**2.1. Zirconium oxidation**

loy-2ratesarehigherthantheZircaloy-3rates.TheZircaloy-2correlationisverifiedforZircaloy-3 by comparison to oxide thickness measurement on Zircaloy-3 coupons oxidized in air for different time periods in the temperature range of 500 to 1100°C: many coupons proceeded to disintegration. Although the latter samples still had a metal layer, oxygen incursion into the metal grain boundaries caused the metal to become brittle and crack like rust. The Kendall correlation is shown to adequately describe the behavior of these samples over the entire range 500 to 1100°C. Maximum oxide limit of 15.52 mils growth for TREAT cladding was deter‐ mined from these data to ensure that the fuel assemblies could still be removed without

The TREAT reactor, a graphite-moderated thermal reactor, is designed primarily for operation in the transient or pulsed mode for destructive testing of prototypic fast reactor fuel pins. It is designed conservatively to produce a pulse with a thermal neutron fluence of at least 3.5 × 1015 neutrons/cm2 averaged over the core. The operating TREAT core temperature limit at the

The standard TREAT fuel assembly consists of upper and lower graphite reflector sections and a central section of uranium oxide-bearing graphite fuel. The fuel section is 4 ft long and contains six fuel blocks, each 8 in. long and 3.96 in. square with chamfered corners. The reactor fuel blocks consist of small particles (mean size, 10 microns) of fully enriched 235U dispersed in a graphite-carbon matrix. The carbon-to-uranium U235 atom ratio is nominally 10,000:1. The

Zirconium alloys are used for cladding in all commercial power thermal reactors because of the high corrosion resistance, low cross section for thermal neutrons, and high temperature capability. As shown later in this chapter, Zircaloy-3 (Zr-3) is more corrosion resistant in air than either Zr-2 or Zr-4 and was used to clad the TREAT fuel. In low-temperature reactors such as TRIGAs, aluminum can be used. Since TREAT has a very thermalized spectrum, the

The compositions of the common zirconium alloys are listed in **Table 1** (Gibbons [1], Blanchard [2] for Zr-2, Zr-4, and Alloy Digest [3] for Zr-3). Zr-3 has much less zinc than either Zr-2 or

**Alloy Zr Sn Fe Cr Ni Nb O C N Hf** Zr-2 98.20 1.50 0.12 0.10 0.05 – 0.13 – – – Zr-4 98.20 1.30 0.22 0.10 – – 0.13 – – – Zr-3 99.42–99.22 0.2–0.3 0.2–0.3 0.05 0.05 – – 0.05 0.01 0.02

A considerable amount of research has been carried out in investigating the oxidation of zirconium alloys used in different environments. The early research was carried out on Zircaloy-2 and the later work was carried out on Zircaloy-4. The recent oxidation research has been carried out because of concern about loss of cooling water from spent fuel pools where

**Table 1.** Composition percentages of commercial Zirconium alloys (w/o).

graphite-carbon-urania blocks are sealed within evacuated Zircaloy-3 cans.

low cross section and high temperature capability were the reasons Zr-3 was used.

disintegration.

58 Nuclear Material Performance

peak is 600°C.

Zr-4.

Lustman [12] summarized the oxidation rates of zirconium in air, oxygen, and nitrogen. The reaction rate of zirconium is higher with air than with oxygen or nitrogen. Lustman explains this by postulating that nitrogen dissolves in ZrO2; since nitrogen is quadrivalent, defects would be created in the oxygen ion lattice, thus permitting a higher rate of diffusion of oxygen through ZrO2.

Phalnikar [13] studied the oxidation behavior of graphite-melted Bureau of Mines zirconium in air from 400 to 1200°C. Both oxygen and nitrogen enter into the reaction, and for tempera‐ tures below 1050°C an outer white or buff monoclinic scale of ZrO2 forms in addition to an inner black scale of monoclinic and tetragonal ZrO2, cubic ZrN, voids, and possibly dissolved nitrogen in the metal [12]. The outer white layer does not form immediately, but requires a definite time to nucleate. At 400°C, this time is 100 hours, whereas at 1300°C only 5 min is required [13]. The appearance of the white scale layer is an indication of an increased rate of reaction at low, but not at, high temperatures. A parabolic relation between weight gain and time occurs before the formation of the white outer scale.

