Determination of the thermodynamic stability of TiB2

Article abstract of DOI:10.1016/j.jallcom.2009.11.058

The standard free energy of formation of titanium boride (TiB₂) was measured by the Electro Motive Force (EMF) method (by using yttria doped thoria (YDT) as the solid electrolyte). Two galvanic cells viz. Cell (I): Pt, TiB₂ (s), TiO<

Full text of DOI:10.1016/j.jallcom.2009.11.058

Journal of Alloys and Compounds 491 (2010) 747–752
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Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jallcom
Determination of the thermodynamic stability of TiB2
Ashish Jaina, R. Pankajavallia, S. Anthonysamya,∗, K. Ananthasivana, R. Babua, V. Ganesana, G.S. Guptab
a Chemistry Group, Indira Gandhi Centre for Atomic Research, Kalpakkam - 603 102, India
b Dept. of Materials Engineering, Indian Institute of Science, Banglore - 560 012, India
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 26 June 2009
Received in revised form 9 November 2009
Accepted 10 November 2009
Available online 14 November 2009
The standard free energy of formation of titanium boride (TiB2) was measured by the Electro Motive
Force (EMF) method (by using yttria doped thoria (YDT) as the solid electrolyte). Two galvanic cells viz.
Cell (I): Pt, TiB2 (s), TiO2 (s), B (s) |YDT| NiO (s), Ni (s), Pt and cell (II): Pt, TiB2 (s), TiO2 (s), B (s) |YDT|
FeO (s), Fe (s), Pt were constructed in order to determine the ꢀfG◦ of TiB2. Enthalpy increments on TiB2
were measured by using inverse drop calorimetry over the temperature range 583–1769 K. The heat
capacity, entropy and the free energy function have been derived from these experimental data in the
Keywords:
Titanium boride
Yttria doped thoria
EMF method
Standard free energy of formation
Enthalpy increment
temperature range 298–1800 K. The mean value of the standard enthalpy of formation of TiB2 (ꢀf H◦
298
ꢀTiB2ꢁ) was obtained by combining these ꢀfG◦ values and the free energy functions of TiB2 derived from
the drop calorimetry data. The mean values of ꢀf H◦ ꢀTiB2ꢁ derived from the ꢀfG◦ data obtained from
298
cell I and II were −322 1.2 kJ mol−1 and −323.3 2.1 kJ mol−1, respectively. These values were found to
be in very good agreement with the assessed data.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
system Ti–B by using the CALPHAD method and by incorporating
more recent experimental data.
TiB2 is a refractory intermetallic compound with high hardness,
low density, high electrical conductivity, good thermal shock resis-
tance, chemical inertness, excellent wear and corrosion resistance
and high elastic modulus [1,2]. These properties render it suitable
for many applications, such as in the manufacture of wear resis-
tant parts, ballistic armour, cathodes and thermocouple sheaths,
crucibles for molten metals, metal evaporation boats and cutting
tools as well as in tribological applications [2–7]. The neutron
absorption properties of 10B coupled with the high temperature
stability of TiB2 (containing 10B) makes it a candidate material
for the manufacture of the control rods for fast breeder reactors
[8–10].
In the recent past many authors have reported the synthesis of
TiB2 and the composites of TiB2 with TiSi2 [11], TiC [12,13], ZrO2
[14], B4C [15,16], TiN [17], TiAl [18]. Advanced methods of synthe-
sis such as electrochemical deposition [19], spark plasma sintering,
combustion synthesis [20,21], sol–gel process and mechanical
milling [22] have been used to synthesize TiB2 and its composites.
The magnetic [23] microstructural, thermal, electrical, electronic
properties as well as bonding properties of TiB2 [24] were also stud-
ied. Witusiewicz et al. [25] have reassessed the phase diagram of the
Fundamental thermodynamic quantities such as the enthalpy of
formation at 298 K, entropy and heat capacity are required in order
to estimate the standard free energy of formation of TiB2. Several
investigators have reported the standard enthalpy of formation of
TiB2 at 298 K (ꢀf H2◦98 ꢀTiB2ꢁ) derived from different techniques,
viz. equilibrium measurements [8,26–28], calorimetry [29–32] and
vapour pressure techniques [33–36]. There is a large spread in these
values (as large as ∼190 kJ mol−1). Moreover, there are discrep-
ancies in the value of ꢀf H298◦ ꢀTiB2ꢁ cited in the compendia on
thermodynamic data [37,38]. The ꢀf H2◦98 value of −280 kJ mol−1
cited in Ref. [37] and that compiled by Hultgren et al. [39] differ
widely from the value of −316 kJ mol−1 suggested in Ref. [38].
