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AC impedance study of corrosion films formed on zirconium based alloys
Electrochimica Acta 45 (1999) 1039 – 1048 www.elsevier.nl/locate/electacta
AC impedance study of corrosion films formed on zirconium based alloys J.J. Vermoyal a,b,*, A. Frichet b, L. Dessemond a, A. Hammou a a
Laboratory of Electrochemistry and Physical-chemistry of Materials and Interfaces, UMR 5631 INPG-CNRS-UJF, 1130 Rue de la Piscine, 38402 Saint Martin d’He`res, France b Framatome Nuclear Fuel, 10 rue Juliette Re´camier, 69006 Lyon, France Received 12 February 1999; received in revised form 30 June 1999
Abstract Oxide films formed by water oxidation (360°C) of two Zr alloys, Zircaloy-4 (Zy-4) and ZrNb(1%)O(0.13%), were studied by impedance spectroscopy (IS) in gaseous atmospheres. Results show that capacitances are frequency dispersed, in agreement with Jonscher’s law of dielectric relaxation. A good correlation was found between oxide thickness calculated from both IS measurements at room temperature and weight gain and those estimated by metallographic examinations. The electrical characteristics of a 2 mm thick film formed on ZrNb(1%)O(0.13%) were investigated as a function of the temperature (25–280°C) at constant oxygen partial pressure (0.3 Pa). Cole – Cole diagrams suggest a frequency-temperature equivalence: low frequency points at low temperatures perfectly superimpose on high frequency points at higher temperatures. This resulting 14 decade ‘master’ curve so obtained can be characterized by the activation energy of the angular frequency v close to 0.8 eV. An equivalent circuit based on an association in series of two layers with different dielectric properties was proposed. By fitting the curves obtained at different temperatures with only a parallel resistance, the thicknesses of the two layers were estimated to be 1.5 and 0.5 mm. Finally, both the Arrhenius diagrams of the total conductivity and the dispersion factor are characterized by a breakdown temperature point with two activation energy values. © 1999 Elsevier Science Ltd. All rights reserved. Keywords: Impedance spectroscopy; Zirconium alloys; Oxidation; Frequency-temperature equivalence; Dielectric dispersion
1. Introduction The corrosion behavior of zirconium alloys used for cladding tubes is one of the most important parameters for optimizing fuel element economy in the nuclear industry. At present, Zircaloy-4 (1.2–1.7 wt% Sn, 0.18– 0.24 wt% Fe and 0.07–0.13 wt% Cr) is used for pressurized water reactors (PWRs) because of its low cross-section for absorption of thermal neutrons, its high mechanical strength and its relatively low corro* Corresponding author. Fax: +33-47-682-6670. E-mail address: [email protected] (J.J. Vermoyal)
sion rate. To increase waterside corrosion resistance, new Zr alloys must be developed and studied before industrial application. The corrosion rate of the cladding depends principally on the alloy composition, the metallurgical treatments, the chemistry and the temperature of the reactor water. The oxidation behavior of Zr alloys is generally described by an initial ‘pre-transition’ stage for which the oxidation rate is either parabolic or cubic. When the oxide reaches a thickness of about 2 to 4 mm, a sharp increase in the oxidation rate occurs and the ‘post-transition’ kinetics is characterized by a quasi linear variation law [1] leading to the degradation of the initial protective oxide film into a partially porous layer.
0013-4686/99/$ - see front matter © 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 3 - 4 6 8 6 ( 9 9 ) 0 0 3 0 7 - 2
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Impedance spectroscopy (IS) was hitherto applied to allow insights into the microstructure of the growing oxide film and more importantly to study the dense layer at the metal–oxide interface and the penetration of the electrolyte into the porous layer on the water side [2–4]. IS results for different materials oxidized under various conditions investigated and manufacturing parameters were correlated to the microstructure [5] and to the pores’ structure of the layer [6]. Nevertheless, experiments were limited to low temperatures and atmospheric pressure, far from corrosive conditions in PWRs at 360°C, implying transition effects between oxidation and the study’s environment [6,7]. This problem has recently been solved by performing IS in situ during oxide film formation [8,9]. In spite of the numerous works based on this method of electrical characterization, little information is available about the transport process of charge carriers and electrical conducting paths in oxide films due principally to the difficulties specific to the IS approach [10]. This study is dedicated to the electrical properties of oxides formed on Zircaloy-4 and ZrNb(1%)O(0.13%) in water at 360°C characterized by IS measurements in gaseous atmospheres. This paper presents the results concerning thickness determination of oxide films carried out to elaborate and test an electrochemical cell. The electrical response of an oxide layer of 2 mm thickness formed on ZrNb(1%)O(0.13%) was investigated as a function of temperature at a constant oxygen partial pressure (0.3 Pa).
2. Experimental Cylindrical cladding tubes of Zy-4 and ZrNb(1%)O(0.13%) were provided by an industrial supplier (Cezus and Zircotube, France) and fabricated according to standard manufacturing routines. The oxide films were formed by oxidation at 360°C in pure water in an autoclave. The thickness of each film was
Fig. 1. Scheme of the electrochemical cell.
calculated from the weight gain, assuming an oxide density of 5.7 g cm − 3 and no dissolution of the oxide during the growth. For scanning electron microscopy (SEM) observations, samples were mechanically polished to diamond paste (1 mm). A thin conductive Au film was sputtered on the surface of the specimen to avoid charging effects. Impedance spectroscopy measurements were performed on a 1.2 cm length cylinder. After cooling and extraction from the autoclave, the samples were ultrasonically washed in alcohol and distilled water for 10 min. A Zr/ZrO2/M (M= Pt, Ag) cell configuration was chosen. A section of the internal side of the cladding tube was partially mechanically eliminated and a Zr alloy ring was spot welded in order to assure an ohmic contact throughout the experiment (Fig. 1). Platinum or silver electrodes were coated on the external side of the oxide film by RF sputtering (Plassys) in high purity argon at room temperature. This electrode was sputtered on an area varying between 0.5 and 3 cm2 far from the singular welded zone to avoid parasitic electric contribution due to possible modification of the Zr phase. The metal deposit is strongly adherent and its thickness could be roughly estimated as 350 nm. Platinum wires were used as current collectors. Oxygen partial pressure was fixed by pure argon (argon U, Air Liquide). The gas flows successively through an oxygen electrochemical pump [11], the working furnace and an oxygen gauge [12] which was used to measure the working oxygen partial pressure (0.3 Pa). The temperature was regulated at 9 1°C and the different parts of the gas circuit were connected by stainless steel tubing and Viton O-ring seals. IS measurements were carried out with an HP4192A impedance analyzer in the 5 – 13 ×106 Hz range. Low frequency points, down to 10 − 4 Hz, were performed with an Autolab potentiostat – galvanostat EcoChemie and a 1250 Solartron coupled with an impedance adaptator allowing high impedance modulus (109 V) measurements. We checked that both apparatus gave the same response for the same cell in the common frequency interval. Experimental data were fitted with the EQUIVALENT CIRCUIT software of Boukamp [13]. Impedance measurements were performed at zero dc polarization. The reliability and the reproducibility of the results were checked by preliminary measurements carried out at ambient temperature for different oxide thicknesses. For the study of the oxide layer of 2 mm thickness between 25 and 280°C, a stationary state was assumed when two successive spectra were identical over the whole frequency range. The temperature of 90°C was chosen as a reference temperature to control any modification of the electrical properties of the oxide films. At the end of the experiments, an impedance diagram was recorded at room temperature on a part of the oxide area not yet studied by IS in
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Fig. 2. Bode diagram (v =2pf ) of a 1.6 mm thickness film on ZrNb(1%)O(0.13%) recorded at room temperature in air (external electrode: platinum). ( ×) impedance ; ( ) phase angle.
where v is the angular frequency. Rc is determined by the high frequency intercept of the impedance diagram and the real axis in the Nyquist plane. Rc values are typically lower than 3 V so the influence of this parameter alters the Cole – Cole diagram shape only for frequencies higher than 106 Hz. The data used for Fig. 1 represented on the Cole – Cole diagram (Fig. 3) exhibit the dielectric dispersion of the oxide film. The observed linearity on a frequency range of 4 decades could be described by the universal law for the dielectric response proposed by Jonscher [14 – 16] : C*=C +
Fig. 3. Cole – Cole diagram of a 1.6 mm thickness film formed on Zr– 1%Nb recorded at room temperature in air (external electrode: platinum).
order to determine the invariance of the oxide film after successive heating and cooling.
