Polyassociative thermodynamic model of A²B⁶ semiconductor meltand phase equilibria in Cd-Hg-Te system. 4. p-T-x diagram of Cd-Hg-Te system
p −T− x diagram of Cd-Hg-Te system is analyzed in the framework of the polyassociative solution model. The temperature dependence of the dissociation constant for ternary complexes, which describes the mixing effects, was determined using the low temperature data on phase equilibrium in the system....
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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irk-123456789-1216112017-06-16T03:03:09Z Polyassociative thermodynamic model of A²B⁶ semiconductor meltand phase equilibria in Cd-Hg-Te system. 4. p-T-x diagram of Cd-Hg-Te system Moskvin, P.P. Khodakovsky, V.V. Rashkovets’kyi, L.V. p −T− x diagram of Cd-Hg-Te system is analyzed in the framework of the polyassociative solution model. The temperature dependence of the dissociation constant for ternary complexes, which describes the mixing effects, was determined using the low temperature data on phase equilibrium in the system. A satisfactory agreement between calculated and experimental data of various works about phase equilibrium was attained. 2006 Article Polyassociative thermodynamic model of A²B⁶ semiconductor meltand phase equilibria in Cd-Hg-Te system. 4. p-T-x diagram of Cd-Hg-Te system / P.P. Moskvin, V.V. Khodakovsky, L.V. Rashkovets’kyi // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 3. — С. 12-16. — Бібліогр.: 16 назв. — англ. 1560-8034 PACS 64.90.+b http://dspace.nbuv.gov.ua/handle/123456789/121611 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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p −T− x diagram of Cd-Hg-Te system is analyzed in the framework of the polyassociative solution model. The temperature dependence of the dissociation constant for ternary complexes, which describes the mixing effects, was determined using the low temperature data on phase equilibrium in the system. A satisfactory agreement between calculated and experimental data of various works about phase equilibrium was attained. |
| format |
Article |
| author |
Moskvin, P.P. Khodakovsky, V.V. Rashkovets’kyi, L.V. |
| spellingShingle |
Moskvin, P.P. Khodakovsky, V.V. Rashkovets’kyi, L.V. Polyassociative thermodynamic model of A²B⁶ semiconductor meltand phase equilibria in Cd-Hg-Te system. 4. p-T-x diagram of Cd-Hg-Te system Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Moskvin, P.P. Khodakovsky, V.V. Rashkovets’kyi, L.V. |
| author_sort |
Moskvin, P.P. |
| title |
Polyassociative thermodynamic model of A²B⁶ semiconductor meltand phase equilibria in Cd-Hg-Te system. 4. p-T-x diagram of Cd-Hg-Te system |
| title_short |
Polyassociative thermodynamic model of A²B⁶ semiconductor meltand phase equilibria in Cd-Hg-Te system. 4. p-T-x diagram of Cd-Hg-Te system |
| title_full |
Polyassociative thermodynamic model of A²B⁶ semiconductor meltand phase equilibria in Cd-Hg-Te system. 4. p-T-x diagram of Cd-Hg-Te system |
| title_fullStr |
Polyassociative thermodynamic model of A²B⁶ semiconductor meltand phase equilibria in Cd-Hg-Te system. 4. p-T-x diagram of Cd-Hg-Te system |
| title_full_unstemmed |
Polyassociative thermodynamic model of A²B⁶ semiconductor meltand phase equilibria in Cd-Hg-Te system. 4. p-T-x diagram of Cd-Hg-Te system |
| title_sort |
polyassociative thermodynamic model of a²b⁶ semiconductor meltand phase equilibria in cd-hg-te system. 4. p-t-x diagram of cd-hg-te system |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2006 |
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http://dspace.nbuv.gov.ua/handle/123456789/121611 |
| citation_txt |
Polyassociative thermodynamic model of A²B⁶ semiconductor meltand phase equilibria in Cd-Hg-Te system. 4. p-T-x diagram of Cd-Hg-Te system / P.P. Moskvin, V.V. Khodakovsky, L.V. Rashkovets’kyi // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 3. — С. 12-16. — Бібліогр.: 16 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-07-08T20:13:12Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 12-16.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
12
PACS 64.90.+b
Polyassociative thermodynamic model of A2B6 semiconductor
melt and phase equilibria in Cd-Hg-Te system.