The standard free energy of formation of TiB2 has not been
experimentally measured, although the estimated data have been
reported in Refs. [37,38]. Even these estimates show significant
scatter, possibly due to the uncertainties in the ꢀf H2◦98 used in
deriving them. Hence, in the present study, the free energy of
formation of TiB2 was determined from the EMF values obtained
by using a galvanic cell that employed YDT as the solid elec-
trolyte and a mixture of Ni, NiO (or Fe, FeO) as the reference
electrode.
Enthalpy increments with TiB2 were measured by using inverse
drop calorimetry in the temperature range 583–1769 K. These were
fitted into a polynomial equation which in turn was used to derive
the temperature dependence of heat capacity, entropy and the free
energy function. These results are presented and compared with
the data cited in the literature.
∗
Corresponding author at: Dept. of Atomic Energy, Indira Gandhi Centre for
Atomic Research, Kalpakkam - 603 102, India. Tel.: +91 44 27480500/24149;
fax: +91 44 27480065.
E-mail address: sas@igcar.gov.in (S. Anthonysamy).
0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.jallcom.2009.11.058

748
A. Jain et al. / Journal of Alloys and Compounds 491 (2010) 747–752
The enthalpy of formation of TiB2 was calculated by the ‘third-
law’ method by using the free energy functions and the free energy
of formation obtained in this study.
2. Experimental
Boron powder with a purity of 99.999% and NiO, FeO and TiO2 with a purity >99%
were procured from M/s. Aldrich, USA. A YDT solid electrolyte cup (10 mm dia and
2 mm tall) was obtained by cutting an YDT tube procured from M/s. Corning Inc.,
USA. Titanium boride was obtained from the Materials Processing Division (MPD),
Bhabha Atomic Research Centre (BARC), Mumbai.
2.1. Chemical purity of the starting material and phase equilibrium studies
In order to ascertain the chemical purity of TiB2 a complete chemical assay of
TiB2 was carried out with the help of an Inductively Coupled Plasma Mass Spec-
trometer (ICPMS, Model: Elan 250, M/s. Sciex, Toronto, Canada). X-ray diffraction
analysis of TiB2 was carried out by using an EXPERT MPD system supplied by M/s.
Philips, The Netherlands.
The test electrode was a mixture of TiB2, TiO2 and B. It was prepared by homog-
enizing an equimolar mixture of the powdered constituents and cold compacting
them in to pellets of 10 mm diameter and 1–2 mm height at a pressure of 100 MPa.
These pellets were heat treated under helium at 900 K for 24 h. The phase purity
of a heat treated pellet was ascertained by XRD analysis and it was found to con-
tain only TiB2, TiO2 and B. These pellets were used as the test electrode in the EMF
experiment.
2.2. EMF measurements
Electromotive Force (EMF) is by definition, the potential difference (voltage)
across the two electrodes of a galvanic cell under open circuit conditions. This
technique facilitates the measurement of thermodynamic properties with a higher
degree of precision as compared to the other experimental methods. In the present
study the attainment of thermodynamic equilibrium was ascertained by the con-
stancy of the EMF. An accurate and precise measurement of the EMF was made
possible by using a high impedance multimeter, Solartron 7150 supplied by M/s.
Schlumberger Electronics (UK) Ltd., UK.
The cells of the following configurations were assembled for the present study:
Pt, TiB2(s), TiO2(s), B(s)||YDT||NiO(s), Ni(s), Pt
(cellI)
Pt, TiB2(s), TiO2(s), B(s)||YDT||FeO(s), Fe(s), Pt
(cellII)
where YDT represents a 7 wt% yttria doped thoria cup.
