) and double-distilled magnesium (99.99% wt. %, TC 1714–001-95, Almaty, Kazakhstan) were used to prepare the alloys. The alloy was prepared in an alundum crucible placed in a steel retort at an argon pressure of 500 kPa and a temperature of 800–1100 °C, depending on the composition. Increased pressure was used to prevent magnesium evaporation. The initial components in the crucible were heated to the specified temperature, held for 5 h, and then cooled by immersion in water.
Table 1.
Composition of Mg–Sn alloys.
| Alloy number | Mass. % | at. % | ||
|---|---|---|---|---|
| Mg | Sn | Mg | Sn | |
| 1 | 58.18 | 48.12 | 85.44 | 14.56 |
| 2 | 35.85 | 64.15 | 73.18 | 26.82 |
| 3 | 23.50 | 76.50 | 60.00 | 40.00 |
| 4 | 15.43 | 85.57 | 47.12 | 52.88 |
| 5 | 9.09 | 90.91 | 32.81 | 67.19 |
An alloy with a content of 60.0 at. % Mg and 40.0 at. % Sn (Fig. 1) corresponds to the composition of the intermetallic compound Mg2Sn–dimagnesium stannide. X-ray structural studies performed on a Bruker D8 Advance diffractometer with copper radiation λkα = 0.154051 nm with graphite monochromator showed (Fig. 2) that the sample contained 97.8% Mg2Sn and 2.8% Sn.
Fig. 1.
Synthesized dimagnesium stannide—appearance.
Fig. 2.
Diffractogram of synthesized dimagnesium stannide.
Research and calculation methods
The determination of the phase transition boundaries between the melt and vapor is based on the values of the saturated vapor pressure of magnesium and tin, which make up the system.
Determination of the dissociation pressure of Mg2Sn.
The isobaric boiling point method was used to determine the saturated vapor pressure. This method was based on a sharp increase in the evaporation rate of the volatile component near the equalization of the saturated vapor pressure of the metal and the corresponding temperature.
The method of determination in this case was as follows. A sample of the Mg2Sn alloy was placed in a quartz crucible and suspended on spring scales in a quartz retort filled with argon. Then, by throttling the inlet of the vacuum pump, the pressure specified by the experimental conditions was set and the crucible was lowered into the shaft furnace. The crucible with the sample was placed in a predefined isothermal zone of the furnace. After that, the furnace was heated at a constant rate. At the same time, the mass loss (Δm) and the corresponding temperature in the system were recorded. The temperature at which a sharp increase in the rate of mass loss was observed at a given pressure was considered equal to the vapor pressure of dimagnesium stannide or its decomposition components. As an example, Fig. 3 shows the change in temperature and mass of the sample when heating Mg2Sn at a pressure of 0.67 kPa.
Fig. 3.
Change of temperature (a) and mass loss of Mg2Sn (b) at a pressure of 0.67 kPa.
The design of the continuous weighing installation to implement the method is shown in 25.
Study of the condensate composition
The composition of the condensate after Mg2Sn evaporation, which allows to judge the evaporation process, was studied during vacuum thermal treatment at a temperature of 850 °C and a pressure of 0.67 kPa on the installation, the diagram of which is shown in Fig. 4.
Fig. 4.
Schematic diagram of the setup to study the condensate composition: 1—container with alloy; 2—condenser; 3—condenser connection line; 4—retort; 5—electric furnace; 6—thermocouple; 7—flow control valve; 8—gas evacuation channel; 9—inert gas supply channel; 10—condensate.
The installation was a quartz retort with a sealed end, in which a porcelain tubular condenser split into two halves along the length was placed. At one end of the condenser a container with a Mg2Sn sample was placed. The retort is sealed with a plug, through which the cover of the chromel-aluminum thermocouple and the channel for the evacuation of gases and the supply of inert gas with a change in the direction of gas movement by means of a leak valve located outside the retort are discharged.
The methodology of the study was as follows. The container with the Mg2Sn sample was placed at one end of the condenser, so that its longitudinal joint was in the horizontal plane, with the condenser containing the compound placed in the sealed end of the retort. The air was evacuated from the system by a vacuum pump. Then, by changing the gas flow direction, the retort was filled with inert gas, in our case—argon.
