STUDY ON CORROSION P HENOMENA OF STEELS IN PB-BI FLOW

11 th International Conference on Nuclear Engineering Tokyo, JAPAN, April -3, 3 ICONE11-36375 STUDY ON CORROSION P HENOMENA OF STEELS IN PB-BI FLOW Yingxia Qi Research Laboratory for Nuclear Reactors Tokyo Institute of Technology -1-1, O-okayama, Meguro-ku Tokyo, 15-855, Japan Phone: 81-3-5734-957 Fax: 81-3-5734-959 e-mail: qiyingia@nr.titech.ac.jp Minoru Takahashi Research Laboratory for Nuclear Reactors Tokyo Institute of Technology -1-1, O-okayama, Meguro-ku Tokyo, 15-855, Japan Phone: 81-3-5734-957 Fax: 81-3-5734-959 e-mail: mtakahas@nr.titech.ac.jp Keywords: Corrosion, Stainless Steel, Liquid Pb-Bi Metals, ab initio Calculation, Test ABSTRACT The corrosions of structure materials such as stainless steel in liquid Pb-Bi metals are a big obstacles for the application of the liquid Pb-Bi into the fast breeder reactors as the coolants. The present work is trying to seek the atomic mechanism of the corrosion phenomena from the point-of-view of interatomic interactions. The interatomic potential energies are calculated by the ab initio method vs. interatomic distance. From the interatomic potential energies, it is cleared that Fe atoms in the pure perfect iron crystals don t diffuse mutually with liquid Pb-Bi atoms. However, Pb atoms may penetrate into the void sites of the crystals of iron through grain boundaries as that the attractive forces from Fe are larger that that from Pb-Bi atoms. Thus, the very small solubility of Fe in liquid Pb-Bi metals may be due to the crystal defects or some accidental reasons. In SUS316, as the larger cohesive forces between Ni and Pb, Bi atoms, t he corrosions of SUS316 in liquid Pb -Bi metals are mainly caused from the mutual diffusions between Ni and Pb-Bi atoms. Also, as the attractive forces from Cr atoms, Pb atoms are easily to penetrate into the SUS316 in addition to the attractive forces from Fe atoms. As a result, with the time evolving, Ni and Cr atoms dissolve gradually into the liquid Pb-Bi metals, while Pb and Bi atoms penetrate into the solids gradually. The corrosion test results verify very well the analytical results based on the calculated interatomic potential energies.. 1. INTRODUCTION Lead-bismuth eutectic (Pb-Bi) has been expected to be one of the candidates of the target of accelerator-driven nuclear transmutation systems (ADS) and the coolant s of the fast breeder reactors (FBR). One of the key issues for the application of Pb-Bi to the systems is the compatibility of the proton beam windows of the ADS and the structural and core materials of the FBR with high temperature Pb -Bi melt. Virtually, the corrosions of solid metals in liquid metals are caused from the motions of their atoms forced by the interatomic interaction forces. The interaction forces between the atoms are dependent upon the species of the atoms available. Here, the functions of the interatomic potential energy vs. interatomic distance for the atoms of steels and Pb -Bi metals are calculated by the ab initio method. The corrosion phenomena happened between the two 1 Copyright 3 by JSME

metals can be predicted and explained by the interatomic potential energy functions. The details will be discussed in the following sections.. ab initio METHOD The potential energy for the two isolated atoms is defined as eq. (1): n n 1 e Z1e Z e Z1Ze φ ( r1) = + +, i j 1 r ij i 1 ri 1 r = = i r1 (1) where, Z is atomic number, r1 the distance between the two nuclei, n the number of the elect ron of the atom, ri the position of the electron i, rij the distance between the electron i and j. The solution of eq. (1) is through the solution of the wavefunction ψ of the electrons of the two atoms. The Schrödinger s equation about ψ is defined as eq. (). ψ + ( / ) E φ( r ) ( ) ψ = m h, () where E is the total energy of the system, ψ the electronic wavefunction including both space and spin variables, φ(r) the potential energy function. The detail solution of the Schrödinger s equation can be referred to the special books about quantum chemistry and mechanics. Here, we use the available code Gaussian 98 [1] developed originally by Carnegie Mellon University to calculate the potential energy function in eq. (). 