CC BY
27
DOI: 10.17277/amt.2020.01.pp.003-007
The p-T-x Phase Diagram of the Cu-Mg System
Yu.V. Levinsky 1*, M.I. Alymov u, L.L. Rohlin2
1 A.G. Merzhanov Institute of Structural Macrokinetics and Materials Science Problems of RAS, 8, Academician Osipyan ul., Chernogolovka, 142432, Russia; 2 Baikov Institute of Metallurgy and Materials Science RAS, 49, Leninsky Prospect, Moscow, 119334, Russia
* Corresponding author. Tel.: +7 496 52 46 384. E-mail: levinsky35@mail.ru
Abstract
The phase equlibria in the copper-magnesium system with participation of the gaze phase were analyzed. Various graphic variants of the equilibria image, the line projections of the maximal solubility on the plane temperature-composition, isobar and isotherm sections of the p-T-x phase diagram and pMg-T phase diagram were proposed.
The findings of the analysis can be useful during optimization of the melting, casting, heat treatment and operation processes of the copper-magnesium system alloys.
Keywords
Phase equilibria; phase diagrams; copper-magnesium alloys; intermetallics.
© Yu.V. Levinsky, M.I. Alymov, L.L. Rohlin, 2020
Alloys of copper and magnesium - magnesium bronzes - find technical applications, in particular, slip rings, collector plates, cables are made from them [1 - 4]. When melting, casting, and heat treating articles made of magnesium bronze, it is necessary to take into account the evaporation of them having high vapor pressure of magnesium. In this regard, the analysis of equilibrium in the copper-magnesium system acquires importance not only taking into account temperature, but also pressure.
The purpose of this article is to build phase diagrams of the copper-magnesium system at various temperatures and pressures.
Two phases are formed in the copper-magnesium system: Mg2Cu (Pearson symbol oF48, space group Fddd) and MgCu2 (Pearson symbol cF24, space group Fd-3m). The projection of curvilinear lines of maximum solubility located in three-dimensional p-T-x space onto the temperature-composition plane is shown in Fig. 1 [5].
The equilibrium gas above the pairs of Cu-Mg alloys consists mainly of magnesium atoms. The total vapor pressure above the alloys, with the exception of very dilute copper solutions, can be taken equal to the partial vapor pressure of magnesium. The equilibrium pressure of magnesium vapor over the melts in a wide
range of concentrations and temperatures is given in Table 1 according to the data of [6 - 8]. The extrapolation of the temperature dependences of the magnesium vapor pressure given in Table 1, before intersecting with the liquidus lines in the diagram in Fig. 1, determines the parameters of three-phase equilibria: (Cu 5 L 5 G); (Cu2Mg 5 L 5 G), (CuMg2 5 5 L 5 G) and (Mg 5 L 5 G).
The diagram in Fig. 1 is a projection of the lines of maximum solubility located in the p-T-x-space of the lines of non-invariant equilibria on the temperature-composition plane. At pressures above 500 Pa, this diagram coincides with the basal section.
Taking these parameters and the data of [5 - 8] into account, Fig. 2 shows the p-T phase diagram of the copper-magnesium system, which is the projection of the spatial lines of three-phase equilibria of this system on the pressure-temperature plane.
In this diagram, curves 1 - 10 and 10 - 17 represent the evaporation and boiling of pure magnesium, respectively, and curves 10 - 15 represent its melting.
Four-phase equilibria are indicated by points 5, 6, and 7. The parameters of these points and the phases involved in them are given in Table 2.
At each point of the invariant four-phase equilibria, four curves of univariate three-phase
20 30 40 50
Cu, mass. % 60 70 80
90
95
100
T, °C 10001
900'
800
700'
600
500
400
300
1 —1— 1 1 - ' 1..... i 1 T i
L
'97° M
725' (CU)
61*9°
N\ \ ✓ Jj "8 ° 552* 1 1 i-.