An open stacked pellet cell assembly as shown in Fig. 1 was used for the exper-
iment. The sample and the reference electrodes were kept in good physical contact
by pressing them against the surface of the YDT cup. In order to ensure that these
electrodes were in good electrical contact with the respective leads, a platinum disc
that was spot welded to the latter was placed on the pellets that constituted the
electrodes. The platinum lead from the electrode at the top along with a Pt–10% Rh
wire encased in a twin bore alumina sheath sealed together by means of Torr seal
(M/s. Inland vacuum industries INC, New York) served as the thermocouple (Type
S). The platinum lead from the electrode at the bottom was routed through a fine
insulating capillary. Three stainless steel extension springs were employed in order
to hold this stacked pellet assembly tightly through an intermediate quartz tube.
The thermocouple (Type S) was calibrated at the freezing points of Sn, Zn, Sb and Ag
as per ITS-90. The hot junction of the thermocouple was positioned in the uniform
temperature zone of the furnace. The reproducibility of the EMF measurements was
established not only by varying the mole ratios of the components of the reference
and test electrodes, but also by thermal cycling and internal consistency checks. All
other experimental details are the same as described elsewhere [40,41].
Fig. 1. Stacked pellets EMF cell assembly.
the desired temperature the specimens were dropped alternatively from the spec-
imen holder, into the sample crucible at the experimental temperature. From the
resultant heat flow signals corresponding to the alumina reference and the TiB2 sam-
ple, the enthalpy increments (TiB2) were measured by using the critically assessed
enthalpy increment values (alumina reference) reportedin Ref. [42]. The mean of five
such heat flow values for the standard and that for the sample were used to compute
the enthalpy increment at that temperature. The experiment was repeated 4 or 5
times at the same temperature and the mean value of the enthalpy increments from
these runs were taken for fitting. The calorimeter and the details of the experimental
procedure have been described elsewhere [43].
2.3. Enthalpy increments measured with TiB2 by drop calorimetry
A “Multi-Detector” High Temperature Calorimeter (MHTC-96) with a drop
detector of M/s. Setaram, France was employed for measuring the enthalpy incre-
ment on TiB2. The tubular calorimetric detector consists of a thermopile having
36 thermocouples in which a sample crucible and an empty reference crucible
are positioned one above the other. These thermocouples cover the whole surface
enabling the measurement of an integrated heat exchange between the crucibles.
In the present study, a drop detector, made up of Pt–30% Rh/Pt–6% Rh thermocou-
ples was employed. This detector is placed in a gas-tight alumina tube which in
turn is placed in the furnace heated by a graphite resistance heating element. In
a typical experiment, five pairs of the samples of ␣-alumina reference (SRM 720)
and TiB2 pellets, each weighing about 150–200 mg, were placed in the individual
slots of the specimen holder maintained at room temperature. The TiB2 samples
and the Al2O3 references were loaded in such a way that each sample was sand-
wiched between two Al2O3 references. The furnace was then gradually heated to the
desired experimental temperature T under argon cover. Once the furnace attained
3. Results and discussion
3.1. Purity of the starting material
All the metallic impurities such as Fe and Ni that could affect
the EMF measurement were found to be less than 100 ppm by
weight. The X-ray diffraction pattern of TiB2 is shown in Fig. 2. It
was observed that all the peaks correspond to the standard pat-

A. Jain et al. / Journal of Alloys and Compounds 491 (2010) 747–752
749
Table 2
Temperature dependence of the measured EMF of cell II.
Cell II
Temperature (K)
EMF (mV)
999
1020
1039
1055
1075
1092
1115
1128
165.7
166.8
167.2
168.3
169.5
170.5
172
172.8
Fig. 2. X-ray diffraction pattern of TiB2.
tern of TiB2 (JCPDS file no. 85-2083). Further, measurement of the
lattice parameter indicated that the sample is stoichiometric TiB2.
This observation is in agreement with the data reported by Murray
et al. [44], Batzner [45] and Ma et al. [46] who considered TiB2 as a
stoichiometric compound up to its melting point.
3.2. Free energy of formation of TiB2
The EMF values obtained by using the galvanic cells I and II are
given in Tables 1 and 2,
respectively. These data are also depicted in Figs. 3 and 4. A linear
regression analysis of the experimental data yielded the following
least-squares expressions, applicable over the temperature range
of the actual measurements:
Fig. 3. Temperature dependence of EMF in cell I.