After that, the sealed end of the retort was placed in a resistance electric furnace so that the container with Mg2Sn was in the isothermal zone during heating. The temperature in the sublimation and condensation zones was monitored using thermocouples. The pressure in the system was maintained by throttling the inlet pipe of the vacuum pump. After the exposure, the retort was filled with argon, removed from the electric furnace, and cooled in the air. The experimental products were weighed and analyzed. The quality of the condensate and its composition were determined by physical and chemical methods.
Automatic control and maintenance of temperature were performed using a microprocessor controller with an accuracy of ± 10 °C. Pressure was measured at the retort outlet with an M110 aneroid barometer with an accuracy of ± 65 Pa.
Determination of the saturated vapor pressure of magnesium and tin above alloys
The saturated vapor pressures of magnesium and tin differ by several orders of magnitude—at the boiling point of magnesium (1373 K), the saturated vapor pressure of tin is 0.1 Pa26. In this regard, the isothermal boiling point method was chosen to determine the values of magnesium vapor pressure above its alloys with tin. The design of the setup to implement the method is shown in25.
The determination method was as follows. A sample of the alloy (up to 2 g) was placed in a crucible, which was suspended in a retort outside the heating zone. The retort was evacuated twice using a vacuum pump and then filled with argon. After this, the lower part of the retort was placed in the isothermal zone of a preheated electric furnace. The retort was heated under an overpressure of 2–5 kPa with an open inert gas supply system to suppress the evaporation of components and compensate for the pressure increase in the retort due to gas expansion during heating. Once the sample reached the target temperature, argon evacuation from the retort volume was initiated while maintaining a constant sample temperature (isothermal mode). At the same time, the loss of the sample in mass and the change in pressure were simultaneously recorded. The pressure at which a sharp increase in the evaporation rate (weight loss) was observed was considered to be equal to the pressure of magnesium vapor above the alloy.
The values of the partial pressures of saturated magnesium vapor of alloys of the same concentration at different temperatures were described by the equation: 
, then the dependence of each of the coefficients A and B was determined as a function of the magnesium concentration in the initial alloy. As a result, the temperature-concentration dependence of the magnesium vapor pressure 
was obtained.
The partial pressure of tin vapor above the magnesium–tin alloy was determined as: 
, where 
is the saturated vapor pressure above elemental tin; 
is the activity of tin in the alloy; 
is the activity coefficient of tin; 
is the concentration of tin in the alloy, equal to 
. Here 
is the concentration of magnesium in the initial alloy.
The activity coefficient of tin was calculated by numerical integration of the Gibbs–Duhem equation, using an auxiliary function 
, proposed by Darken26. After transformation27 and substitution into the equation: 
, this function relates 
and 
in a form convenient for numerical integration: 
.
Determination of thermodynamic functions and phase transition boundaries
Due to the absence of boiling of liquid metal melts due to the high density of the components, the boiling point was determined to be equal to the temperature at which the sum of the partial pressures of magnesium and tin, in accordance with Dalton’s law, is equal to atmospheric pressure (101.3 kPa) or another pressure corresponding to the conditions of vacuum technologies.
The composition of the vapor phase (the concentration of magnesium 
and tin 
) above the melts at the boiling point of the melt with a certain ratio of components was determined as the ratio of the partial pressure of magnesium or tin to the total vapor pressure above the melt: 
.
The value of the energy functions of alloy formation was determined based on the dependence: 
, where 
is the partial Gibbs mixing energy of magnesium or tin; 
is the thermodynamic activity of magnesium or tin in their alloys. 
is defined as the ratio of the partial pressure of magnesium above the alloy to the vapor pressure above the pure element at the same temperature: 
. Based on this dependence, the partial mixing entropy of magnesium and tin (
) was determined: 
, and further the mixing enthalpy (
): 
.
The integral values of the entropy and enthalpy of mixing were calculated by summing the fractions of the partial functions in the initial alloy: 
and 
.