42 Bit ,68
0.013 V 485° o! 1 r;
1
0 10 20 30 40 50 60 Mg Cu, at. %
70 80 90 100 Cu
Fig. 1. The projection of the lines of maximum solubility of the copper-magnesium system on the temperature - composition plane [5]
Table 1
Temperature dependence of the partial vapor pressure of Mg over equilibrium melts Cu-Mg [lgPMg(Pa) = -AIT+B]
Source
[6]
ion, Mg at. % A B Temperature, °C
22.4 7760 9362 815 - 927
33.0 7630 9705 823 - 888
52.1 6910 9607 669 - 781
58.1 6850 9609 652 - 729
66.7 6760 9682 618 - 683
76.5 6670 9710 608 - 687
85.7 6630 9726 599 - 668
93.6 6590 9728 592 - 667
11.0 8720 9460 900 - 1069
18.0 8520 9736 875 - 959
22.0 8420 9896 740 - 948
29.0 8260 10127 800 - 915
37.0 8000 10202 812 - 866
42.0 7830 10159 775 - 837
50.0 7630 10123 776 - 837
66.0 7390 10213 572 - 749
76.0 7260 10228 640 - 730
90.0 7190 10279 619 - 730
17.29 8337 9550 900 - 974
23.36 8097 9570 886 - 957
30.07 7867 9709 829 - 963
37.04 7670 9733 809 - 870
44.49 7463 9794 789 - 876
50.53 7299 9902 833 - 848
67.28 7004 9920 707 - 800
65.52 6905 9936 683 - 778
90.05 6840 9964 706 - 783
[7]
[8]
0
103/T K-1
log p, Pa
3
0
400 500 600 700 800 T, °C
Fig. 2. p-T phase diagram of the Cu-Mg system
Four-phase equilibrium points of the Cu-Mg system
Table 2
Point number in the diagram of Fig. 2 Temperature, °C Pressure, Pa Equilibrium phases
5 485 10 Mg, CuMg2, G, L
6 552 10 Cu2Mg, CuMg2, L, G
7 725 30 Cu, Cu2Mg, L, G
equilibria end. The phases involved in these equilibria are shown in Fig. 2. In the diagram in Fig. 2, there are two more points of non-invariant equilibria 8 and 9, which correspond to congruent melting of Cu2Mg and CuMg2.
The isobar p = 100 Pa crosses the curves of three-phase equilibria 5 - 12, 5 - 10, 6 - 13, 6 - 9, 7 - 10, 9 - 7 and 7 -11 on the p-T-diagram (the point of intersection of the isobar with the melting curve of copper is not shown) In accordance with this, eight contour lines of non-invariant equilibria are shown in the isobaric section of Fig. 3. A characteristic feature of this diagram is the presence of three closed regions of the liquid. Of interest is also the heating behavior of mixtures of intermetallic compounds Cu2Mg and MgCu2. First, when mixtures are heated, they melt at a temperature of 552 °C, then at a temperature of 660 °C, the formed melt solidifies with the release of magnesium vapor, then at a temperature of 700 °C the remaining Cu2Mg melts again to form a liquid already rich in copper, which in turn at a temperature of 840 °C hardens again with the release of magnesium vapor and copper-based solid solutions. At an even higher
temperature close to the melting point of copper, these solutions, enriched with magnesium, melt again.
The isotherm T = 740 °C intersects the equilibrium curves 7 - 11, 7 - 9, 6 - 9 on the p-T diagram. In accordance with this, in the isothermal section at a temperature of 740 °C (Fig. 4) there are three horizontal horizons of unvariant equilibria. As follows from Fig. 4, in the indicated pressure range there is a region of a solid solution of magnesium in copper, a solid intermetallic compound Cu2Mg, and two liquid regions, one of which is rich in copper and the other is rich in magnesium.
Of practical interest is the diagram of the first kind [7] for the Cu - Mg system in pMg -T coordinates, which is shown in Fig. 5. Taking into account the fact that the total equilibrium pressure of solutions based on copper gas over all alloys, except for very dilute solutions based on copper, can be replaced without partial error by partial pressure of magnesium, the diagram in Fig. 5 can easily be transformed from the diagram in Fig. 2, removing all equilibrium curves involving only condensed phases.