3. Results
3.1. Thickness determination Bode diagrams obtained at ambient temperature and room atmosphere give prominence to the capacitive behavior for the different layers investigated. Fig. 2 shows the Bode diagram recorded on a 1.6 mm oxide film formed on ZrNb(1%)O(0.13%). The electrical properties described in the Cole–Cole representation allow predominantly capacitive systems to be studied due to the normalization of the admittance by angular frequency (v=2pf ). Assuming that the complex impedance Z*=Z%−jZ%%, where Z% and Z%% are the real and the imaginary parts, respectively, is equivalent to an association in series of a complex capacitance C*= C%− jC%% and a pure resistance Rc, measured at high frequency, i.e. the overall resistance of contacts and connection wires to the electrochemical cell, expressions of C% and C%% take on the following forms: C% =
1 Z% v (Z −Rc)2 +Z%2
(1)
1 Z%−Rc v (Z%−Rc)2 +Z¦2
(2)
C¦ =
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B ( jv)1 − n
(3)
where C* is the complex capacitance of the film, C is a pure capacitance related to the oxide thickness which is defined as the limit of the complex capacitance C% at infinite frequency. B is a constant related to the dielectric dispersion and n is a constant parameter characteristic of the constant phase angle between the real axis and the experimental curve. C is obtained from the high frequency intercept of the linear extrapolation defined by the experimental curve on the real axis in the Cole – Cole representation. One can note that Eq. (3) is related to the well known constant phase element (CPE) to which a real capacitance C is added in parallel. This association allows to take into account that the extrapolation of the linear experimental curve has a real and finite value (C ) whereas that for a simple CPE this value is zero. In spite of the cylindrical cell configuration, the film thickness allows the more convenient planar capacitance relation to be used (assuming the homogeneity of the oxide layer): d=
oro0A C
(4)
where d is the oxide thickness, o0 the vacuum permittivity, or the relative permittivity of the oxide and A the area of the noble metal used for the external electrode. The main inaccuracy in the thickness value is related to the electrode area determination (5%). With a zirconia dielectric constant of 20 for an oxide formed on ZrNb(1%)O(0.13%) [17] and 22 on Zy-4 [18,19], the values of the calculated thicknesses are listed in Table 1. Results show that the Cole – Cole curves are independent of the nature and the area of the electrode sputtered on ZrO2. Moreover, the difference between several samples cut in the same cladding was in the majority close to 0.1 mm which demonstrated excellent measurements reproducibility. These values were compared with those estimated from microscopic observations and weight gain (WG) taking 1 mm for 15 mg dm − 2 [20]. SEM examinations of the oxide layers were carried out on more than 20 zones arbitrarily chosen
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Table 1 Nature and area of the electrode deposit on the oxidea Zr alloys
Zy-4 (or = 22)
ZrNb(1%)O(0.13%) (or = 20)
Metal electrode and area (cm2)
Thickness of oxide films (mm) Weight gain
IS
SEM
Ag/0.36 Pt/2.9 Pt/3.1 Pt/3 Pt/3 Pt/3.2
1 2 1.6 1.6 1.6 1.6
0.96 2.01 1.7 1.72 1.67 1.65
0.97 1.95 1.65 ndb 1.57 ndb
Pt/1.1 Pt/1.6 Ag/0.8 Pt/2.5 Pt/0.85 Pt/1.55 Pt/1.8
1.9 1.9 1.9 1.9 2.55 3 3.46
1.9 1.69 2 2.1 2.6 3.1 3.55
1.89 (0.19) ndb 2.05 (0.2) ndb 2.8 (0.18) 3.05 (0.16) 3.55 (0.11)
(0.07) (0.12) (0.2) (0.25)
a Thickness of oxide films formed on Zy-4 and ZrNb(1%)O(0.13%) determined by weight gain. IS (room temperature-ambient atmosphere) and SEM (standard deviation is indicated within brackets). b nd: not determined.
around the external side of the tubes. The result for a 3.5 mm oxide film formed on ZrNb(1%)O(0.13%) is given in Fig. 4. Dark strips will not be discussed in this paper but were generally identified in the literature as pores or cracks [21]. The values of the oxide thicknesses calculated from IS are in excellent agreement with those determined from WG and SEM investiga-
tions and allow the satisfactory covering of the sputtering noble metal deposit to be assumed. These experimental results corroborate those found using evaporated electrodes [22,23] and emphasize the interest of such a technique compared to a liquid metal electrode which can often lead to inadequate wetting of the oxide films [23].
Fig. 4. Back-scattered electron image of a cross-section of specimen Zr – 1%Nb magnification : × 4000 (white, metal; grey, oxide; black, resin).
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Table 2 Nature and area of the electrode deposit on the oxidea Zr alloy
Sample 1 Sample 2 Sample 3
Metal electrode and area (cm2)
Ag/0.8 Pt/2.5 Pt/2.7
Thickness of the oxide films (mm) Weight gain
IS (or =20) (ambient temperature-room atmosphere)
SEM
1.9 1.9 1.9
1.97 2.09 2.11
2.02 (0.23) 2.06 (0.19) 2.04 (0.18)
a Thickness of oxide films formed on ZrNb(1%)O(0.13%) determined by weight gain. IS (room temperature-ambient atmosphere) and SEM (standard deviation is indicated within brackets). The samples investigated were cut in the same cladding.
It must be mentioned that oxide thickness could only be determined by IS for layers thicker than 1 mm. Below this value, most oxide films are short-circuited or exhibit very low resistances. Intermetallic particles (Zr(Fe,Cr)2 for Zy-4) are generally thought to be the cause of the local conduction giving rise to the shortcircuit [19,23,24]. Nevertheless, the electrons’ pathway leading to the electrical breakdown of the oxide has not yet been completely identified. The preferred sites for cathodic reduction of copper at room temperature were shown to be scratches and cracks in thin oxides on zircaloy and not the intermetallics [25]. In the case of ZrNb(1%)O(0.13%), the influence of the second phase particles, consisting mainly of b-Nb with a mean diameter close to 50 nm and few Zr(NbFe)2 lower than 300 nm, is strongly unlikely in a charge percolation process. Moreover, short-circuits were observed in oxides on pure zirconium containing very few second phase particles [23]. Accordingly, intermetallics could not be regarded as the only origin of the short circuit conduction pathways. The constant phase angle observed in Fig. 3 is often related to the microstructure of the oxide. It was assumed that electron-conducting paths due to localized regions of high electrical conductivity like metallic precipitates could give rise to the CPE behavior [4,24–28]. In our studies, such a behavior was also observed in
spite of very low second phase particles’ concentration. In order to avoid any electrical short-circuit, the electrical behavior of a 2 mm oxide film formed on ZrNb(1%)O(0.13%) was studied as a function of temperature.