The oxidation buildup is nearly linear with time on a log log plot, indicating a power relation between weight gain and time. The curves for 800°C and below all have a significant bend in them, indicating a change from a low reaction rate regime to a much higher one at later time. The change is referred to as the regime transition. The post-transition regime is a linear relation and the reaction rate is much higher than the pre-transition regime. Reactions at temperatures of 900°C and above do not exhibit this bend because of a change in the zirconium crystal structure from the alpha phase to the beta phase which occurs at 862°C [14].

## **2.2. Oxidation rates of Zircaloy-2**

Kendall [11] measured the corrosion rates of sponge zirconium and Zircaloy-2 in dry air at 500, 600, and 700°C. Consistent with the previous discussion, he states that the reaction proceeds in two stages: initially the rate decreases with exposure time, approximating a cubic relationship. After sufficient time of exposure (after transition), the rate becomes a constant independent of time.

TREAT fuel was built in 1958 and its cladding oxidation rate estimates were based on the alloy research of Kendall [11]. Kendall measured the reaction rates on many different samples for different air flow rates, metal geometries, cold working, annealing, and at three different temperatures, 500, 600, and 700°C. He concluded temperature and metal composition are the important parameters which determine the reaction rate. **Figure 1** illustrates the uncertainty in the measurements [11].

**Figure 1.** Weight gain of Zircaloy-2 at 600°C.

The two oxide growth measurements in **Figure 1** are for two samples cut from the same sheet and exposed to the same environment at 600°C. Oxidation growth for the other samples run at 600°C fell within these two extremes. Since the curves are almost parallel, the data obtained for each temperature were averaged to produce a single curve for each temperature. The averaged results are included in **Table 2** for Zircaloy-2 for the three different temperatures.


**Table 2.** Oxidation gains Zircaloy-2

tures below 1050°C an outer white or buff monoclinic scale of ZrO2 forms in addition to an inner black scale of monoclinic and tetragonal ZrO2, cubic ZrN, voids, and possibly dissolved nitrogen in the metal [12]. The outer white layer does not form immediately, but requires a definite time to nucleate. At 400°C, this time is 100 hours, whereas at 1300°C only 5 min is required [13]. The appearance of the white scale layer is an indication of an increased rate of reaction at low, but not at, high temperatures. A parabolic relation between weight gain and

The oxidation buildup is nearly linear with time on a log log plot, indicating a power relation between weight gain and time. The curves for 800°C and below all have a significant bend in them, indicating a change from a low reaction rate regime to a much higher one at later time. The change is referred to as the regime transition. The post-transition regime is a linear relation and the reaction rate is much higher than the pre-transition regime. Reactions at temperatures of 900°C and above do not exhibit this bend because of a change in the zirconium crystal

Kendall [11] measured the corrosion rates of sponge zirconium and Zircaloy-2 in dry air at 500, 600, and 700°C. Consistent with the previous discussion, he states that the reaction proceeds in two stages: initially the rate decreases with exposure time, approximating a cubic relationship. After sufficient time of exposure (after transition), the rate becomes a constant

TREAT fuel was built in 1958 and its cladding oxidation rate estimates were based on the alloy research of Kendall [11]. Kendall measured the reaction rates on many different samples for different air flow rates, metal geometries, cold working, annealing, and at three different temperatures, 500, 600, and 700°C. He concluded temperature and metal composition are the important parameters which determine the reaction rate. **Figure 1** illustrates the uncertainty

structure from the alpha phase to the beta phase which occurs at 862°C [14].

time occurs before the formation of the white outer scale.

**2.2. Oxidation rates of Zircaloy-2**

independent of time.

60 Nuclear Material Performance

in the measurements [11].

**Figure 1.** Weight gain of Zircaloy-2 at 600°C.

Although it appears from the table that very few data points were obtained and only two data points at 700°C, there was a large amount of data obtained for each data point presented and then they were averaged to produce the few results shown. In fact, the two 700°C points represent the average of about 10 data points each. Plots of these data are shown in **Figure 2** in log-log coordinates. As stated previously, the bend in the 500 and 600°C curves is referred to as the transition point between the initial (parabolic to cubic) reaction regime and the post transition linear reaction rate regime.

**Figure 2.** Averaged weight gain of Zircaloy-2, specimens at 500, 600, and 700°C [11].

Since the data appear as straight lines in each regime, the weight gain, *M*, in each section can be represented by a the product of the rate constant *k* and the time *t*.

$$M'' = kt \tag{1}$$

The values of *n* and *k* for each straight line section of a plot can be determined by first taking the log of this equation and evaluating it at two data points and subtracting one from the other to obtain

$$\begin{aligned} m^\* \left( \log \left( M\_\odot \right) - \log \left( M\_\downarrow \right) \right) &= \left( \log \left( t\_\odot \right) - \log \left( t\_\downarrow \right) \right); \text{is rearranged to;}\\ m^\* \log \left( M\_\downarrow \left/ M\_\downarrow \right) &= \log \left( t\_\uparrow \left/ t\_\downarrow \right) \end{aligned} \tag{2}$$

so that

$$m = \frac{\log\left(t\_2 \mid t\_1\right)}{\log\left(M\_2 \mid M\_1\right)} \text{ and } k = \frac{M\_1}{t\_1}^\* \tag{3}$$

Kendall's Zirconium constants [11] and this work's slightly improved constants for Zircaloy-2 are presented in Table 2. Kendall [11] states that, "From the shapes of the curves and the calculated values of *n*1 and *n*2 above, it is evident that the same reactions control the rates at the different temperatures and that the reaction of Zircaloy-2 and zirconium are determined by the same mechanism. Variations in the values of *n* and *k* are then due to experimental error. A major source of error results from spalling of the reaction products. The reaction products of Zircaloy-2 are adherent and tough while those of zirconium are fragile and flaky." Kendall concludes that the exponents for the pre-transition regime are *n*1 = 2.58 and linear, *n*2 = 1 , for the post-transition regime (**Table 3**).


\*Average of values at 500 and 700°C; data at 600°C inadequate for direct determination because of sample failure. *k*<sup>2</sup> calculated from this average value. (Units of w are mg/cm2 and unit of *t* is hours for these values of *k*1 and *k*2.)

**Table 3.** Reaction constants.

The rate coefficients for Zircaloy-2 are plotted in **Figure 3** and the logarithms are seen to be linear with 1/*T*, which shows that an Arrhenius equation can be used to fit these data.

Oxidation, Embrittlement, and Growth of TREAT Zircaloy-3 Cladding http://dx.doi.org/10.5772/62708 63

**Figure 3.** Rate constants for Zircaloy-2.

The values of *n* and *k* for each straight line section of a plot can be determined by first taking the log of this equation and evaluating it at two data points and subtracting one from the other

*n MM tt* (2)

*MM t* <sup>=</sup> <sup>=</sup> (3)

)

and unit of *t* is hours for these values of *k*1 and *k*2.)

*<sup>n</sup>*/hour *n2*

( ( ) ( ) ( ) ( ))

*nM M t t*


2 1 21

( ) ( )

log /

**Initial Reaction After Transition**

)

log / and

*<sup>n</sup> t t <sup>M</sup> n k*

2 1 1 2 1 1

Kendall's Zirconium constants [11] and this work's slightly improved constants for Zircaloy-2 are presented in Table 2. Kendall [11] states that, "From the shapes of the curves and the calculated values of *n*1 and *n*2 above, it is evident that the same reactions control the rates at the different temperatures and that the reaction of Zircaloy-2 and zirconium are determined by the same mechanism. Variations in the values of *n* and *k* are then due to experimental error. A major source of error results from spalling of the reaction products. The reaction products of Zircaloy-2 are adherent and tough while those of zirconium are fragile and flaky." Kendall concludes that the exponents for the pre-transition regime are *n*1 = 2.58 and linear, *n*2 = 1 , for

*<sup>n</sup>*/hour *n2 k*2 (mg/cm2

500 7.43 × 10−3 2.49 1.25 × 10−2 1.13 600 1.34 × 10−1 2.41 1.31 × 10−1 0.98 700 Not determined – 9.18 × 10−1 1.01

 3.34 × 10−3 2.64 3.52 × 10−3 1.14 5.62 × 10−2 2.41 (2.57 × 10−2) 1.11\* 8.93 × 10−1 2.82 1.57 × 10−1 1.07 \*Average of values at 500 and 700°C; data at 600°C inadequate for direct determination because of sample failure. *k*<sup>2</sup>

The rate coefficients for Zircaloy-2 are plotted in **Figure 3** and the logarithms are seen to be

linear with 1/*T*, which shows that an Arrhenius equation can be used to fit these data.

