Journal of Alloys and Compounds 604 (2014) 363–372
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jalcom
Thermochemistry of the Cu2Se–In2Se3 system
M. Ider a,⇑, R. Pankajavalli b, W. Zhuang c, J.Y. Shen d, T.J. Anderson e
a
Department of Chemical Engineering, Usak University, 64200 Usak, Turkey
Thermodynamics and Kinetics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India
c
General Research Institute for Nonferrous Metals, Grirem Advanced Materials Co., Ltd., Beijing 100088, China
d
General Research Institute for Nonferrous Metals, Beijing 100088, China
e
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, United States
b
a r t i c l e
i n f o
Article history:
Received 20 February 2014
Received in revised form 15 March 2014
Accepted 17 March 2014
Available online 1 April 2014
a b s t r a c t
Solid state electrochemical cells were employed to obtain standard Gibbs energy of formation of CuInSe2
as well as the temperature and enthalpy of the a to d-CuInSe2 transformation in the Cu2Se–In2Se3
pseudo-binary system. The reversible EMF data of the following solid-state electrochemical cell were
measured:
Pt; InðlÞ; In2 O3 ðsÞ kYSZk In2 O3 ðsÞ; Cu2 SeðsÞ; CuðsÞ; CuInSe2 ða or dÞ; C; Pt Cell I
Keywords:
System Cu2Se–In2Se3
Phase diagram
Gibbs energy of formation
Copper indium di-selenide
Solid electrolyte EMF measurements
Thermodynamic assessment
The calculated standard molar Gibbs energy of formation of a and d-CuInSe2 from measured data are
given by
DGf CuInSe2 ðaÞ 0:0003 ¼ 0:0051T ðKÞ 220:92 kJ=mol ð949—1044 KÞ
DGf CuInSe2 ðdÞ 0:0004 ¼ 0:0043T ðKÞ 210:92 kJ=mol ð1055—1150 KÞ
The a to d phase transition temperature Ttrans and the enthalpy of transition DHtrans for CuInSe2 were
determined to be 1064 K and 10.0 kJ/mol respectively. DStrans was calculated as 9.4 J/mol K.
The thermodynamic and phase diagram data in the Cu2Se–In2Se3 pseudo-binary system were critically
assessed. A self consistent set of thermochemistry and phase diagram data was obtained with the help of
measured data. The liquid phase along the Cu2Se–In2Se3 pseudo-binary was calculated with the Redlich–
Kister model. The b-Cu1In3Se5 and c-Cu1In5Se8 phases were represented by the sub-regular model. The
ordered non-stoichiometric a-CuInSe2 and d-CuInSe2 phases were modeled by using a three-sublattice
formalism. The calculated phase diagram and thermochemical data show reasonable agreement.
Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction
CuInSe2 (CIS) is becoming one of the most promising materials
for solar cell applications. Its band gap (1.04 eV) and good absorption coefficient (105 cm1) for solar spectrum make this material
an excellent candidate for a solar cell absorber layer. Although
the electrical properties of CIS are relatively well-known, some ternary phase diagram regions were not completely studied experimentally. The knowledge of phase diagram and thermochemistry
of CIS along with its constituent binaries will provide helpful information on the processing conditions and development of new thin
film and bulk production methods. For the thermodynamic assessment of phase diagram, the phase stability and Gibbs energy of
compounds are essential. According to the recent pseudo-binary
⇑ Corresponding author. Tel.: +90 27622121362720; fax: +90 2762212137.
E-mail address: [email protected] (M. Ider).
http://dx.doi.org/10.1016/j.jallcom.2014.03.129
0925-8388/Ó 2014 Elsevier B.V. All rights reserved.
diagram reported by Chang [1], four ternary compounds CuInSe2,
Cu2In4Se7, CuIn3Se5 and CuIn5Se8 exist in the Cu2Se–In2Se3 section.
However; critically assessed Gibbs energy expressions are missing
and the stability of the compounds are not experimentally established. For this reason, the thermochemical data for Cu2Se–In2Se3
pseudo-binary region was assessed. Solid state galvanic cell experiments were performed to measure Gibbs energy data of selected
ternary compounds and the pseudo-binary phase diagram was calculated by optimizing the experimental data.
2. Literature review
CuInSe2 has two solid modifications separated by a first order transition
between chalcopyrite and sphalerite structures. The d-CuInSe2 sphalerite phase is
stable with a wide homogeneity range between the temperatures of 1090 and
1280 K. The low temperature a-CuInSe2 phase crystallizes in the chalcopyrite form
with a contracting homogeneity range at low temperature. The melting point
Tm(CuInSe2) = 1254 ± 5 K and lattice constants (a = 0.577 nm c = 1.156 nm) of
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M. Ider et al. / Journal of Alloys and Compounds 604 (2014) 363–372
CuInSe2 were reported by Rigan et al. [2]. Mechkovski et al. [3] also studied the
melting and phase transition temperatures. He determined the melting enthalpy
of CuInSe2 by DTA experiments as DHmelt = 83.6 kJ/mol.
Wei et al. [4] stated a first order transition for CuInSe2 and calculated the order–
disorder transition temperature as Ttr = 1125 ± 20 K, which is similar to the experimental value of 1083 K reported by Shay and Wernick [5].
Bachmann et al. [6] measured the low temperature CuInSe2 heat capacity by
pulsed calorimetry and semi-adiabatic techniques. He derived the entropy value
at 298 K as S298 ¼ 1:5773 kJ=mol K and reported the Debye temperature for CuInSe2.
However, his heat capacity data is limited to only low temperature (<300 K).
Khriplovich et al. [7] measured the heat capacity of CuIn2Se3.5 at low temperatures with a vacuum adiabatic calorimeter. On the other hand, these results were
not supported by structural analysis to check whether it was a single phase or
two-phase sample.
A number of papers were also published stating the lattice parameters and stability of intermediate phases; however, some results are inconsistent. Range [8]
reported the formation of a cubic high-pressure zincblende structure for CuInSe2.
Kotkata and Al-Kotb [9] reported lattice parameters of CuInSe2. The lattice parameters of Cu1In3Se5 were measured by Palatnik and Rogacheva [10]. Neuman [11]
also reported the lattice parameters for CuInSe2 and CuGaSe2. Fearheiley and Bachmann [12] reported the lattice parameters of CuInSe2 (a = 5.814 ± 0.003 Å and
c = 11.63 ± 0.04 Å) and compared his results with Hahn et al.’s [13] results which
were close (a = 5.782 Å c = 11.621 Å). He concluded that the lattice constant of CuInSe2 and non-stoichiometric defect structures vary within its homogeneity range.
This suggestion is supported by the fact that a few other authors also observed
slightly different lattice parameters within homogeneous single-phase CIS.
Matsuhita et al. [14] determined the melting and transition points of I–III–VI
compounds by DTA, including those for CIS. It was stated that enthalpies of fusion
and transition depend on mean atomic weight and ionicity, that the melting point
was influenced by the lattice strain. It was found that fusion and transition enthalpies of their solid solutions are much lower than the end members of their
compounds.
Zargarova et al. [15] constructed the CuInSe2–InSe phase diagram section and
reported a transition temperature between a-CuInSe2 and d-CuInSe2 at 1103 K.
Two phase coexistence between CuInSe2 and InSe was observed by micro-structural
examination at low temperatures. An event at 1083 K that was attributed to cation
ordering was reported. Above 868 K only liquid, L + a-CuInSe2 and L + InSe stability
were reported. No other experimental information is available for (a,d)-CuInSe2–
In2Se3, and (a,d)-CuInSe2–In4Se3, (a,d)-CuInSe2–In6Se7. Aside from Zargarova’s
results, there is not much stability information about Cu1In3Se5–InxSey and Cu1In5Se8–InxSey (x = 1, 2, 4, 6; y = 1, 3, 7) systems.