3.2. Electrical beha6ior of an oxide layer of 2 mm thickness IS measurements were performed on three samples of ZrNb(1%)O(0.13%) originating from the same cladding (Table 2). As expected for an activated conduction process, the impedance modulus in Bode diagrams is a decreasing function of the temperature (Fig. 5). When the temperature is raised, diagrams show that the phase angle decreases from − 90 close to −80°, suggesting a deviation from an ideal capacitor behavior. The continuous change in the phase angle with frequency has sometimes been related to the Young’s model [29] for insulating oxides with exponential profiles of conductivity. Nevertheless, the infinite slope and so the bent curve obtained in Cole – Cole diagram for such an electrical response disagree with the linearity of the experimental data. For the three studied cells, the electrical responses were found to be identical whatever the thermal history of the sample, the nature and the area of the noble
Fig. 5. Bode diagrams (v= 2pf ) for sample 3 at different temperatures. Empty symbols: impedance; full symbols, phase angle.
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Fig. 6. Nyquist diagrams recorded at 210°C normalized to the area of the external electrode. Sample 1(*), sample 2 ( + ), sample 3 ().
metal used as the electrode (Fig. 6). Moreover, IS diagrams recorded at the reference temperature (90°C) remain unchanged after an increase to 280°C indicating neither significant modification of the electrical properties of the film nor oxide growth. This was confirmed by SEM examinations and IS measurements on uncoated area of the samples at the end of the experiments.
Fig. 7. Variation of the extrapolated capacitance at infinite frequency C on the Cole–Cole diagram as a function of temperature. Increasing temperature ( × ), decreasing temperature ().
The extrapolated capacitance at infinite frequency was found to be constant up to 150°C followed by a decrease (Fig. 7). The reversibility in temperature and the constant value of C at 90°C attest that this temperature dependence could not be attributed to the oxide growth. As the film remains unchanged in terms of geometrical dimensions, a decrease in the oxide dielectric constant as a function of the temperature could be assumed. In fact, the explanation of the C decrease was obtained by plotting Cole – Cole diagrams recorded at different temperatures on the same curve (Fig. 8). The graph demonstrates that between 105 and 1 Hz, low frequency points measured at low temperature perfectly superimpose on the high frequency points determined at higher temperature. For frequencies typically lower than 1 Hz, the resistive contribution of the oxide film prevents the superimposition on the complete frequency range studied. In the Cole – Cole plane, a resistive contribution associated to a Jonscher’s dispersion modifies the linearity at low frequency and led to a sharp increase in the slope of the curve. Consequently, an increasing temperature leads to an increase of oxide conductivity and thus to a modification of frequency localization of the curve linearity break. Therefore, we assume that the frequency – temperature equivalence is only significant for the dielectric behavior of the oxide film. Without taking into account the coverage frequency range, one can draw a continuum curve of about 14 frequency decades by plotting the points measured between 105 and 103 Hz for the temperatures investigated. Although this frequency – temperature equivalence have already been found for the conductivity of ionically and electronically conducting amorphous solids, it is always the result from data normalization [30] or curves’ translation [14]. In this study, we superimposed high frequency impedance data on the Cole – Cole diagram without making any assumption on the electrical properties of the oxide film.
Fig. 8. Superimposition of Cole–Cole diagrams recorded between 1 and 105 Hz as a function of temperature: 90 ( ), 128 (×), 147 (), 186 (2), 227 () and 260°C ( ). Dashed line: slope of the high and low frequency dispersion. Solid line: slope of the middle frequency dispersion.
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Fig. 9. Bode diagram (v = 2pf ) of the master curve calculated at 90°C. (×) impedance ; ( ) phase angle. The continuous line represents the fit using the equivalent circuit (see text for further explanations).
This kind of representation allows a complete vision of the system’s impedance and is not reduced to only the real part of the impedance as in conductivity studies. As mentioned before, the geometric parameters and the sample’s resistance were not found to vary between 90 and 280 °C. From the master curve, we can ensure that the temperature dependence of C is not related to the modification of the oxide dielectric constant. In fact, by varying the temperature, we modify the window of the measurement on a simple curve. For temperatures higher than 150°C, the dielectric response associated to the total oxide thickness is henceforth not accessible in the frequency range investigated. Thus, the linear extrapolation of C on the Cole–Cole diagram can not be directly correlated to the film thickness. This is the cause of the decrease of the dielectric constant previously mentioned when using the extrapolation of the experimental curve to determine the C values. The frequency corresponding to the superimposed points obtained at different temperatures exhibits a temperature dependence. The observed variation obeys an Arrhenius law with an activation energy close to 0.8 eV on the whole frequency range. Let us mention that the physical meaning of this parameter is still unknown. By using the thermal activation of the measuring frequency and Eqs. (1) and (2), the master Cole–Cole curve was extrapolated in Bode plane at a fixed temperature (Fig. 9). Based on 14 frequency decades, an equivalent circuit could then be accurately established. Another parameter, the dispersion factor F(v), could be used to describe the frequency dispersion of the capacitance of the oxide layer [10]. F(v) is defined by the relation: F(v)=
C(v) −C% C%
to dispose of the most complete electrical description of the film. Note that F(v) is normalized by the oxide thickness and is absolutely independent of the equivalent circuit. An Arrhenius diagram of the dispersion factor (Fig. 10) depicts two linear sections. The two activation energies (Ea) of about 0.4 and 0.16 eV were determined, respectively, above and below 170°C. These will be discussed later. On the master curve in the Cole – Cole plane (Fig. 8), two linear sections of the same slope separated by a transient segment of a higher slope were observed. Simulation of several electrical circuits allowed us to assert that such an intermediary electrical signature ‘inserted’ in a more extended frequency range indicates a contribution of two dielectric relaxation processes strictly connected in series. The parallel association of two dielectric relaxations results in only two successive slopes, with the highest one obtained at low frequencies in total contradiction with our results. This suggests that the oxide film is in fact composed of two layers having different dielectric properties. This is not an unrealistic assumption if one refers to the literature regarding zirconium alloys [10]. On Bode diagrams, as no inflection point was detected, no specific resistance of each layer could be
(5)
It could be calculated at each frequency but we chose the lowest one to determine this value (1 mHz) in order
Fig. 10. Arrhenius diagram of the dispersion factor F(v).
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Fig. 13. Arrhenius diagram of the conductance (1/R).
Fig. 11. Equivalent circuit used to fit the experimental curves. (2) R is the total oxide resistance, C (1) Jonscher and C Jonscher are Jonscher’s capacitances associated with the different dielectric layers. L is the inductance corresponding to electrical wires and Rc is the overall resistance of connections.
achieved. Modulation of the amplitude of the measuring signal between 10 and 500 mV did not induce any modification of either the impedance diagram shape or impedance modulus. Consequently, the low frequency resistance was attributed to the total oxide resistance rather than a charge transfer resistance. The chosen equivalent circuit is shown in Fig. 11. It is a series association of a contact resistance and a self inductance, due to the platinum wires, whose behavior is depicted at the highest frequencies. These components are connected in series with a parallel combination of two Jonscher’s capacitors in series and a resistance describing the overall conductivity properties of the oxide film. By using the proposed equivalent circuit, an excellent agreement was achieved between experimental
and calculated data (Fig. 9). The relative error of calculated electrical parameters was estimated to be lower than 5%. Concerning the temperature variations of Jonscher’s parameters, Fig. 12 shows thicknesses and n values for the two layers indexed 1 and 2 for the first (high frequency) and the second dielectric responses (low frequency), respectively. IS results do not allow the spatial localization of the two layers in relation to the metal – oxide interface and the corrosive solution to be distinguished. The corresponding parameters of both layers are constant within the temperature range and are respectively around 1.5 mm and n1 = 0.6 for the high frequency dispersion and 0.5 mm and n2 = 0.4 for the low frequency one. For temperatures higher than 250°C, the second relaxation process was almost unobservable (Fig. 8) because of the technical limitation of high frequency measurements. This explains the slight modification of the calculated layers’ thickness. An Arrhenius diagram of the electrical conductance (1/R) of the film is shown in Fig. 13. As for the dielectric dispersion, the plots could be separated into two linear sections. Activation energies of 0.5 and 0.4
Fig. 12. Variation of the thickness of layers 1, 2 and the total oxide, and variation of n1 and n2 values as a function of temperature. Layer 1 (2), layer 2 (), total oxide ( ), n1 (*) and n2 (× ).
