PERITECTIC DIAGRAMS OF ASSOCIATED SOLUTIONS

Shunyaev K.Yu1., Pechischeva N.V1., Zinigrad M.I.2

1Institute of metallurgy, Ural’s Branch of Russian Academy of Science,

101, Amundsen Str., Ekaterinburg, 620016, Russia,

2College of Judea and Samaria, Ariel, Israel

The ideal associated solution model has been successfully applied to evaluation of thermodynamic characteristics of mixing of systems with a strong interaction between theire components [1-4]. We have supposed the original version of the model, taking into account the possibility of existence of associates with various compositions, sizes and shapes [5-9]. It was shown that the model could be applied to vast variety of the systems, including monoatomic systems, simple eutectics and systems with unlimited solubility at liquid state as well as at solid ones nearthe liquidus and solidus. It was shown also that the model allowed calculating both mixing characteristics and the melting ones, including balance state phase diagrams.

The case of the solution melting has been considered in [9]. As solid it is a regular solution with components having melting points at 700 and 1000 K respectively. As liquid this system presents an ideal associated solution, consisting of associates of various dimensions with arbitrary stoichiometry. It has been supposed, that energy parameter wasnot changing during melting, and so, there was only one model parameter to change. It has been shown in the model example that the type of an equilibrium diagram was depending on value and sign of the model parameter. There are 4 possible types of equilibrium diagrams in this case, namely eutectic, “cigar”-type and azeotropic type diagrams with both upper and lower azeotropic points. But the question about peritectic equilibrium existence possibility is still opened.

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The work is realized with financial support by the Russian Foundation for Basic Research (project № 04-03-33109), Special Federal Program “Intergation” (project Б 0035), grant "Leading scientific schools" (НШ-2022.2003.3).

The present work deals with search of conditions, allowing appearance of peritectic point on equilibrium diagram.

Let’s consider a model regular solid solution, looking for the peritectic equilibrium at varied melting point of its components. In the tables 1 and 2 one may see that appearance of peritectic point is only possible when a difference between melting points of the components is great (TB/ TA > 2.25). The equilibrum diagrams of real systems such as Cu-Ir, Pd-W, U-Ta, Ni-Re etc. demonstrate the similar picture, though there are some exception there.

For instance, the Co-Cu, Au-Cr systems are not possessed a great difference between the melting points of their components [10]. The possible types of equilibrium diagrams are given on fig. 1 on dependence of value and sign of the interaction energy parameter. It has been supposed that the components had melting points 100 and 500K and they formed a solution with f.c.c. lattice at solid phase. Comparing given diagrams and that obtained for a system with small difference of components melting points [9] one may notes following features:

  • change of diagram shape (e.g. an increasing of “cigar” width);
  • absence of diagram type with lower azeotropic point;
  • appearance of diagram type with peritectic equilibrium.

Let’s note as a conclusion, that if for example the solution is subregular in the solid phase with a strong asymmetry of properties compared with equiatomic composition, the obtained relation between melting points of the components providing the possibility of peritectic equilibrium existence will able to change considerably.

Table 1. Minimum value of second component melting point (TA) allowing appearance of peritectic equilibrium for given melting point the first component (TB)

TB (K) / 100 / 200 / 300 / 400 / 500 / 700 / 800 / 900 / 1200 / 1300 / 1400 / 1500
TA (K) / 250 / 500 / 700 / 950 / 1150 / 1600 / 1850 / 2050 / 2700 / 2950 / 3150 / 3400

Table 2. The analysis of conditions of peritectic equilibrium existence in the model taking into account existence of arbitrary stoichiometry associates. Solid phase is a regular solution. W is an energy parameter

TA (K) / TB (K) / W / Cperitec / Tperitec
500 / 100 / -500 / 0.022 / 101.5
500 / 100 / -400 / 0.03 / 109.5
500 / 100 / -360 / 0.042 / 121.7
600 / 100 / -400 / 0.017 / 113.5
700 / 200 / -700 / 0.086 / 213.0
800 / 200 / -800 / 0.054 / 207.24
1000 / 300 / -1000 / 0.102 / 324.93
1000 / 300 / -1100 / 0.088 / 304.88
1400 / 400 / -1300 / 0.102 / 460.84
1400 / 500 / -1600 / 0.139 / 509.2
1600 / 500 / -1600 / 0.117 / 552.19
1600 / 500 / -1800 / 0.097 / 504.75
1800 / 700 / -2100 / 0.168 / 714.47
1800 / 700 / -2050 / 0.175 / 733.42
1900 / 800 / -2300 / 0.194 / 804.78
2000 / 800 / -2400 / 0.174 / 801.38
2100 / 900 / -2550 / 0.201 / 907.2
2300 / 900 / -2650 / 0.174 / 932.4
2700 / 1200 / -3337 / 0.213 / 1200
3000 / 1300 / -3650 / 0.206 / 1312
3150 / 1400 / -3890 / 0.213 / 1401
3200 / 1400 / -3920 / 0.208 / 1407
3400 / 1500 / -4180 / 0.211 / 1505
3400 / 1500 / -4190 / 0.211 / 1501

a /
b

c /
d

e / Fig. 1. Changes of phase diagram shape for a regular solution with great difference of melting points of their components at varying value of the interaction energy parameter:
W = 1000 J/mol (a); W = 0 (b);
W = -200 J/mol (c); W = -300 J/mol (d);
W = -400 J/mol (e)

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