Determination of standard free energy of formation for niobium silicides by EMF measurements

Article abstract of DOI:10.1149/1.1591757

EMF measurements were carried out at temperatures ranging from 1280 to 1490 K in the following cells: Mo, Si + NbSi₂ + SiO₂/SiO₂-sat. Li₂O-SiO₂/NbSi₂ + Nb₅Si₃ + SiO₂, Mo ⊕, Mo, Si + NbSi₂ + SiO₂/SiO₂-sat. Li₂O-SiO₂/Nb₅Si₃ + NbO + SiO₂, Mo⊕, and Mo, NbSi₂ + Nb₅Si₃ + SiO₂/SiO₂-sat. Li₂O-SiO₂/Nb₅Si₃ + NbO + SiO₂, Mo⊕, using SiO₂-saturated lithium silicate liquid electrolyte. Each of the cells showed a reliable electromotive force (emf) corresponding to the difference in silicon potential between the electrodes. Based on these emf values measured, the molar standard free energy of formation for NbSi₂ and Nb₅Si₃ were determined to be ΔG°_NbSi2/kJ = -165 + 0.008 (T/K) ± 13 and ΔG°_Nb5Si3/kJ = -526 + 0.009 (T/K) ± 63, respectively.

Full text of DOI:10.1149/1.1591757

Journal of The Electrochemical Society, 150 ͑8͒ J43-J48 ͑2003͒
J43
0
013-4651/2003/150͑8͒/J43/6/$7.00 © The Electrochemical Society, Inc.
Determination of Standard Free Energy of Formation for
Niobium Silicides by EMF Measurements
Hiroyasu Fujiwara,a,z Yukitomi Ueda, Alok Awasthi, Nagaiyar Krishnamurthy,
and Sheo Parkash Garg
a
b
b
b
a
Graduate School of Energy Science, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
Bhabha Atomic Research Center, Materials Processing Division, Mumbai 400085, India
b
EMF measurements were carried out at temperatures ranging from 1280 to 1490 K in the following cells: ꢀMo, Si ϩ NbSi2
ϩ SiO /SiO -sat. Li O-SiO /NbSi ϩ Nb Si ϩ SiO , Mo ꢁ , ꢀMo, Si ϩ NbSi ϩ SiO /SiO -sat. Li O-SiO /Nb Si
3
2
2
2
2
2
5
3
2
2
2
2
2
2
5
ϩ NbO ϩ SiO , Mo ꢁ , and ꢀMo, NbSi ϩ Nb Si ϩ SiO /SiO -sat. Li O-SiO /Nb Si ϩ NbO ϩ SiO , Mo ꢁ , using
2
2
5
3
2
2
2
2
5
3
2
SiO -saturated lithium silicate liquid electrolyte. Each of the cells showed a reliable electromotive force ͑emf͒ corresponding to
2
the difference in silicon potential between the electrodes. Based on these emf values measured, the molar standard free energy of
o
o
formation for NbSi2 and Nb Si were determined to be ⌬G
/kJ ϭ Ϫ165 ϩ 0.008 (T/K) Ϯ 13 and ⌬G
/kJ ϭ Ϫ526
5
3
NbSi
Nb Si
2
5
3
ϩ 0.009 (T/K) Ϯ 63, respectively.
2003 The Electrochemical Society. ͓DOI: 10.1149/1.1591757͔ All rights reserved.
©
Manuscript submitted October 15, 2002; revised manuscript received February 17, 2003. Available electronically July 1, 2003.