In general, there is a lack of experimental data on the thermochemistry of CIS
and related ternaries except a few estimation calculations. Mooney and Lamoreaux
[16] reported the enthalpy of formation of CuInSe2 and presented enthalpy data of
binary associates. The Gibbs energy of formation data was also calculated using
approximate equality equation by Lamoreaux et al. [17]. Neumann [18] also
reported the heats of atomization for CIS and Nomura et al. [19] analyzed the mechanism of the phase change from Cu2xSe to CuInSe2 by the absorption of indium selenide. Some of literature enthalpy and transformation data are summarized in
Tables 1 and 2.
A few studies on phase equilibrium in the Cu2Se–In2Se3 pseudo-binary system
have been reported. Cu5InSe4, CuInSe2, Cu2In4Se7, CuIn3Se5 and CuIn5Se8 are the
most widely referred intermediate compounds. Many other compounds were also
stated to exist between chalcopyrite and In2Se3 compositions in the pseudo-binary
section. However, X-ray and structural data are not in good agreement and this
region requires further structure studies and justification. There is not much thermodynamic data available on the stability of these ternary phases except the standard enthalpy and absolute entropy of formation, DHf;298 and S298 of CuInSe2.
A general review was published on production methods of CIS films by Rockett
and Birkmire [20]. Production analysis and performance of photovoltaic devices
based on CIS materials were discussed. Cahen and Noufi [21] summarized
thermodynamic data available on CIS related compounds. Gibbs energies of compounds and species that are involved in preparation of CIS films were calculated.
A number of possible formation reaction Gibbs energy and free energy function
data, as well as formation enthalpy data are available in this paper.
Bachmann et al. [22] published a Cu2Se–In2Se3 pseudo-binary phase diagram.
He reported the congruent melting point for Cu5InSe4 as T = 943 °C with two eutectics at xIn2 Se3 ¼ 0:11 and xIn2 Se3 =0.17. Folmer et al. [23] studied the composition
range greater than 50 mol% In2Se3 and suggested three new hexagonal phases in
high In2Se3 region of Cu2Se–In2Se3 pseudobinary.
Fearheiley et al. [24] reviewed the phase relations in the Cu–In–Se system and
the crystal growth of single crystals. Cu–In, In–Se and Cu–Se phase diagrams were
reported. He also reported the pseudo-binary section of Cu2Se–In2Se3 containing
the intermediate compounds Cu2In4Se7 [25] Cu1In3Se5 [26], Cu3In5Se9 [27],
Cu5InSe4 [22] and CuIn5Se8 [28]. The pseudo-binary section of Cu–CuInSe2 was
reported with a wide range of coexistence up to 900 K.
Fearheiley et al. [24] reported Cu2In4Se7 as incongruently melting and Cu1In3Se5
as congruent melting compounds. However, Schock [29] did not report a Cu2In4Se7
phase although he reported an incongruent CuIn3Se5 intermediate. Schock [29] also
stated that the solubility of excess Cu in CuInSe2 is very small. A summary of collected phase diagram data from several references was presented.
Hanada et al. [30] studied the crystal structure of CuIn3Se5 by combination of
electron and X-ray diffractions. He determined that CuIn3Se5 is a stable compound
semiconductor, which is different from CIS and not a vacancy ordered compound or
a defect chalcopyrite. He measured lattice parameters by XRD at 700 °C as
a = 0.574 nm and c = 1.1518 nm. Schumann et al. [31] measured diffraction patterns
of CuIn2Se3.5 compound. It was claimed that CuIn2Se3.5 has a structure type with
defects that is a derivative of chalcopyrite. However, the lattice parameters reported
by Schumann et al. [31] for CuIn2Se3.5 do not agree with two earlier reports. The fact
that the diffraction patterns of Cu2In4Se7 are very similar to CIS with the chalcopyrite structure suggest a possibility that Cu2In4Se7 composition range may lie in a
homogeneity range or in a two phase region of CuInSe2–Cu1In3Se5 or CuInSe2 and
some other composition.
Koneshova et al. [32] constructed a Cu2Se–In2Se3 phase diagram from previously published results and suggested the co-existence of CuInSe2 and Cu1In3Se5
phases in the phase diagram. Koneshova et al. [32] also claimed that some of the
ternary phases, which were previously assumed to be stable, in fact were two phase
regions. Instead of the Cu2In4Se7 modification, a stable phase corresponding to the
Cu1In3Se5 composition was outlined in the phase diagram. Two phase coexistence
between the CuInSe2 and Cu1In3Se5 modifications was also assumed. On the other
hand the limits of high temperature stable modification were greater than other
reports and Cu1In3Se5 phase was reported to be stable only below 900 °C. Additionally, a thin range of coexistence between Cu1In3Se5 and possibly a compound, which
lies in the composition range of Cu1In5Se8 compositions, was depicted. However,
the limits seem too narrow.
Boehnke and Kuhn [33] emphasized that numerous compounds were stated in
the literature to exist along Cu2Se–In2Se3 line and the reported data showed evident
differences in structure and homogeneity ranges and thermal behavior. Boehnke
and Kuhn [33] concluded from X-ray, EPMA (electron microprobe analysis), optical
microscopy and DTA measurements that only 4 ternary phases with extended
homogeneity range were stable. He verified d (sphalerite) phase first time by high
temperature X-ray diffraction. It was asserted that a beta phase extending between
xIn2 Se3 ¼ 0:67 and xIn2 Se3 ¼ 0:80 crystallizes in an ordered chalcopyrite-like defect
structure. From a comparison of X-ray data with those of literature data for Cu2In4Se7, Cu1In3Se5, Cu8In18Se32, and Cu7In19Se32, he concluded that all belong to a b
(Cu1In3Se5) phase. He also reports that the c (Cu1In5Se8) phase has a typical layered
structure with hexagonal and trigonal modifications along with strong lattice
parameter dependence on compositions. This approach with respect to limits of stabilities of ternary compounds seems reasonable.
Godecke et al. [34] published a detailed paper about phase diagram of CIS and
related binaries. His results are consistent with Boehnke et al.’s [33] results, except
the limits of two phase region of high temperature sphalerite phase and b
Table 1
Comparison of a-CuInSe2 to d-CuInSe2 enthalpy of transformation data.
Solid phase
Ttrans (K)
DHtrans (kJ/mol)
References
CuInSe2
1058–1083
1083
1125
–
1095–1099
1064
1050
–
–
10.0
15.9
16.2
10.0
21.7
[47]
[48,3]
[4]
[49]
[14]
This work (Cell I)
[35]
Solid phase
Melting temperature (K)
DHmelting (kJ/mol)
Heat of fusion (kJ/mol)
DSmelting (kJ/mol)
References
CuInSe2
1259
1269
83.6
–
–
88.62
0.0664
–
[3]
[14]
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M. Ider et al. / Journal of Alloys and Compounds 604 (2014) 363–372
Table 2
Comparison of the standard enthalpy of formation, DHf;298 , and standard molar entropy, S298 of the ternary and some binary compounds in the Cu–In–Se system.