The values of the partial evaporation functions were determined in accordance with the dependence: 
, where 
is the partial Gibbs energy of evaporation of magnesium or tin; 
is the partial pressure of saturated magnesium or tin vapor in their alloys. Hence: 
, 
, where 
and 
are the partial entropy and enthalpy of evaporation of magnesium or tin, respectively.
The integral thermodynamic functions of evaporation of the magnesium–tin system were calculated similarly to those for the formation of solutions.
Results and their discussion
Information on the behavior of Mg2Sn during the transition to the gas phase is absent. This is of great importance in constructing a complete phase diagram, including the boundaries of the liquid—vapor phase transition. Thus, if the compound has a sufficiently high vapor pressure and transitions to vapor without decomposing, this will lead to a deterioration in the quality of the magnesium distillate due to the presence of tin. In this regard, we conducted a study on the behavior of dimagnesium stannide in a vacuum.
The results of the experiments on the decomposition of Mg2Sn in vacuum: the pressure at which the experiments were performed; the decomposition temperature of the compound; the calculated pressure value obtained by approximation of the determination results; and the deviation (Δ) of the pressure value from the calculated one are given in Table 2.
Table 2.
Dissociation pressure of dimagnesium stannide Mg2Sn.
| Experimental pressure, Pa | Temperature, K | Calculated pressure, Pa | Δ, % |
|---|---|---|---|
| 130 | 975 | 134 | + 0.74 |
| 983 | 160 | + 16.87 | |
| 670 | 1046 | 590 | − 13.06 |
| 1043 | 556 | − 19.87 | |
| 6670 | 1187 | 6586 | − 1.21 |
| 1191 | 6994 | + 4.69 | |
| 13,330 | 1237 | 13,580 | + 1.82 |
| 1244 | 14,858 | + 10.16 | |
| 40,000 | 1320 | 40,000 | 0 |
| 1313 | 36,706 | − 8.97 | |
| |Δ|avg = 7.74 | |||
The total error in the determination of dimagnesium stannide decomposition is calculated as the sum of the errors in independent measurements, %: temperature − 1; weighing – 0.1; pressure 0.5; approximation of experimental data − 7.74, equal to 9.34%.
The values of the decomposition pressure—dissociation of dimagnesium stannide (pD) depending on temperature were approximated by the expression:
ln pD [Pa] = 26.695–21,250 × T−1. The dissociation temperature at atmospheric pressure corresponds to 1401 ± 131 K = 1128 ± 105 °C.
The enthalpy of magnesium dissociative evaporation, calculated from the equation of magnesium vapor pressure dependence on temperature, is 176.7 ± 16.5 kJ/mol, entropy—126.1 ± 11.8 J/(mol × K).
Mg2Sn undergoes decomposition into constituent metals during dissociative evaporation. Decomposition process of the compound at a temperature of 850 °C and a pressure of 0.67 kPa was performed using an installation to confirm such decomposition.
As a result of the experiment, a significant number of spherical granules were found in the distillation residue, indicating coalescence of tin droplets after magnesium evaporation from the alloy. X-ray phase analysis of the condensate sample revealed 91.6% Mg, 1.52% Mg2Sn, and 6.95% SiO2. X-ray fluorescence analysis revealed 95.35% magnesium, 0.25% tin, and 4.84% silicon. The presence of Mg2Sn can be explained by entrainment of the initial alloy by the magnesium vapor flow formed during compound dissociation. The presence of SiO2 is apparently due to contamination of the condensate sample during removal from the condenser.
The values of the partial pressure of magnesium vapor above its melts with tin are given in Table 3, which also shows the vapor pressure of tin and the error of the experimental determinations.
Table 3.