Pure niobium is commercially produced by a process involving
a , for points B and C are related to the standard free energy of
Si
aluminothermic reduction of niobium pentoxide. Another method
o
o
formation for niobium silicides, ⌬G
and ⌬G
, respec-
proposed by the present authors1,2 is a silicothermic process involv-
NbSi2
Nb5Si3
tively. In other words, if a at point B and C is obtained, both
Si
ing reduction of niobium pentoxide and deoxidation of as-reduced
niobium metal by silicon. In considering this process, thermody-
namic data such as heat capacity, heat of formation, and free energy
of formation for the compounds in the Nb-Si binary system became
necessary. However, only limited information is available on these
o
o
⌬
G
and ⌬G
can be determined. Considering that the main
NbSi
Nb Si
2
5
3
o
objective of the present work is the determination of ⌬G
and
NbSi
2
o
⌬
G
, measurements of emf corresponding to the difference in
3
Nb Si
5
3
4-14
aSi between points A and B, and between A and C in Fig. 2, are most
suitable. However, because the experimental conditions are limited
to the composition of SiO2 saturation and metallic niobium and
SiO2 can never co-occur in Nb-Si-O ternary systems emfs corre-
sponding to the difference in aSi among points A, B, and D are
measured in this study. The line CD corresponds to the following
equilibrium
in the literature. Most of the reports
for the heat of formation for
NbSi and Nb Si are calculated and estimated values, except for
2
5
3
1
0
11
the report by Gorelkin et al. and that by Meschel and Kleppa. In
1
0
these reports combustion calorimetry for Nb Si and direct syn-
5
3
thesis calorimetry11 for NbSi and Nb Si were performed. Experi-
2
5
3
mental evaluation of the heat capacity for NbSi and Nb Si are also
2
5
3
1
5,16
limited.
Further, no experimental work on the direct determina-
tion of the standard free energy of formation for niobium silicides
has been reported.
1
0NbO͑s͒ ϩ 6Si͑s͒ ϭ 2Nb Si ͑s͒ ϩ 5O ͑g͒ K͑1͒
͓1͔
5
3
2
In the present study, electromotive force ͑emf͒ measurements
were carried out to determine the standard free energy of formation
for NbSi and Nb Si . The temperature range investigated is 1280-
Thus
6
5
1
5
2
5
3
log pO2
ϭ
log aSi
ϩ
log K͑1͒
͓2͔
1490 K. Based on the results, the standard heats of formation at 298
K for NbSi and Nb Si have also been obtained.
2
5
3
where pO2 and K(1) are the partial pressure of oxygen and the equi-
Thermodynamic Considerations
According to the binary Nb-Si phase diagram17 shown in Fig. 1,
librium constant for Reaction 1. The slope of this line is the fixed
numerical value of 6/5, and the location of point D can be deter-
mined by the measurement of the difference in aSi between points A
and D. Then, aSi at point C can be derived by using pO2 at point C,
which is the intersection of the line CD and the line corresponding
to the pO2 at the two-phase equilibria of Nb ϩ NbO in Nb-O sys-
two niobium silicides, i.e., Nb Si and NbSi , are stable at 1373 K.
5
3
2
In the Nb-O binary system,17 three niobium oxides exist. Although
the phase relation is clear for each of the binary systems in Fig. 1,
the phase relation for the ternary Nb-Si-O system is not certain. In
order to draw the isothermal section of the ternary phase diagram, a
potential diagram, in which thermodynamically stable phases are
related to the oxygen and silicon potentials, is constructed as in Fig.
tem.
o
o
In this way, aSi at point B and C, i.e., for ⌬G
and ⌬G
,
3
NbSi
Nb Si
2
5
2
. The free energy of formation for each of the compounds that is
can be obtained. It should be noted, however, that the standard free
necessary for this potential calculation has been obtained from Bar-
in’s table. Solid solubilities and the possibility of ternary com-
pounds are ignored in this calculation.
In Fig. 2, three-phase equilibria is represented as a point and
two-phase equilibria is represented as a line, except for the cases of
o
energy of formation of NbO, ⌬G
, is necessary for determination
4
NbO
o
o
of ⌬G
and ⌬G
and that the accuracy of the literature data
NbSi
o
Nb Si
2
5
3
for ⌬GNbO influences the results of the present study.
Experimental
SiO and Si ͑these single-phase regions are shown as gray lines͒.
2
The isothermal section for Nb-Si-O ternary at 1373 K shown in Fig.
Assembled cells.—Three kinds of electrodes, in which the silicon
potential is fixed by three-phase equilibria of Nb-Si-O ternary, were
1
is based on this potential diagram. Points A-F in Fig. 2 correspond
to the three-phase triangles A-F, in Fig. 1. Locations of these points
in Fig. 2 depend on the free energies of formation for the corre-
sponding compounds. For example, the values of silicon activity,
used for emf measurements, i.e., electrode A: Si(s) ϩ NbSi (s)
2
ϩ SiO (s); electrode B: NbSi (s) ϩ Nb Si (s) ϩ SiO (s); and
2
2
5
3
2
electrode D: Nb Si (s) ϩ NbO(s) ϩ SiO (s). The letter represent-
5
3
2
ing each electrode corresponds to the characters used in Fig. 1 and 2.