Solid phase
DHf;298 (kJ/mol)
Method
References
S298 (J/mol K)
Method
References
a-CuInSe2
267.4
260.2
280.0
204.0
204.7
189.8
202.9
204.4
117.8
78.0
679.6
41.8
65.2
200.3
754.2
Mass spectrometry
Calculated
Calculated
Calculated
Optimized
Calculated
EMF
Calculated
Calculated
Calculated
Calculated
Calculated
Calculated
Optimized
Calculated
[50]
[51]
[52]
[53]
This work
[54]
This work
[16]
[16]
[16]
[16]
[16]
[16]
This work
[54]
157.7
158.2
Pulsed calorimetry
Calculated
[6]
[55]
472.9
266.9
664.6
285.7
Calculated
Optimized
Calculated
Optimized
[54]
This work
[54]
This work
182.83
520.0
513.0
354.8
Optimized
Adiabatic calorimetry
Calculated
Calculated
This work
[7]
[55]
[55]
551.5
Calculated
[55]
InSe
In2Se3
In5Se6
CuSe
Cu2Se
d-CuInSe2
Cu2In4Se7
b-CuIn3Se5
c-CuIn5Se8
(Cu1In3Se5) phase. There is not much known in the high temperature regions of this
section. Godecke’s results were based on experimental studies by differential thermal analysis, light optical microscopy, scanning electron microscopy, transmission
electron microscopy, and X-ray diffraction. In short, Godecke [34] identified four
different ternary phases: a-CuInSe2, c-CuIn5Se8, d-CuIn3Se5 and high temperature
phase of Cu13In3Se11. Some of the crystal structure data of the compounds in the
Cu–In–Se system are summarized in Table 3.
3. Experimental procedure
The EMF of galvanic cells was measured as a function of temperature. The Gibbs energy of the cell reaction and phase transformation temperature was obtained from the measured open circuit
potential of the cells over a temperature range. Based on the coexistence information available in the Cu–In–Se system, the test electrode materials were prepared from the following sample:
1 Cu2Se(s) + CuInSe2 (a or d) two phase mixture was prepared
by mixing Cu2Se (Johnson Matthey) and In2Se3 (Johnson Matthey)
compounds with the mole ratio of
nIn2 Se3
¼ 0:3 Cell I
nIn2 Se3 þ nCu2 Se
The EMF data for cell I was measured over the ranges 949–
1150 K. A 15% w/w yittria stabilized zirconia was employed as
the solid oxide electrolyte against an In(s,l)–In2O3(s) two phase
mixture reference electrode. Using literature data for the standard
Gibbs energy functions of Cu, In, In2O3 and Cu2Se along with standard Gibbs energy change of appropriate cell reactions, the standard Gibbs energy of formation for a-CuInSe2, d-CuInSe2 and
enthalpy of transformation data were calculated. An optimized
version of the pseudo-binary phase diagram is obtained by computing critically evaluated data in accordance with the measured
EMF data.
3.1. Cell materials
Reagent grade Cu2Se (Johnson Matthey) and In2Se3 (Johnson
Matthey), Cu powder (Alfa Aesar), In shots (Aldrich) and Se pellets
(Atomergic Chemicals) all of which were of 99.99% purity or better
were used as the starting materials. Solid mixtures of Cu2Se and
In2Se3 in the mole ratios 70:30 were powdered and individually
encapsulated in silica ampoules under vacuum of less than 10 Pa.
In this procedure, the silica ampoule was heated in stages at
1333 K for 40 h, 1148 K for 70 h followed by cooling to room temperature. The ampoules were broken and the solid mixtures were
ground in an agate mortar. All the samples were characterized by
X-ray Diffraction (XRD) method to ensure the desired phases were
obtained [35]. Comparisons of structural data analysis for the test
electrode materials were made using XRD powder patterns of the
samples before and after each EMF experiments. Analysis of Xray powder diffractograms taken from samples (Cu2Se)1x (In2Se3)x
with x = 0.3 (cell I) (at.%) using Philips 3720 X-ray Diffractometer
before the experiment showed the presence of a-CuInSe2–Cu2Se
phases. The X-ray analysis of the powdered mixtures after the
experiment showed peaks of a-CuInSe2–Cu2Se + In2O3 + Cu phases.
In powder (Strem Chemicals, mass fraction of In, 0.9999) and In2O3
(Johnson Matthey, mass fraction of In2O3, 0.9999) were used as
received to fabricate reference electrodes.
3.2. EMF measurements
The test electrodes were made by intimately mixing the coexisting phases with one third of their mass of In2O3 powder. These
mixtures were then allowed to equilibrate within the cell at the
lowest temperature of measurement. Before cell I EMF measurements, excess Cu(1Cu + 1cell I sample w/w) was added to test electrode sample to ensure the co-existence stoichiometry of Cu2Se, Cu
and CuInSe2. The reference electrode was made from a mixture of
0.88 In + 0.12 In2O3 w/w. Both pellet and powder samples were
used in experiments. The pellet samples were prepared by using
a macro/micro 13 mm KBr die set (International Crystal Labs). A
maximum force of 10 tons was applied on each sample by a
hydraulic press.
The EMF measurements were made on the following galvanic
cell:
Pt; InðlÞ; In2 O3 ðsÞ==YSZ==In2 O3 ðsÞ; Cu2 SeðsÞ; CuðsÞ;
CuInSe2 ða or dÞ; C; Pt Cell I
where YSZ denotes 15 mass percent Y2O3 (yittria) stabilized ZrO2
(zirconia) solid electrolyte, C denotes graphite cups and Pt denotes
the platinum wire used as the electrical contact. High density
nuclear grade graphite cups and alumina crucibles were used to
contain the test electrode materials. The absence of asymmetric
potentials due to the graphite cups was tested by measuring the
symmetrical galvanic cell with identical (In/In2O3) electrodes.
Nearly null (±1 mV) EMF was measured in the above symmetric cell
over the experimental range of 900–1200 K. The absence of asymmetric potentials and the location of the electrodes in the isothermal zone of the furnace were carefully verified. In measurements,
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M. Ider et al. / Journal of Alloys and Compounds 604 (2014) 363–372
3.3. Results
Table 3
Lattice structures of the compounds in the Cu–In–Se system.
CuInSe2
(a)
CuInSe2
(d)
Beta
Cu2In4Se7
CuIn3Se5
CuIn5Se8
Tetragonal
Cubic
–
Tetragonal
Tetragonal
Hexagonal
Lattice parameter
References
ao = 0.5785 nm
Co = 1.157 nm
ao = 0.5782 nm
Co = 1.1621 nm
ao = 0.5780 nm
Co = 1.161 nm
ao = 0.577 nm
Co = 1.156 nm
ao = 0.5781 nm
Co = 0.1164 nm
ao = 0.5814 nm
Co = 0.1163 nm
ao = 0.5785 nm
Co = 1.1621 nm
xCu = 0.258, xIn = 0.249, xSe = 0.493
ao = 0.5780 nm
Co = 1.161 nm
xCu = 0.221, xIn = 0.27, xSe = 0.509
ao = 0.586 nm
Co = 0.558 nm
ao = 0.584 nm
xCu = 0.244, xIn = 0.256, xSe = 0.500
ao = 0.5755 nm
xCu = 0.14, xIn = 0.323, xSe = 0.537
ao = 0.5766 nm
Co = 1.1531 nm
xCu = 0.15, xIn = 0.31, xSe = 53.8
ao = 0.5751 nm
Co = 1.1520 nm
xCu = 0.115, xIn = 0.329, xSe = 55.6
ao = 0.5762 nm
Co = 1.153 nm
ao = 0.5765 nm
Co = 1.153 nm
ao = 0.5754 nm
Co = 1.1518 nm
ao = 0.575 nm
Co = 1.150 nm
ao = 1.2147 nm
Co = 4.6010 nm
ao = 1.212 nm
Co = 4.604 nm
xCu = 0.073, xIn = 0.35, xSe = 0.577
ao = 1.212 nm
Co = 4.604 nm
xCu = 0.07, xIn = 0.356, xSe = 0.574
Ao = 0.404 nm
Co = 0.404 nm
xCu = 0.043, xIn = 0.372, xSe = 0.585
(high T phase)
[13]
Measured open circuit potentials at each measurement temperature are plotted in Fig. 1. The data were fitted using linear regression analysis and the following expressions resulted:
[3]
Ea 1:47 ðmVÞ ¼ 343:85 0:18828T ðKÞ ð949—1044 KÞ
ð1Þ
[9]
Eb 0:45 ðmVÞ ¼ 309:26 0:15580T ðKÞ ð1055—1150 KÞ
ð2Þ
[2]
[11]
[12]
[33]
[33]
[8]
3.4. Discussion
3.4.1. Gibbs energy of a-CuInSe2 and d-CuInSe2
The half cell reaction of the cell I can be written as
1=2In2 O3 ðsÞ þ 2Cu2 SeðsÞ þ 3e
$ CuInSe2 ða or dÞ þ 3CuðsÞ þ 3=2O2 ðgÞ
ð3Þ
InðlÞ þ 3=2O2 ðgÞ $ 1=2In2 O3 ðsÞ þ 3e
ð4Þ
[33]
For the passage of 3 equivalent of electrons, the over-all cell
reaction per mole of CIS can be represented as
[33]
2Cu2 SeðsÞ þ InðlÞ $ CuInSe2 ða or dÞ þ 3CuðsÞ
[33]
The Gibbs energy change of the overall cell reaction is directly
related to the measured EMF by the Nernst equation,
[33]
DGR ¼ nFE
[31]
[31]
ð5Þ
ð6Þ
where E is the measured open circuit value between test and reference electrodes, n is the number of equivalent charges transferred