Magnesium vapor pressure values determined experimentally, calculated using the approximate equation, calculated tin vapor pressure values, approximate equation coefficients, experimental determination error.
| [Mg], at. % | T, K |
 , experiment, kPa |
 , calculation, kPa |
 , calculation, kPa |
 |
Δ, % | |
|---|---|---|---|---|---|---|---|
| B | A | ||||||
| 100 | 1023 | 1.73 | 1.72 | – | 23.429 | − 16,346 | + 0.52 |
| 2.00 | + 16.21 | ||||||
| 1.47 | − 14.58 | ||||||
| 1273 | 38.00 | 39.68 | – | − 4.22 | |||
| 37.20 | − 6.24 | ||||||
| 38.80 | − 2.21 | ||||||
| 85.44 | 1073 | 2.27 | 2.367 | 4.55 × 10–11 | 23.319 | − 16,687 | − 4.09 |
| 2.46 | + 3.93 | ||||||
| 1273 | 26.85 | 27.235 | 8.40 × 10–8 | − 4.13 | |||
| 27.56 | + 1.1 | ||||||
| 73.18 | 1073 | 1.06 | 1.14 | 7.92 × 10–10 | 24.511 | − 18,755 | − 6.77 |
| 1.21 | + 6.42 | ||||||
| 1273 | 17.16 | 17.71 | 4.42 × 10–7 | − 3.13 | |||
| 18.15 | + 2.46 | ||||||
| 60.00 | 1173 | 2.14 | 2.44 | 1.05 × 10–7 | 25.277 | − 20,516 | − 12.33 |
| 2.71 | + 11.02 | ||||||
| 1373 | 30.51 | 30.51 | 1.48 × 10–5 | 0 | |||
| 31.04 | + 1.74 | ||||||
| 47.12 | 1273 | 4.31 | 4.44 | 7.00 × 10–6 | 24.647 | − 20,693 | -3.02 |
| 4.52 | + 1.71 | ||||||
| 1473 | 39.13 | 40.12 | 4.66 × 10–4 | − 2.47 | |||
| 41.13 | + 2.51 | ||||||
| 32.81 | 1273 | 1.88 | 1.65 | 3.63 × 10–6 | 23.819 | − 20,904 | + 14.08 |
| 1.42 | − 13.83 | ||||||
| 1473 | 14.92 | 15.34 | 2.45 × 10–4 | − 2.73 | |||
| 15.46 | + 0.80 | ||||||
| Symbols: [Mg]—magnesium content in the alloy, the rest is tin; Δ – relative error | |Δ|av. = 5.47 | ||||||
The total measurement error is defined as the sum of the errors of independent measurements: temperature – 1%, weighing – 0.1%, pressure 0.5%, approximation of experimental data – 5.47%, equal to 7.07%.
The values of the partial pressure of saturated magnesium vapor 
above tin alloys are given in Table 3 and are approximated by the dependence:
 |
where: 
– atomic fraction of magnesium in the alloy; T – temperature, K.
The saturated vapor pressure above elemental cadmium corresponds to the equation:
.
The partial pressure of saturated tin vapor in the Mg – Sn system, calculated by numerical integration of the Gibbs – Duhem equation, corresponds to the dependence:
 |
The dependence of the vapor pressure above elemental tin was taken from paper28 and converted by us to the form: 
.
The decomposition temperature of dimagnesium stannide (1401 ± 131 K), determined by the boiling point method (isobaric variant) within the limits of the determination errors, coincides with the boiling point of the melt (1494 ± 105 K), determined by the same method (isothermal variant).
Based on the dependencies of the partial pressure of magnesium and tin vapor, the boundaries of the vapor–liquid equilibrium fields of the Mg–Sn system at atmospheric pressure and vacuum (0.7 kPa) are calculated (highlighted with dotted lines). The pressure value of 0.7 kPa is due to the fact that at lower pressures, crystallization of dimagnesium stannide from the melt is possible.
The complete magnesium–tin phase diagram, including the boundaries of the liquid—vapor phase transition, is shown in Fig. 5.
Fig. 5.
Complete phase diagram of the magnesium—tin system.
The boiling point of magnesium, determined on the basis of the partial vapor pressure, is 1100 °C at atmospheric pressure and 695 °C in a vacuum, while that of tin is 2609 °C and 1791 °C, respectively. The areas of coexistence of liquid and vapor are large in terms of temperature. The boiling point of the melt in a vacuum (821 °C), corresponding to dimagnesium stannide, exceeds the melting point of the compound by ⁓50–770.5 °C.