By choosing two electrodes from these three, three kinds of cells
were constructed:
z
E-mail: fujiwara@energy.kyoto-u.ac.jp
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J44
Journal of The Electrochemical Society, 150 ͑8͒ J43-J48 ͑2003͒
Figure 1. Phase diagrams of Nb-Si, Nb-O, and Si-O binary systems and
isothermal section of Nb-Si-O ternary system at 1373 K.
cell AB: ꢀ Mo, electrode-A/SiO -sat. Li O-SiO /
2
2
2
Figure 2. Potential diagram of Nb-Si-O ternary system at 1373 K. Points
A-F correspond to the three-phase region shown in Fig. 1.
electrode-B, Mo
ꢁ
͓3͔
͓4͔
͓5͔
cell AD: ꢀ Mo, electrode-A/SiO -sat. Li O-SiO /
2
2
2
electrode-D, Mo
ꢁ
ment ͑i.e., during ‘‘equilibration’’͒, these residual reactants reacted
and the electrode reached equilibrium. The electrodes were analyzed
by XRD after the emf measurements, which confirmed disappear-
ance of all these residual reactants. This disappearance suggests that
these compounds do not participate in the three-phase equilibria of
the electrodes.
cell BD: ꢀ Mo, electrode-B/SiO -sat. Li O-SiO /
2
2
2
electrode-D, Mo
ꢁ
Sakao and Elliott18 have reported measurement of silicon activity
in Ag-Si alloys using lithium silicate electrolyte. In order to ensure
the working of the present experimental setup, activity of Si in
Ag-Si alloy using lithium silicate electrolyte was first measured, and
the values obtained were compared with the values reported by
them. The cell constructed for this purpose is:
Lithium silicate was prepared by heating in air the mixture of
Li CO and SiO at 1173 K for 43.2 ks in a SiO crucible. Disso-
2
3
2
2
ciation of CO from carbonate was ensured by weight change. The
2
electrolyte composition was 86 mass % SiO . This composition
2
corresponds to the SiO -liquidus at 1573 K in Li O-SiO binary
2
2
2
1
9
phase diagram. Ag-Si alloy used for cell͑Ag͒, Eq. 6, was prepared
by melting the pure metals in a graphite crucible under argon atmo-
sphere.
cell͑Ag͒: ꢀ Mo, electrode-A/SiO -sat. Li O-SiO /
2
2
2
Ag-Si͑xSi ϭ 0.054͒, Mo
ꢁ
͓6͔
Apparatus and procedure.—A schematic illustration of the ex-
perimental setup is shown in Fig. 3. A silicon carbide resistance
furnace equipped with mullite reaction tube ͑g͒ of 52 mm i.d., 60
mm o.d., and 1000 mm length was used. Temperature was measured
Materials.—SiO2 used was extra-pure grade from Wako Pure
Chemical Industries, Ltd. NbSi2 and Nb Si3 were synthesized by
5
vacuum heating of the mixture of pure elements. Appropriate
amounts of niobium powder ͑99.9%, less than 74 ␮m, Furuuchi
Chemical Co.͒ and silicon powder ͑99.999% less than 50 ␮m, Fur-
uuchi Chemical͒ were mixed and pressed into 10 mm diam pellets.
The pellets were placed on a molybdenum plate and heated inside a
by a Pt ϩ (Pt-13%Rh) thermocouple ͑i͒ placed inside a SiO pro-
2
tection tube ͑h͒ and was controlled by PID type controller to Ϯ1 K.
The cells were placed inside an outer SiO2 crucible ͑c͒ of 36 mm
o.d., 32 mm i.d., and 100 mm height, which in turn was placed in a
graphite protection crucible ͑f͒.
Ϫ2
Ϫ3
vacuum graphite furnace (10 to 10 Pa) at 1473 K for 7.2 ks. To
complete the solid-solid reaction, they were continuously heated at
At first, a molybdenum lead wire ͑j͒ of 0.5 mm diam and the
pelletized electrodes ͑a͒, which was prepared by pressing the pow-
der mixture of one set of the three compounds, were placed into an
inner SiO2 crucible ͑d͒ of 12 mm o.d., 10 mm i.d., and 10 mm
height. A mullite insulating tube ͑e͒ was pushed into the gap be-
tween the inner SiO2 crucible and the electrode pellet in order to
avoid direct contact of molybdenum lead wire with the electrolyte.
