Additive Element Effects on Electronic Conductivity of Zirconium Oxide Film

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1 Journal of NUCLEAR SCIENCE and TECHNOLOGY, 31[6], pp. 546~551 (June 1994). Additive Element Effects on Electronic Conductivity of Zirconium Oxide Film Yusuke ISOBE, Motomasa FUSE and Kinya KOBAYASHI Energy Research Laboratory, Hitachi Ltd.* (Received April 23, 1993) A theoretical study on the electronic structure of zirconium oxide using a molecular orbital method was carried out to investigate the additive element effects on the electronic conductivity of oxide film formed on Zr-alloys. The atomic clusters used were (MZr12O8)36+ (M=Zr, 3d-transition metals and alkali metals). To simulate the electron conduction process in the oxide, calculations for a cluster with oxygen vacancy (V0) were also carried out. The energy gap Eg between electron-occupied and empty levels was evaluated, and the electronic conductivity was estimated qualitatively. Opposite effects on the electronic conductivity were found for additions of 3d-transition metals and alkali metals. The latter increased the electronic conductivity by forming impurity levels with small Eg. The former, however, induced compressive strain in the oxide, resulting in a lowering of electronic conductivity due to widening of the energy gap at the oxygen vacancy. KEYWORDS: zirconium oxides, electronic conductivity, energy gap, computer simulation, molecular orbital method, additives, impurities, zirconium alloys, corrosion I. INTRODUCTION Because of their good characteristics, Zralloys have been widely used as fuel cladding or fuel assembly materials in light water reactors. However, their corrosion resistance should be improved to satisfy future requirements of higher burnup reactor designs. Corrosion behavior of Zr-alloys is greatly influenced by several properties of the oxide film at the surface, including the electronic conductivity. In Zr-alloys, oxidation of metals occurs at the metal/oxide interface, and the oxide film grows thicker as oxidation proceeds. There are two flows of species through the oxide film in the corrosion process. One is the flow of oxygen ions from the surface to the metal/oxide interface. The oxygen ions which come to the interface form a new oxide layer. The other flow is the counter-flow of electrons which released from metal atoms through the oxidation reaction. The electrons are consumed in a cathodic reaction occurring at the surface. Therefore, the oxide film in which mobilities of such species are low, i.e. the oxide film with low electric conductivity, acts as an effective barrier against corrosion. (Here, electric conductivity means both ionic and electronic conductivities.) It has been found that the electric conductivity of oxide film was affected by additive elements in the oxide. Kubo & Uno(1)(2) reported that the oxide film of alloys with the higher corrosion resistance showed the lower electric conductivity, and that the conductivity changed with Fe content in the alloy (Fe content in the oxide was considered to follow that of Fe content in the alloys). The corrosion resistance of Zircaloy is improved by p-quenching(3)(4). This has been attributed to the dissolution of constituent atoms, such as Fe, Cr and Ni, into the oxide film, giving rise to the decreased conductivity. In spite of the importance of the electronic conductivity of oxide films and effects of additive elements on it, a detailed mechanism for their conductivity change has not been * Omika-cho, Hitachi-shi

2 Vol. 31, No. 6 (June 1994) 547 presented. The authors have investigated additive element effects on the electronic conductivity of oxide film. For this, we carried out a theoretical determination of the electronic structure of zirconium oxide (ZrO2) using a molecular orbital method. The changes in electronic energy levels caused by impurity levels or lattice strains were calculated. Then we considered the mechanism of the electronic conductivity change at an atomistic level. II. CALCULATION METHOD The molecular orbital method based on density functional theory(5) was employed here because of its suitability to calculations of a large atomic cluster including heavy atoms, such as Zr. The local spin density approximation (LSDA) was applied and molecular orbitals were expanded by Slater-type minimum atomic orbitals. The ZrO2 has three phases, i.e. monoclinic, tetragonal and cubic. The monoclinic phase is the stable one below about 1,273 K, but tetragonal and cubic phases have been observed in oxide film near the metal/oxide interface(6)(7) and they are thought to be a better corrosion barrier than the monoclinic phase. Therefore, we used atomic clusters modeled on tetragonal and cubic lattice structures as shown in Fig. 1. Lattice constants of the tetragonal cluster were those measured by Teufer(8). The lattice constant of the cubic cluster was assumed to be the same as one of the tetragonal constants (0.515 nm). Both types of clusters have the same number of nuclei and electrons [(Zr13O8)36+]. are constituents of Zircaloy (Fe, Cr and Ni) and the other was composed of alkali metals. Among the latter, Li is known to accelerate the corrosion rate of Zircaloy(9). All additive atoms were substituted for the Zr atom which was located at the center of the atomic cluster. In order to simulate an actual electron conduction process, calculations for clusters with an oxygen vacancy were also carried out. An oxygen vacancy was introduced by removing one oxygen atom from the cluster. Table 1 Additive elements used in this study and their atomic orbitals, together with the data of Zr and O Since the electron conduction mechanism of ZrO2 is expected to be a band mechanism such as that seen in semiconductors, electronic conductivity p is related to the energy gap E, between electron-occupied and empty levels where k is the Boltzmann constant and T the temperature. Using the above relation, we made qualitative analyses of electronic conductivity of various clusters by evaluating each cluster's Eg. (1) IL RESULTS AND DISCUSSION Fig. 1 Atomic clusters used in this study, (a) tetragonal and (b) cubic clusters Additive elements considered were divided into two groups as shown in Table 1. The first group included 3d-transition metals which 1. Electronic Structure of Pure Cluster Figure 2 shows calculated electron energy levels and density of states for (a) tetragonal and (b) cubic clusters with no additive elements or oxygen vacancy (pure clusters). Density of states n(s) was evaluated by overlapping of the Gaussian functions(10) 51