4. xTp −− diagram of Cd-Hg-Te system
P.P. Moskvin1, V.V. Khodakovsky1, L.V. Rashkovets’kyi2
1Zhitomir State Technological University, 103, Chernyakhovs’kogo str., 10005 Zhitomir, Ukraine
E-mail: moskvin@us.ztu.edu.ua
2V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
45, prospect Nauky, 03028 Kyiv, Ukraine
Abstract. xTp −− diagram of Cd-Hg-Te system is analyzed in the framework of the
polyassociative solution model. The temperature dependence of the dissociation constant
for ternary complexes, which describes the mixing effects, was determined using the low
temperature data on phase equilibrium in the system. A satisfactory agreement between
calculated and experimental data of various works about phase equilibrium was attained.
Keywords: phase equilibrium, associates and complexes in liquid phase.
Manuscript received 23.03.06; accepted for publication 23.10.06.
It was shown in our previous works [1-3] that the
polyassociative model of the liquid phase can be
successfully applied to the description of phase
equilibrium both in binary systems Cd-Te, Hg-Te and in
the range of the quasibinary CdTe-HgTe phase diagram.
In the work [3], when processing the data on phase
equilibrium along the quasibinary CdTe-HgTe diagram,
it was shown that mixing effects in a multicomponent
melt are well explained by presence of associates
CdHgTe and CdHgTe3 in it. For quasibinary diagram
temperatures, the values of dissociation constants of
mentioned complexes have been found. It has allowed
describing the phase equilibria at high temperatures with
a high accuracy. In this work, temperature dependences
of dissociation constants for complexes CdHgTe and
CdHgTe3 were obtained, and using them analyzed were
phase equilibria in the system for the whole range of
compositions and for a wide temperature range.
Temperature dependences of the dissociation
constants CdHgTeK ,
3CdHgTeK and solid phase interact-
tion parameter )(α TS were carried out by processing
the experimental data on phase equilibria for low
temperatures both for the part of the diagram enriched
with metals, and in its tellurium corner.
Precomputations have shown that equilibrium
curves of the phase diagram are displaced in the same
way while changing the concentrations of each of
associates, responsible for effects of mixing in this
ternary system. It means that increase of the
concentration in the melt of complexes CdHgTe or
CdHgTe3 each, due to the reduction of dissociation
constants, results in decrease of the liquidus temperature
at the same total concentrations of a component in a
liquid phase. This result is represented to be natural and
corresponding to data of the theoretical analysis of
behavior of the liquidus binary system depending on the
degree of liquid phase dissociation, which has been
performed in the generalizing work [4]. The increase in
the concentration of complexes in the liquid phase
displaces a liquidus line to the place of more
concentrated melts, reducing the distance between it and
a solidus line. For the present calculations, such
information is useful, since it allows separating the
composition melt where the influence of each associate
on liquidus position is determinative. Proceeding from
the stated reasons, the following approach of obtaining
the dissociation parameters at low temperatures was
formulated. In fact, the complex with the large
concentration of tellurium CdHgTe3 should be contained
in the greater concentration in the melt enriched with a
metalloid component. That’s why, its formation
parameters should be obtained, basing on experimental
data of phase equilibrium in tellurium enriched corner of
the diagram. At the same time, an influence of a
complex CdHgTe should affect more essentially the
equilibrium lines in the part of the diagram enriched
with metals, where its formation conditions are more
preferable. These conclusions have allowed getting,
finally, temperature dependences of dissociation
constants without using long mathematical procedures.
The temperature dependences of the required parameters
found by the mentioned way, as well as other
thermodynamic data on the initial binary systems, found
by us in [1, 2] and necessary for calculations of p–T–x
equilibria in such a binary system, are shown in Table.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 12-16.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
13
Table. Thermodynamic parameters of polyassociative model for Cd–Hg–Te system.
Dissociation parameters of complexes
System
FT ,
К
FSΔ ,
e. u.
Sl
pC −Δ ,
Кmole
cal
⋅
ATe 2ATe TeA2 32TeA
TeCd − 1365.1 8.8 1.88
ТTe
5
2
8 10289,2105541.1245.78 ⋅−
⋅
+
TТe
4
2
6 10828.110314.756.5 ⋅−+
0.02
TTe
5
2
8 1012.30817.1511.120 ⋅−
1
⋅+
TeHg − 943.1 9.25 0.98
Tе
5591372.7 +−
TTe
4
2
7 10004.810809.2987.53 −⋅+ 0.6
TTe
5
2
7 10359.10641.5249.76 ⋅−
1
⋅+
TeHgCd −−
CdHgTeK = Te
5000
3104 ⋅⋅ − 3CdHgTeK = Te
2653
4109.8
−
− ⋅⋅
S
HgTeCdTeα ⋅ = )18.32320( T−
mole
cal
Fig. 1. Liquidus temperature of the Cd-Hg-Te system vs the
concentration of tellurium in the melt for different values of
the parameter
HgCd
Cd
XX
X
Z
+
= at Z = 0.05, 0.1, 0.2, 0.3, 0.4.