The composition of the equilibrium vapor phase is represented by magnesium in practically the entire range of component concentrations. Thus, at a content of 0.1 wt. % Mg (1 × 10–3 at. %) in the melt, the vapor phase will contain 99.73–99.76 wt. % magnesium, with the remainder being tin. That is, the separation of the liquid magnesium—tin alloy by distillation of magnesium does not present any technological difficulties.
However, when magnesium is distilled in a vacuum, there is a restriction on the degree of vacuum—the pressure above the melt must exceed 0.7 kPa to avoid the potential crystallization of the Mg2Sn intermetallic compound.
The thermodynamic activities of the components were calculated based on the partial pressures of magnesium and tin vapor (Fig. 6). It can be seen that the results of our experiments satisfactorily coincide with the data of studies by other authors19,29. This confirms the correctness of the obtained vapor pressure values.
Fig. 6.
Activities in the magnesium—tin system: 1–4—magnesium; 5–7—tin; 1, 4, 5, 7—at a temperature of 1073 K; 2, 6—at 1273 K; 3—at 1350 K; 1, 2, 5, 6—our data; 4—data19; 7—data29.
The energy functions of the Mg–Sn system mixture were calculated based on the values of thermodynamic activity (Tables 4, 5).
Table 4.
Partial and integral mixing entropies of the Mg–Sn system.
| Composition of alloys, at. % |
 , J/(mol × K) |
 , J/(mol × K) |
 , J/(mol × K) |
|
|---|---|---|---|---|
| Mg | Sn | |||
| 100 | 0 | 0 | – | 0 |
| 95 | 5 | 3.80 ± 0.27 | − 76.82 ± 5.43 | − 0.24 ± 0.02 |
| 90 | 10 | 3.47 ± 0.25 | − 75.20 ± 5.32 | − 4.40 ± 0.31 |
| 80 | 20 | − 3.46 ± 0.24 | − 36.14 ± 2.56 | − 9.99 ± 0.71 |
| 70 | 30 | − 11.16 ± 0.79 | − 12.27 ± 0.87 | − 11.49 ± 0.81 |
| 60 | 40 | − 14.21 ± 1.00 | − 6.13 ± 0.43 | − 10.98 ± 0.78 |
| 50 | 50 | − 11.38 ± 0.80 | − 9.39 ± 0.66 | − 10.39 ± 0.73 |
| 40 | 60 | − 5.60 ± 0.40 | − 14.15 ± 1.00 | − 10.73 ± 0.76 |
| 30 | 70 | − 3.90 ± 0.28 | − 15.24 ± 1.08 | − 11.84 ± 0.84 |
| 20 | 80 | − 17.29 ± 1.22 | − 11.08 ± 0.78 | − 12.32 ± 0.87 |
| 10 | 90 | − 60.00 ± 4.24 | − 3.91 ± 0.28 | − 9.52 ± 0.67 |
| 5 | 95 | − 96.40 ± 6.82 | − 0.99 ± 0.07 | − 5.77 ± 0.41 |
| 0 | 100 | – | 0 | 0 |
Table 5.
Partial and integral enthalpies of mixing for the Mg – Sn system.
