Determination of the standard free energies of formation for tungsten silicides by EMF measurements using lithium silicate liquid electrolyte

Article abstract of DOI:10.1016/j.jallcom.2004.08.100

EMF measurements on silicon concentration cell were carried out using lithium silicate electrolyte in the temperature range 1300-1500 K. Using the EMF-temperature relations obtained, the standard free energies of formation for W₅Si₃ and WSi₂ have been calculated as functions of temperature: ΔG⁰(W₅Si₃) (kJ mol^-1) = -128.6 - 0.0132 (T (K)) ± 0.42 and ΔG ⁰(WSi₂) (kJ mol^-1) = -98.5 + 0.0095 (T (K)) ± 0.15, respectively. Combining the results with thermodynamic data, the standard enthalpies of formation for silicides at 298 K have been obtained as ΔH⁰(W₅Si₃, 298) (kJ mol^-1) = -133 ± 25 and ΔH⁰(WSi₂, 298) (kJ mol ^-1) = -82 ± 6, respectively. A new eutectoid reaction W ₅Si₃ ? W + WSi₂ occurring around 700 K is suggested in W-Si binary system. Published by Elsevier B.V.

Full text of DOI:10.1016/j.jallcom.2004.08.100

Journal of Alloys and Compounds 391 (2005) 307–312
Determination of the standard free energies of formation for tungsten
silicides by EMF measurements using lithium silicate
liquid electrolyte
Hiroyasu Fujiwaraa,∗, Yukitomi Uedaa, Alok Awasthib,
Nagaiyar Krishnamurthyb, Sheo Parkash Gargb
a
Graduate School of Energy Science, Kyoto University, Yoshida-honmachi, Sakyo-ku, 606-8501Kyoto, Japan
b
Materials Processing Division, Bhabha Atomic Research Centre, Mumbai 400085, India
Received 17 August 2004; accepted 31 August 2004
Available online 28 November 2004
Abstract
EMF measurements on silicon concentration cell were carried out using lithium silicate electrolyte in the temperature range 1300–1500 K.
Using the EMF–temperature relations obtained, the standard free energies of formation for W5Si3 and WSi2 have been calculated as func-
tions of temperature: ꢀG0(W5Si3) (kJ mol−1) = −128.6 − 0.0132 (T (K)) 0.42 and ꢀG0(WSi2) (kJ mol−1) = −98.5 + 0.0095 (T (K)) 0.15,
respectively. Combining the results with thermodynamic data, the standard enthalpies of formation for silicides at 298 K have been ob-
tained as ꢀH0(W5Si3, 298) (kJ mol−1) = −133 25 and ꢀH0(WSi2, 298) (kJ mol−1) = −82 6, respectively. A new eutectoid reaction
W5Si3 ⇒ W + WSi2 occurring around 700 K is suggested in W–Si binary system.
© 2004 Published by Elsevier B.V.
Keywords: High temperature alloy; Electrochemical reactions; Intermetallics
1. Introduction
thalpy of formation at 298 K for W5Si3 was reported by
Tomaszkiewicz et al. [3], while that for WSi2 was done by
Robins and Jenkins [4] and by O’Hare [5]. A work on high
temperature heat capacity by Bondarenko et al. [6] provides
thedataforbothW5Si3 andWSi2. However, thedataforWSi2
are not consistent with the results by Callanan et al. [7], in
which experimentally determined low temperature heat ca-
pacity was combined with the reported values by Mezaki
et al. [8].
The EMF measurements have been widely used for ther-
modynamic activity determination. Unfortunately, applica-
tion to the refractory metal silicide systems was not so
popular, because of high reactivity of silicon and low par-
tial pressure of oxygen determined by Si/SiO2 equilibrium.