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eV were calculated for temperatures both higher and lower than 170°C. These values are close to 0.56 eV determined by Dawson et al. [31] on anodic ZrO2 within the temperature range of 250–300°C. However, they are almost two times lower than for ionic conduction in zirconia based conductors (0.8–1 eV), regardless of the crystallographic structures. In our unpublished works, an activation energy close to 1 eV was determined for both tetragonal and monoclinic pure zirconias. This discrepancy suggests that the related conduction processes are different for each material.
4. Discussion For an oxide film in pre-transition kinetic step, we observed in Section 3.2 that the superimposition of Cole–Cole diagrams depicts a frequency–temperature equivalence for the dielectric part of the IS response. Although this phenomenon needs more theoretical work to access the associated physical meaning, this is an interesting experimental fact to study IS data as a function of the temperature. We will now discuss the nature of the two dielectric layers. Two allotropic forms of ZrO2, monoclinic and tetragonal, have been identified in the scales formed on Zr alloys [32]. Several works have suggested that a part of the oxide crystallites formed initially at the oxide–metal interface has a tetragonal structure which could be stabilized by the high compressive stress [33,34], the small grain size [35] or point defects [36]. The activation energies of the film conductance are nevertheless too different from classical ZrO2 to ascribe the two dielectric responses we observed by IS measurements to these two different structures. Recently, Barberis and Frichet [10] investigated the IS response in liquid medium at room temperature of oxide films formed on Zy-4 in preand post-transition. In agreement with several structural observations [37,38] and IS measurements [5], they stated that the film is constituted of a dense layer and a porous layer, even before the kinetic transition. The penetration of the electrolyte in the porous layer enhances its conductivity and allows the bilayered structure of the film to be identified. The IS signature is depicted at a higher frequency for the porous layer than for the dense layer [10]. As an opposite, the gaseous atmosphere used in our study could be assumed to decrease the conductivity of the porous layer compared to the dense one. Remembering that the porosity has not been observed by TEM up to now, the nanometer size of the ‘cracks’ could bring about a relative homogeneity in the conduction process between the two layers and could also clarify the single resistance we observed for the total oxide film. As a contrast, the dielectric properties would allow the two constituent structures of the oxide film to be differentiated.
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Consequently, our IS results could be interpreted as follows: The signature of the dense layer at high frequencies characterized by a thickness of 1.5 mm and a Jonscher’s parameter n1 of 0.6. The electrical response of the 0.5 mm porous layer at low frequencies with a n2 factor of 0.4, indicative of more energy losses during the sinusoidal alternative measuring signal than for the inner film. A value of 0.65 n51 is often identified with the presence of hopping conduction by electrons and this close to 0.4 could be related to a dielectric behavior of a p-n junction [14]. Complementary studies have to be made in order to identify the electrical or the structural nature of the two film components observed by IS and to establish the correlation degree with either the tetragonal-monoclinic structure or the porous and the dense layers. In spite of the impossibility of determining the total oxide thickness by direct linear extrapolation of C on Cole – Cole diagram at temperatures above 150°C, this value could be deduced from the sum of the two layers. It would therefore be feasible to follow oxide growth by in situ IS measurements in gaseous atmospheres. Moreover, the fact that the sum of the two layer thicknesses independently calculated by IS with o = 20 is equal, on the whole temperature range, to the total oxide thickness determined by weight gain or SEM, undoubtedly demonstrates the validity of the assumption concerning the independence of the dielectric constant to the temperature revealed by the Cole – Cole master curve. The two linear parts of the Arrhenius diagram are a common manifestation of the conductance of the film, calculated from the equivalent circuit, and the dispersion factor determined without any assumption on the significance of IS data. Such a behavior could be related to the modification of the transport process in terms of concentration or mobility of the charge carriers in the overall film or to the intrinsic properties of each layer, which are predominant within a specific temperature range. The detail of the nature and the charge transport mechanism will be discussed in a future publication [39]. 5. Conclusion Preliminary IS investigations carried out at room temperature on oxide films with different thicknesses and natures established the interest of using Cole – Cole diagrams to study capacitive systems. We have shown that The electrical response could be associated to the dielectric relaxation model proposed by Jonscher. The thickness of the oxide films could be accurately determined by IS measurements in agreement with weight gain and SEM examinations.
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Using the Cole–Cole representation, the superimposition of data obtained between 25 and 280°C for a 2 mm thickness film gave prominence to a frequency–temperature equivalence characterized by the activation energy of the angular frequency close to 0.8 eV. From the 14 frequency decade’s master curve, an equivalent circuit is proposed involving two dielectric layers. However, the nature (microstructure, composition) of these two layers is yet to be identified.
References [1] B. Cox, Can. Rep. AECL (1967) 2668. [2] B. Cox, J.P. Pemsler, J. Nucl. Mater. 28 (1968) 73. [3] L. Durand-Kelikian, G. Cragnolino, D.D. Macdonald, Corros. Sci. 32 (1991) 347. [4] O. Gebhardt, A. Hermann, Electrochim. Acta 41 (1996) 1181. [5] F. Garzarolli, H. Seidel, R. Tricot, J.P. Gros, ASTM-STP 9 (1132) (1991) 395. [6] B. Cox, Y. Yamaguchi, J. Nucl. Mater. 210 (1994) 303. [7] H. Go¨hr, J. Schaller, C.A. Schiller, Electrochim. Acta 38 (1961) 1993. [8] H. Go¨hr, J. Schaller, H. Ruhman, F. Garzarolli, ASTMSTP 11 (1295) (1996) 181. [9] B. Sala, I. Bobin-Vastra, A. Frichet, Proceedings of the 8th International Symposium on Nuclear Power Systems, Amelia Island, 2, 1997, American Nuclear Society, Inc., La Grange Park, Illinois, USA, 1005. [10] P. Barberis, A. Frichet, J. Nucl. Ind. 273 (1999) 182. [11] A. Caneiro, M. Bonnat, J. Fouletier, J. Appl. Electrochem. 11 (1981) 83. [12] J. Fouletier, G. Vitter, M. Kleitz, J. Appl. Electrochem. 5 (1975) 111. [13] B. Boukamp, Equivalent Circuit, University of Twente, Twente, The Netherlands, 1989. [14] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics Press, London, 1983. [15] A.K. Jonscher, J. Mater. Sci. 16 (1981) 2037.