� – the experimental data [13] which have been taken from the
figure of the work [5]; ,,, o+◊ × – the data [9] for Z = 0.05,
0.1, 0.2, 0.3, respectively.
The found thermodynamic parameters (Table) have
allowed making calculations of liquidus and solidus lines
in the system Cd-Hg-Te for all compositions of the
diagram in a wide temperature range. The basic results of
calculations are submitted in Figs 1-6. In Figs 1-2,
together with the experimental data [5, 9, 13], the
calculated system Cd-Hg-Te liquidus curves are given for
various sections of the state diagram and at different
temperatures in the part enriched with tellurium. If to take
into account an essential differences between experi-
mental results of various authors, which is especially
distinctly observed in Fig. 2, for example, for liquidus at
500 and 550 ºC, then it is possible to consider conformity
of calculations to the experiment as quite satisfactory.
In Fig. 3, the dependences of the concentration of
the most numerous complexes in melts on total tellurium
concentration along the section of the diagram with Z =
0.2 are submitted. So for chosen Z , at the tellurium
concentrations in the range XTe ≈ 0.5 at. frac., the
complex HgTe as well as free atoms Hg and Te
dominate as melt components whereas the concentration
of other associates in the liquid phase, as a whole, does
not exceed 7 %. These small concentrations of melt
components insignificantly affect the position of
calculated liquidus, but essentially influences on partial
pressures of components. The interaction of complexes
is essentially changed at enrichment of solution by
tellurium, while the equilibrium temperature is
decreased. So at XTe ≥ 0.75 at. frac. multiatomic
complexes HgTe2, Hg2Te3, and CdHgTe3 begin to play a
dominating role in the melt, and the concentration of the
two-atomic complex HgTe sharply decreases. Such a
situation in a multicomponent liquid phase corresponds
to the general fact that, while the temperature decreases,
the concentration of multinuclear complexes should
increase, whereas the content of simple associates
sharply decreases. Such a change of the complexes in the
melt versus temperature is responsible for the unusual
shape of liquidus, and as it was discussed by us in [1],
during a substantiation of enthalpy signs of free energies
of associate formation and changing the associate
composition of the melt versus temperature.
More difficult situation is observed when
comparing the calculations to experimental data for the
dependence of the grown layers composition on the
initial liquid phase composition (Fig. 4). The
experimental data, as a rule, are obtained in the course of
crystallization of a solid solution by liquid phase epitaxy
(LPE). From Fig. 4, it follows that these experimental
data are groupped, basically, near respective calculated
solidus lines though accuracy in the description of
system behaviour for this parameter nevertheless is not
so high, even considering essential difference between
experimental data of various authors. Mentioned above
concerns, first of all, to the practical coincidence of
results obtained by various authors under rather different
temperature conditions. As an example, we can compare
the data [9] to the results [11] when practically from
same melt a solid solution of the same composition is
crystallized at the temperatures distinguished almost by
T
°C
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 12-16.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
14
Fig. 2. Low-temperature liquidus of the Cd-Hg-Te system for
enriched with tellurium part of the diagram. �, o,+ –
experimental data [8] for temperatures 500, 550, 600 ºС,
respectively; ×, ◊ – the data [10, 15] for T = 500 ºС.
XTe, at. fraction
Fig. 3. Associate concentration vs the total tellurium content in
Cd-Hg-Te melt at Z = 0.2. 1 – Hg, 2 – Te, 3 – HgTe, 4 –
HgTe2, 5 – Hg2Te3, 6 – CdHgTe, 7 – CdHgTe3.
30-50 K. Such a situation doesn’t allow hastening with
critical conclusions about applicability of the
polyassociative solution model to the description of a
solidus line in the system, and demands more thorough
examination of a question about applicability of the
equilibrium analysis for the description of the
experimental data obtained by LPE methods. Really,
when the calculations are compared with experimental
data for the state diagram in multicomponent systems,
it’s necessary to be attentive. The numerous factors that
influence on growing system in a real crystallization
process can be the reason of a discrepancy of phase
equilibrium model to experimental data [8].