1
873-1973 K for 7.2 ks. NbO was prepared by vacuum heating of
the mixture of niobium powder and Nb O ͑99.9%, Nakarai Chemi-
cal Co.͒. The heating operation was similar to that for silicides.
Synthesized silicides and NbO were examined by X-ray diffraction
2
5
͑
XRD͒ analysis.
The oxides and silicides thus prepared contained small amounts
of some residual reactants, i.e., NbO in NbO, Nb Si in NbSi , and
Nb in Nb Si . This was apparently caused by evaporation of the
2
5
3
2
Four such inner SiO crucibles ͑d͒ were used in every heating op-
2
5
3
high-vapor-pressure substances during the synthesis process. How-
ever, because of the preheating of the cell before the emf measure-
eration ͑Fig. 3, top view͒. Then these inner SiO2 crucibles were put
into the outer SiO crucible ͑c͒ with powder SiO and electrolyte
2
2
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Journal of The Electrochemical Society, 150 ͑8͒ J43-J48 ͑2003͒
J45
Figure 4. Observed emf of the cell ͓ꢀ Mo, Si ϩ NbSi2
ϩ SiO /SiO -sat. Li O ϩ SiO /Ag ϩ Si(x ϭ 0.054), Mo ꢁ͔ as a func-
2
2
2
2
Si
1
8
tion of temperature and comparison with literature data.
before starting the emf measurement. Each emf was obtained after
holding at a constant temperature for more than 2.4 ks. Only emf
values stable within 1 mV for 600 s were considered as equilibrium
value. EMF was measured by digital voltmeter with 1 G⍀ inner
electric resistance. Reversibility of the electrochemical reaction was
checked occasionally by passing a small amount of outer current
through the cell for a moment. In this operation, emf was restored
eventually. Stability of the emf was tested by holding the cell at a
constant temperature for 43.2 ks. Measured emf values were repro-
ducible within 1 mV.
Experimental procedure for cell͑Ag͒ was almost the same as that
for silicide electrodes, except for the location of the alloy electrode.
To ensure good contact of the molten Ag-Si alloy with the electro-
lyte, the molten alloy was placed inside a SiO tube ͑12 mm o.d., 10
2
mm i.d., and 60 mm length͒ with holes and kept on the electrolyte.
The molybdenum lead wire was dipped into the molten alloy for
measuring emf. After emf measurements, solidified Ag-Si alloy was
dissolved in HF ϩ HNO solution and the silicon content was de-
3
termined by inductively coupled plasma spectrometry.
Results and Discussion
Activity of silicon in Ag-Si alloy.—As electrode A contains pure
silicon, the activity of silicon in this electrode is unity. Then the emf
for this cell is given
Figure 3. Schematic illustration of experimental apparatus: ͑a͒ electrode
pellet, ͑b͒ SiO -saturated liquid electrolyte, ͑c͒ outer SiO crucible, ͑d͒ inner
RT
2
2
E ϭ Ϫ
ln aSi ͑in alloy͒
͓7͔
4
F
SiO crucible, ͑e͒ mullite insulating tube, ͑f͒ graphite protection crucible, ͑g͒
2
mullite reaction tube, ͑h͒ SiO2 protection tube, ͑i͒ thermocouple, and ͑j͒
molybdenum lead wire.
The emf values of the cell represented Eq. 7 are plotted against
temperature in Fig. 4. In this figure, the results of Sakao and Elliott18
for alloys with nearby compositions (xSi ϭ 0.0474 and 0.0661͒ are
also shown. The slope of the relation obtained by the present study
is comparable to those reported by them, indicating that equilibrium
was reached at various temperatures. Activity of silicon in the Ag-Si
(xSi ϭ 0.054) alloy at temperatures ͑1323 and 1423 K͒ obtained
͑
b͒. The upper part of each of the inner SiO crucibles ͑d͒ was fully
2
covered with electrolyte.