\* log log ) (log log ;is rearranged to;

( ) ( )

=

\*log / log /

the post-transition regime (**Table 3**).

Temperature, °C *k*1 (mg/cm2

calculated from this average value. (Units of w are mg/cm2

2 1 21

to obtain

62 Nuclear Material Performance

so that

Zircaloy-2

Zirconium

**Table 3.** Reaction constants.

The rate constants in **Figure 3** are fit with the Arrhenius equation of the form

$$k = A \, ^\ast e^{\left(\frac{-Q}{RT}\right)}\tag{4}$$

where *k* is the rate coefficient, *A* is the "frequency factor", *Q* is the activation energy,

*R* is the gas constant = 1.9872 cal/(g-mole°K), and *T* is the absolute temperature, °K.

The activation energy, *Q*, is determined by taking the logrithm of both sides of the Arrhenius expression, evaluating at two data points, subtracting and solving for *Q* and *A*

$$\ln k = \ln A - \frac{\mathcal{Q}}{RT}\mathcal{Q} = R\frac{\ln \frac{k\_1}{k\_2}}{\left(\frac{1}{T\_2} - \frac{1}{T\_1}\right)}\\A = k\_i e^{+\frac{\mathcal{Q}}{RT\_i}}\tag{5}$$

Constants for both the pre-transition and post-transition regions were determined by Kendall [11]. The calculated values of A and Q that he reported for his data for both the pre-transition and the post-transition regions for both Zirconium and Zircaloy-2 are listed in Table 4.


**Table 4.** Values of *A* and *Q* in the Arrhenius equation for Zircaloy-2 and Zirconium in dry air [11].

The final equation is obtained by substituting the Arrhenius expression into Equation 1

$$M\_{\rm gain} = \left\{ \mathbf{A} \ast \mathbf{t} \ast \mathbf{e}^{\left(\frac{-Q}{RT}\right)} \right\}^{\frac{1}{\mathbf{n}}} \tag{6}$$

So, for example, the predicted amount of the oxide deposit after 10 hours at 500°C obtained from the above equation is calculated to be

$$M\_{\rm gain} = \left\{ 1.1 \ge 10^9 \, \* \, 10 \, \* \, e^{\left(\frac{-3.94 \times 10^4}{2^4 \left(800 + 273\right)}\right)} \right\}^{\frac{1}{2.98}} = 0.40001 \, 1 \, \text{mg} \, / \, \text{cm} \tag{7}$$

**Figure 4.** Comparison of final equations to original data.

The calculated results from the above correlation are compared in **Figure 4** to the original averaged data of **Figure 2**. It is seen the correlation values are all greater than the experimental values. So the constants in Table 4 will be used since they overestimate the total oxidation.

Equation 3, the above table, and graph list the weight gain per unit area from the reaction. The quantities of interest are: (1) the oxide thickness and (2) the loss of Zircaloy metal. These are obtained from Equation 3 for weight gain per unit area with the following relations.

The mass gain per unit area, *Mgain*(*mg*/*cm*<sup>2</sup> ) , due to Zr being oxidized to ZrO2, is given by

$$\mathbf{M}\_{\text{gain}} \triangleq \mathbf{M}\_{\text{ZrO}\_2} \text{ - } \mathbf{M}\_{\text{Zr}} \tag{8}$$

*MZrO*<sup>2</sup> = mass per unit area of the oxide gained and *MZr* = mass per unit area of the metal lost. *M*ZrO2 and *M*Zr to be related by the ratio of molecular weights as

$$M\_{Zo\_2} = M\_{Zr} \left(\frac{mw\_{Zo\_2}}{mw\_{Zr}}\right) \text{or transposing } M\_{Zr} = M\_{Zo\_2} \left(\frac{mw\_{Zr}}{mw\_{Zo\_2}}\right) \tag{9}$$