The two half-cell reactions of cell I are given by
TiB2(s) + 2O2− → TiO2(s) + 2B(s) + 4e−
2NiO(s) + 4e− → 2Ni(s) + 2O2−
EMFI = [338.6 + 0.0919T (K)] 0.6 (mV) (887–1131 K)
EMFII = [71.3 + 0.1046T (K)] 0.4 (mV) (832–1003 K)
(1)
(2)
(3a)
(3b)
Table 1
For the passage of 4 Faraday of charge, the over-all chemical
reaction could be represented by Eq. (4):
Temperature dependence of EMF in cell I.
Cell I
TiB2(s) + 2NiO(s) → TiO2(s) + 2B(s) + 2Ni(s)
(4)
Temperature (K)
EMF (mV)
887
900
911
922
936
420
421.7
422.2
423.3
424.2
425
940
948
953
958
969
970
970
984
986
425.4
425.6
426.9
427.6
426.8
428.2
430.3
429.7
432
999
1016
1038
1051
1062
1074
1085
1100
1112
1124
1131
433
434
435.5
436.3
437
438
439.5
440.8
442
442.4
Fig. 4. Temperature dependence of EMF in cell II.

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A. Jain et al. / Journal of Alloys and Compounds 491 (2010) 747–752
Table 3
Some thermodynamic functions of TiB2.
T (K)
HT◦ − H2◦98 (kJ mol−1
)
T (K)
HT◦ − H2◦98 (kJ mol−1
)
Cp (J K−1 mol−1
)
ST◦ (J K−1 mol−1
)
−(GT − H2◦98)/T
(J K−1 mol−1
)
Measured
Fit
583
18.314
24.007
29.769
36.993
45.898
54.241
64.249
69.110
76.628
86.230
99.062
105.057
113.325
–
–
–
–
16.535
23.424
30.637
37.976
45.791
53.684
61.879
70.205
78.737
87.560
96.496
105.630
113.171
–
–
–
–
298
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
0
44.271
44.585
56.282
62.702
67.044
70.406
73.244
75.779
78.125
80.348
82.487
84.566
86.603
88.608
90.588
92.550
94.498
28.472
28.747
43.378
56.683
68.519
79.115
88.706
97.482
105.589
113.140
120.223
126.908
133.250
139.293
145.075
150.626
155.971
28.472
28.473
30.388
34.342
39.071
44.048
49.040
53.942
58.706
63.315
67.766
72.060
76.206
80.212
84.087
87.839
91.476
684
785
884
986
1086
1187
1287
1387
1488
1588
1688
1769
–
0.082
5.196
11.170
17.669
24.547
31.733
39.186
46.882
54.807
62.949
71.302
79.861
88.622
97.582
106.739
116.091
–
–
–
The standard free energy change, ꢀrG◦ of the above reaction
in excellent agreement with each other and with the value of
−300.6 kJ mol−1 cited in Ref. [38], while the values cited in Ref. [22]
are higher (−264.2 kJ mol−1).
(4)
is calculated by using the Nernst relation,
ꢀrG◦ = −4FE
(5)
(6)
(4)
3.3. Enthalpy increments by drop calorimetry
ꢀrG◦ = [−130.7 − 0.0355T (K)] 0.2 (kJ mol−1
)
(4)
where ꢀrG(◦4) is the change in standard free energy for the reaction,
F is the Faraday’s constant and E is the EMF of the cell.
By combining Eq. (6) with the auxiliary data on the free energy of
formation of TiO2 [38] and NiO [38], an expression for the standard
free energy of formation of TiB2 was obtained (Eq. (7)):
The enthalpy increment values measured in the temperature
range of 583–1769 K were fitted in to a 4-term polynomial function
using the least-squares method:
HT − H2◦98/(J mol−1) = 61.427(T/K) + 9.360 × 10−3(T/K)2
+ 20.212 × 105(K/T) − 25, 926
(12)
ꢀf G◦ < TiB2 > = [−340.4 + 0.0414T (K)] 2.2 (kJ mol−1
× (887–1131 K)
)
(7)
The◦following constraints were used for fitting the data: (a)
HT − H298 = 0 at 298 K and (b) the first derivative of this expression
with respect to temperature at 298 K is equal to the value of heat
capacity of TiB2 at 298 K. The standard error in the fit was 3% and
The two half-cell reactions pertaining to cell II could be repre-
sented as follows:
the standard deviation of the fit was estimated to be 1.7 kJ mol−1
.