per mole of reaction and Faraday’s constant, F is equal to
96485.3 C/mol.
[30]
[10]
[23]
[33]
[33]
[33]
both cell electrodes were located in isothermal zone of the furnace.
This enabled the solid oxide ion conductor to be in its ionic conduction domain at both electrodes. The temperature range of adopted
measurements was high enough that there was no detrimental
influence from the partial electronic conduction. A nearly static
atmosphere of purified argon was provided for the electrodes of
the cell compartment. The temperature of the cell was measured
using a Pt–10%Rh/Pt thermocouple whose junction was located
near the electrodes of the cell in the isothermal zone of the furnace.
The reversibility of the EMF readings was ascertained by checking the
reproducibility in thermal cycling as well as by micro-polarization.
The equilibrium nature of the EMF was verified by a 5–10%
variation in the composition of the co-existing phases of the test
electrodes from one experimental run to another. The test
electrodes were examined by XRD at the end of each experiment
to confirm the absence of changes in phase composition. Other
experimental details such as temperature control, argon purification system, and voltage measurement are given elsewhere
[36–38].
3.4.2. Gibbs energy of Cu2Se, Cu and In
Cu2xSe is a defect compound with a fair homogeneity range.
Although the phase diagram and thermochemistry of Cu–Se system were studied before, the literature data is subject to controversy. There is some inconsistency and uncertainty in published
data for the Gibbs energy function and enthalpy of formation.
The Cu–Se system was recently assessed by Chang [1]. The a
and b Cu2xSe defect phases were described by a 3 sublattice model
using the formula(Cu,Va)1(Se,Va)1(Cu)1. The other intermediate
phases were treated as line compounds. Liquid phase was
described by the associated model developed by Sommer [39].
However, the optimized Gibbs energy function of Cu2xSe is not
in good agreement with Barin and Knacke’s [40] assessment.
Although Barin and Knacke’s [40] recommendation assumes only
170
Run 1
Run 2
Run 3
160
E (mV)
Compound Crystal
system
150
140
130
120
900
950
1000
1050
1100
1150
T (K)
Fig. 1. Temperature dependence of the EMF of cell I.
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M. Ider et al. / Journal of Alloys and Compounds 604 (2014) 363–372
one solid transformation at 395.4 K, the Gibbs energy data display
a parabolic character at higher temperature. The reason why there
is a distinct bend in the Gibbs energy functions is not clear since
Chang’s [1] assessment does not suggest any phase transformation
or multi-phase equilibrium between 395.4 and 1300 K. However, it
may be related to defect formation reactions and the large difference in the entropy function may be responsible for the large deviation in the Gibbs energy function. Cahen and Noufi [21] reported a
slightly different Gibbs energy of formation data although his
Gibbs energy functions are similar to Barin and Knacke’s [40].
The difference comes from Cahen and Noufi’s [21] DHf;298 ¼
60:00 kJ=mol and Barin and Knacke’s [40] DHf;298 ¼
65:27 kJ=mol assumptions. Shen [41] recently re-optimized the
Cu–Se system. The a-Cu2xSe and b-Cu2xSe phases were described
by the sublattice model with two Cu sublattices and one Se sublattice represented by the formula (Cu,Va)1(Se,Va)1(Cu)1. The liquid
phase was described by an ionic sublattice model with two sublattices schematically described as (Cu+1,Cu+2)p(Se2,Va1,Se)q.
Shen’s [41] and Cahen and Noufi’s [21] results in general are consistent, although Shen’s [41] DHf;298 (-52.46 kJ/mol) slightly differ
from Cahen and Noufi’s [21] (60.00 kJ/mol). When direct values
of Gibbs energies were used in calculation, third law analysis
showed that Barin and Knacke’s [40] data introduced a trend of
slight temperature dependency. After analyzing all the available
data, Shen’s [41] latest assessment results were adopted in this
assessment since the calculated values are consistent with the
other binaries. Interpolated values of Barin and Knacke’s [40] data
were used when critical data was missing. The Gibbs energy
changes for cell reactions were calculated using both Gibbs energy
of formation of compounds and Gibbs energy functions to check
the consistency of reference data. The data for elements Cu(s)
and In(l) were obtained from Barin and Knacke [40], Cahenand
and Noufi [21] and Shen’s [41] assessment. ThermoCalc files and
the results from direct Gibbs energy calculations were compared
for consistency.
3.4.3. First order transition between a-CuInSe2 and d-CuInSe2
The Gibbs energy of the CuInSe2 compound can be easily calculated from the following relations:
DGRða
or dÞ
¼ GCuInSe2 þ 3GCu 2GCu2 Se GIn
ð7Þ
DGRða
or dÞ
¼ DGf CuInSe2 ða or dÞ 2DGf Cu2 SeðsÞ
ð8Þ
Expressions for the standard Gibbs energy changes DGR(a) and
DGR(d) for the reaction were calculated using Eqs. (1), (2), and (6).
DGR;a ¼ 0:0545T ðKÞ 99:52 kJ=mol
ð9Þ
DGR;d ¼ 0:0451T ðKÞ 89:52 kJ=mol
ð10Þ
Eqs. (9) and (10) are valid for the a (Chalcopyrite) and d (Sphalerite)
phases of CuInSe2 in the temperature ranges indicated in Eqs. (1)
and (2). Since there is no phase transition in Cu2Se, In and Cu in
the temperature range of 949–1150 K, the difference in DGR calculated from Eqs. (9) and (10) must correspond to the standard Gibbs
energy change DGR(a–d) for the a to d transition in CuInSe2. Thus, by
solving Eqs. (9) and (10), one obtains
DGRða-dÞ ðkJ=molÞ ¼ 10:0 0:0094T ðKÞ
ð11Þ
Since the Gibbs energy change is zero for the equilibrium, a–d
transformation temperature of 1064(±20) K is obtained by solving
Eq. (11). Correspondingly, the standard enthalpy of transition,
DHtrans is found as 10.0 kJ/mol and the standard entropy of transformation, DStrans , is found as 9.4 J/mol K.