3. INTERACTION BETWEEN PURE IRON AND PB-BI. The potential energy functions between two atoms are calculated by the ab initio method. As it is unknown how the electrons of the two atoms dispose between the two nuclei, the potential energy functions are calculated under the possible spin multiplicities. The spin multiplicity is defined as S = n s + 1 (3) 1 where s = ±1/, n is the total valence electrons in the outmost shells of the two atoms. For α electrons, s = 1/ while for β electrons, s = -1/. One α and a β electrons comprise an antiparallel pair with s =. When the electrons between the two atoms comprise more pairs, S will be smaller, the cohesive energies between the two atoms are stronger. Conversely, when the electrons between the two atoms can t be paired, S will be larger, the cohesive energies between the two atoms are weaker. The possible spin multiplicities are determined by the valence electrons of the atoms. The calculated potential energy functions between Fe atoms are shown in Fig. 1. Here it should be noted that the possible spin multiplicities S are 13 and 17 as only under these spin multiplicities, the potential energies can be given a convergent value over a large range of the interatomic distances. Moreover the curves of the potential functions are continuously smooth and approach to zero at the large interatomic distances as shown in Fig. 1. The case S=17 means that all of the eight valence electrons of Fe atom don t pair up with the another s, while S=13 means that the two electrons of one Fe atom are paired up with the two electrons of the another Fe atom. Potential energy (ev) - S=13 S=17 V eff Fe-Fe - Fig. 1 Potential energy functions for Fe-Fe atoms. It has been found that the effective potential function V eff is obtained by the fractional average of the potentials S=13 and S=17 as the following: V, a < 1. eff = avs = 13 + ( 1 a ) VS=17 The criteria for the effective potential function are the experimental data such as the crystal structure, the melting temperature of the solid iron, the self-diffusivity and the atomic pair distribution functions of the liquid iron. From Fig. 1, we can see that there is a well below zero in the potential energy functions. The minimum position of the well is approximately equal to the nearest-distance between the atoms. From the point-of-view of the molecular dynamics, the interatomic forces between the two atoms are derived from the derivatives of the potential functions as equation (4): F = ( r) φ r, (4) Therefore, the attractive forces exert bet ween the atoms at the rights of the minimum position while the repulsive forces exert at the left of the minimum position. Usually, the deeper of the well of the potential energy function, the larger the attractive forces, and the larger the cohesive energy between the Copyright 3 by JSME

two atoms. For the potential energy function of S=13, only the repulsive forces exist with the attractive forces are nearly zero. In the following discussions, the forces between the two atoms will be compared by the depth of the well of the potential energy functions...1 -.1 Pb-Bi Pb-Pb Bi-Bi Pb-Bi -. Fig. Effective potential functions for Pb -Bi metals. In Fig., the calculated effective potential functions for Pb liquid metals, Bi liquid metals and Eutectic Pb-Bi liquid metals are expressed. The criteria for the potentials are the experimental data of the self-diffusivity and the atomic pair distribution functions of these liquid metals. By comparison of the well depth of the effective potential function curves in Fig. 1 and Fig., it can be seen that the cohesive forces for Fe-Fe atoms are stronger than for Pb-Bi atoms from the depth of the well. This is in agreement with the fact that the melting temperature of iron metals are higher than Pb, Bi and eutectic Pb-Bi metals. The calculated potential energy functions for Fe-Pb atom pair and Fe-Bi atom pair are shown in Fig. 3 and 4, respectively. - S=7 S=11 S=13 Fe-Pb - Fig. 3 Potential energy functions for Fe-Pb atoms. The possible spin multiplicities for Fe-Pb atom pair are S=7,11,13. Of them, obviously, the cohesive forces for S=7 are largest. However, for Fe-Bi atom pair, just S=8 is possible. Fe-Bi S=8 - Fig. 4 Potential energy functions for Fe-Bi atoms. In Fig. 3, the potential