9.8.2. Appendix 9.2: Thermodynamics and Kinetics Parameters of Fuel Constituent Redistribution Model

Diffusion constant and activation energy, heat of transport, and solubility limits for the phases present are given in Table 9.8.1, Table 9.8.2, Table 9.8.3, Table 9.8.4, respectively. Eq. (9.8-1) and Eq. (9.8-2) are used to predict the phase transition temperatures. Ref. [9-11] and [9-27] has been utilized to obtain most of the diffusion constants, diffusion activation energies and heat of transport values. Similar to Ref. [9-11] and [9-27], diffusion constants and heat of transport values are used as fitting parameters. Some of those parameters differs from the corresponding references. Phase transition Equations (Eq. (9.8-1) and Eq. (9.8-2)) are modeled as given in Ref. [9-11].

Table 9.8.1 Zirconium diffusion constant (m \(^2\)/s)

Phase	Pu < 7 at%	Pu \(\geq\) 7 at %
\(\alpha\)	2.0e-07	4.0e-06
\(\delta\)	2.0e-07	4.0e-06
\(\beta\)	5.7e-06	7.0e-04
\(\gamma\)	\(0.4 \times 10^{-5.1-8.05C_{Zr}+9.13C_{Zr}^2}\)	\(10^{-5.1-8.05C_{Zr}+9.13C_{Zr}^2}\)

Table 9.8.2 Zirconium activation energy \(Q_0\) (kJ/mol)

Phase	Pu < 7 at%	Pu \(\geq\) 7 at %
\(\alpha\)	170.0	170.0
\(\delta\)	150.0	150.0
\(\beta\)	180.0	180.0
\(\gamma\)	\(128 - 107 C_{Zr} + 174 C_{Zr}^2\)	\(128 - 107 C_{Zr} + 174 C_{Zr}^2\)

Table 9.8.3 \(Q_h\) - Heat of Transport (kJ/mol)

Phase	Pu < 7 at%	Pu \(\geq\) 7 at %
\(\alpha\)	0	150
\(\delta\)	0	150
\(\beta\)	0	650
\(\gamma\)	-80	-200

Table 9.8.4 Zr Solubility Limit

Phase	Zr Solubility limit (at %)
\(\alpha\)	5
\(\delta\)	40
\(\beta\)	5

(9.8-1)\[T_{\alpha + \delta \leftarrow \beta +\gamma} = \frac{a_{Pu}}{0.164} \left( 868.15 - 935.15 \right) + 935.15\]

(9.8-2)\[T_{\beta +\gamma \leftarrow \gamma } = \frac{a_{Pu}}{0.164} \left( 923.15 - 965.15 \right) + 965.15\]