In the previous work by the authors [9], lithium silicate
electrolyte was utilized for EMF measurements of the sil-
icon concentration cells in order to determine the standard
free energies of formation for niobium silicides. Because
of the potential utility of the method adopted in the pre-
Transition metal silicides are effective oxidation-resistant
protective coating on the metals. Although thermodynamic
properties of the tungsten silicides have a bearing on vari-
ous practical applications, direct measurements of them have
been performed only to a limited extent. The experimental
work on the direct determination of the standard free en-
ergies of formation for tungsten silicides has been reported
by Chart [1]. He measured the vapor pressure of SiO for
the mixture of SiO2 + tungsten silicides by Knudsen-effusion
method. Kematick [2] reported the standard enthalpies of
formation at 298 K for the silicides, combining the latest
heat capacity data with the relation between silicon vapor
pressure and temperature obtained by high temperature mass
spectrometry. Calorimetric determination of the standard en-
∗
Corresponding author. Tel.: +81 75 753 5437; fax: +81 75 753 5437.
E-mail address: fujiwara@energy.kyoto-u.ac.jp (H. Fujiwara).
0925-8388/$ – see front matter © 2004 Published by Elsevier B.V.
doi:10.1016/j.jallcom.2004.08.100

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H. Fujiwara et al. / Journal of Alloys and Compounds 391(2005) 307–312
vious work, this has been applied for tungsten silicides in
the present study. The temperature range investigated is
1300–1500 K. Based on the results, the standard enthalpies
of formation at 298 K for W5Si3 and WSi2 have also been
obtained.
2. Experimentals
2.1. Phase relation and potential diagram
Fig. 1 is the binary W–Si phase diagram [10]. According
to this phase diagram, two tungsten silicides, i.e., W5Si3 and
WSi2, are stable at 1373 K. The lower part of Fig. 1 shows
the isothermal section of W–Si–O ternary system at 1373 K.
The isothermal section is constructed based on the potential
diagram shown in Fig. 2. In calculation of the relations in
Fig. 2, Barin’s data [11] of the standard free energy of for-
mation were used. The solid lines in Fig. 2 correspond to
the two-phase equilibria except for the lines for SiO2 and Si
(these are represented as gray lines). The points A, B, C and
D in Fig. 2 correspond to the three-phase triangles A, B, C
and D in the isothermal section shown in Fig. 1. As will be
mentioned later in Section 3.1, dashed lines were calculated
from the results of the present study. Within the area of quad-
rangle W–WO2–SiO2–Si in the isothermal section (Fig. 1),
no intermediate compounds were reported. In addition to this,
the partial pressure of oxygen at point D is calculated to be
much higher than that at point C. Thus, each of the phases
in W–Si binary system, W, W5Si3 and WSi2, coexists with
SiO2 at this temperature.
Fig. 2. Potential diagram of W–Si–O ternary system at 1373 K. Points A–D
correspond to the three-phase regions shown in Fig. 1.
2.2. Configuration of the cells
Three kinds of cells were used for EMF measurements,
i.e.,
cell(1) (−)Mo, reference/electrolyte/W + W5Si3
+ SiO2, Mo(+)
(1)
(2)
(3)
cell(2) (−)Mo, reference/electrolyte/W5Si3 + WSi2
+ SiO2, Mo(+)
cell(3) (−)Mo, W5Si3 + WSi2 + SiO2/electrolyte/W
+ W5Si3 + SiO2, Mo(+)
In the reference electrode of the cells (1) and (2), the activity
of silicon was fixed as unity. For this purpose, liquid silver
alloy saturated with Si and SiO2 was chosen. However, three-
phase mixture of Si, SiO2 and WSi2 or NbSi2 was used for
some of the initial experiments. Right hand sides of the cells
(1) and (2) correspond to the three-phase equilibria of C and B
inFigs. 1and2, respectively. Theoverallcompositionofthese
electrodes for each individual runs has been shown in the
isothermal section in Fig. 1. The EMF measurements of cell
(3) were also performed independently. However, only two of
them are arithmetically independent. The electrolyte used in
all the cells was molten lithium silicate saturated with SiO2.
The ionic conductivity of this electrolyte can be assumed
unity [12]. The electrolyte composition was 86 mass% SiO2.
This composition corresponds to the SiO2 liquidus at 1573 K
in Li2O–SiO2 binary phase diagram [13].