energy function of S=7 is considered to be appropriate, because the minimum position of the well is nearly equal to the distance of the addition of Fe and Pb atom radius. At this case, the spin multiplicity S=8 for Fe-Bi atoms is just 1 higher than S=7 for Fe-Pb atoms, being consistent with that the atomic number of Bi is 1 larger than Pb atom. - Fe-Fe Pb-Bi Pb-Pb Bi-Bi Fe-Bi Fe-Pb - Fig. 5 Comparison of the potential functions for Fe-Fe, Pb-Bi, Fe-Pb and Fe-Bi atoms. Table 1 Comparisons of well depth of the potential functions for Fe-Fe, Pb-Bi, Fe-Pb, Fe-Bi atoms Fe-Fe Pb-Bi Fe-Pb Fe-Bi depth (ev) -.6 -.1 -.3. The comparisons of the potential energy functions for Fe, Pb-Bi metals and Fe-Pb, Fe-Bi atoms are shown in Fig. 5. The comparisons of the well depth of the potential functions are shown in Table 1. From Fig. 5 and Table 1, it can be known that the cohesive forces between Fe-Pb and Fe-Bi atoms are smaller than that between Fe-Fe atoms. Therefore, it is very difficult for Fe atoms in iron metals to dissolve into liquid Pb-Bi through the attract ive forces from Pb and Bi atoms by broking the cohesive forces between Fe-Fe atoms. In fact, according to ref. 4, the solubility of Fe in liquid Pb and Bi is very small, 8.5 1-4 at.% Fe and 1.83 1 - at.% Fe at 873K, respectively. 3 Copyright 3 by JSME

However, the cohesive forces between Fe-Pb atoms are larger than that between Pb-Bi atoms. Therefore it is possible for Pb atoms to penetrate into the iron crystals by the attractive forces from Fe atoms when the void sites are available in the crystals. And as the cohesive forces between Pb-Bi atoms are slight larger than that between Bi-Bi atoms, Bi atoms will also possibly penetrate into the iron crystals by accompanying Pb atoms. That is, the corrosions of solid iron in liquid Pb -Bi are almost caused from the penetration of Pb and Bi atoms into the iron crystals. As the cohesive forces near the grain boundary are usually weak, the routes of penetration should be along the grain boundaries. The corrosion processes of solid Fe in liquid Pb -Bi are simulated by molecular dynamics method using the potential functions in Fig. 5. The simulated iron solid has a perfect crystal lattice with two sides of the free surfaces immerged in a liquid Pb -Bi as shown in Fig. 6. After a short time of the relaxing process, with running 1 step at time step of fs at 8K, the system reached the configuration as shown in Fig. 6. It can be seen that iron crystal wasn t destroyed at all, and no iron atoms dissolving into the liquid Pb-Bi. liquid Pb-Bi iron crystals liquid Pb-Bi Fig. 6 Snapshots of perfect crystal iron in liquid Pb -Bi. However, even though the solubility of solid Fe in liquid Pb-Bi is very small, there should be a small amount of Fe atoms dissolved into the liquid Pb-Bi. This may be caused by some lattice-defects, surface-defects and grain boundary which often occur in the practical iron crystals. 4. INTERACTION BETWEEN STAINLESS STEEL AND LIQUID PB-BI The calculated potential energy functions for Cr-Pb, Cr-Bi and Ni-Pb, Ni-Bi atom pairs are shown in Fig. 7, 8, 9 and 1, respectively. It is considered that the depth of the well in the potential functions is related with the solubility of one specie in another specie. The deeper of the well, the larger the solubility. In Fig. 7, for Cr-Pb atom pairs, the potential function for spin multiplicity S=9 is considered to be appropriate as of the same reason for Fe-Pb atom pair. In Fig. 8, for Ni-Pb atom pair, the potential function for spin multiplicity 5 is considered to be appropriate as the solubility of Ni in liquid Pb is about 3 at. % Ni at 643K [5] which is not very small, in addition to the same reason for Fe-Pb atoms. - S=9 S=11 S=13 Cr-Pb - Fig. 7 Potential energy functions for Cr-Pb atoms. - - Ni-Pb S=3 S=5 S=7 S=9 S=11 - Fig. 8 Potential energy functions for Ni-Pb atoms. In Fig. 9, the potential energy function for Cr-Bi atom pair is shown. The result of no cohesive forces between Cr and Bi atoms is inconsistent with the experimental results that Cr and Bi metals are immiscibility in both the liquid and the solid state [5]. - Cr-Bi S=1 - Fig. 9 Potential energy functions for Cr-Bi atoms. In Fig. 1, for Ni-Bi atoms, the potential function for spin multiplicity S= is considered to be 4 Copyright 3 by JSME