Substituting in gives

**Before Transition After Transition**

**Table 4.** Values of *A* and *Q* in the Arrhenius equation for Zircaloy-2 and Zirconium in dry air [11].

2.58/hour *Q*1 cal/mole *n*<sup>1</sup> *A*2 (mg/cm2

The final equation is obtained by substituting the Arrhenius expression into Equation 1

gain A\*t\*

*RT M e*

1 n

*Q*

æ ö ç ÷ è ø ì ü ï ï <sup>=</sup> í ý ï ï î þ

> 1 3.94 10 2.58

So, for example, the predicted amount of the oxide deposit after 10 hours at 500°C obtained

( ) 4

æ ö - ç ÷ <sup>+</sup> è ø

gain 1.1x10 \*10 \* 0.400011mg / cm *x*

The calculated results from the above correlation are compared in **Figure 4** to the original averaged data of **Figure 2**. It is seen the correlation values are all greater than the experimental values. So the constants in Table 4 will be used since they overestimate the total oxidation.

9 2\* 500 273

ì ü ï ï = = í ý ï ï î þ

Zircaloy-2 1.1 × 109 3.94 × 104 2.58 8.5 × 106 3.10 × 104 1 Zirconium 1.8 × 109 4.14 × 104 2.58 7.9 × 105 2.98 × 104 1

)/hour *Q*2 cal/mole *n*<sup>2</sup>

(6)

(7)

A1 (mg/cm2 )

64 Nuclear Material Performance

from the above equation is calculated to be

**Figure 4.** Comparison of final equations to original data.

*M e*

$$M\_{\rm gain} = M\_{\rm Zro\_1} - M\_{\rm zr} = M\_{\rm zr} \triangleq \left(\frac{m\nu\_{\rm zro\_1}}{m\nu\_{\rm zr}} - 1\right) = M\_{\rm Zo\_1} \left(1 - \frac{m\nu\_{\rm zr}}{m\nu\_{\rm zro\_2}}\right) \tag{10}$$

Solving for *MZr* and *MZrO*<sup>2</sup> from these equations and dividing by the densities *ρZr* = 6.52 gm/cm3 *<sup>ρ</sup>ZrO*<sup>2</sup> = 6.0 gm/cm3 , the thickness of metal lost and oxide gained are obtained.

The thickness of metal loss, *TZr* , in mils is given as

$$\mathrm{T}\_{\mathrm{z}} = \frac{M\_{\mathrm{z}\mathrm{i}}}{\rho\_{\mathrm{z}}} = \frac{M\_{\mathrm{gain}} \left\{ \frac{\mathrm{mg}}{\mathrm{cm}^{2}} \right\}}{6.52 \frac{\mathrm{g}}{\mathrm{cm}^{3}} \ast 2.54 \frac{\mathrm{cm}}{\mathrm{in}} \ast \left( \frac{123.224}{91.224} \mathrm{l} \right)} \frac{1 \,\mathrm{gm}}{10^{3} \,\mathrm{mg}} \frac{10^{3} \,\mathrm{miles}}{\mathrm{in}} = 0.172 \,\mathrm{^{\circ}M}\_{\mathrm{gain}} \tag{11}$$

Similarly, the thickness of the oxide layer is

$$\mathrm{T}\_{\mathrm{ZnO\_2}} = \frac{M\_{\mathrm{ZnO\_2}}}{\rho\_{\mathrm{ZnO\_2}}} = \frac{M\_{\mathrm{gain}} \left\{ \frac{\mathrm{mg}}{\mathrm{cm}^2} \right\}}{6.0 \, ^\circ 2.54 \, ^\circ \left( 1 \, \frac{91.224}{123.224} \right)} = 0.253 \, ^\circ M\_{\mathrm{gain}} \tag{12}$$

So in summary, the thickness of the oxide layer in mils is 0.253 times the weight gain in mg/ cm2 . The reduction in metal thickness in mils is 0.172 times the weight gain in mg/cm2 .

**Figure 4** shows the post-transition period produces the highest rate of oxidation (i.e., slope or derivative, mg/cm2 /hr) so that use of the post-transition equation to estimate the oxidation rate, the oxide accumulation, and metal loss will overestimate these quantities. Since the weight gain post-transition is linear with time, this conservative oxidation rate is constant for a given temperature.

The oxidation rate in the post-transition region is the derivative of correlation equation (2a) or

$$\mathbf{R} = \frac{\mathbf{dM}}{\mathbf{dt}} = \mathbf{A} \triangleq e^{\mathbf{A}\frac{\mathbf{-Q}}{RT}}\tag{13}$$

Kendall [11] used the values of *A* and *Q* from Table 4 to extrapolate the reaction rates to temperatures below 500°C without the benefit of additonal data but based on the applicability of the Arrhenius expression. Kendall's post-transition correlation is used in this document to conservatively estimate the oxidation rate over the range of interest from room temperature to 820°C. Additional data are referenced in the following discussion to show that use of his correlation conservatively bounds the Zircaloy-3 data obtained by Argonne at 600, 700, and 800°C and that his correlation conservatively bounds literature values of on Zircaloy-2 below 500°C even though his data were limited to the 500 to 700°C range.

#### **2.3. Oxidation rates of Zircaloy-3 and low temperature data on Zircaloy-2**

Boland [15] states that, "Data from the literature, (Kendall [11]; Lustman [12] and Tipton [16]) indicate that zirconium is more resistant to oxidation in air than Zircaloy-2, but no directly comparable data were found on the oxidation of Zircaloy-3 so that experimental data were obtained to supply the missing information. Since Zircaloy-3 contains less tin and more iron than Zircaloy-2, information in the literature would indicate that it should be more resistant to oxidation in air than Zircaloy-2. The published experimental data on oxidation has a scatter of about 50% and can be used only as a guide in estimating how fast oxidation occurs in alloys or environments that differ from those actually tested.

To obtain Zircaloy-3 oxidation data under temperature conditions similar to those expected in the reactor, samples of the cladding, which were removed from a fuel element after 805 transients, were tested in a furnace in the TREAT reactor building. Samples were cycled from room temperature to 600°C thirty-five times with a total time at 600°C of 69 hours. One of these samples was then heated to 800°C for 2 hours to simulate the cladding temperature that might follow an accident. The sample heated to 800°C showed an oxide penetration of about 2 mils while the other sample showed an oxide penetration of less than 0.5 mils." Boland did not translate the above into rates at 600 and 800°C, but instead reported corrosion rates for 600, 700, and 800°C.

Zirconium and Zircaloy-2 corrosion rates were computed at 500, 600, and 700°C using Kendall's constants substituted in Equation 2a. These and the Zircaloy-3 corrosion rates at 600, 700, and 800°C reported by Boland [15] are shown in **Table 5**. Boland did not include any details about the measurement or about whether they were based on the post-transition kinetics or simply the total corrosion weight divided by the time at temperature. The 0.5 mils at 600°C corresponds to 2.07 mg/cm2 and if divided by 69 hours to a rate of 0.029 mg/cm2 /hour which is less than the 600°C value in Table 5. The 2.0 mils corresponds to 8.26 mg/cm2 and if divided by 2 hours to a rate of 4.13 mg/cm2 /hr. The latter value is higher than the data in Table 5. A value of 0.21 mg/cm2 /hour reported by Freund [17] (converted from 0.9 mil/day) at 700°C is also included in the table and is close to the Boland number. The table values of Zircaloy-3 are less than those of Zircaloy-2 and slightly greater than zirconium.


**Table 5.** Comparison of corrosion rates (mg/cm2 /hour).

**Figure 4** shows the post-transition period produces the highest rate of oxidation (i.e., slope or

the oxide accumulation, and metal loss will overestimate these quantities. Since the weight gain post-transition is linear with time, this conservative oxidation rate is constant for a given

The oxidation rate in the post-transition region is the derivative of correlation equation (2a) or

Kendall [11] used the values of *A* and *Q* from Table 4 to extrapolate the reaction rates to temperatures below 500°C without the benefit of additonal data but based on the applicability of the Arrhenius expression. Kendall's post-transition correlation is used in this document to conservatively estimate the oxidation rate over the range of interest from room temperature to 820°C. Additional data are referenced in the following discussion to show that use of his correlation conservatively bounds the Zircaloy-3 data obtained by Argonne at 600, 700, and 800°C and that his correlation conservatively bounds literature values of on Zircaloy-2 below