Similarly the Gibbs energy functions of a and d-CuInSe2 are
found as:
367
Ga—CuInSe2 ¼ 0:2227T ðKÞ 129:35 kJ=mol
ð12Þ
Gd-CuInSe2 ¼ 0:2189T ðKÞ 134:85 kJ=mol
ð13Þ
The following Gibbs energy expressions for Cu(s), Se(l) and In(l)
are used:
GCu ¼ 0:0619T þ 15:747 kJ=mol ðfit 800—1100 KÞ
ð14Þ
GSe ¼ 0:0902T þ 26:576 kJ=mol ðfit 800—1100 KÞ
ð15Þ
GIn ¼ 0:0915T þ 15:415 kJ=mol ðfit 500—1100 KÞ
ð16Þ
All the Gibbs energy expressions are given relative to reference
state of 298 K at which the Gibbs formation energies of pure elements were taken as zero. The expressions for pure elements were
interpolated from the curve fit expressions of tabulated values of
Barin and Knacke [42] in the temperature range of experimental
measurements (800–1100 K). The Gibbs energy function of Cu2Se(solid) was taken from the latest assessment results by Shen
[41] (0.24185T 0.0002329 kJ/mol). The Gibbs energy of formation of Cu2Se(solid) was obtained from formation reaction from
elements. From this value, the Gibbs energy of formation of CuInSe2 compound was calculated by using Eq. (8). The calculated
Gibbs energy of formation functions can be represented as:
DGf Cu2 SeðsÞ ¼ 0:024695T ðKÞ 60:698 kJ=mol
ð17Þ
DGf CuInSe2 ðaÞ ¼ 0:0051T ðKÞ 220:92 kJ=mol
ð18Þ
The Gibbs energy of a-CuInSe2, d-CuInSe2, enthalpy of transformation and DHf;298 data are compared in Tables 1 and 2.
3.4.4. Computation of DHf;298 of CuInSe2(a)
A third-law analysis was conducted on cell I data to assess the
temperature dependent errors in the EMF measurements and their
consistency with the calorimetric data. For this purpose, Gibbs
energy expressions for Cu, In, Cu2Se and CuInSe2 from Cahen and
Noufi [43] and Shen [41] were combined with the DGR values cal
culated from each EMF value along with DGf of Cu2Se at each
experimental temperature in order to derive those for DHf;298 at
different temperatures. A third-law plot of DHf;298 CuInSe2 is shown
in Fig. 2. The mean value of DHf;298 CuInSe2 was found to be
202.92 kJ/mol. This value is compared with those of other literature values along with S298 in Table 2.
Due to the lack of reliable data for the free energy functions, no
third-law analysis was performed for the Cu1In3Se5 and Cu1In5Se8
phases. However, the pseudo-binary phase diagram of Cu2Se and
In2Se3 system was critically optimized and all compound Gibbs
energy data were calculated in accordance with published phase
diagram data. The recently measured Gibbs energy functions by
Ider [35] for Cu1In3Se5 and Cu1In5Se8 phases were also used in
the optimization. The CALPHAD method of phase diagram calculation was used in the optimization with the help of ThermoCalc
computer program. The estimated and calculated data are compared in Tables 1, 2 and 4.
3.4.5. Pseudo-binary phase diagram assessment of the Cu2Se–In2Se3
system
The Cu2Se–In2Se3 pseudo-binary phase diagram is one of the
most studied sections of the Cu–In–Se system. Although many provisional phase diagrams were suggested, there is still some inconsistency especially in the CuInSe2–In2Se3 section of the phase
diagram. The difficulty in interpreting the crystal structure data,
which displays compositional dependency in non-homogeneous
structure regions, is responsible for most of the confusion. The performance of a critical assessment should be helpful in interpreting
the phase diagram data.
368
M. Ider et al. / Journal of Alloys and Compounds 604 (2014) 363–372
ΔHof,298 (CuInSe2) (kJ / mol )
-100
Table 4
Optimized parameters according to the analytical description of the phases.a
This work by emf
Average
-150
Phase,
modification
or function
Parameters
Liquid
GlCu2 Se ¼ GCu2 Se
GlIn2 Se3 ¼ GIn2 Se3
-200
-250
-300
700
d-CuInSe2
800
900
1000
1100
1200
1300
T (K)
a-CuInSe2
Fig. 2. Third-law determination of the standard enthalpy of formation of a-CuInSe2.
In this assessment, the Cu2Se–In2Se3 system is characterized by
the occurrence of three stable ternary compounds with wide
homogeneity ranges: CuInSe2, Cu1In3Se5 and Cu1In5Se8. CuInSe2
can be described with two polymorphs: the chalcopyrite a-CuInSe2
and the high temperature modification of d-CuInSe2 with the
sphalerite structure, while the b-phase can be represented with
the numerical formula Cu1In3Se5, which can be described as an
ordered defect structure. The c phase, represented by the numerical formula of Cu1In5Se8, can be described by a non-homogenous
layered structure. The liquid phase does not exhibit miscibility
gaps. However, there are 2 eutectic (17 mol% In2Se3, 95 mol% In2Se3) and 2 peritectic reactions (73 and 84.5 mol% In2Se3) in the
pseudo-binary section of Cu2Se–In2Se3 system.
In the present investigation, the temperature of phase transformation of CuInSe2 from the ordered chalcopyrite to sphalerite
structure was observed over the range 1000–1100 K. It was
observed that the EMF readings were sporadic beyond 1150 K,
which indicated some phase change or co-existence phases going
to liquidus range. A critical construction of partial isothermal section of the Cu–In–Se phase diagram was performed by combining
XRD measurements, phase transition temperatures and standard
enthalpy data from the literature along with the calculated Gibbs
energy functions. Furthermore, an optimization of selected data
was performed based on the measured and evaluated phase diagram and the reported thermodynamic data. Various models,
including the Redlich–Kister polynomial [44] with two coefficients,
sub-regular model, and sub-lattice models [45,46], were used to
describe the solution phases in this system. A self-consistent set
of phase diagram and thermodynamic data was obtained through
this assessment.
3.5. Thermodynamic models
3.5.1. Pure elements and stoichiometric compound phases
The Gibbs energy functions for Cu2Se were taken from Shen
[41]. The Gibbs energy functions for In2Se3 were taken from the
recent assessment of Chang [1]. The Cu2Se compound was reported
with two modifications, a-Cu2xSe and b-Cu2xSe in Shen’s [41]
recent re-optimization study. The a-Cu2xSe and b-Cu2xSe phases
were described by the sublattice model with two Cu sublattices
and one Se sublattice represented by the formula (Cu,Va)1
(Se,Va)1(Cu)1. These optimized functions were adopted and the
values for the stoichiometric compositions were directly used in
this assessment.