Fig. 1. Phase diagram of W–Si binary system and isothermal section of
W–Si–O ternary system at 1373 K. Each of the three-phase regions of A–D
corresponds to the point A–D in Fig. 2. Initial compositions used in elec-
trodes are marked in the three-phase regions B and C.

H. Fujiwara et al. / Journal of Alloys and Compounds 391(2005) 307–312
309
3. Results and discussion
3.1. EMF and activity of the three-phase equilibrium
EMF of the cells (1), (2) and (3), E(1), E(2) and E(3), are
shown in Fig. 4. The EMF–temperature relations obtained by
the linear regression are:
E(1) (mV) = +111.1 + 0.0114 (T (K)) 0.36
E(2) (mV) = +134.7 − 0.0224 (T (K)) 0.23
E(3) (mV) = −28.5 + 0.0371 (T (K)) 0.30
(4)
(5)
(6)
respectively. The errors in these equations represent the 95%
confidence interval for the least square regression. It is clear
that the temperature dependence of EMF is relatively small
for all the three cells. This is so because only condensed
phases are involved in the overall cell reactions, for which
the entropy change is known to be small. EMF measurements
were carried out by increasing and decreasing temperature,
showing no systematic errors in the results.
Fig. 3. Schematic illustration of experimental apparatus.
2.3. Procedure and materials
As mentioned before only two of the EMF–temperature
relations are arithmetically independent amongst the Eqs.
(4)–(6). Consistency in measurements can be ensured by
comparing measured EMF–temperature relation (6) with the
following Eq. (7):
The experimental details have been reported elsewhere
[9]. However, major modifications were made in reference
electrode assembly. A schematic illustration of the cell as-
sembly is shown in Fig. 3. The reference electrode consisted
of a holder tube made of SiO2 in which silver alloy saturated
with silicon was placed. The upper and the lower parts of the
silver alloy had different compositions, 40 and 80 mass% Si,
respectively. It may be noted that the maximum solubility of
silver in silicon is 4 × 10−4 at.% Ag at about 1523 K [14]. The
reference electrode assembly was placed vertically inside the
SiO2 crucible. The preparation of the upper part was done
by melting at 1673 K in graphite crucible. The lower part
was prepared by pressing the powder mixture into a pellet
followed by sintering at 1473 K for more than 3.6 ks under
Ar + 3% H2 atmosphere. Because the lower part contained
more silicon, i.e., more solid phase, than the upper part at the
experimental temperature, the shape of the pellet remained
unchanged and admixing of the molten alloy and the elec-
trolyte was avoided. The molybdenum lead wire immersed
into the upper part of the alloy was separated from the elec-
trolyte in this manner. Electrical contact of the alloy and the
electrolyte was achieved at the bottom of the electrode. The
reason for this modification and the results will be discussed
in Section 3.1.
E (mV) = −23.6 + 0.0338 (T (K)) 0.43
(7)
calculated using Eqs. (4) and (5). The EMF values ob-
tained from Eqs. (6) and (7) are respectively 23.4 0.30 and
23.7 0.43 mV at an average temperature of 1400 K.
W5Si3 and WSi2 were synthesized by vacuum heating of
the mixture of pure elements (W: 99.9%, less than 74 ␮m; Si:
99.999% less than 50 ␮m, Furuuchi Chemical Co.) at 1473 K
for 7.2 ks and at 1873 K for 7.2 ks, respectively. Lithium
silicate used as electrolyte was prepared from Li2CO3 and
SiO2. The mixture of Li2CO3 and SiO2 was de-carbonated
at 1173 K in platinum crucible for 43.2 ks and pre-melted at
1473 K in graphite crucible. Surface carbon of the pre-melted
drop of lithium silicate was eliminated by heating at 1273 K
in air.
Fig. 4. Observed EMF of the cells (1), (2) and (3) plotted against tem-
perature. Solid marks indicate results obtained by using solid silicides in
reference electrode.