TiB2(s) + 2O2− → TiO2(s) + 2B(s) + 4e−
2FeO(s) + 4e− → 2Fe(s) + 2O2−
(8a)
(8b)
The experimentally measured enthalpy increment and the data
obtained from the fit are given in Table 3. The s◦298 value needed
for the computation of the entropy and free energy functions were
obtained from Ref. [9]. In addition, the calculated heat capacity,
entropy and free energy functions at suitable temperature intervals
(100 K) are also given in Table 3.
In Fig. 5, the measured and the fit values of enthalpy incre-
ments obtained from the present study are compared with the
values given in Ref. [37]. It is seen that these two are in good agree-
ment (within 1.7%). It is evident from Fig. 6 that the heat capacity
values obtained in this study agree with those cited in Ref. [37].
The agreement between the present heat capacity is within 2% at
temperatures below 1600 K and within 3% at temperatures above
1600 K, respectively.
For the passage of 4 Faraday of charge, the over-all chemical
reaction could be represented by
TiB2(s) + 2FeO(s) → TiO2(s) + 2B(s) + 2Fe(s)
(9)
The ꢀrG◦ of this reaction was found to be
(9)
ꢀrG◦ = [−27.5 − 0.0403T (K)] 0.2 (kJ mol−1
)
(10)
(9)
Combining the above expression (Eq. (10)) with the molar free
energies of formation of FeO [47] and TiO2, an expression for the
molar free energy of formation of TiB2 was calculated to be:
ꢀf G◦ < TiB2 > = [−389.6 + 0.0902T (K)] 2.5 (kJ mol−1
× (832–1003 K)
)
3.4. Errors in EMF measurement
(11)
The EMF data represented by Eqs. (1) and (2) are precise within
0.6 (mV) and 0.4 (mV), respectively. These values would introduce
an error of 0.2 kJ mol−1 in the ꢀrG◦ values derived through Eqs. (6)
and (10). Other possible uncertainties which will contribute to the
over-all error in the calculation of standard free energy of formation
Eq. (7) was derived from as many as 25 measurements obtained
by using the cell I in the temperature range 887–1131 K, while Eq.
(11) was obtained from 8 measurements by using cell II in the
temperature range 832–1003 K. Values obtained by using the cell
II were used to validate the results obtained from cell I. The val-
ues of −299 kJ mol−1 and −299.4 kJ mol−1 at 1000 K for the free
energy derived from these two independent measurements are
of TiB2
[
2.2 kJ mol−1 (Eq. (7)) and 2.5 kJ mol−1 (Eq. (11))] are due
to the errors in the free energy of formation of TiO2, NiO and FeO
obtained from Ref. [39].

A. Jain et al. / Journal of Alloys and Compounds 491 (2010) 747–752
751
“third-law” analysis [48] was carried out. This method verifies if
the values of ꢀf H2◦98 derived from the experimental data show any
temperature dependence. This analysis is carried out by using the
free energy functions (fef) cited in the literature. These (fefs) are
auxiliary functions derived from independent experimental deter-
minations. In this study the fef pertaining to various compounds
involved in the equilibrium reactions were obtained from different
standard compilations [37,38]. The ‘fef’ is defined as follows:
GT◦ − H2◦98
fef =
(13)
T
where GT◦ is the standard free energy of formation at temperature
T, H2◦98 is the standard enthalpy at 298 K. The ꢀf H2◦98 ꢀTiB2ꢁ value
thus obtained was compared with the values cited in the literature
(Table 4). Several investigators have experimentally determined
the heat of formation of TiB2 at 298 K [8,26–36]. The assessed val-
ues of ꢀf H2◦98 are presented in Refs. [37,38] and are summarized in
Table 4. Brewer and Haraldsen [26] have determined the thermody-
namic stability of refractory borides by establishing an equilibrium
between nitrogen and the boride phases. They found the value
of ꢀf H2◦98 ꢀTiB2ꢁ to be −301 kJ mol−1, that was further confirmed
by Samsonov [27]. However, the mass spectrometric studies by
Schissel and Williams [33] yielded a value of −134 kJ mol−1 for
ꢀf H2◦98. The high temperature calorimetric measurement by Lowell
and Williams [29] and the high temperature Knudsen effusion mass
spectrometric studies by Schissel and Trulson [34] yielded ꢀf H2◦98
ꢀTiB2ꢁ values of −209 kJ mol−1 and −218 kJ mol−1, respectively.