2
1
Mg, mass. % 20 40
60 80 100 X_L
20
40 60
Mg, at. %
80
100
Fig. 3. Isobaric section of the phase diagram of the Cu-Mg system at a pressure of 100 Pa
QLL.Mg
C^ 2-
M
0
Cu
20
i r
40
60
80
Mg
Mg, at. %
Fig. 4. Isothermal section of the phase diagram of the Cu-Mg system at a temperature of 740 °C
Examples of isobaric and isothermal sections of the phase diagram of the copper-magnesium system are shown in Figs. 4 and 5.
The whole diagram of Fig. 5 is divided into five single-phase regions (two regions of solid solutions based on copper and magnesium, liquid, regions of solid phases Cu2Mg and CuMg2), separated by the boundaries of two-phase equilibria. The compositions of the phases located in these equilibria can be determined using the diagram in Fig. 1. To determine the composition of alloys in single-phase regions of
Fig. 5, the presence of isobars or isotherms of solubility of magnesium is necessary. In particular, the compositions of alloys, in particular liquids, in the diagram of Fig. 5, limited by the curve 10 - 5 - 6 - 7 -8, can be calculated from the information given in Table 1.
The presented options for graphic equilibrium in the copper-magnesium system can be useful in choosing the optimal conditions for melting, casting, and heat treatment of alloys of the copper-magnesium system.
0
0
3
1
1.4
1.2
1.0
103/T, K-1
0
g, Pa ________ - ! ............. L
Jt / /S9 / / V ________V
MgyT \/ 6<4L................. t .........................../ / / /7 Z,*-" ..... 0
/ /CuMg #2 - f / Cu2Mg i i 2 / 1 t 2! ! V ; Cu I 1 1 I
400 500 600 700 800 T, °C
Fig. 5. pMg-T phase diagram of the Cu-Mg system
Conclusions
Based on the analysis of equilibria involving the gas phase in the copper-magnesium system, a p-T diagram of this system, examples of isobaric and isothermal sections of a triple p-T-x phase diagram and a pMg-T phase diagram are presented.
References
1. Nikolaev A.K., Kostin S.A. Med' i zharoprochnyye mednyye splavy [Copper and heat resistant copper alloys]. Moskva: DPK Press, 2012, 720 p.
2. Ten E.B., Badmazhalova I.B. Polucheniye kachestvennykh litykh zagotovok iz Cu-Mg splavov. [Preparing high-quality cast billets from Cu-Mg alloys]. Izv. VUZov. Tsvetnaya metallurgiya. 2013, 1, 45-49.
3. Ten E.B., Nam C.U Nepreryvnaya plavka beskislorodnoy medi [Continuous smelting of oxygen-free copper]. Izvestiya VUZov. Tsvetnaya metallurgiya. 2000, 6, 22-24.
4. Ten E.B. Nepreryvnoye gorizontal'noye lit'ye beskislorodnoy medi. [Continuous horizontal casting of oxygen-free copper]. Liteynoyeproizvodstvo. 2003, 7, 7-10.
5. Diagrammy sostoyaniya dvoynykh metallicheskikh sistem. Spravochnik. [Phase diagrams of binary metal systems. Directory]. Ed. by N.P. Lyakishev. Moscow: Mashinostroyeniye. 1997, 2, 1024 p.
6. Sieben P., Schmal H.G. Vapour Pressure and Activity of Magnesium in the Binary Alloy Systems with Nickel and Vapour Pressure of Some Pure Metals. Giesserei. 1966. B. 18 (14), 197-211.
7. Gard S.P., Bhatt Y.J., Sundaram C.V. Thermodynamic Study of Liquid Cu-Mg Alloys by Vapour Pressure Measurement. Metal. Trans. 1973, 4, 283-289.
8. Juneja J.M., Iyngar G.N.K., Abraham K.P. Thermodynamic Properties of Liquid (Magnesium + Copper) Alloys by Vapour-Pressure Measurement Made by a Boiling-Temperature Method. J. Chem. Thermodynamic. 1986, 18, 1025-1035.
9. Levinsky Yu.V., Lebedev M.P. R-T-x-diagrammy sostoyaniya dvoynykh metallicheskikh sistem [p-T-x-state diagrams of binary metal systems]. Moscow, Nauchnyy mir, 2014. 200 p.
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