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H. Fujiwara et al. / Journal of Alloys and Compounds 391(2005) 307–312
17 W5Si3 (s) + Si (s) = 5 WSi2 (s)
(13)
Because the activity of silicon, aSi, at the reference elec-
trode is unity, the EMF values, E(1) and E(2), are given as:
7
respectively. Then, the standard free energy of formation for
W5Si3, ꢀG0(W5Si3), and that for WSi2, ꢀG0(WSi2), can be
related to the activity of silicon at points C and B respectively
by the following equations:
ꢀ
ꢁ
RT
E(1) = −
ln aCSi
ln aBSi
(8)
(9)
4F
ꢀ
ꢁ
RT
ꢀ
ꢁ
E(1) = −
4F
13 ꢀG0(W5Si3) + RT ln
= 0
(14)
1
aCSi
The superscript in aSi, denotes the region of the three-phase
equilibria in Fig. 1. Then, silicon activities at these three-
phase equilibria are obtained as functions of temperature
within the experimental temperature range (1300–1500 K):
ꢀ
ꢁ
57 ꢀG0(WSi2) − ꢀG0(W5Si3) + RT ln
= 0 (15)
1
7
1
aBSi
Combining the Nernst’s equation and Eqs. (8) and (9), Eqs.
(14) and (15) are rewritten as:
log aCSi = −0.230 − 2240 (T (K))−1 0.0056
log aBSi = +0.452 − 2715 (T (K))−1 0.0036
By using these equations, the upper and lower limits of
(log aSi) for W5Si3 stability at 1373 K were calculated to be
−1.525 and −1.861, respectively. As shown in Fig. 2, this
range is relatively small as compared to that calculated from
the literature data [11].
(10)
(11)
ꢀG0(W5Si3) = −12FE(1)
(16)
(17)
ꢀG0(WSi2) = −12 FE(1)
−
28 FE(2)
5
5
Thus, the standard free energies of formation for the silicides
are given as functions of temperature:
ꢀG0(W5Si3) (kJ mol−1
= −128.6 − 0.0132 (T (K)) 0.42
)
The three-phase mixture of Si, SiO2 and WSi2 was used at
first as the reference electrode. However, it was occasionally
observed that the EMF values for the cells (1) and (2) became
lower after several hours of use. On the other hand, no de-
crease in EMF was observed for the cell (3) in which silicon
activities for both of the electrodes were lower than unity.
These facts indicate that the “life time” of the reference elec-
trode was not long enough. This phenomena did not seem re-
producible, but depended on the thermal history and the setup
of the electrolyte, electrode and lead wire. Replacement of
WSi2 with NbSi2 was not effective to resolve this problem. It
wasassessedthatthisphenomenonwascausedbyirreversible
local reactions between molybdenum lead wire, pure silicon
and electrolyte. Thus, in order to separate molybdenum lead
wire from electrolyte in high silicon activity region, silver al-
loy saturated with silicon put into SiO2 tube was used as the
reference electrode as shown in Fig. 3. The modified refer-
ence electrode allowed satisfactory EMF measurements for
more than 48 h. For the cells (1) and (2), the initial data ob-
tained by using solid silicides in reference electrode are also
plotted in Fig. 4. These results agree with that obtained by
modified reference electrode.
(18)
ꢀG0(WSi2) (kJ mol−1) = −98.5 + 0.0095 (T (K)) 0.15
(19)
In calculation of the standard free energy of formation, solid
solubilities in the terminal phases and non-stoichiometry of
silicides should be considered. Because oxygen solubilities in
W and Si phases are negligibly small [10] and there are no re-
ports on those in silicide phases, the effect of oxygen addition
to the W–Si binary system is not considered. Kocherzhinskii
et al. [15] reported Si solubility in W phase as 2.35 at.% Si
at 2273 K and 0.97 at.% Si at 1823 K and homogeneity range
of W5Si3 phase as 37.5–40.0 at.% Si at 2073 K. However,
information for the range 1300–1500 K is not available. In
addition, there are no reports which show a possibility of
non-stoichiometric WSi2 and solid solution of Si phase. Ac-
cordingly, the accuracies in Eqs. (18) and (19) were estimated
from the experimental errors in EMF measurements of the
cells (1) and (2), ignoring the presence of the solid solution
of terminal phases and non-stoichiometry of the silicides.