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[16] A.K. Jonscher, Nature 253 (1975) 717. [17] A. Frichet, J.P. Mardon, in: A.M. Garde, E.R. Bradley (Eds.), Proceedings of the 10th International Symposium on Zirconium in the Nuclear Industry, ASTM, Baltimore, June 21 – 24, 1993. [18] C. Bataillon, S. Brunet, Electrochim. Acta. 39 (1994) 455. [19] O. Gebhardt, M. Gehringer, T. Graber, A. Hermann, Mater. Sci. Forum 192-194 (1995) 587. [20] IAEA-TECDOC-996, IAEA, Vienna, 1998. [21] B. Cox, Adv. Corros. Sci. Tech. 5 (1973) 173. [22] B. Cox, F. Gascoin, Y.M. Wong, J. Nucl. Mater. 218 (1995) 113. [23] B. Cox, Y.M. Wong, J. Nucl. Mater. 218 (1995) 324. [24] O. Gebhardt, J. Nucl. Mater. 203 (1993) 17. [25] B. Cox, F. Gauducheau, Y.M. Wong, J. Nucl. Mater. 189 (1992) 362. [26] N. Ramasubramanian, J. Nucl. Mater. 55 (1975) 134. [27] A. Urqhardt, D. Vermilyea, W. Rocco, J. Electrochem. Soc. 125 (1975) 199. [28] R. Kruger, R. Adamson, S. Brenner, J. Nucl. Mater. 189 (1992) 318. [29] L. Young, Trans. Faraday Soc. 51 (1955) 1250. [30] S.R. Elliott, Solid State Ionics 70/71 (1994) 27. [31] D. Dawson, R. Creamer, Br. J. Appl. Phys. 16 (1965) 1643. [32] C. Roy, G. David, J. Nucl. Mater. 37 (1970) 71. [33] J. Godlewski, P. Bouvier, G. Lucazeau, L. Lafayette, Proceedings of the 12th International Symposium on Zirconium in the Nuclear Industry, Toronto, ASTM-STP, June 15 – 18, 1998. [34] J. Godlewski, ASTM-STP 10 (1245) (1994) 663. [35] P. Barberis, J. Nucl. Mater. 226 (1995) 34. [36] D. Pe´cheur, F. Lefe`vre, A.T. Motta, C Lemaignan, D. Charquet, ASTM-STP 10 (1245) (1994) 687. [37] B. Cox, J. Nucl. Mater. 27 (1968) 1. [38] P. Bossis, G. Lelie`vre, P. Barberis, X. Iltis, F. Lefe`vre, Proceedings of the 12th International Symposium on Zirconium in the Nuclear Industry, Toronto, ASTM-STP, June 15 – 18, 1998. [39] J.J. Vermoyal, A. Frichet, L. Dessemond, A. Hammou, submitted for publication.
AC impedance study of corrosion films formed on zirconium based alloys J.J. Vermoyal a,b,*, A. Frichet b, L. Dessemond a, A. Hammou a a
Laboratory of Electrochemistry and Physical-chemistry of Materials and Interfaces, UMR 5631 INPG-CNRS-UJF, 1130 Rue de la Piscine, 38402 Saint Martin d’He`res, France b Framatome Nuclear Fuel, 10 rue Juliette Re´camier, 69006 Lyon, France Received 12 February 1999; received in revised form 30 June 1999
Abstract Oxide films formed by water oxidation (360°C) of two Zr alloys, Zircaloy-4 (Zy-4) and ZrNb(1%)O(0.13%), were studied by impedance spectroscopy (IS) in gaseous atmospheres. Results show that capacitances are frequency dispersed, in agreement with Jonscher’s law of dielectric relaxation. A good correlation was found between oxide thickness calculated from both IS measurements at room temperature and weight gain and those estimated by metallographic examinations. The electrical characteristics of a 2 mm thick film formed on ZrNb(1%)O(0.13%) were investigated as a function of the temperature (25–280°C) at constant oxygen partial pressure (0.3 Pa). Cole – Cole diagrams suggest a frequency-temperature equivalence: low frequency points at low temperatures perfectly superimpose on high frequency points at higher temperatures. This resulting 14 decade ‘master’ curve so obtained can be characterized by the activation energy of the angular frequency v close to 0.8 eV. An equivalent circuit based on an association in series of two layers with different dielectric properties was proposed. By fitting the curves obtained at different temperatures with only a parallel resistance, the thicknesses of the two layers were estimated to be 1.5 and 0.5 mm. Finally, both the Arrhenius diagrams of the total conductivity and the dispersion factor are characterized by a breakdown temperature point with two activation energy values. © 1999 Elsevier Science Ltd. All rights reserved. Keywords: Impedance spectroscopy; Zirconium alloys; Oxidation; Frequency-temperature equivalence; Dielectric dispersion
1. Introduction The corrosion behavior of zirconium alloys used for cladding tubes is one of the most important parameters for optimizing fuel element economy in the nuclear industry. At present, Zircaloy-4 (1.2–1.7 wt% Sn, 0.18– 0.24 wt% Fe and 0.07–0.13 wt% Cr) is used for pressurized water reactors (PWRs) because of its low cross-section for absorption of thermal neutrons, its high mechanical strength and its relatively low corro* Corresponding author. Fax: +33-47-682-6670. E-mail address: [email protected] (J.J. Vermoyal)
sion rate. To increase waterside corrosion resistance, new Zr alloys must be developed and studied before industrial application. The corrosion rate of the cladding depends principally on the alloy composition, the metallurgical treatments, the chemistry and the temperature of the reactor water. The oxidation behavior of Zr alloys is generally described by an initial ‘pre-transition’ stage for which the oxidation rate is either parabolic or cubic. When the oxide reaches a thickness of about 2 to 4 mm, a sharp increase in the oxidation rate occurs and the ‘post-transition’ kinetics is characterized by a quasi linear variation law [1] leading to the degradation of the initial protective oxide film into a partially porous layer.
0013-4686/99/$ - see front matter © 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 3 - 4 6 8 6 ( 9 9 ) 0 0 3 0 7 - 2
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Impedance spectroscopy (IS) was hitherto applied to allow insights into the microstructure of the growing oxide film and more importantly to study the dense layer at the metal–oxide interface and the penetration of the electrolyte into the porous layer on the water side [2–4]. IS results for different materials oxidized under various conditions investigated and manufacturing parameters were correlated to the microstructure [5] and to the pores’ structure of the layer [6]. Nevertheless, experiments were limited to low temperatures and atmospheric pressure, far from corrosive conditions in PWRs at 360°C, implying transition effects between oxidation and the study’s environment [6,7]. This problem has recently been solved by performing IS in situ during oxide film formation [8,9]. In spite of the numerous works based on this method of electrical characterization, little information is available about the transport process of charge carriers and electrical conducting paths in oxide films due principally to the difficulties specific to the IS approach [10]. This study is dedicated to the electrical properties of oxides formed on Zircaloy-4 and ZrNb(1%)O(0.13%) in water at 360°C characterized by IS measurements in gaseous atmospheres. This paper presents the results concerning thickness determination of oxide films carried out to elaborate and test an electrochemical cell. The electrical response of an oxide layer of 2 mm thickness formed on ZrNb(1%)O(0.13%) was investigated as a function of temperature at a constant oxygen partial pressure (0.3 Pa).