The In–Se system was recently assessed by Chang [1] with nine
intermediate phases including four stable phases corresponding to
b-Cu1In3Se5
c-Cu1In5Se8
l
0 l
LCu2 Se;In2 Se3 ¼ 25; 930
1 l
LCu2 Se;In2 Se3 ¼ 18; 000
2 l
LCu2 Se;In2 Se3 ¼ 14; 500
a
GCu2 Se:In2 Se3 ¼ 0:5 GCu2 Se b þ 0:5 GIn2 Se3 d
a
GIn2 Se3 :Cu2 Se ¼ 0:5 GCu2 Se b þ 0:5 GIn2 Se3 d
0 a
LCu2 Se;Cu2 Se ¼ GCu2 Se b þ 2000
0 a
LIn2 Se3 ;In2 Se3 ¼ GIn2 Se3 d þ 4120
17; 000 þ T
þ 17; 000 T
0
La:Cu2 Se;In2 Se3 ¼ 15; 000 3T
0
LaCu2 Se;In2 Se3 : ¼ 18; 050 30T
GaCu2 Se:In2 Se3 ¼ 0:5 GCu2 Se
b
þ 0:5 GIn2 Se3
d
19; 350 þ 3T
GaIn2 Se3 :Cu2 Se ¼ 0:5 GCu2 Se
b
þ 0:5 GIn2 Se3
d
þ 19; 250 3T
0
LaCu2 Se;Cu2 Se ¼ GCu2 Se
0
LaIn2 Se3 ;In2 Se3 ¼ GIn2 Se3
0
La:Cu2 Se;In2 Se3 ¼ 15; 000
b
þ 8000
d
0
LaCu2 Se;In2 Se3 : ¼ 8000
GlCu2 Se ¼ GCu2 Se
GlIn2 Se3 ¼ GIn2 Se3
b
d
þ 4000
þ 5000 þ 7T
þ 3500 þ 4T
0 l
LCu2 Se;In2 Se3 ¼ 60; 000
1 l
LCu2 Se;In2 Se3 ¼ 80; 000
l
GCu2 Se ¼ GCu2 Se b þ 7000
GlIn2 Se3 ¼ GIn2 Se3
0 l
LCu2 Se;In2 Se3
1 l
LCu2 Se;In2 Se3
Function
l
d
þ 6T
þ 4000 þ 4T
¼ 1000 þ T
¼ 179; 000
GCu2 Se a ¼ 80217:34 þ 288:16728T
59:0572T ln T 0:0375096T 2
ð298 6 T 6 395Þ
=98255.14 + 662.67401T 120.090000Tln T
+ 0.0400000T2
0.6967E05T3 + 1,020,000T1 (395 6 T 6 800)
GCu2 Se b ¼ GCu2 Se a þ 6830 17:29114T
GCu2 Se l ¼ GCu2 Se b þ 16; 000 11:422T
GIn2 Se3 l ¼ GIn2 Se3 d þ 88763:31 75:84304T
GIn2 Se3 c ¼ 350296:2 þ 559:60784T
113:41683T ln T 0:0179945T 2 ð298 6 T 6 1018Þ
=
354076.2
+ 554.14084T
d
113.41683Tln T 0.0179945T2 (298 6 T 6 1018)
=323687.73 + 770.53003T 151Tln T (1018 6 T 6 6000)
GIn2 Se3
a
Temperature (T) is in Kelvin. The Gibbs energies are in J/mol.
In2Se3 compositions. The a-In2Se3, b-In2Se3, c-In2Se3, and d-In2Se3
phases were modeled as line compounds. However, only the
c-In2Se3 and d-In2Se3 phases were included in this assessment.
The three-term equation given below was used to represent the
temperature dependence of the Gibbs energies of the end
members,
G ¼ a þ bT þ cT ln T
ð19Þ
where °G is the standard Gibbs energy, T is the absolute temperature, and a, b and c are constants whose values are estimated from
optimization of experimental data.
3.5.2. Liquid phase
With a view towards predicting higher order systems, a simplified model for the liquid is preferred such as the Redlich–Kister
[44] expansion. The general formula for the liquid solution can
be represented as
Gl ¼ ref Gl þ id Gl þ E Gl
ð20Þ
369
M. Ider et al. / Journal of Alloys and Compounds 604 (2014) 363–372
ref
with
Gl ¼ xCu2 Se GlCu2 Se þ xIn2 Se3 GlIn2 Se3
ð21Þ
Gl ¼ RT xCu2 Se ln xCu2 Se þ xIn2 Se3 ln xIn2 Se3
ð22Þ
ref
id
where xi refers to the fraction of species i in liquid phase. The terms
Gli represent the Gibbs energies of the pure liquid phase of species i.
E l
G , the excess Gibbs energy, can be expressed by the following
regular solution model,
0
00
u
þ y0In2 Se3 y00In2 Se3 Gu
In2 Se3 :In2 Se3 þ yIn2 Se3 yCu2 Se GIn2 Se3 :Cu2 Se
id
E
Gl ¼ xCu2 Se xIn2 Se3
2
X
i l
LCu2 Se;In2 Se3
xCu2 Se xIn2 Se3
i
0
00
u
Gu ¼ y0Cu2 Se y00In2 Se3 Gu
Cu2 Se:In2 Se3 þ yCu2 Se yCu2 Se GCu2 Se:Cu2 Se
h 0
0
Gu ¼ RT p y0Cu2 Se lnyCu2 Se þ y0In2 Se3 lnyIn2 Se3
i
00
þq y00In2 Se3 lnyIn2 Se3 þ y00Cu2 Se ln y00Cu2 Se
ð35Þ
and the excess function is given by
E
ð23Þ
Gu ¼ y0Cu2 Se y0In2 Se3 y00Cu2 Se LCu2 Se;In2 Se3 :Cu2 Se þ y00In2 Se3 LCu2 Se;In2 Se3 :In2 Se3
þ y00In2 Se3 y00Cu2 Se y0In2 Se3 LIn2 Se3 :In2 Se3 ;Cu2 Se þ y0Cu2 Se LCu2 Se:In2 Se3 ;Cu2 Se
i¼0
ð36Þ
where L is the binary interaction parameter to be optimized in the
present work. The temperature dependence of L may be represented as
i l
LCu2 Se;In2 Se3
¼ ai þ bi T
ð24Þ
3.5.3. Ordered non-stoichiometric compound phases
b-Cu1In3Se5 and c-Cu1In5Se8 phases can be represented by the
sub-regular model, which is a modified version of the general Redlich–Kister model [44] with 2 coefficients. The general representation of the Gibbs energy of b and c phases is the same as Eq. (20),
where l is replaced with b or c
For b and c phases, the reference terms can be represented as
ref
ref
b
G ¼
xCu2 Se GbCu2 Se
c
þ xIn2 Se3
c
GbIn2 Se3
ð25Þ
c
G ¼ xCu2 Se GCu2 Se þ xIn2 Se3 GIn2 Se3
ð26Þ
where xi refers to the fraction of species i in b or c phase. The terms
Gbi and Gci represent the standard Gibbs energy of stoichiometric
reference phases of species i. The ideal terms can be expressed with
the following expressions:
id b
G ¼ RT xCu2 Se ln xCu2 Se þ xIn2 Se3 ln xIn2 Se3
ð27Þ
Gc ¼ RT xCu2 Se ln xCu2 Se þ xIn2 Se3 ln xIn2 Se3
ð28Þ
id
Similarly the excess terms are given by the following relation:
E
Gb ¼ xCu2 Se xIn2 Se3
1
X
i l
LCu2 Se;In2 Se3
xCu2 Se xIn2 Se3
i
ð29Þ
i
ð30Þ
i¼0
E
Gc ¼ xCu2 Se xIn2 Se3
ð34Þ
1
X
i l
LCu2 Se;In2 Se3
xCu2 Se xIn2 Se3
y0i
y00i
In these expressions
and
refer to the site fractions of the
species i on the first and second sublattices, respectively. The standard Gibbs energy of stoichiometric a-CuInSe2 terms Gu
Cu2 Se:In2 Se3
and Gu
In2 Se3 :Cu2 Se with the parameters estimated in this study are
modeled according to following relations:
Gu
Cu2 Se:In2 Se3 ¼ 0:5 Gb-Cu2 Se þ 0:5 Gd-In2 Se3 þ a1 þ b1 T
ð37Þ
Gu
In2 Se3 :Cu2 Se ¼ 0:5 Gd-In2 Se3 þ 0:5 Gb-Cu2 Se þ a1 þ b1 T
ð38Þ
The Gibbs energies for the other two terms in the Eq. (34) are
expressed as
Gu
Cu2 Se:Cu2 Se ¼ Gb-Cu2 Se þ a1 þ b1 T
ð39Þ
Gu
In2 Se3 :In2 Se3 ¼ Gd-In2 Se3 þ a1 þ b1 T
ð40Þ
where Gb-Cu2 Se and Gd-In2 Se3 are the standard Gibbs energy of stoichiometric b-Cu2Se and d-In2Se3 phases. The ai and bi are the model
parameters to be optimized.