3 548 J. Nucl. Sci. Technol., are also very similar. From these results, we conclude that the calculated electronic structures of these clusters represent that of the actual ZrO2 crystal. In the following, the cubic cluster is mainly used and additive elements or an oxygen vacancy are inserted into this cluster. Fig. 2 Electron energy levels and density of states calculated for (a) tetragonal and (b) cubic clusters These clusters have no additive elements. where el is the energy of the l-th electron level. The width in the Gaussian function was chosen as s=0.5 ev. Electronic structures of tetragonal and cubic clusters are very similar. Because these atomic clusters are pure clusters Eg's, which are defined by the energy difference between the LUMO (Lowest Unoccupied Molecular Orbital) and HOMO (Highest Occupied Molecular Orbital) in this case, correspond to optical gaps of ZrO2. The estimated Eg's are 4.44 and 4.23 ev for tetragonal and cubic clusters, respectively, and these values coincide with the experimental value (4.5 ev)(11). Figure 3 shows the electronic structure of the cubic cluster together with experimental results observed by ESCA(12). The positions of each band are almost the same for calculated and experimental results. Electronic structures of the cubic and tetragonal clusters (2) Fig. 3 Experimental and calculated results of electronic structure of ZrO2 2. Effects of Impurity Levels In this section, impurity levels accompanied by additive elements or oxygen vacancy are estimated, and their effects on the electronic conductivity are discussed. At first, impurity (defect) levels due to an oxygen vacancy were examined. The ZrO2 crystal has a nonstoichiometry and the electron conduction types of ZrO2_. and ZrO2+x are n-type and p-type, respectively(13). The electron conduction type of oxide film on Zr-alloy after a corrosion test has been reported to be n-type(14), so the oxygen vacancy is considered to be the major defect and it plays a key role in the electron conduction of oxide film. Figure 4 shows an electronic structure for a cluster including the oxygen vacancy. Due to the appearance of defect levels, the HOMO is present in the conduction band, i.e. this electronic structure represents n-type electron conduction the same as the experimental results. The energy gap Ea for this cluster (Eg(V0)) is estimated at 0.65 ev. 52

4 Vol. 31, No. 6 (June 1994) 549 Fig. 4 Electron energy levels and density of states calculated for cluster with oxygen vacancy value is quite large compared with Eg(V0). On the other hand, the Eg for the cluster with Li is less than 0.01 ev. Figures 6 and 7 show electron energy levels for the clusters with other 3d-transition metals and alkali metals, respectively. In Fig. 6, energy levels for the pure cluster and the cluster with an oxygen vacancy are also shown. Solid and broken lines in these figures represent occupied and empty levels, respectively. The number of circles on the Electronic structures for clusters including Fe and Li are shown in Fig. 5(a) and (b), respectively. Both show p-type electron conduction (the HOMO is present in the valence band), which reflects the substitution of lower valence elements, Fe and Li, for Zr. However, Eg's for each cluster are very different. The E, for the cluster with Fe is 1.76 ev ; this Fig. 6 Electron energy levels calculated for clusters with 3d-transition metals, together with results for pure cluster and cluster with oxygen vacancy Fig. 5 Electron energy levels and density of states calculated for cluster with Fe and Li Fig. 7 Electron energy levels calculated for clusters with alkali metals 53