Fig. 5 shows the temperature dependence of ꢀG0(W5Si3)
and ꢀG0(WSi2) together with the literature data. Chart [1]
reported ꢀG0(W5Si3) and ꢀG0(WSi2) at 1500 K and sum-
marized the results in a set of data: the standard enthalpies
and entropies of formation at 298 K and heat capacity for
the silicides. The accuracies of ꢀG0(W5Si3) and ꢀG0(WSi2)
calculatedusingtheresultswerereportedtobe24and9 kJ, re-
spectively. Kematick [2] reported the values of ꢀG0(W5Si3)
and ꢀG0(WSi2) at 2073 K based on the experimental results
obtained at the temperature above the melting point of sili-
con. The lines in this figure were calculated from the temper-
ature dependence of the vapor pressure originally reported
in these publications. The present results agree well with the
As plotted in the isothermal section in Fig. 1, the over-
all composition of the electrode was occasionally changed;
however, no difference in the results was observed. The X-ray
diffraction analysis of the used electrode showed the presence
of the solid phases corresponding to each three-phase equi-
librium.
3.2. Standard free energy of formation for silicide
The overall cell reactions for the cells (1) and (2) are given
as:
53 W (s) + Si (s) = 1 W5Si3 (s)
(12)
3

H. Fujiwara et al. / Journal of Alloys and Compounds 391(2005) 307–312
311
2ꢀG0(W5Si3) − 3ꢀG0(WSi2) = 0
(21)
The temperature value of this point is estimated to be
700 30 K. This suggests an eutectoid reaction expressed
by W5Si3 (s) → W (s) + WSi2 (s) occurring at this tempera-
ture. Eutectoid temperature estimated by using Chart’s data
shown in this figure almost agrees with the present value.
Inaccuracy of the calculated eutectoid temperature is not
small due to relatively small temperature dependence of
the standard free energies of formation for the silicides,
and extrapolation of about 600 K to the lower temperature
region.
3.3. The standard enthalpy of formation of silicide
By applying the third law method, the standard enthalpy of
Fig. 5. The standard free energies of formation for W5Si3 and WSi2 com-
pared with the literature data.
formation for silicide at 298 K, ꢀH0(silicide, 298), is given
as:
reported values for both W5Si3 and WSi2 by Chart [1]. The
value of ꢀG0(W5Si3) by Barin [11] is about 25–30 kJ mol−1
lower than the other three results, while the temperature de-
pendence is almost the same at the temperature below and
above the melting point of silicon. This may be caused by
inappropriate selection in the standard enthalpy of formation
for W5Si3 at 298 K in Barin’s assessment.
Fig. 6 is the Ellingam diagram for W–Si system. The free
energy change of the individual reactions in this figure is
calculated using Eqs. (18) and (19) and is including 1 mol
of silicon. As shown in this figure, three lines intersect each
otheratonepoint. Thisintersectionpointofthethreerelations
is calculated by using the reaction:
ꢀH0(silicide, 298) = ꢀG0(silicide, T) − ꢀfef × T
(22)
where ꢀfef is the change in the free energy function for the
formation reactions of the silicides. The fef values for the
elements were taken from JANAF table [16]. Those for the
silicides were calculated using the heat capacity, Cp (sili-
cide), and the standard entropy at 298 K, ꢀS0(silicide, 298).
For the case of W5Si3, because of the lack of reliable data in
literature, Cp (W5Si3) calculated from the Neumann–Kopp
rule and ꢀS0(W5Si3, 298 K) estimated by Chart [1] were
used. For the case of WSi2, precise experimental values of
ꢀS0(WSi2, 298 K) [7] and Cp (WSi2) in the temperature
range from 298 to 1000 K [7,8] are available. These are com-
bined with Cp (WSi2) at temperature range from 1000 to
1500 K calculated based on the Neumann–Kopp rule. The re-
sults of calculation and the literature data are listed in Table 1.