In order to establish the equilibrium between electrode and elec-
trolyte, the cell was first heated to 1423-1473 K for 7.2-14.4 ks
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J46
Journal of The Electrochemical Society, 150 ͑8͒ J43-J48 ͑2003͒
respectively. It is clear that the temperature dependence of emf is
Table I. Activity of silicon in Ag-Si alloy „xSi ϭ 0.054….
relatively small for all three cells. This is so because only condensed
phases are involved in the overall cell reactions, for which the en-
tropy change is known to be small. Although emf measurements
were carried out by increasing and decreasing temperature, no sys-
tematic difference was observed in the results. Each of the emf
measurements of the cells were carried out independently. However,
only two of them are arithmetically independent. Consistency in
measurements can be seen by comparing measured emf-temperature
relation ͑Eq. 10͒ with the following equation ͑Eq. 11͒
Sakao and Elliotta
Temperature, T/K
Present study
1
1
323
423
0.190
0.126
0.186
0.130
a
Values read from graph.
presently are listed in Table I along with those of Sakao and Elliott.
The present results compare well with these values. The use of
lithium silicate electrolyte in the present study was essentially the
same as that by Sakao and Elliott. However, few points relating to
the experiments were different, e.g., the electrode without molten
alloy and the electrolyte with a slightly different composition. These
results apparently indicate that no problem was caused by these
differences under the present experimental conditions.
EBD /mV ϭ ϩ239 Ϫ 0.004 ͑T/K͒ Ϯ 1.5
͓11͔
calculated using Eq. 8 and 9. The EBD /mV values obtained at an
average temperature of 1400 K from Eq. 10 and 11 are 234.8
Ϯ 1.1 and 233.4 Ϯ 1.5, respectively.
Because aSi at electrode A is unity, for cell AB and AD, the emf
values, EAB and EAD , are given as
EMF and activity of the three-phase equilibrium.—EMF of the
cell AB, AD, and BD, EAB , EAD , and EBD , are shown in Fig. 5.
The emf-temperature relations obtained by the linear regression are
RT
B
EAB ϭ Ϫ
ln a
ln a
͓12͔
͓13͔
Si
4
F
RT
D
Si
EAB /mV ϭ ϩ111 Ϫ 0.012 ͑T/K͒ Ϯ 0.9
EAD /mV ϭ ϩ350 Ϫ 0.016 ͑T/K͒ Ϯ 1.2
EBD /mV ϭ ϩ225 ϩ 0.007 ͑T/K͒ Ϯ 1.1
͓8͔
͓9͔
EAD ϭ Ϫ
4
F
Then aSi at the three-phase equilibrium at points B and D are ob-
tained as functions of temperature within the experimental tempera-
ture range ͑1280-1490 K͒
͓10͔
B
log a ϭ ϩ0.24 Ϫ 2240/͑T/K͒ Ϯ 0.02
͓14͔
͓15͔
Si
D
Si
log a ϭ ϩ0.32 Ϫ 7060/͑T/K͒ Ϯ 0.02
Using these equations, log a values at points B and D at 1373 K are
Si
calculated to be Ϫ1.39 and Ϫ4.82, respectively. The former value is
about a 0.8 order of magnitude lower than that shown in Fig. 2.
Standard free energy of formation for silicides.—As mentioned
previously, the only two emfs of the three cells AB, AD, and BD are
arithmetically independent. Because the standard deviation of the
linear regression is relatively low, emf of cells AB and BD are used
for the calculation of the standard free energy of formation for sili-
cides.
At electrodes B and D, the following equilibria are achieved,
respectively
1
7
5
Nb Si ͑s͒ ϩ Si͑s͒ ϭ NbSi ͑s͒
͓16͔
͓17͔
5
3
2
7
1
0
1
2
5
NbO͑s͒ ϩ Si͑s͒ ϭ
Nb Si ͑s͒ ϩ
SiO2
5
3
1
11
11
Thus, the activities of silicon at electrodes B and D are given as
5
1
7
B
o
o
RT ln a ϭ ϩ ⌬G
Ϫ
⌬G
͓18͔
͓19͔
Si
NbSi
Nb Si
7
2
5
3
2
RT ln a ϭ ϩ ⌬G
5
10
11
D
Si
o
o
o
NbO
ϩ
⌬G
Ϫ
SiO
2
⌬G
Nb Si
11
5
3
11
o
SiO
o
NbO
where ⌬G
and ⌬G
are the standard free energy of formation
2
for SiO and NbO, respectively. The emf of cells AB and BD can be
2
related to the standard formation free energy for silicides as
5
1
7
o
o
4
FEAB ϭ Ϫ ⌬G
ϩ
⌬G
͓20͔
NbSi
Nb Si
7
2
5
3
5
25
5
10
11
o
o
o
SiO
o
NbO
4
FEBD ϭ ϩ ⌬G
Ϫ
⌬G
Ϫ
⌬G
ϩ
⌬G
NbSi
Nb Si
2
77
5
3
11
2
Figure 5. Observed emf of cells AB, AD, and BD plotted against tempera-
7
ture.