When carrying out the LPE process, one of the
main reasons responsible for mentioned distinctions is
the absence of thermodynamic equilibrium between a
binary compound substrate and a liquid three-component
phase. Really, the absence of thermodynamic
equilibrium in the growing system provides the
realization of the crystallization process. At the same
time, various initial supercoolings of an initial solution
determine different growth rates which reflects on the
composition of layers during crystallization. Many
authors observed such influence of growing rates on
layer parameters for LPE manufacturing the
multicomponent solid solutions [8]. The absence of the
direct control of a liquid phase liquidus temperature,
from which the crystallization begins, is responsible for
different growth rates of layers in each specific
technological process. It quite naturally provides the
various composition of grown layers. A confirmation of
the fact that such kinetic effects can be essential lies in
rather large values of equilibrium distribution
coefficients of a solid solution main component, which
were obtained in our calculations. So, for the equilibrium
partial distribution coefficient, for example, cadmium,
which is 0
CdK = LO
Cd
SO
CdTe 2/ XX , where SO
CdTeX , LO
CdX
are the equilibrium concentrations of cadmium in a solid
and liquid phases (the factor 2 appears when
recalculating the mol. fractions into the atomic ones), it
is possible to obtain the value of 0
CdK in the range of 30
to 80. For such a large distribution coefficient, the
diffusion rate limits of a substance supplied to the
growth front can essentially reduce it. The effect of
equilibrium distribution coefficient transformation into
the effective one according to the model of diffusion-
limited crystallization is analyzed in [12] with reference
to the system Ga-In-P-As. The calculations from [12]
have shown that slowness of a mass transfer to the front
of growth can reduce the value of the distribution
coefficient by several times. If to take into account rather
high tellurium melt viscosity, the mentioned effect can
be essential, and its account can provide conformity of
growing phase composition calculations to experimental
data. Naturally, theoretical consideration of such
phenomena is beyond notions about equilibrium
crystallization when compositions of contacting phases
submit only to the state diagram of the system.
Mechanical strains in a film, which are caused by
lattice mismatch between a layer and a massive
substrate, can render an essential influence on the
composition of grown layers. This effect is known in the
literature as a composition-pulling effect [8]. It can
influence both on a composition of growing solid
solution and on the phase equilibrium temperature
because of the occurrence of contact supercooling in the
system. Generally, this effect is described by the
coherent state diagram, which takes into account the
X
i,
m
ol
. f
ra
ct
io
n
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 12-16.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
15
Fig. 4. Cadmium concentration in the solid solution versus that
in the initial liquid phase. + – [15] for T = 450 ºС; ×, o –
[10, 11] for T = 500 ºС; �, ◊ – [9] for T = 550 ºС.
Fig. 5. CdTe substrate solubility in liquid mercury at various
temperatures. Experimental data are taken from Fig. of [6].
contribution of the mechanical strains in a layer under
the general condition of heterophase equilibrium [8]. In
other words, the mentioned phenomenon is possible to
be estimated only by comparing the calculation data
obtained from the equations of the traditional state
diagram and coherent one [8]. At this analysis of LPE
processes in the system, it is difficult to estimate
accurately the contribution of this factor into the
composition change of the elastically strained layer. At
the same time, a small distinction of lattice parameters of
solid solution mixed components, which does not exceed
0.32 %, testifies that this contribution can be
insignificant. This assumption was established by the
fact that according to our data (Table) and the data [6, 7]
on Sα , this parameter is in the interval of values from
−1500 up to 2000 cal/mol. Such a value of the reduced
excess energy of mixture Sα does not provide affinity of
a condition of a solid phase to the limit of spinodal
disintegration. It is known that the composition-pulling
effect is the most significant, when the solid phase is
thermodynamically unstable [12]. Proceeding from the
mentioned facts at the following stage of calculations, it
is possible to consider that the mentioned effect should
not essentially displace the system from a condition of
thermodynamic equilibrium. Taking into account a
significant disorder of experimental data, the description
of low temperature solidus in the part of the diagram
enriched with tellurium can be considered as the
satisfactory one.
In Fig. 5, the results of modeling of substrate CdTe
dissolution in mercury at various temperatures are shown.