The estimation of errors listed in this table was made by us-
ing the error in ꢀG0(silicide, T) represented by Eqs. (18)
and (19) and that in fef. The error fef is estimated to be
16 J K−1 mol−1 for W5Si3 and 3.6 J K−1 mol−1 for WSi2,
respectively. Each of them results in the error of 25 and
6 kJ mol−1 in ꢀH0(silicide, 298). As the difference in cal-
culated values by using the free energy values of 1300 and
1500 K was less than 1 kJ mol−1, the average of them are
adopted in the table. Considering the error limits, the present
result for W5Si3 is in accord with the reported values. The
present result for WSi2 almost agrees with the values by Ke-
matick [2] and O’Hare [5]. Although the result for WSi2 by
Chart is about 10 kJ negative than the results of these three,
recalculation by Kematick using the latest heat capacity and
the standard entropy of WSi2 yields almost the same value,
−81.3 kJ mol−1. There is a good agreement among the val-
ues observed by the third law treatment of three different
experimental results. These values also agree with the recent
calorimetric results, thus establishing the reliability of the
present study.
3WSi2 (s) + 7W (s) = 2W5Si3 (s)
(20)
Fig. 6. Ellingam diagram for W–Si system.

312
H. Fujiwara et al. / Journal of Alloys and Compounds 391(2005) 307–312
Table 1
Comparison of the standard enthalpies of formation for W5Si3 and WSi2 reported by various workers
Author
Method
ꢀH0(W5Si3, 298) (kJ mol−1
)
ꢀH0(WSi2, 298) (kJ mol−1
)
Present study
Robinson and Jenkins [4]
Chart [1]
Kematick [2]
O’Hare [5]
Electromotive force, third law
Reaction calorimetry
Knudsen effusion, third law
Mass spectrometry, third law
Reaction calorimetry
−133 25
−82
6
−93.7
−135
−92.7 (−81.3)a
−138 32
−78.6
−79
3
5
Tomaszkiewicz et al. [3]
a
Reaction calorimetry
−126 18
Recalculation by Kematick [2] using the standard entropy at 298 K and heat capacity by Callanan et al. [7].
4. Conclusions
ꢀH0(W5Si3, 298) (kJ mol−1) = −133 25
The standard free energies of formation for tungsten sili-
cides at temperatures from 1300 to 1500 K were determined
by EMF measurements by using lithium silicate electrolyte.
The results are summarized as follows:
ꢀH0(WSi2, 298) (kJ mol−1) = −82
6
(i) The EMF–temperature relations are
Acknowledgement
E (mV) = +111.1 + 0.0114 (T (K)) 0.36
This study was financially supported by grant-in-aid of
Japanese Ministry of Education, Culture, Sports and Tech-
nology (#14550722).
(−)Mo, Si+ (Ag alloy or silicide) + SiO2/electrolyte/
W + W5Si3 + SiO2, Mo(+)
E (mV) = +134.7 − 0.0224 (T (K)) 0.23
(−)Mo, Si+ (Ag alloy or silicide) + SiO2/electrolyte/
References
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log aSi = +0.452 − 2715 (T (K))−1
0.0036 (for W5Si3 + WSi2 + SiO2)
respectively.
(iii) The standard free energies of formation for tungsten sili-
cides are:
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ꢀG0(W5Si3) (kJ mol−1
= −128.6 − 0.0132 (T (K)) 0.42
)
(18’)
ꢀG0(WSi2) (kJ mol−1
)
[15] Yu.A. Kocherzhinskii, O.G. Kulik, E.A. Shishkin, L.M. Yupko, Dok-
lady Chem. 212 (1973) 782–784.
[16] M.W. Chase Jr., NIST-JANAF Thermochemical Tables, 4th ed., ACS,
AIP and NIST, New York, 1998.
= −98.5 + 0.0095 (T (K)) 0.15
(19’)
(iv) The standard enthalpies of formation for tungsten sili-
cides at 298 K are: