2.13.3.1 Zr-C Phase Diagram

The most recent critical assessment of the Zr-C system was carried out by Fernandez-Guillermet14 and is depicted in Figure 3. The phase diagram shows the formation of a monocarbide phase which exists between 37.5 and 49.5 at.% C (ZrC06-098 with extent of phase field temperature-dependent), melts congruently at 3700K and 46at.% C (ZrC0 85), and forms a eutectic with carbon at 3200 K at 67.6 at.% C. Solid solubility of C in Zr has not been established conclusively but is estimated to be between 1 and 3 at.% C by Sara15, Rudy,16 and Kubaschewski-von Goldbeck.17 The Zr + ZrC eutec­tic is close to the melting temperature of bcc Zr, 2127 K, contributing to the assessment of low carbon solubility. Solubility of Zr in C is taken as nil.

Figure 4 shows the results of experimental phase diagram studies superimposed on the assessed dia­gram. Phase boundaries of the ZrC phase were estab­lished via ceramography by Farr,18 Sara and Doloff,19 Sara et al.,20 Sara,15 and Rudy et al.,21 while Storms and Griffin13 used C and Zr activity values deter­mined during a Knudsen effusion study. Rudy et al. prepared mixtures of Zr, ZrH2, or graphite with ZrC and determined ZrCx solidus temperatures and ZrC-C eutectic temperature via differential thermal analysis (DTA), ceramography, or melting in a Pirani furnace. As described by Rudy and Progulski,22 the Pirani technique subjects a bar specimen with a central blackbody hole to resistance heating; melting is determined by the temperature at which liquid forms in the blackbody hole. The technique is noted to be most precise for isothermal transformations (i. e., congruent melting or eutectic), as the sample often collapses or the blackbody hole closes before the liquidus is reached. Sara15 prepared zirconium car­bides having various C/Zr ratios from mixtures of ZrH2 and graphite to determine melting tempera­tures and the congruent melting temperature and composition. Adelsberg etal.23 performed ceramogra — phy on C-Zr diffusion couples to contribute data points to the low-carbon liquidus line; ZrC-C eutec­tic temperature was also determined by ceramogra — phy. Zotov and Kotel’nikov24 placed ZrCx bars with a radial hole under axial loading and resistance heating; fracture of the sample at the temperature at which the hole melted determined ZrCx solidus. For the ZrC0.88 sample, at least, their value is

C/Zr ratio

0 0.2 0.4 0.6 0.8 1 1.4 2

Figure 3 Zr-C phase diagram, as assessed by Fernandez-Guillermet.14

4000

3500

anomalously high. Heating the sample in an effusion cell, Bhatt et a/.25 determined Zr-ZrC eutectic tem­perature by an optical pyrometric ‘spot technique.’

2.13.3.2 Enthalpy of Formation

Other properties on which the current phase diagram is based include enthalpy of formation, enthalpy increment or heat content, specific heat capacity (Cp), and activity of C and Zr in ZrC. Standard enthalpy of formation, AHf, of ZrCx as a function of the C/Zr ratio is plotted in Figure 5. A quadratic fit to the reviewed data is provided by

AHf° = 2.03 x 105×2 — 5.04 x 105x — 9.92 x 104 [2]

where x is the C/Zr ratio and A Hf is in units of joules per mole. Within the compositional range, AHf is most negative at the stoichiometric composi­tion and the recommended value is -197 kJ mol-1.26 Toth3 attributes this to decreasing ZrCx bond strength with removal of C from the lattice.

2.13.3.3 Enthalpy and Heat Capacity

Enthalpy increment of ZrCx with respect to 298 K (HT — H298) is plotted as a function of tempera­ture in Figure 6 and as a function of C/Zr ratio at 1600 K in Figure 7. Storms and Griffin report the following equation to fit the experimental values of

Mezaki et a/.,27 Levinson,28 Kantor and Fomichev,29 and Turchanin and Fesenko30:

HT-H298 = -2.14 x 104 + 56.86T-5.46×10-3T2 1.456 x 106

T

where H is in units of joules per mole and T is absolute temperature, valid from 298 to 3200 K. From their low-temperature heat capacity measure­ments on ZrC0 96, Westrum and Feick31 determined a value of H298 — H0 of 5.9 kJ mol-1 and an entropy, S298 — S0 of 33.3Jmol-1.

Heat capacity of ZrCx is plotted as a function of temperature in Figure 8 and as a function of C/Zr ratio at 298 K in Figure 9. Heat capacity is equal to the first derivative of enthalpy with temperature, and the function recommended by Storms and Griffin13 is

Cp = 56.86 — 0.0109T + 5.586 x 10-6T2

1.456 x 106 [4]

T2

where Cp is in units of joules per mole per kelvin.

Low-temperature heat capacity of ZrC0.96 was measured by Westrum and Feick31 by adiabatic calo­rimetry between 5 and 350 K. No data are available for more carbon-deficient compositions, limiting efforts to quantify the entropy of mixing introduced by carbon vacancies. High-temperature drop calorimetry

Temperature (K)
Figure 6	Enthalpy of ZrCx as a function of temperature.
T
66 x 103
1600K ♦ Neel et a/.32 ■» Levinson28 A Kantor and Fomichev29 Bolgar et a/33 ♦ Turchanin and Fesenko30 ♦ Storms and Griffin13
♦ A
64 x 103
62 x 103
60 x 103
58 x 103
56 x 103
54 x 103
………..
_l_d
0.6	0.7	0.8 C/Zr ratio

Temperature (K) Figure 8 Heat capacity of ZrCx as a function of temperature.
I………….	……….. I…………….
40
Ж Westrum and Feick31 X Bolgar et al.33 IX Kantor and Fomichev29 Storms and Griffin13 a Storms and Wagner35
39
~o E 72, ЪА
38	, Art
37
га ‘о
36
Ай
35
34
Ай
33 0.6
C/Zr ratio

measurements were made on ZrCo.92-1 by Neel eta/.,32 Mezaki et a/.,27 Levinson,28 Bolgar et a/.,33 Kantor and Fomichev,29 and Turchanin and Fesenko.30 Petrova and Chekhovskoi34 determined heat capacity, using a pulsed electric current method to measure thermal diffusivity. Storms and Wagner35 used the laser flash method to measure thermal diffusivity for ZrC0.64-1 at 300 K and estimated Cp for these compositions, using a known value for ZrC09631 and by assuming a curve parallel to that established for NbCx as a function of C/Nb ratio.36 Heat capacity increases sharply between 0 and 500 K, saturates, then begins to increase more rapidly near the melting point. Both room — temperature heat capacity and high-temperature enthalpy increase with C/Zr ratio in the homogeneity range. Room-temperature heat capacity of ZrC096 is 38Jmol-1K-1.31,35