These data are obtained at low temperatures and
correspond to the part of the state diagram enriched with
metals. Calculations have shown that it is possible to get
satisfactory conformity of calculations to experiments in
this part of the diagram at so low temperatures only by
taking into consideration sharper temperature dependence
of the solid phase interaction parameter. This functional
dependence for the description of experimental data was
as follows: =Sα )1900024.8( −⋅T cal/mol.
The analysis of the associate concentration in a
liquid phase under conditions that are resulted in Fig. 5
has shown that the melt in practice consists completely
of free atoms of mercury, tellurium and cadmium, and
elementary associate HgTe and is the only liquid phase
complex. Thus, its mol. fraction does not exceed 0.002
at temperatures near 500 ºС, decreasing with its
downturn. It means that the value of a dissociation
constant of the complex in the melt under such
circumstances weakly influences on the position of a
calculated curve. Liquidus lines in this part of the
diagram are determined by the content of free atoms of
the main solution component. These values are
connected, first of all, with fusion entropies of
compounds and their possible temperature dependence
in the temperature range from 200 to 1100 °С. In the
calculations of the state diagrams in a wide temperature
interval, this factor was discussed by us in [1] when
analyzing the phase equilibrium in initial binary systems
in a wide temperature range. Due to these amendments
and use of obtained )(α TS , the conformity to the
experiment in Fig. 5 was reached.
In Fig. 6, temperature dependences of partial
pressure along lines of xTp −− equilibrium versus
composition of a solid solution CdxHg1−xTe are
submitted. Considering the significant disorder of
experimental data [7, 14] and not high reliability of their
production at high temperatures, the conformity of
calculations to experiment can be considered as
satisfactory.
Successful application of the theory of the associated
solutions with several complexes of different
compositions to the description of phase equilibrium in a
system allows making the following conclusion. Really,
the polyassociative solution model is the attempt to
expand the use of ideal solution laws to a set of
multicomponent systems. Thus, it was considered that the
deviation from Raoult’s law and the deviation of liquidus
lines from ideal solutions predicted by the model is caused
only by incorrect calculation of number of particles
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 12-16.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
16
Fig. 6. Partial pressure of tellurium along a three-phase curves
for various solid solutions CdxHg1−xTe. SX CdTe = 0.1, 0.2, 0.4,
0.6, 0.8 mol. frac. �, o,, ×+ – experimental data [7, 14] for
SX CdTe = 0.1, 0.2, 0.4, 0.6 mol. frac.
existing in melt, whereas the approximation of ideal liquid
phase remains acceptable. The reality of such an approach
to the description of multicomponent systems has been
stated in [16] when modeling the thermodynamic
functions of organic materials. It is possible to assume that
the approach with use of several associates in the melt can
replace Lewis' standard method based on the application
of activity coefficients when modeling the complex
systems with strong interaction.
In conclusion, it is necessary to note that the
dissociation parameters of Cd-Hg-Te melt complexes are
self-connected. In practice, it means that it is impossible
to take any of dissociation parameters from the data in
Table and estimate by using it the concentration of one
specific complex, ignoring thus the presence of other
associates in the melt. Really, the concentrations of
complexes are interconnected through the equations of
quasi-chemical reactions, and the condition of the
balance of substance and change in the concentration of
one of the complexes inevitably causes the variation of
the others. Such a situation is not new and is typical for
thermodynamic calculations on phase equilibrium for
other multicomponent systems, even when they are
carried out with use of other models of solutions [8].
Nevertheless, ignoring this circumstance, especially
when applying the polyassociative solution model with a
set of complexes in the melt, will inevitably yield an
incorrectness in use of the model and lead to essential
mistakes in calculation results. Thus, it can be asserted
that the model of polyassociative solutions with the
dissociation parameters found in the work is capable to
describe successfully xTp −− equilibrium in system
Cd-Hg-Te. Attempts to achieve higher accuracy in the
description of technological processes for preparing
materials according to equilibrium thermodynamics due
to a variation of dissociation parameters were inefficient.
Obviously, it is possible to assert that the accuracy of
calculations based on representations about the
equilibrium phase diagram is achieved. It seems, a
perspective way to increase the reliability of calculations
is connected with the transition to kinetic non-
equilibrium models considering process of
crystallization, proceeding in time and when occurring
the external factors. The developed thermodynamic
model of phase equilibrium can be successfully applied
as the first approximation for the choice of growth
conditions of a solid solution CdxHg1−xTe with a
necessary composition.
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