4. Optimization procedure
A selected set of thermodynamic and phase diagram data and our
EMF experimental data were used for the optimization of thermodynamic model parameters of the Cu2Se–In2Se3 system. The optimization was performed using the PARROT module of the Thermo-Calc
program package. First, the calculated and estimated values of Gibbs
energy of known compounds were entered. Second, single phase
and two phase boundary limits are outlined by reviewing the latest
phase diagram data. Then, unknown Gibbs energy functions were
estimated from enthalpy of formation, standard entropy, heat
i¼0
i c
LCu2 Se;In2 Se3
¼ ai þ bi T
¼ ai þ bi T
ð31Þ
ð32Þ
The high temperature modification d-CuInSe2 sphalerite and aCuInSe2 chalcopyrite phases can be described using the sublattice
model developed by [45,46] with the following formula:
ðCu2 Se;In2 Se3 Þ1 ðIn2 Se3 ; Cu2 SeÞ1
Liquid
1265 K
δ+L
Cu2Se + δ
1188.2 K
1265 K
δ
1096 K
1062.7 K
Cu2Se + CuInSe2
1213 K 1183 K
α
1161 K
δ+β
998 K
α+β
993 K
β
ð33Þ
To model the homogeneity range, the ordered non-stoichiometric a-CuInSe2 and d-CuInSe2 phases are described using a
three-sublattice formalism. The Gibbs energy of such a phase u
(u = a-CuInSe2 or d-CuInSe2) can be represented by Eq. (20), where
l is replaced by u, as:
Cu2Se
MOLE_FRACTION In2Se3
γ
γ + In2Se3
i b
LCu2 Se;In2 Se3
1400 K
TEMPERATURE_KELVIN
where xi refers to the fraction of species i in b or c phase and L is the
binary interaction parameter to be optimized in the present work.
The temperature dependence of L may be represented as
In2Se3
Fig. 3. Calculated Cu2Se–In2Se3 phase diagram based on the optimized parameters.
370
M. Ider et al. / Journal of Alloys and Compounds 604 (2014) 363–372
Table 5
Invariant equilibria in the Cu2Se–In2Se3 system.
Phases
Composition (at.% In2Se3)
Temperature (K)
Reaction type
References
Liquid/d-CuInSe2
50
50
50
50
53
50
50
50
50–53
50
54
16–18
16
21.56
42
43
43
45
46.6
43
47.0
47.3
50
50
50
50
50
50
50
50
50
50
50
68
67
55
62
61.8
66–68
56
19–20
17
21
22
22
11
22
20–23
11
16.8
96
95
95
67
75.2
73.5
83
84.3
1263
1254
1259
1275
1280
1259
1280
1258
1275
1259
1265
1223
1216
1220
1053
1053
1053
1060
1058
1053
1063
1062.7
1103
1103
1083
1100
1088
1091
1083
1083
1087
1096
1123
833
868
1075
978
793
940–950
998
1168
1163
1208
1215
1055
1053
1188
1188
1216
1188.2
1133
1143
1158
1198
1173
1213
1153
1183.5
Congruent melting
[5]
[2]
[3]
[32]
[24]
[48]
[2]
[33]
[1]
[20]
This
[24]
[22]
[1]
[32]
[24]
[48]
[2]
[1]
[20]
[22]
This
[15]
[32]
[48]
[2]
[33]
[1]
[20]
[22]
[56]
This
[56]
[32]
[48]
[2]
[33]
[1]
[20]
This
[24]
[22]
[1]
[1]
[32]
[24]
[48]
[20]
[22]
This
[33]
[1]
This
[33]
[1]
This
[33]
This
Liquid/Cu5InSe4
Liquid/Cu13In3Se11
d-CuInSe2/Cu2Se_b/a-CuInSe2
d-CuInSe2/a-CuInSe2
n-CuInSe2/d-CuInSe2
d-CuInSe2/a-CuInSe2/b-Cu1In3Se5
Liquid/Cu5InSe4/d-CuInSe2
Liquid/Cu2Se_b/Cu13In3Se11
Liquid/Cu13In3Se11/d-CuInSe2
Liquid/Cu2Se_b/d-CuInSe2
Liquid/c-Cu1In5Se8/In2Se3_d
Liquid/d-CuInSe2/b-Cu1In3Se5
Liquid/b-Cu1In3Se5/c-Cu1In5Se8
capacity, transition enthalpy and temperature, and melting information. Third, fixing the calculated Gibbs energy data of a-CuInSe2
from EMF experiments, the coefficients of ordered non-stoichiometric phases were roughly estimated. Fourth, after obtaining
estimated parameters for a-CuInSe2, d-CuInSe2, b-Cu1In3Se5 and
c-Cu1In5Se8, phase solution parameters were also calculated.
Finally, all the calculated and optimized parameters were optimized
based on the available thermodynamic and phase diagram data.
5. Results and discussion
The optimized parameters of the stable phases in the Cu2Se–
In2Se3 system are listed in Table 4. The phase diagram and
Congruent melting
Congruent melting
Eutectoid
Congruent transformation
Congruent transformation
Eutectoid
Eutectic
Eutectic
Eutectic
Eutectic
Eutectic
Peritectic
Peritectic
work
work
work
work
work
work
work
work
thermodynamic properties of this system were calculated with
the Poly-3 module of the ThermoCalc program package. The calculated phase diagram is given in Fig. 3. Table 5 displays the experimental and calculated temperatures and compositions of the
invariant reactions in the system. The calculated values are well
within the uncertainty of experimental data. The high temperature
phase of d-CuInSe2 phase limits are well defined and the stability
ranges of b-Cu1In3Se5 and c-Cu1In5Se8 phases seem to be consistent with the experimental data published in this region. Comparison between the calculated Cu2Se–In2Se3 phase diagram and
various experimental data are given in Figs. 4–6. Fig. 5 reveals a
more complicated region of the phase diagram where there were
no consistent explanation of numerous and conflicting data.
M. Ider et al. / Journal of Alloys and Compounds 604 (2014) 363–372
Liquid
β
α
Cu2Se + CuInSe2
Cu2Se
α+β
γ
γ + In2Se3
δ
Cu2Se + δ
MOLE_FRACTION In 2Se3
In2Se3
Fig. 4. Comparison between the calculated Cu2Se–In2Se3 phase diagram and
various experimental data.
δ
δ+β
γ
β
α+β
MOLE_FRACTION In 2Se3
Fig. 5. Comparison between the Cu2Se–In2Se3 phase diagram and various experimental data in the vicinity of In2Se3 rich section.
Liquid
TEMPERATURE_KELVIN
This region appears with two peritectic reactions involving
d-liquid, b-liquid and c-liquid coexistence regions at high temperature. The eutectic at around 1150 K is also clearly represented.
Fig. 6 shows a comparison between the calculated Cu2Se–In2Se3
phase diagram and various experimental data from 0.35 to
0.65 mol fraction of In2Se3.
The assessed and calculated standard enthalpies of formation of
the intermediate compounds at 298 K are presented in Table 2.
Although there is broad inconsistency in the literature, these optimization results are within the reported limits.
6. Conclusion
A thermodynamic description of the Cu2Se–In2Se3 was obtained
by optimization of the available phase equilibrium and thermodynamic information along with the direct results of EMF experiments. The Redlich–Kister model with 3 coefficient expression
was employed to define the Gibbs energy of the liquid phase.
The a and d modification of CuInSe2 phases were modeled with a
specific sublattice model. A reasonable agreement between the
model calculated values and the thermodynamic phase equilibrium data was achieved. Importantly, a conclusion for the conflicting phase stability regions of b-Cu1In3Se5 and c-Cu1In5Se8 phases
along with the high temperature homogeneity limits of d-CuInSe2
sphalerite formation was described. The calculated phase diagram
can further be improved with a study towards confirmation of beta
and gamma phase Gibbs energy functions.