Williams [28] analyzed the above values [29,34] and recommended
a value of −209 kJ mol−1. Yurick and Spear [8] re-determined the
enthalpy of formation of TiB2 by an equilibrium study on the Ti–B–N
system and obtained a value of −304 kJ mol−1 through a third-law
analysis of their data. This value differs from the assessed values of
−280 kJ mol−1 [37,39] and −316 kJ mol−1 [38]. The ꢀf H2◦98 ꢀTiB2ꢁ
value of about −280 kJ mol−1 presented in Ref [37] as well as by
Hultgren et al. [39] were derived by assessing the calorimetric
heats [29,30], vapour pressures [34–36] and equilibrium mea-
surements involving TiB2 [26–28]. Huber [31] performed oxygen
bomb calorimetry of TiB2 and reported a value of −324 kJ mol−1 for
ꢀf H2◦98 ꢀTiB2ꢁ. Akhachinskij and Chirin [32] used the direct prepara-
tion of TiB2 from its constituent elements in a Calvet calorimeter in
order to derive a value of −319 kJ mol−1 for ꢀf H2◦98 ꢀTiB2ꢁ. Guzman
et al. [49] quoted the value of −323.8 kJ mol−1 for ꢀf H2◦98 ꢀTiB2ꢁ.
In order to determine the value of ꢀf H◦ ꢀTiB2ꢁ from the data
obtained in this study, the free energy func2t9io8ns of TiB2 were com-
puted by combining the drop calorimetry data with the free energy
functions of Ti and B obtained from Hultgren et al. [39]. The follow-
ing reaction (14) was considered in the computation of this free
Fig. 5. Measured values of the enthalpy increments of TiB2.
Fig. 6. Temperature dependence of Cp of TiB2.
3.5. Third-law analysis of the EMF data
In order to examine if ꢀfG◦ values obtained in this investi-
gation are free from temperature dependent systematic errors, a
Table 4
Comparison of the values of ꢀf H298◦ ꢀTiB2ꢁ.
ꢀfG◦ (kJ mol−1) = (A + BT (K))
Temperature (K)
ꢀf H◦ ꢀTiB2ꢁ (kJ mol−1
)
References
298
A
B
−340.4
0.0414
0.0902
0.0167
0.0167
887–1131
832–1003
600–1100
600–1100
−322.0
−323.3
−315.9
−279.5
−301.0
−134
This study-cell I
This study-cell II
−389.6
−317.3
[38]a
[37,39]a
[26,27]
[33]
[28]
[34]
[29]
[8]
[3]
[32]
−280.9
–
–
–
–
–
–
–
–
–
2270
–
1900–2250
2100–2400
−209
−218
–
−209
1850–2100
−304
–
–
–
−324
−319
−323.8
[49]
a
Computed from the free energy data.

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A. Jain et al. / Journal of Alloys and Compounds 491 (2010) 747–752
providing TiB2 powder for this study. Authors are also grateful to
Dr. K. Nagarajan, Chemistry Group, Indira Gandhi Centre for Atomic
Research, for providing support in the calorimetric measurements
on the TiB2 sample.
References
[1] R. Telle, G. Petzow, Mater. Sci. Eng. A 105–106 (1988) 97–104.
[2] U. Demircan, B. Derin, O. Yucel, Mater. Res. Bull. 42 (2007) 312–318.
[3] T.S.R.Ch. Murthy, B. Basu, A. Srivastava, R. Balasubramaniam, A.K. Suri, J. Eur.
Ceram. Soc. 26 (2006) 187–192.
[4] C. Morz, D. Titanium, Am. Ceram. Soc. Bull. 74 (1995) 158–159.
[5] J.J. Gamgler, J. Am. Ceram. Soc. 33 (1950) 367–374.
[6] B. Basu, G.B. Raju, A.K. Suri, Int. Mater. Rev. 51 (2006) 352–372.
[7] J.J. Fang, Z.X. Li, Y.W. Shi, Appl. Surf. Sci. 254 (2008) 3849–3858.
[8] T.J. Yurick, K.E. Spear, Thermodynamics of TiB2 from Ti–B–N studies, IAEA-SM-
236/53, 1980, pp. 73–90.
[9] E.F. Westrum Jr., G.A. Clay, J. Chem. Thermodyn. 10 (1978) 629–636.
[10] C. Subramanian, T.S.R.Ch. Murthy, A.K. Suri, Int. J. Refract. Met. Hard Mater. 25
(2007) 345–350.
[11] T.S.R.Ch. Murthy, C. Subramanian, R.K. Fotedar, M.R. Gonal, P. Sengupta, S.
Kumar, A.K. Suri, Int. J. Refract. Met. Hard Mater. 27 (2009) 629–636.
[12] D. Vallauri, I.C. Atías Adrián, A. Chrysanthou, J. Eur. Ceram. Soc. 28 (2008)
1697–1713.
[13] C.L. Yeh, Y.L. Chen, J. Alloys Compd. 463 (2008) 373–377.
[14] B. Basu, J. Vleugels, O. Van der Biest, J. Eur. Ceram. Soc. 25 (2005) 3629–
3637.
[15] L.Z. Pei, H.N. Xiao, J. Mater. Process. Technol. 209 (2009) 2122–2127.
[16] H. Itoh, K. Sugiura, H. Iwahara, J. Alloys Compd. 232 (1996) 186–191.
[17] C.L. Yeh, G.S. Teng, J. Alloys Compd. 424 (2006) 152–158.
[18] C.L. Yeh, S.H. Su, J. Alloys Compd. 407 (2006) 150–156.
[19] U. Fastner, T. Steck, A. Pascual, G. Fafilek, G.E. Nauer, J. Alloys Compd. 452 (2008)
32–35.
[20] L. Zhan, P. Shen, S. Jin, Q. Jiang, J. Alloys Compd. 480 (2009) 315–320.
[21] Z.I. Zaki, E.M.M. Ewais, M.M. Rashad, J. Alloys Compd. 467 (2009) 288–292.
[22] A. Calka, D. Oleszak, J. Alloys Compd. 440 (2007) 346–348.
[23] G.E. Grechnev, A.V. Fedorchenko, A.V. Logosha, A.S. Panfilov, I.V. Svechkarev,
V.B. Filippov, A.B. Lyashchenko, A.V. Evdokimova, J. Alloys Compd. 481 (2009)
75–80.
Fig. 7. Third-law analysis of the experimental (EMF) data.
energy function (ꢀfef):
Ti(s) + 2B(s) → TiB2(s)
(14)
The values of ꢀrG◦ and ꢀrG(◦9) were computed for each exper-
(4)
imental temperature using the EMF data listed in Tables 1 and 2.
These free energy data were combined with the corresponding val-
ues of ꢀfG◦ ꢀNiOꢁ or (ꢀfG◦ ꢀFeOꢁ) and ꢀfG◦ ꢀTiO2ꢁ in order to derive
ꢀfG◦ ꢀTiB2ꢁ from cells I and II. The ꢀf H2◦98 ꢀTiB2ꢁ value pertaining
to each measurement was computed by using Eq. (15):
ꢀf H2◦98K(TiB2) = ꢀf G◦(TiB2) − T × ꢀfef
(15)
[24] Y. Han, Y. Dai, D. Shu, J. Wang, B. Sun, J. Alloys Compd. 438 (2007) 327–331.
[25] V.T. Witusiewicz, A.A. Bondar, U. Hecht, S. Rex, T.Ya. Velikanova, J. Alloys
Compd. 448 (2008) 185–194.
[26] L. Brewer, H. Haraldsen, J. Electrochem. Soc. 102 (1955) 399–406.
[27] G.V. Samsonov, J. Appl. Chem. (USSR) 28 (1955) 975.
[28] W.S. Williams, J. Phys. Chem. 65 (1961) 2213–2216.
[29] C.E. Lowell, W.S. Williams, Rev. Sci. Instrum. 32 (1961) 1120–1123.
[30] V.A. Epel’baum, M.L. Starostina, Bor. Trudy Konf. Khim., Bora i Ego Soedinenii.
(1958) 97.
[31] E.J. Huber Jr., J. Chem. Eng. Data 11 (1966) 430–431.
[32] V.V. Akhachinskij, N.A. Chirin, Proceeding of Symposium on Thermodynamics
of Nuclear Materials, Vol. 2, IAEA, Vienna, 1975, pp. 467–472.
[33] P.O. Schissel, W.S. Williams, Bull. Am. Phys. Soc. Ser. II 4 (3) (1959).
[34] P.O. Schissel, O.C. Trulson, J. Phys. Chem. 66 (1962) 1492–1496.