͓21͔
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Journal of The Electrochemical Society, 150 ͑8͒ J43-J48 ͑2003͒
J47
are calculated to be Ϯ13 and Ϯ63 kJ molϪ1, respectively. The ex-
perimental error in temperature measurements is ignored because of
its relatively minor effect. Considering that 5 mol of niobium is
consumed in the formation reaction of 1 mol Nb Si , the fact that
5
3
o
the calculated inaccuracy of ⌬G
is five times as large as that of
Nb Si
5
3
o
⌬
G
indicates the very large uncertainty that could be introduced
NbO
o
by uncertainty of the value of ⌬G
. As far as the present experi-
NbO
mental method is applied, the electrode composition is limited to
SiO saturation. In other words, emf measurements corresponding to
2
the difference in Si potential between point C and point A or B in
Fig. 2 cannot be performed, as pointed out previously. Thus, the
relatively high level of inaccuracy cannot be avoided.
Figure 6 shows the standard free energy of formation of niobium
silicides. As shown in this figure, temperature dependence of the
standard free energies is negligibly small. The present results for
4
Nb Si agree with the literature data and the temperature depen-
5
3
dence of the free energy for both silicides is coincident. The present
result for NbSi is about 40 kJ lower than the literature data in the
2
experimental temperature range. Even if the accuracy of the present
data is considered, this difference is apparent.
The standard heats of formation of silicides.—By applying the
third law method, the standard heat of formation of silicides at 298
o
i
K, ⌬H (298), is given as
o
i
o
i
⌬
H ͑298͒ ϭ ⌬G ͑T͒ Ϫ ⌬fef • T
͓24͔
Figure 6. Comparison of standard free energies of formation for NbSi and
2
Nb Si obtained with the literature data.
5
3
where ⌬fef is the change in the free energy function for the forma-
By solving these equations and using literature data20 for ⌬Go
4
SiO
tion reactions of the silicides. The calculated values are listed in
2
o
NbO
o
o
o
and ⌬G
, ⌬G
and ⌬G
are obtained as functions of
Table II. As the difference in ⌬H
1/3(298) and
NbSi
Nb Si
(NbSi )
2
5
3
2
o
temperature
⌬
H(
1/8(298) calculated by using the free energy values of
3
Nb Si )
5
o
1300 and 1400 K was less than 0.3 kJ, the averages of them are
adopted in the Table. The estimated error in this Table was calcu-
⌬
G
/kJ ϭ Ϫ165 ϩ 0.008 ͑T/K͒ Ϯ 13
/kJ ϭ Ϫ526 ϩ 0.009 ͑T/K͒ Ϯ 63
͓22͔
͓23͔
NbSi
2
o
lated from Eq. 22 and 23.
⌬
G
Nb Si
5
3
o
i
As mentioned before, the experimental data for ⌬H (298) were
1
0
reported by Gorelkin et al. (i ϭ Nb Si ) and Meschel and
5
3
The experimental errors in emf measurements of cells AB and
BD are 0.9 and 1.1 mV, respectively. These errors result in 1 and 3
kJ mol in accuracy of ⌬G
11
Kleppa (i ϭ NbSi2 and Nb Si ). The present results for NbSi
5
3
2
Ϫ1
o
o
and Nb Si agree with these literature data within the error limits,
5 3
and ⌬G
. Inaccuracies of
NbSi
Nb Si
6
2
5
3
respectively. Based on the assessed data by Chart, Kubaschewski
o
SiO
o
NbO
5
4
⌬
G
and ⌬G
are estimated from the standard heat of forma-
et al., and Barin and on the experimental data by Meschel and
2
Ϫ1 20
11
o
tion of SiO and NbO, and are Ϯ1.7 and Ϯ12.6 kJ mol
tively. Therefore, the overall inaccuracies for ⌬G
,
respec-
Kleppa, ⌬H (298) for Nb Si is more negative than that for
i
5 3
2
o
o
and ⌬G
NbSi . This tendency is in accord with the present results.