5 550 J. Nucl. Sci. Technol., HOMO represents the maximum number of electrons which can occupy this level, and filled circles denote actual electron occupancy in the ground state. When the HOMO is not fully occupied, Eg is defined as the energy gap between the partially and the highest fully occupied level. Energy gaps for each cluster depicted in Figs. 6 and 7 are summarized in Table 2. Table 2 Calculated Eg for clusters with oxygen vacancy or additive elements Figure 8(a), (b) shows calculated force vectors acting on ions in the cluster with (a) Fe and (b) Li. Force vectors are obtained as the differential of the cluster's total energy based on positions of nuclei. In this study, strong repulsive, Coulomb forces act between ions even in the pure cluster because the cluster size is rather small. So, the force vector F shown in Fig. 8 was determined by the following equation, F=F (Cluster with additive element) -F (Pure cluster).(3) Fig. 8 Calculated force vectors acting on ions in cluster with (a) Fe and (b) Li Figure 6 reveals that positions of impurity levels vary systematically with atomic number of additive element. Energy gaps for clusters with 3d-transition metals are all larger than Eg(V0) which governs the electronic conductivity of oxide film. Moreover, these Eg's are too large to cause additional electron conduction. These results suggest that impurity levels due to the introduction of 3d-transition metals in the oxide have little effect on the electronic conductivity of oxide. In contrast to 3d-transition metal, Eg's for clusters with alkali metals are all very small compared with Eg(V0) as shown in Fig. 7 and Table 2. This implies that the electronic conductivity is increased by impurity levels due to the presence of alkali metals in the oxide. 3. Effects of Lattice Strain In the oxide film, lattice strain is expected to be induced around additive elements and the electronic structure is altered by this. Therefore, we estimated the lattice strain caused by 3d-transition metals and alkali metals, and its effects on Eg(V0). In Fig. 8(a), all forces acting on Zr are toward the central Fe, but O experience almost no forces (actually, O experiences a small force directly opposite Fe). These directions of the force vectors are thought to be determined by the following mechanism. With substitution of lower valence Fe for Zr, Coulomb forces between the central Fe and other ions are weakened compared to the pure cluster. So Zr which receives repulsive forces from Fe has forces which are going to be toward Fe, and O which receives attractive forces from Fe has forces which are going to be aways from Fe. The result of Fig. 8(a) shows that the compressive strain is induced around Fe. In contrast to the Fe case, forces arising around Li are at random. This strain may be caused by the Jahn-Teller effect because electron energy levels near the HOMO are very close to each other for alkali metals (cf. Fig. 7). Lattice strains around other 3d-transition metals and alkali metals have almost the same tendency as those around Fe and Li, respectively. 54

6 Vol. 31, No. 6 (June 1994) 551 Figure 9 shows the lattice constant dependency of Eg(V0). Each point in Fig. 9 was obtained by altering the lattice constant of cluster with an oxygen vacancy. The Eg(V0) becomes larger when the lattice constant is smaller, i.e. the electronic conductivity is suppressed when compressive strain acts around the oxygen vacancy. Results of Figs. 8 and 9 suggest that the compressive strain induced by the addition of 3d-transition metals in the oxide makes Eg(V0) of the strained region larger, and suppresses the electronic conductivity of the oxide. As the amount of the strain around the additive element cannot be evaluated quantitatively, the predicted suppression of the conductivity is only qualitative. The effect of random strain arising around alkali metals on Eg(V0) is not clear yet. But the release of degenerated levels and broadening of the band width, caused by the random strain may make Eg(V0) smaller. Fig. 9 Relation between Eg (V0) and lattice constant of cluster N. CONCLUSION Effects of additive elements on the electronic conductivity of zirconium oxide film were estimated by using a molecular orbital method. The energy gap between electronoccupied and empty levels was calculated and the mechanism of the electronic conductivity change by additive elements was discussed qualitatively. The conclusions are summarized here. (1) Impurity levels caused by the addition of 3d-transition metals had little effect on the electronic conductivity of oxide film. (2) The addition of alkali metals increased the electronic conductivity by forming impurity levels that have small Eg. (3) Compressive strain was induced around 3d-transition metals, and this strain decreased the electronic conductivity by making Eg(V0) larger. The mechanism of the electronic conductivity change discussed in this study could explain the favorable effects on the corrosion property of zirconium alloy from addition of Fe, Cr and Ni and undesirable effects by addition Li. REFERENCES (1) KUBO, T., UNO, M.: J. Nucl. Sci. Technol., 28[2], 122 (1991). (2) idem: ASTM STP 1132, 476 (1991). (3) URQUHART, A. W., VERMILYEA, D. A.: J. Nucl. Mater., 62, 111 (1976), (4) ANDERSSON, Th., VESTERLUND, G.: ASTM STP 754, 75 (1982). (5) KOHN, W., et al.: Phys. Rev., 104, A1133 (1965). (6) PLOC, R. A.: J. Nucl. Mater., 61, 79 (1976). (7) GODLEWSKI, J., CADALBERT, R.: A new method of residual stress distribution analysis for corroded zircaloy-4 cladding, Proc. Int. Symp. on Material Chemistry in Nuclear Environment, Tsukuba, Mar. 1992, p. 3. (8) TEUFER, G. : Acta. Cryst., 15, 1187 (1962). (9) PERKINS, R. A., et al.: ASTM STP 1132, 595 (1991). (10) SATOKO, C., TSUKADA, M., ADACHI, H.: J. Phys. Soc. Jpn., 45, 1333 (1978). (11) FRANDON, J., at al. : Phys. Stat. Sol., b98, 379 (1980). (12) TSUDA, N., et al.: J. Phys. Soc. Jpn., 36, 523 (1974). (13) KUMAR, A., RAJDEV, D., DOUGLASS, D.L.: J. Amer. Ceram. Soc., 55, 439 (1972). (14) INAGAKI, M., KANNO, M., MAKI, H.: ASTM STP 1132, 437 (1991). 55

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