Boland [15] states that, "Data from the literature, (Kendall [11]; Lustman [12] and Tipton [16]) indicate that zirconium is more resistant to oxidation in air than Zircaloy-2, but no directly comparable data were found on the oxidation of Zircaloy-3 so that experimental data were obtained to supply the missing information. Since Zircaloy-3 contains less tin and more iron than Zircaloy-2, information in the literature would indicate that it should be more resistant to oxidation in air than Zircaloy-2. The published experimental data on oxidation has a scatter of about 50% and can be used only as a guide in estimating how fast oxidation occurs in alloys

To obtain Zircaloy-3 oxidation data under temperature conditions similar to those expected in the reactor, samples of the cladding, which were removed from a fuel element after 805 transients, were tested in a furnace in the TREAT reactor building. Samples were cycled from room temperature to 600°C thirty-five times with a total time at 600°C of 69 hours. One of these samples was then heated to 800°C for 2 hours to simulate the cladding temperature that might follow an accident. The sample heated to 800°C showed an oxide penetration of about 2 mils while the other sample showed an oxide penetration of less than 0.5 mils." Boland did not translate the above into rates at 600 and 800°C, but instead reported corrosion rates for 600,

Zirconium and Zircaloy-2 corrosion rates were computed at 500, 600, and 700°C using Kendall's constants substituted in Equation 2a. These and the Zircaloy-3 corrosion rates at 600, 700, and 800°C reported by Boland [15] are shown in **Table 5**. Boland did not include any details about the measurement or about whether they were based on the post-transition

*Q RT e* æ ö ç ÷

dM R A\* dt

500°C even though his data were limited to the 500 to 700°C range.

or environments that differ from those actually tested.

**2.3. Oxidation rates of Zircaloy-3 and low temperature data on Zircaloy-2**

/hr) so that use of the post-transition equation to estimate the oxidation rate,

è ø = = (13)

derivative, mg/cm2

66 Nuclear Material Performance

temperature.

700, and 800°C.

Causey [18] of Sandia reports that a considerable amount of data on Zircaloy-2 have been obtained since the work of Kendall [11]. He states: "There are a substantial number of reports dealing with the oxidation of Zircaloy at temperatures of 527°C and below. Regardless of the type of oxidant (oxygen, water, water vapor, CO, etc.) to which zirconium or its alloys such as Zircaloy-2 and 4 are exposed, the general behavior of the process is more or less the same. The reaction rate depends more on the pressure of the gas than the composition and that it applies to air as well. Oxidation occurs at the same rate in air or in water and proceeds in ambient condition or in high vacuum. He reports the dependence of the post-transition oxidation rate R on temperature and pressure as

$$R = 13.9 \, P^{\frac{1}{66}} \exp\left(\frac{1.47}{\mathbf{k}\_{\theta} T}\right) \tag{14}$$

where *R* is oxidation rate gram/(cm2 ·second); *P* is the pressure in atmospheres (note the factor *P*1/6 = 1 at ambient pressure; the activation energy is 1.47 eV; *k*B is the Boltzmann constant (8.617 × 10−5 eV/°K).

This correlation is plotted in **Figure 5** along with Kendall's Zr-2 extrapolated correlation down to 200°C. It agrees well with the Kendall Zircaloy-2 correlation over the temperature range of 200 to 800°C. It is lower below 500°C than the Kendall Zircaloy-2 correlation extrapolated below 500°C, which means the Kendall correlation conservatively overestimates the rates below 500°C. And the Kendall correlation fits the Zircaloy-2 data in the medium temperature range of 500 to 700°C range where Kendall took his data. The Kendall correlation (extrapolated to 800°C) is also higher than the Argonne 600 to 800°C Zircaloy-3 data. Therefore, the Kendall correlation which is used by TREAT to estimate the amount of oxide which has formed on the fuel does so conservatively. Note no transients performed so far have brought the fuel or cladding above 600°C.

**Figure 5.** Comparison of the Kendall and Sandia correlations and Argonne Zircaloy-3 values.