2
NbSi
Nb Si
2
5
3
Table II. Comparison of values of standard heats of formation of niobium silicides reported by various workers.
o
i
Ϫ1
⌬fH (298)/kJ mol
Source
Reference
Method
(NbSi2)1/3
(Nb Si )
5 3 1/8
Present study
Barin
Kubaschewskii et al.
Chart
Niessen and Boer
Kaufmann
Fernandes et al.
Fernandes et al.
Gorelkin et al.
Mischel and Kleppa
Schafer
EMF measurement
Assessment
Assessment
Assessment
Calculation
Calculation
Calculation
Calculation
Calorimetry
Calorimetry
Estimation
Ϫ53.9 Ϯ 4.2
Ϫ41.8
Ϫ46.0 Ϯ 13.9
Ϫ46.0
Ϫ62.2 Ϯ 7.9
Ϫ63.8
Ϫ56.5 Ϯ 13.6
Ϫ60.7
4
5
6
7
8
Ϫ46
Ϫ90.7
Ϫ55.5
Ϫ56.0
Ϫ65.3
Ϫ62.7
Ϫ60.9
a
9
9
a
10
11
12
13
14
Ϫ63.8 Ϯ 11.5
Ϫ64.6 Ϯ 2.4
ϹϪ13.3
Ϫ33 Ϯ 16
Ϫ13 to Ϫ98
Ϫ53.7 Ϯ 1.6
Searcy
Brewer and Krikorian
Estimation
Estimation
Ϫ42 Ϯ 20
Ϫ24 to Ϫ78
a
Two different models are applied.
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J48
Journal of The Electrochemical Society, 150 ͑8͒ J43-J48 ͑2003͒
o
Conclusions
⌬
H͑
1/8͑298͒/kJ ϭ Ϫ62.2 Ϯ 7.9
3
Nb Si ͒
5
In order to determine the standard free energy of formation of
niobium silicides, emf measurements were conducted at tempera-
tures ranging from 1280 to 1490 K. The results are as follows:
Acknowledgment
1
. The emf-temperature relations are
E/mV ϭ ϩ111 Ϫ 0.012 ͑T/K͒ Ϯ 0.9
ꢀMo, Si ϩ NbSi ϩ SiO /SiO -sat. Li O-SiO /NbSi
2
Honest experimental works done by Mr. Ishiwari ͑former under-
graduate student of Kyoto University͒ and helpful comments and
suggestions by Dr. Asano ͑Professor Emeritus, Kyoto University͒
and Dr. Wakasugi ͑Kyoto Institute of Technology͒ are gratefully
acknowledged. This study was financially supported by a Grant in
Aid of the Japanese Ministry of Education, Culture, Sports and
Technology ͑no. 14550722͒.
͑
2
2
2
2
2
ϩ Nb Si ϩ SiO , Mo ꢁ ͒
5
3
2
E/mV ϭ ϩ350 Ϫ 0.016͑T/K͒ Ϯ 1.2
ꢀMo, Si ϩ NbSi ϩ SiO /SiO -sat. Li O-SiO /Nb Si ϩ NbO
͑
Kyoto University assisted in meeting the publication costs of this article.
2
2
2
2
2
5
3
ϩ SiO , Mo ꢁ ͒
References
2
1
2
3
4
5
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. The standard free energy of formation for niobium silicides are
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o
⌬
G
/kJ ϭ Ϫ165 ϩ 0.008 ͑T/K͒ Ϯ 13
/kJ ϭ Ϫ526 ϩ 0.009 ͑T/K͒ Ϯ 63
3
NbSi
2
o
⌬
G
Nb Si
5
1
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4
. The standard heats of formation for niobium silicides at 298 K
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2
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o
⌬
H͑
1/3͑298͒/kJ ϭ Ϫ53.9 Ϯ 4.2
NbSi ͒
2
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