[35] G.M. Kibler, T.F. Lyon, M.J. Linevsky, V.J. Desantis, Technical Report No. WADD-
TR-60-646. Part III, vol. 2, General Electric Co., Evandale, OH, 1964.
[36] V.V. Fesenko, A.S. Bolgar, Sov. Powder Metall. Met. Ceram. 1 (1963) 11–15.
[37] M.W. Chase Jr., C.A. Davis, J. Downey Jr., D.J. Frurip, R.A. Mcdonald, A.N. Syveud,
JANAF Thermochemical Tables, III ed., 1985, pp. 274–275.
[38] O. Knacke, O. Kubaschewski, K. Hesselmann (Eds.), Thermochemical Properties
of Inorganic Substances, second ed., Springer–Verlag, Germany, 1991.
[39] R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley, Selected Values of
the Thermodynamic Properties of Binary Alloys, American Society for Metals,
Metals Park, OH, 1973, pp. 516–521.
The ꢀfef values interpolated at the actual temperature at
which the EMF measurement was carried out were combined with
the computed values of ꢀfG◦ ꢀTiB2ꢁ in order to derive ꢀf H2◦98
ꢀTiB2ꢁ. A third-law plot of ꢀf H2◦98 ꢀTiB2ꢁ (Fig. 7) indicates that our
experimental measurements do not suffer from significant tem-
perature dependent errors. The values of −322 1.2 kJ mol−1 and
−323.3 2.1 kJ mol−1 were derived for ꢀf H2◦98 ꢀTiB2ꢁ from cells
I and II, respectively. The enthalpy of formation of TiB2 at 298 K
obtained from our measurements are in good agreement with the
data reported in the standard reference [38] as well as with those
reported by most of the investigators (Table 4).
4. Conclusions
The standard free energy of formation of TiB2 was determined
for the first time by using an EMF method that employed yttria
doped thoria as the oxide solid electrolyte. Enthalpy increments
of TiB2 were measured by using inverse drop calorimetry over the
temperature range 583–1769 K. By using the measured values of
the enthalpy increments, other thermodynamic functions viz., heat
capacity, entropy and the free energy function have been derived
in the temperature range 298–1800 K. Two independent EMF mea-
surements (cell I and cell II) carried out in this study yielded ꢀf H2◦98
values of −322 1.2 kJ mol−1 and −323.3 2.1 kJ mol−1, respec-
tively. These values agree with those cited in the literature as
well.
[40] A.M. Azad, O.M. Sreedharan, J. Appl. Electrochem. 17 (1987) 949–955.
[41] R. Pankajavalli, K. Ananthasivan, S. Anthonysamy, P.R. Vasudeva Rao, J. Nucl.
Mater. 336 (2005) 177–184.
[42] Synthetic Sapphire Al2O3, Certificate of Standard Reference Materials, SRM 720,
National Bureau of Standards, U.S. Department of Commerce, Washington, DC,
USA, 1982.
[43] R. Kandan, R. Babu, P. Manikandan, R. Venkata Krishnan, K. Nagarajan, J. Nucl.
Mater. 384 (2009) 231–235.
[44] J.L. Murray, P.K. Liao, K.E. Spear, in: J.L. Murray (Ed.), Phase Diagrams of Binary
Titanium Alloys, ASM International, Materials Park, OH, 1987, pp. 33–38.
[45] C. Batzner, ‘System B-Ti’, COST507, in: I. Ansara, A.T. Disdale, M.H. Rand (Eds.),
Thermochemical Database for Light Metal Alloys, European Commission, Lux-
embourg, 1998.
[46] X. Ma, C. Li, Z. Du, W. Zhang, J. Alloys Compd. 370 (2004) 149–158.
[47] O.M. Sreedharan, C. Mallika, A Compilation of Gibbs Energy Data for 40 Metal
Oxide Buffers, Report RRC – 69, 1984, pp. 1–34.
Acknowledgements
[48] O. Kubaschewskii, High Temp. High Pressure 4 (1972) 1–5.
[49] L. Guzman, M. Elena, A. Miotello, P.M. Ossi, D.C. Kothari, Vacuum 46 (1995)
951–954.
The authors wish to thank Mr. C. Subramanian, Materials Pro-
cessing Division, Bhabha Atomic Research Centre, Mumbai for