| Composition of alloys, at. % |
 , kJ/mol |
 , kJ/mol |
 , kJ/mol |
|
|---|---|---|---|---|
| Mg | Sn | |||
| 100 | 0 | 0 | – | 0 |
| 95 | 5 | 3.58 ± 0.25 | − 177.98 ± 12.58 | − 5.50 ± 0.39 |
| 90 | 10 | 1.80 ± 0.13 | − 158.81 ± 11.23 | − 14.26 ± 1.01 |
| 80 | 20 | − 10.23 ± 0.72 | − 90.51 ± 6.40 | − 26.29 ± 1.86 |
| 70 | 30 | − 24.18 ± 1.71 | − 47.80 ± 3.34 | − 31.27 ± 1.50 |
| 60 | 40 | − 33.18 ± 2.35 | − 30.49 ± 2.16 | − 32.11 ± 2.27 |
| 50 | 50 | − 35.72 ± 2.53 | − 27.20 ± 1.92 | − 31.45 ± 2.22 |
| 40 | 60 | − 35.36 ± 2.50 | − 27.56 ± 1.95 | − 30.69 ± 2.10 |
| 30 | 70 | − 40.84 ± 2.89 | − 24.89 ± 1.76 | − 29.68 ± 2.10 |
| 20 | 80 | − 66.13 ± 4.67 | − 16.88 ± 1.19 | − 26.73 ± 1.89 |
| 10 | 90 | − 130.32 ± 9.21 | − 6.08 ± 0.43 | − 18.51 ± 1.31 |
| 5 | 95 | − 184.40 ± 13.04 | − 1.79 ± 0.13 | − 10.92 ± 0.77 |
| 0 | 100 | – | 0 | 0 |
The change in the integral mixing entropy has a negative value, which indicates the ordering of atoms. In the first case, a minimum of the function is noted at a magnesium content in the alloy of about 60 at. %, which approximately corresponds to the composition of dimagnesium stannide and its congruent melting. The second minimum is located between 20 and 10 percent magnesium concentration in the alloy, which is apparently due to the proximity of the Sn–Mg2Sn eutectic – 9.6 at. % Mg, and the shift in concentration to the higher side is due to experimental errors.
The minimum integral mixing enthalpy (− 32.11 ± 2.27 kJ/mol) coincides exactly with the composition of Mg2Sn and confirms the presence of the compound in the liquid phase.
Conclusion
As a result of research using the boiling point method, the values of the partial pressure of magnesium above the alloys of the magnesium–tin system were determined for the entire concentration range, represented by the temperature–concentration dependence. Preliminary, using the boiling point method (isobaric variant) and vacuum distillation, the decomposition of dimagnesium stannide into its constituent metals was established. The pressure of magnesium above the intermetallic compound (pD) corresponds to the equation: ln pD [Pa] = 26.695–21,250 × T−1. The decomposition temperature of Mg2Sn at atmospheric pressure corresponds to the value (1401 ± 131 K), which, within the limits of determination errors, coincides with the boiling point of the melt (1494 ± 105 K).
Based on the thermodynamic activity of the melt components, the partial and integral mixing functions – entropy and enthalpy – were determined and presented in tabular form.
Based on the partial values of the vapor pressure of magnesium and tin, the boundaries of the vapor–liquid equilibrium fields at atmospheric pressure (101.3 kPa) and in a vacuum (0.7 kPa) were calculated. A complete phase diagram was constructed, including the boundaries of the liquid–vapor phase transition at the specified pressures. A pressure drop in the system below 0.7 kPa may be accompanied by the crystallization of dimagnesium stannide from the melt.
The boiling point of magnesium at atmospheric pressure is 1100 °C, in a vacuum—695 °C, tin – 2609 °C and 1791 °C, respectively. The areas of coexistence of liquid and vapor are large in terms of temperature. The boiling point of the melt in a vacuum (821 °C), corresponding to dimagnesium stannide, exceeds the melting point of the compound by ⁓50 °C – 770.5 °C.
The composition of the equilibrium vapor phase is represented by magnesium in practically the entire range of component concentrations—at a content of 0.1 wt. % Mg (1 × 10–3 at. %) in the melt, the vapor phase will contain 99.73–99.76 wt. % magnesium, with the remainder being tin. That is, the separation of liquid magnesium—tin alloys by distillation of magnesium in a vacuum does not present any technological difficulties. Distillation separation of magnesium—tin melts is difficult due to the high temperature of the process and the high activity of magnesium in relation to the components of the gas phase.
Acknowledgements
The authors gratefully acknowledge the support extended by the Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan for funding this research.
Author contributions
V.V. conceived and supervised the project. V. V., S. T., X. L., A. M., T. C., A. N., and N. B. wrote the code and performed the experiments. V. V., S. T., X. L., A. M., T. C., A. N., and N. B. analyzed the results. V. V., S. T., X. L., A. M., T. C., A. N., and N. B. wrote the manuscript. All authors reviewed the manuscript.
Funding
The work was supported by the Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant AP 26196623).
Data availability
All data generated or analyzed during this study are included in this published article.
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
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