2. Experimental Cylindrical cladding tubes of Zy-4 and ZrNb(1%)O(0.13%) were provided by an industrial supplier (Cezus and Zircotube, France) and fabricated according to standard manufacturing routines. The oxide films were formed by oxidation at 360°C in pure water in an autoclave. The thickness of each film was
Fig. 1. Scheme of the electrochemical cell.
calculated from the weight gain, assuming an oxide density of 5.7 g cm − 3 and no dissolution of the oxide during the growth. For scanning electron microscopy (SEM) observations, samples were mechanically polished to diamond paste (1 mm). A thin conductive Au film was sputtered on the surface of the specimen to avoid charging effects. Impedance spectroscopy measurements were performed on a 1.2 cm length cylinder. After cooling and extraction from the autoclave, the samples were ultrasonically washed in alcohol and distilled water for 10 min. A Zr/ZrO2/M (M= Pt, Ag) cell configuration was chosen. A section of the internal side of the cladding tube was partially mechanically eliminated and a Zr alloy ring was spot welded in order to assure an ohmic contact throughout the experiment (Fig. 1). Platinum or silver electrodes were coated on the external side of the oxide film by RF sputtering (Plassys) in high purity argon at room temperature. This electrode was sputtered on an area varying between 0.5 and 3 cm2 far from the singular welded zone to avoid parasitic electric contribution due to possible modification of the Zr phase. The metal deposit is strongly adherent and its thickness could be roughly estimated as 350 nm. Platinum wires were used as current collectors. Oxygen partial pressure was fixed by pure argon (argon U, Air Liquide). The gas flows successively through an oxygen electrochemical pump [11], the working furnace and an oxygen gauge [12] which was used to measure the working oxygen partial pressure (0.3 Pa). The temperature was regulated at 9 1°C and the different parts of the gas circuit were connected by stainless steel tubing and Viton O-ring seals. IS measurements were carried out with an HP4192A impedance analyzer in the 5 – 13 ×106 Hz range. Low frequency points, down to 10 − 4 Hz, were performed with an Autolab potentiostat – galvanostat EcoChemie and a 1250 Solartron coupled with an impedance adaptator allowing high impedance modulus (109 V) measurements. We checked that both apparatus gave the same response for the same cell in the common frequency interval. Experimental data were fitted with the EQUIVALENT CIRCUIT software of Boukamp [13]. Impedance measurements were performed at zero dc polarization. The reliability and the reproducibility of the results were checked by preliminary measurements carried out at ambient temperature for different oxide thicknesses. For the study of the oxide layer of 2 mm thickness between 25 and 280°C, a stationary state was assumed when two successive spectra were identical over the whole frequency range. The temperature of 90°C was chosen as a reference temperature to control any modification of the electrical properties of the oxide films. At the end of the experiments, an impedance diagram was recorded at room temperature on a part of the oxide area not yet studied by IS in
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Fig. 2. Bode diagram (v =2pf ) of a 1.6 mm thickness film on ZrNb(1%)O(0.13%) recorded at room temperature in air (external electrode: platinum). ( ×) impedance ; ( ) phase angle.
where v is the angular frequency. Rc is determined by the high frequency intercept of the impedance diagram and the real axis in the Nyquist plane. Rc values are typically lower than 3 V so the influence of this parameter alters the Cole – Cole diagram shape only for frequencies higher than 106 Hz. The data used for Fig. 1 represented on the Cole – Cole diagram (Fig. 3) exhibit the dielectric dispersion of the oxide film. The observed linearity on a frequency range of 4 decades could be described by the universal law for the dielectric response proposed by Jonscher [14 – 16] : C*=C +
Fig. 3. Cole – Cole diagram of a 1.6 mm thickness film formed on Zr– 1%Nb recorded at room temperature in air (external electrode: platinum).
order to determine the invariance of the oxide film after successive heating and cooling.
3. Results
3.1. Thickness determination Bode diagrams obtained at ambient temperature and room atmosphere give prominence to the capacitive behavior for the different layers investigated. Fig. 2 shows the Bode diagram recorded on a 1.6 mm oxide film formed on ZrNb(1%)O(0.13%). The electrical properties described in the Cole–Cole representation allow predominantly capacitive systems to be studied due to the normalization of the admittance by angular frequency (v=2pf ). Assuming that the complex impedance Z*=Z%−jZ%%, where Z% and Z%% are the real and the imaginary parts, respectively, is equivalent to an association in series of a complex capacitance C*= C%− jC%% and a pure resistance Rc, measured at high frequency, i.e. the overall resistance of contacts and connection wires to the electrochemical cell, expressions of C% and C%% take on the following forms: C% =
1 Z% v (Z −Rc)2 +Z%2
(1)
1 Z%−Rc v (Z%−Rc)2 +Z¦2
(2)
C¦ =
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B ( jv)1 − n
(3)
where C* is the complex capacitance of the film, C is a pure capacitance related to the oxide thickness which is defined as the limit of the complex capacitance C% at infinite frequency. B is a constant related to the dielectric dispersion and n is a constant parameter characteristic of the constant phase angle between the real axis and the experimental curve. C is obtained from the high frequency intercept of the linear extrapolation defined by the experimental curve on the real axis in the Cole – Cole representation. One can note that Eq. (3) is related to the well known constant phase element (CPE) to which a real capacitance C is added in parallel. This association allows to take into account that the extrapolation of the linear experimental curve has a real and finite value (C ) whereas that for a simple CPE this value is zero. In spite of the cylindrical cell configuration, the film thickness allows the more convenient planar capacitance relation to be used (assuming the homogeneity of the oxide layer): d=
oro0A C
(4)
where d is the oxide thickness, o0 the vacuum permittivity, or the relative permittivity of the oxide and A the area of the noble metal used for the external electrode. The main inaccuracy in the thickness value is related to the electrode area determination (5%). With a zirconia dielectric constant of 20 for an oxide formed on ZrNb(1%)O(0.13%) [17] and 22 on Zy-4 [18,19], the values of the calculated thicknesses are listed in Table 1. Results show that the Cole – Cole curves are independent of the nature and the area of the electrode sputtered on ZrO2. Moreover, the difference between several samples cut in the same cladding was in the majority close to 0.1 mm which demonstrated excellent measurements reproducibility. These values were compared with those estimated from microscopic observations and weight gain (WG) taking 1 mm for 15 mg dm − 2 [20]. SEM examinations of the oxide layers were carried out on more than 20 zones arbitrarily chosen
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Table 1 Nature and area of the electrode deposit on the oxidea Zr alloys
Zy-4 (or = 22)
ZrNb(1%)O(0.13%) (or = 20)
Metal electrode and area (cm2)
Thickness of oxide films (mm) Weight gain
IS
SEM
Ag/0.36 Pt/2.9 Pt/3.1 Pt/3 Pt/3 Pt/3.2
1 2 1.6 1.6 1.6 1.6
0.96 2.01 1.7 1.72 1.67 1.65
0.97 1.95 1.65 ndb 1.57 ndb
Pt/1.1 Pt/1.6 Ag/0.8 Pt/2.5 Pt/0.85 Pt/1.55 Pt/1.8
1.9 1.9 1.9 1.9 2.55 3 3.46
1.9 1.69 2 2.1 2.6 3.1 3.55
1.89 (0.19) ndb 2.05 (0.2) ndb 2.8 (0.18) 3.05 (0.16) 3.55 (0.11)
(0.07) (0.12) (0.2) (0.25)
a Thickness of oxide films formed on Zy-4 and ZrNb(1%)O(0.13%) determined by weight gain. IS (room temperature-ambient atmosphere) and SEM (standard deviation is indicated within brackets). b nd: not determined.
around the external side of the tubes. The result for a 3.5 mm oxide film formed on ZrNb(1%)O(0.13%) is given in Fig. 4. Dark strips will not be discussed in this paper but were generally identified in the literature as pores or cracks [21]. The values of the oxide thicknesses calculated from IS are in excellent agreement with those determined from WG and SEM investiga-
tions and allow the satisfactory covering of the sputtering noble metal deposit to be assumed. These experimental results corroborate those found using evaporated electrodes [22,23] and emphasize the interest of such a technique compared to a liquid metal electrode which can often lead to inadequate wetting of the oxide films [23].
Fig. 4. Back-scattered electron image of a cross-section of specimen Zr – 1%Nb magnification : × 4000 (white, metal; grey, oxide; black, resin).
