COST 507 - Repositório Aberto da Universidade do Porto

only fit the high­temperature asymptot and obtained a reasonably good description of
data for H­H 298 at high temperatures, very close to Jonsson's. However, in the lowtemperature
region they had to accept the deviation from a straight line that C fccT p '+
Cp Eraphlte gave. This situation is almost the same for Seifert et al. who used an
expression for C p = C hcpTi p + c***** ­ c ­ 2dT.
The assessments by Albertsen et al. and by Seifert et al. are related because they both
did not fit the C P data down to room temperature. In this respect the assessments by
Albertsen et al. and by Seifert et al. are not very satisfactory. It should also be
mentioned that Seifert et al. predict decreasing values of C P for TiC at high
temperatures. That is an unfortunate artifact caused by their strategy of primarily
considering the difference in C P between TiC and a mixture of graphite and hep Ti
and also accepting a gradual decrease of C P for hep Ti above the melting point of Ti,
according to the description given by Dinsdale [91 Din].
The complete expression for the Gibbs energy of TiC used by Jonsson was
°G TiC ­ H SER = a + bT + cTlnT + dT 2 + eT 1 + fT" 3 . He determined the b parameter by
fitting the value of S 298 evaluated by Kelley and King [61 Kel] by integration of C P
from 0 K. Finally, the a parameter could be evaluated from the heat of formation at
298 K. It was measured to ­183.47 kJ/mol TiC by Humphrey [51 Hum] but was also
measured by others, [61 Low], [91 Lin], [78Mas], [89Ber], [92Kor] and [61Fuj]. De
Boer's [88DeB] value is about 30 kJ/mol TiC higher and such a high value is
supported by other studies. This difference would decrease the solubility product of
TiC in various solvents by a factor of about exp(30000/8.31451473)=12 at 1473 K. It
is unfortunate that this information shows such a strong scatter. See Fig.7. Jonsson
first tried to use Humphrey's value after a small correction, A f "H m (29S) = - 184.4
kJ/mole TiC, but was not able to fit all the information on the ô­TiC]. x solution phase
very well. The a parameter was then used as an adjustable parameter in the
subsequent assessment of the whole Ti­C system.
However, Jonsson realised that information can also be obtained from ternary systems
showing equilibria with TiC. He thus combined his assessment with information on
the ô­Ti(C,N)+graphite +gas equilibrium in the Ti­C­N system. His final value was
Δ¡ "HJ29S) = - 188.0 kJ/mole TiC, which differs by only 4.5 from the experimental
value by Humphrey. The experimental uncertainty was given as ± 11.6. Jonsson then
found that the same value worked well in the Ti­W­C [96dJon] and Ti­C­N [96cJon]
systems. When determining the a and b parameters, Albertsen et al. did not use the
value of S 298 which would not have been logical because their C P values are not
accurate down to that temperature. Instead, they combined information on
A 7 °// m (298) with information on the ô­TiCi_ x solution phase to evaluate both a and b.
Unfortunately, they used information on activities of Ti presented by themselves in a
recent paper and that information differs significantly from the results of other
studies. Albertsen et al. did not check on the consequences for the Ti­C­N or W­Ti­C,
nor for Fe­Ti­C for which Jonsson's, [96dJon] and [97Jon], assessments were not yet
available. The situation was similar for Seifert et al. and they used the same strategy
and determined the a and b parameters from an assessment of the whole Ti­C system.
Their main objection to Jonsson's assessment of the Ti­C system is his choice of
value for A f °H s TiC at 298 K. Seifert et al. found that a less negative value, in
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