Thermal expansion has been investigated via low — and high-temperature X-ray diffraction,60-67 neutron diffraction,68 and dilatometry.32,54,57,69-74 Elongation (AL/L298) and linear coefficient of ther­mal expansion (CTE) are plotted as a function of temperature with respect to 298 K in Figures 18 and 19, respectively. Elongation results are gener­ally consistent between lattice parameter and dila — tometric methods, diverging at high temperatures. Scatter is magnified on the CTE versus T curve, which is akin to the second derivative of length versus T experimental data. Elongation is fairly linear, permitting authors to report a mean CTE over various temperature ranges; slope increases slightly with temperature, consistent with an observed rising CTE with temperature. Increase in CTE is more pronounced at temperatures up to 500 K with a more modest increase at higher tem­perature, although more lower-temperature values are needed to fully understand this behavior. At subambient temperatures, elongation (or contrac­tion, as the reference temperature is 298 K) is non­linear with temperature.

CTE values with respect to 298 K lie in the range (5-7) x 10~6K~ but the degree of scatter

-0.005

Figure 18 Elongation with respect to 298 K of ZrCx as a function of temperature.

precludes a more precise recommended value. Thermal expansion coefficient at 1273 K as a func­tion of C/Zr ratio is plotted in Figure 20, where a trend of increasing CTE with deviation from
stoichiometry can be seen. This composition depen­dence of CTE confirms the general picture of decreasing bond strength as C atoms are removed from the lattice.5

2.13.4.2 Diffusion

The results of diffusion studies are summarized in Table 1. The temperature dependence of diffusion
coefficient conforms to an Arrhenius relationship, according to

D(T) = D0e~Q/RT [10]

aZotov and Tsedilkin,75 14C tracer diffusion. bAgarwala and Paul,76 14C tracer diffusion on Zr rod, vacuum. cPavlinov and Bykov,77 ZrI4/14C-ZrI4 diffusion couple, vacuum. dAndrievskii et a/.,78 14C tracer diffusion on ZrI4, vacuum.

eUshakov et a/. ,79 rate of ZrC layer growth on alternating ZrI4 and graphite pellets stacked in Mo crucible, vacuum. fAdelsberg et a/. ,23 rate of ZrC layer growth on Zr bar melted in graphite crucible, vacuum.

9Andrievskii et a/. ,80 14C tracer diffusion on hot-pressed ZrC0 96, He atmosphere.

hSarian and Criscione,81 14C tracer diffusion on single crystal and arc-melted ZrC0 965, vacuum.

‘Andrievskii et a/. ,82 14C tracer diffusion on hot-pressed ZrC0 85, Ar atmosphere.

‘Andrievskii et a/. ,83 14C tracer diffusion on hot-pressed ZrC0 97 (Zr self-diffusion composition-independent from ZrC0 84-0 .97).

where Tis absolute temperature, R is the gas constant, Qis the activation energy for diffusion (kJ mol-1), and D0 is a preexponential factor having the same units as D, the diffusion coefficient, (cm2 s — ).

Diffusion of carbon in a-Zr (hcp) and p-Zr (bcc) has been investigated through diffusion of 14C tracer deposited onto Zr75-79 and by the rate of ZrC layer growth on Zr in contact with graphite.23,79

Self-diffusion of C in ZrCx has been determined by tracer diffusion.80-83 The study by Andrievskii et a/.83 provides the only reported value for self-diffusion of Zr in ZrC, which was found to be independent of C/Zr ratio. Activation energy for C self-diffusion in ZrCx increased with decreasing C/Zr ratio, while diffusion coefficient at a given temperature increased with increasing C/Zr ratio. However, O (0.16-0.19 wt%) and N (0.27-0.55 wt%) impurity content was substan­tial and varied for different samples. No further studies of C self-diffusion in ZrCx as a function of C/Zr ratio are available to clarify differences between C self­diffusion in pure ZrCx versus oxycarbonitride phases.

Carbon and zirconium self-diffusion in ZrC is slower than the inter-diffusion of C in Zr, with cor­respondingly higher preexponential factors and acti­vation energies. Pavlinov and Bykov77 remarked that the activation energy for C diffusion in Zr was close to that of Zr self-diffusion in Zr. As for self-diffusion,

Zr diffuses much slower than C, which may be under­stood in terms of the interstitial nature of C in ZrC: the smaller C atom is able to diffuse via either ther­mal metal vacancies or interstitial sites, the latter dwarfing the former in most cases.

Matzke84 proposed three potential mechanisms for C self-diffusion in ZrC. First, a C atom may jump along (110) directions to its nearest neighbor vacant C octahedral interstitial site, which, according to the author, requires a large lattice strain and the movement of two Zr atoms. Second, a C atom may jump along (111 ) directions to its nearest neighbor vacant C octahedral interstitial site via an unoccu­pied tetrahedral interstice, requiring lower strain energy. Third, a C atom may jump to a vacant octa­hedral site via a thermal metal vacancy. The author proposes that this divacancy mechanism requires the lowest energy, close to the activation energy for gen­eration of a metal vacancy.

The operative diffusion mechanism depends on the C/Zr ratio. Upadhyaya5 suggested that carbon diffu­sion in near-stoichiometric compositions occurs via thermal metal vacancies, while jumps via tetrahedral interstices are favored at higher carbon vacancy con­centration. No adequate explanations are available for the composition dependence of activation energy of C in ZrC, or the composition independence of that of Zr. Other properties (formation enthalpy, hard­ness) indicate a decrease in bond strength as the C/Zr ratio decreases, which would suggest that dif­fusion would be enhanced as well. This stands in opposition to measured activation energies for the diffusion of C in ZrC0.84-o.97, which increased with deviation from stoichiometry.83 As for Zr diffusion, Upadyaya5 suggested that two effects in operation when the C/Zr ratio decreases, a decrease in the energy required to form thermal metal vacancies, and an increase in the energy required for metal vacancy motion due to the decreased interatomic distance, cancel each other out.

Further discussion of diffusion mechanisms in the context of mechanical creep are considered in Section 2.13.5.6.