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Table 2 Nature and area of the electrode deposit on the oxidea Zr alloy
Sample 1 Sample 2 Sample 3
Metal electrode and area (cm2)
Ag/0.8 Pt/2.5 Pt/2.7
Thickness of the oxide films (mm) Weight gain
IS (or =20) (ambient temperature-room atmosphere)
SEM
1.9 1.9 1.9
1.97 2.09 2.11
2.02 (0.23) 2.06 (0.19) 2.04 (0.18)
a Thickness of oxide films formed on ZrNb(1%)O(0.13%) determined by weight gain. IS (room temperature-ambient atmosphere) and SEM (standard deviation is indicated within brackets). The samples investigated were cut in the same cladding.
It must be mentioned that oxide thickness could only be determined by IS for layers thicker than 1 mm. Below this value, most oxide films are short-circuited or exhibit very low resistances. Intermetallic particles (Zr(Fe,Cr)2 for Zy-4) are generally thought to be the cause of the local conduction giving rise to the shortcircuit [19,23,24]. Nevertheless, the electrons’ pathway leading to the electrical breakdown of the oxide has not yet been completely identified. The preferred sites for cathodic reduction of copper at room temperature were shown to be scratches and cracks in thin oxides on zircaloy and not the intermetallics [25]. In the case of ZrNb(1%)O(0.13%), the influence of the second phase particles, consisting mainly of b-Nb with a mean diameter close to 50 nm and few Zr(NbFe)2 lower than 300 nm, is strongly unlikely in a charge percolation process. Moreover, short-circuits were observed in oxides on pure zirconium containing very few second phase particles [23]. Accordingly, intermetallics could not be regarded as the only origin of the short circuit conduction pathways. The constant phase angle observed in Fig. 3 is often related to the microstructure of the oxide. It was assumed that electron-conducting paths due to localized regions of high electrical conductivity like metallic precipitates could give rise to the CPE behavior [4,24–28]. In our studies, such a behavior was also observed in
spite of very low second phase particles’ concentration. In order to avoid any electrical short-circuit, the electrical behavior of a 2 mm oxide film formed on ZrNb(1%)O(0.13%) was studied as a function of temperature.
3.2. Electrical beha6ior of an oxide layer of 2 mm thickness IS measurements were performed on three samples of ZrNb(1%)O(0.13%) originating from the same cladding (Table 2). As expected for an activated conduction process, the impedance modulus in Bode diagrams is a decreasing function of the temperature (Fig. 5). When the temperature is raised, diagrams show that the phase angle decreases from − 90 close to −80°, suggesting a deviation from an ideal capacitor behavior. The continuous change in the phase angle with frequency has sometimes been related to the Young’s model [29] for insulating oxides with exponential profiles of conductivity. Nevertheless, the infinite slope and so the bent curve obtained in Cole – Cole diagram for such an electrical response disagree with the linearity of the experimental data. For the three studied cells, the electrical responses were found to be identical whatever the thermal history of the sample, the nature and the area of the noble
Fig. 5. Bode diagrams (v= 2pf ) for sample 3 at different temperatures. Empty symbols: impedance; full symbols, phase angle.
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Fig. 6. Nyquist diagrams recorded at 210°C normalized to the area of the external electrode. Sample 1(*), sample 2 ( + ), sample 3 ().
metal used as the electrode (Fig. 6). Moreover, IS diagrams recorded at the reference temperature (90°C) remain unchanged after an increase to 280°C indicating neither significant modification of the electrical properties of the film nor oxide growth. This was confirmed by SEM examinations and IS measurements on uncoated area of the samples at the end of the experiments.
Fig. 7. Variation of the extrapolated capacitance at infinite frequency C on the Cole–Cole diagram as a function of temperature. Increasing temperature ( × ), decreasing temperature ().
The extrapolated capacitance at infinite frequency was found to be constant up to 150°C followed by a decrease (Fig. 7). The reversibility in temperature and the constant value of C at 90°C attest that this temperature dependence could not be attributed to the oxide growth. As the film remains unchanged in terms of geometrical dimensions, a decrease in the oxide dielectric constant as a function of the temperature could be assumed. In fact, the explanation of the C decrease was obtained by plotting Cole – Cole diagrams recorded at different temperatures on the same curve (Fig. 8). The graph demonstrates that between 105 and 1 Hz, low frequency points measured at low temperature perfectly superimpose on the high frequency points determined at higher temperature. For frequencies typically lower than 1 Hz, the resistive contribution of the oxide film prevents the superimposition on the complete frequency range studied. In the Cole – Cole plane, a resistive contribution associated to a Jonscher’s dispersion modifies the linearity at low frequency and led to a sharp increase in the slope of the curve. Consequently, an increasing temperature leads to an increase of oxide conductivity and thus to a modification of frequency localization of the curve linearity break. Therefore, we assume that the frequency – temperature equivalence is only significant for the dielectric behavior of the oxide film. Without taking into account the coverage frequency range, one can draw a continuum curve of about 14 frequency decades by plotting the points measured between 105 and 103 Hz for the temperatures investigated. Although this frequency – temperature equivalence have already been found for the conductivity of ionically and electronically conducting amorphous solids, it is always the result from data normalization [30] or curves’ translation [14]. In this study, we superimposed high frequency impedance data on the Cole – Cole diagram without making any assumption on the electrical properties of the oxide film.
Fig. 8. Superimposition of Cole–Cole diagrams recorded between 1 and 105 Hz as a function of temperature: 90 ( ), 128 (×), 147 (), 186 (2), 227 () and 260°C ( ). Dashed line: slope of the high and low frequency dispersion. Solid line: slope of the middle frequency dispersion.
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Fig. 9. Bode diagram (v = 2pf ) of the master curve calculated at 90°C. (×) impedance ; ( ) phase angle. The continuous line represents the fit using the equivalent circuit (see text for further explanations).
This kind of representation allows a complete vision of the system’s impedance and is not reduced to only the real part of the impedance as in conductivity studies. As mentioned before, the geometric parameters and the sample’s resistance were not found to vary between 90 and 280 °C. From the master curve, we can ensure that the temperature dependence of C is not related to the modification of the oxide dielectric constant. In fact, by varying the temperature, we modify the window of the measurement on a simple curve. For temperatures higher than 150°C, the dielectric response associated to the total oxide thickness is henceforth not accessible in the frequency range investigated. Thus, the linear extrapolation of C on the Cole–Cole diagram can not be directly correlated to the film thickness. This is the cause of the decrease of the dielectric constant previously mentioned when using the extrapolation of the experimental curve to determine the C values. The frequency corresponding to the superimposed points obtained at different temperatures exhibits a temperature dependence. The observed variation obeys an Arrhenius law with an activation energy close to 0.8 eV on the whole frequency range. Let us mention that the physical meaning of this parameter is still unknown. By using the thermal activation of the measuring frequency and Eqs. (1) and (2), the master Cole–Cole curve was extrapolated in Bode plane at a fixed temperature (Fig. 9). Based on 14 frequency decades, an equivalent circuit could then be accurately established. Another parameter, the dispersion factor F(v), could be used to describe the frequency dispersion of the capacitance of the oxide layer [10]. F(v) is defined by the relation: F(v)=
C(v) −C% C%
to dispose of the most complete electrical description of the film. Note that F(v) is normalized by the oxide thickness and is absolutely independent of the equivalent circuit. An Arrhenius diagram of the dispersion factor (Fig. 10) depicts two linear sections. The two activation energies (Ea) of about 0.4 and 0.16 eV were determined, respectively, above and below 170°C. These will be discussed later. On the master curve in the Cole – Cole plane (Fig. 8), two linear sections of the same slope separated by a transient segment of a higher slope were observed. Simulation of several electrical circuits allowed us to assert that such an intermediary electrical signature ‘inserted’ in a more extended frequency range indicates a contribution of two dielectric relaxation processes strictly connected in series. The parallel association of two dielectric relaxations results in only two successive slopes, with the highest one obtained at low frequencies in total contradiction with our results. This suggests that the oxide film is in fact composed of two layers having different dielectric properties. This is not an unrealistic assumption if one refers to the literature regarding zirconium alloys [10]. On Bode diagrams, as no inflection point was detected, no specific resistance of each layer could be
(5)
It could be calculated at each frequency but we chose the lowest one to determine this value (1 mHz) in order
Fig. 10. Arrhenius diagram of the dispersion factor F(v).
