PERITECTIC DIAGRAMS OF ASSOCIATED SOLUTIONS
Shunyaev K.Yu1., Pechischeva N.V1., Zinigrad M.I.2
1
Institute of metallurgy, Ural’s Branch of Russian Academy of Science,
101, Amundsen Str., Ekaterinburg, 620016, Russia, shun@ural.ru
2
College 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 near the 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 was not 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.
________________________________________________________________
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).
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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 500 K 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
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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
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T (K) 600
T (K) 800
700
500
600
400
500
400
300
300
200
200
100
100
0
0
0,5
0
1
cA
0
0,5
cA
1
b
a
T (K)600
T (K) 600
500
500
400
400
300
300
200
200
100
100
0
0
0
0,5
cA
0
1
0,5
cA
1
d
c
Fig. 1. Changes of phase diagram shape for a
T (K) 600
regular solution with great difference of melt-
500
ing points of their components at varying val-
400
ue of the interaction energy parameter:
300
W = 1000 J/mol (a); W = 0 (b);
200
W = -200 J/mol (c); W = -300 J/mol (d);
100
0
W = -400 J/mol (e)
0
0,5
1
e
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