References
γ + In2Se3
TEMPERATURE_KELVIN
Liquid
371
δ
Cu2Se + δ
Cu2Se + α
α
α+β
MOLE_FRACTION In 2Se3
Fig. 6. Comparison between the calculated Cu2Se–In2Se3 phase diagram and
various experimental data from 0.35 to 0.65 mol fraction of In2Se3.
[1] C.-H. Chang, Ph.D. Dissertation, University of Florida, Gainesville, FL, 1999.
[2] M.Y. Rigan, V.I. Tkachenko, N.P. Stasyuk, L.G. Novikova, Inorganic Materials,
1991, p. 304.
[3] L.A. Mechkovski, S.A. Alfer, I.V. Bodnar, A.P. Bologa, Thermochim. Acta 93
(1985) 729.
[4] S.H. Wei, L.G. Ferreira, A. Zunger, Phys. Rev. 45 (5) (1992) 2533.
[5] L. Shay, J.H. Wernick, Ternary Chalcopyrite Semiconductors, Pergamon, Oxford,
1975;
L.S. Palatnik, E.J. Rogacheva, Dokl. Akad. Nauk SSSR 174 (1967) 80 (Sov. Phys.
Dokl. 12 (1967) 503).
[6] K.J. Bachmann, F.S.L. Hsu, F.A. Thiel, H.M. Kasper, J. Electron. Mater. 6 (1977)
431.
[7] L.M. Khriplovich, I.E. Paukov, W. Moller, Kuhn, Russ. J. Phys. Chem. 58 (1984)
619.
[8] Z. Range, Naturforsch., B: Anorg. Chem. 23 (1968) 1262.
[9] M.F. Kotkata, M.S. Al-Kotb, Proc. Int. Conf. Condens Matter. Phys. Appl. (1992)
262–265.
[10] L.S. Palatnik, E.I. Rogacheva, Izvestiya Akademii Nauk SSSR, Neorganischke
Mater. 2 (3) (1966) 478–484.
[11] H. Neumann, Cryst. Res. Technol. 29 (7) (1994) 985–994.
[12] M.L. Fearheiley, K.J. Bachmann, J. Electron. Mater. 14 (6) (1985).
[13] H. Hahn, G. Frank, W. Klinger, A.D. Meyer, G. Storger, Z. Anorg. Allg. Chem. 271
(1953) 153.
[14] H. Matsuhita, S. Endo, T. Irie, Jpn. J. Appl. Phys. Part 1 Reg. Pap. Short Note 30
(6) (1991) 1181–1185.
[15] M.F. Zargarova, P.K. Babaeva, D.S. Azhdarova, Z.D. Mekhtieva, S.A. Mekhtieva,
Inorg. Mater. 32 (1995) 282.
[16] J.B. Mooney, R.H. Lamoreaux, Solar Cells 16 (1986) 211.
[17] R.H. Lamoreaux, K.H. Lau, R.D. Brittain, Final Report, SERI Subcontract XZ-202001, 1983.
[18] H. Neumann, Cryst. Res. Technol. 18 (1983) 665.
[19] S. Nomura, H. Matsuhita, T. Takizawa, Jpn. J. Appl. Phys. 30 (1991) 3461–3464.
[20] A. Rockett, R.W. Birkmire, J. Appl. Phys. 70 (7) (1991).
[21] D. Cahen, R. Noufi, J. Phys. Chem. Solids 53 (1992) 991–1005.
[22] K.J. Bachmann, M.L. Fearheiley, Y.H. Shing, Trans. Appl. Phys. Lett. 44 (1984)
407.
[23] J.C.W. Folmer, J.A. Turner, R. Noufi, D. Cahen, J. Electrochem. Soc. 132 (6)
(1985) 1319.
[24] M.L. Fearheiley, Solar Cells 16 (1986) 91.
[25] R. Lesuer, C. Djega-Mariadassau, P. Charpin, J.H. Albany, Inst. Phys. Conf. Ser. 35
(1977) 15.
[26] L.S. Palatnik, Y.F. Komnik, E.I. Rogacheva, Ukr. Fiz. Zh. 9 (1964) 862.
[27] V.I. Tagirov, N.F. Gakhramanov, A.G. Guseinov, F.M. Aliev, G.G. Guiseinov, Sov.
Phys. Semicond. 14 (1980) 831.
[28] C. Manolikas, J. van Landuyt, R. de Ridder, S. Amelinckx, Phys. Status Solidi A 55
(1979) 709.
[29] H.W. Schock, Adv. Solid State Phys. 34 (1994) 147–161.
372
M. Ider et al. / Journal of Alloys and Compounds 604 (2014) 363–372
[30] T. Hanada, A. Yamana, Y. Nakamura, O. Nittono, Technical Digest of the
International PVSEC-9, 1996.
[31] B. Schumann, G. Kuhn, U. Boehnke, H. Neels, Sov. Phys. Crystallogr. 26 (6)
(1981) 678.
[32] T.I. Koneshova, A.A. Babitsyna, V.T. Kalinnikov, Inorg. Mater. 18 (9) (1983)
1267.
[33] U.C. Boehnke, G. Kuhn, J. Mater. Sci. 22 (1987) 1635.
[34] T. Godecke, T. Haalboum, F. Ernst, Z. Metall. 91 (2000) 651–662.
[35] M. Ider, Ph.D. Dissertation, University of Florida, Gainesville, FL, 2003.
[36] T.J. Anderson, L.F. Donaghey, J. Chem. Thermodyn. 9 (1977) 603.
[37] T.J. Anderson, T.L. Aselage, L.F. Donaghey, J. Chem. Thermodyn. 15 (1983) 927.
[38] Y. Feutelais, B. Legendre, S. Misra, T.J. Anderson, J. Phase Equilib. 15 (1994)
171–177.
[39] F. Sommer, Z. Metall. 73 (1982) 72.
[40] Barin, O. Knacke, in: Thermochemical Properties of Inorganic Substances,
Springer-Verlag, Berlin, 1973.
[41] J.Y. Shen, Private Communication.
[42] I. Barin, O. Knacke, in: Thermochemical Properties of Inorganic Substances,
Springer-verlag, Berlin, 1973.
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
[53]
[54]
[55]
[56]
D. Cahen, R. Noufi, J. Phys. Chem. Solids 52 (1991) 947.
O. Redlich, A. Kister, Ind. Eng. Chem. 40 (1948) 345.
M. Hillert, L.I. Staffanson, Acta Chim. Scand. 24 (1970) 3618.
B. Sundman, J. Agren, J. Phys. Chem. Solids 42 (1981) 297.
I.V. Bodnar, B.V. Korzun, Mater. Res. Bull. 18 (1983) 519.
L.S. Palatnik, E.I. Rogacheva, Sov. Phys. Dokl. 12 (1967) 503.
L. Garbato, F. Ledda, A. Rucci, Prog. Cryst. Growth Charact. 15 (1987) 1–41.
L.I. Berger, S.A. Bondar, V.V. Lebedev, A.D. Molodyk, S.S. Strel’chenko, Nauka
Tekh. (1973) 248.
V.M. Glazov, V.V. Lebedev, A.D. Molkyn, A.S. Pashinkin, Inorg. Mater. 15 (1979)
1865.
E. Gombia, F. Leccabue, C. Pelosi, Mater. Lett. 2 (1984) 429.
C. Mallika, Private Communication.
S.H. Wei, Private Communication.
C.H. Chang, Private Communication.
K.J. Bachmann, H. Goslowsky, S. Fiechter, J. Cryst. Growth 89 (1988) 160.