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Fig. 13. Arrhenius diagram of the conductance (1/R).
Fig. 11. Equivalent circuit used to fit the experimental curves. (2) R is the total oxide resistance, C (1) Jonscher and C Jonscher are Jonscher’s capacitances associated with the different dielectric layers. L is the inductance corresponding to electrical wires and Rc is the overall resistance of connections.
achieved. Modulation of the amplitude of the measuring signal between 10 and 500 mV did not induce any modification of either the impedance diagram shape or impedance modulus. Consequently, the low frequency resistance was attributed to the total oxide resistance rather than a charge transfer resistance. The chosen equivalent circuit is shown in Fig. 11. It is a series association of a contact resistance and a self inductance, due to the platinum wires, whose behavior is depicted at the highest frequencies. These components are connected in series with a parallel combination of two Jonscher’s capacitors in series and a resistance describing the overall conductivity properties of the oxide film. By using the proposed equivalent circuit, an excellent agreement was achieved between experimental
and calculated data (Fig. 9). The relative error of calculated electrical parameters was estimated to be lower than 5%. Concerning the temperature variations of Jonscher’s parameters, Fig. 12 shows thicknesses and n values for the two layers indexed 1 and 2 for the first (high frequency) and the second dielectric responses (low frequency), respectively. IS results do not allow the spatial localization of the two layers in relation to the metal – oxide interface and the corrosive solution to be distinguished. The corresponding parameters of both layers are constant within the temperature range and are respectively around 1.5 mm and n1 = 0.6 for the high frequency dispersion and 0.5 mm and n2 = 0.4 for the low frequency one. For temperatures higher than 250°C, the second relaxation process was almost unobservable (Fig. 8) because of the technical limitation of high frequency measurements. This explains the slight modification of the calculated layers’ thickness. An Arrhenius diagram of the electrical conductance (1/R) of the film is shown in Fig. 13. As for the dielectric dispersion, the plots could be separated into two linear sections. Activation energies of 0.5 and 0.4
Fig. 12. Variation of the thickness of layers 1, 2 and the total oxide, and variation of n1 and n2 values as a function of temperature. Layer 1 (2), layer 2 (), total oxide ( ), n1 (*) and n2 (× ).
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eV were calculated for temperatures both higher and lower than 170°C. These values are close to 0.56 eV determined by Dawson et al. [31] on anodic ZrO2 within the temperature range of 250–300°C. However, they are almost two times lower than for ionic conduction in zirconia based conductors (0.8–1 eV), regardless of the crystallographic structures. In our unpublished works, an activation energy close to 1 eV was determined for both tetragonal and monoclinic pure zirconias. This discrepancy suggests that the related conduction processes are different for each material.
4. Discussion For an oxide film in pre-transition kinetic step, we observed in Section 3.2 that the superimposition of Cole–Cole diagrams depicts a frequency–temperature equivalence for the dielectric part of the IS response. Although this phenomenon needs more theoretical work to access the associated physical meaning, this is an interesting experimental fact to study IS data as a function of the temperature. We will now discuss the nature of the two dielectric layers. Two allotropic forms of ZrO2, monoclinic and tetragonal, have been identified in the scales formed on Zr alloys [32]. Several works have suggested that a part of the oxide crystallites formed initially at the oxide–metal interface has a tetragonal structure which could be stabilized by the high compressive stress [33,34], the small grain size [35] or point defects [36]. The activation energies of the film conductance are nevertheless too different from classical ZrO2 to ascribe the two dielectric responses we observed by IS measurements to these two different structures. Recently, Barberis and Frichet [10] investigated the IS response in liquid medium at room temperature of oxide films formed on Zy-4 in preand post-transition. In agreement with several structural observations [37,38] and IS measurements [5], they stated that the film is constituted of a dense layer and a porous layer, even before the kinetic transition. The penetration of the electrolyte in the porous layer enhances its conductivity and allows the bilayered structure of the film to be identified. The IS signature is depicted at a higher frequency for the porous layer than for the dense layer [10]. As an opposite, the gaseous atmosphere used in our study could be assumed to decrease the conductivity of the porous layer compared to the dense one. Remembering that the porosity has not been observed by TEM up to now, the nanometer size of the ‘cracks’ could bring about a relative homogeneity in the conduction process between the two layers and could also clarify the single resistance we observed for the total oxide film. As a contrast, the dielectric properties would allow the two constituent structures of the oxide film to be differentiated.
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Consequently, our IS results could be interpreted as follows: The signature of the dense layer at high frequencies characterized by a thickness of 1.5 mm and a Jonscher’s parameter n1 of 0.6. The electrical response of the 0.5 mm porous layer at low frequencies with a n2 factor of 0.4, indicative of more energy losses during the sinusoidal alternative measuring signal than for the inner film. A value of 0.65 n51 is often identified with the presence of hopping conduction by electrons and this close to 0.4 could be related to a dielectric behavior of a p-n junction [14]. Complementary studies have to be made in order to identify the electrical or the structural nature of the two film components observed by IS and to establish the correlation degree with either the tetragonal-monoclinic structure or the porous and the dense layers. In spite of the impossibility of determining the total oxide thickness by direct linear extrapolation of C on Cole – Cole diagram at temperatures above 150°C, this value could be deduced from the sum of the two layers. It would therefore be feasible to follow oxide growth by in situ IS measurements in gaseous atmospheres. Moreover, the fact that the sum of the two layer thicknesses independently calculated by IS with o = 20 is equal, on the whole temperature range, to the total oxide thickness determined by weight gain or SEM, undoubtedly demonstrates the validity of the assumption concerning the independence of the dielectric constant to the temperature revealed by the Cole – Cole master curve. The two linear parts of the Arrhenius diagram are a common manifestation of the conductance of the film, calculated from the equivalent circuit, and the dispersion factor determined without any assumption on the significance of IS data. Such a behavior could be related to the modification of the transport process in terms of concentration or mobility of the charge carriers in the overall film or to the intrinsic properties of each layer, which are predominant within a specific temperature range. The detail of the nature and the charge transport mechanism will be discussed in a future publication [39]. 5. Conclusion Preliminary IS investigations carried out at room temperature on oxide films with different thicknesses and natures established the interest of using Cole – Cole diagrams to study capacitive systems. We have shown that The electrical response could be associated to the dielectric relaxation model proposed by Jonscher. The thickness of the oxide films could be accurately determined by IS measurements in agreement with weight gain and SEM examinations.
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Using the Cole–Cole representation, the superimposition of data obtained between 25 and 280°C for a 2 mm thickness film gave prominence to a frequency–temperature equivalence characterized by the activation energy of the angular frequency close to 0.8 eV. From the 14 frequency decade’s master curve, an equivalent circuit is proposed involving two dielectric layers. However, the nature (microstructure, composition) of these two layers is yet to be identified.
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