appropriate because it has been known that the chemical compounds are formed between Ni and Bi atoms as NiBi 3 or NiBi. The minimum position of the well for S= potential function is nearly equal to the interatomic distance between Ni and Bi atoms. - S= S=6 S=8 S=1 Ni-Bi - Fig. 1 Potential energy functions for Ni-Bi atoms. - Cr-Pb Ni-Pb Cr-Bi Ni-Bi - Fig. 11 Comparison of the potential functions of Cr-Pb, Ni-Pb and Cr-Bi, Ni-Bi atoms Table Comparisons of well depth of the potential functions for Cr-Pb, Ni-Pb, Cr-Bi, Ni-Bi atoms Cr-Pb Ni-Pb Cr-Bi Ni-Bi depth (ev) -.4 --.37. -.86 The comparisons of the selected potential functions for Cr-Pb, Ni-Pb and Cr-Bi, Ni-Bi atoms are shown in Fig. 11, and the well depths of these curves are shown in Table. From Fig. 5 and 11, it is known that the potential function shape for Cr-Bi atoms is similar to that for Fe-Bi atoms, no cohesive forces between these atom pairs. As the chemical reaction between Ni and Bi atoms, it can be predicted that Ni and Bi atoms will mutually diffuse into each other. This will be a most important factor for the corrosion of the stainless steel in liquid Pb -Bi metals. Besides, it is possible for Pb atoms to penetrate into the crystals because of the attractive forces from Cr and Ni atoms in addition to Fe atoms. Whether Cr atoms dissolve into the liquid Pb-Bi metals is determined by if the cohesive forces between Cr-Pb atoms are larger than between Cr-Fe atoms. If we suppose that the cohesive forces between Cr-Fe atoms are smaller than between Cr-Pb, Cr atoms will dissolve into the liquid Pb-Bi metal s. Due to the lattice voids in the steel crystals formed by the dissolved Ni and Cr atoms, Fe atoms will transfer within these voids and very small of them may diffuse into the liquid Pb-Bi metals. Conclusively, the corrosions of the stainless steel will evolve with the Ni and Cr atoms dissolving into the liquid Pb-Bi metals and Pb and Bi atoms penetrating into the crystals. However, Fe atoms almost stay in the crystals.. 5. CORROSION TEST The corrosion test of SUS316 in a Pb-Bi flow was conducted for 1 hrs in our lab [6]. The contents of elements in SUS316 are listed in Table 3. The working fluid was 45%Pb-55%Bi alloy with the melting point of 398K. The test pieces were 15 mm wide, 1 mm long and mm thick. Two Pb -Bi flow channels above and below the test pieces were 13 mm wide, mm high and 45 mm long. The liquid metal was circulated and heated up to 673K in the cold section from the cooler to the heater and to 83K in the hot section from the heater to the cooler including the test section. From Fig. 1, it could be found that two layers are observed over the steel base in SEM analysis, i.e., a thick adherent Pb-Bi layer that covered the steel surface and a damaged layer ~1µm in depth inside the steel base. By Comparison of the counts of Ni, Cr and Fe atoms over the layer of adherent Pb-Bi, it is clearly known that there are more Ni atoms dissolved into the liquid Pb-Bi, less are Cr atoms while Fe atoms are lest. These experimental results are in good agreement with the analytical results discussed in the last section. Observing the counts of Pb and Bi atoms over the damaged layer, it is known that Pb and Bi atoms penetrated into the steel base. These results are in good agreement with the predictions discussed above. The interesting matter is that the counts of Fe atoms over the damaged layer. It is not continuous for the counts vs. position. In some place, the counts are higher than the original while some place are very low. This may be interpreted as that Fe atoms transfer within the voids formed by the dissolved Ni and Cr atoms to accumulate, leaving the other place fewer atoms. At the interface between the damaged layer and the adherent Pb -Bi layer, only the counts of Fe atoms decrease sharply, indicating that Fe atoms don t diffuse in Pb-Bi met als. This confirms again the ab 5 Copyright 3 by JSME

initio calculation results discussed above. Table 3 Contents of elements in SUS316 Cr Ni Mo Mn Si 16-18 1-14 -3 <. <.1 steel damaged adherent [3]. Y. Waseda, The Structure of Non-crystalline materials, McGraw-Hill International Book Company. [4]. O. Kubaschewski, IRON-Binary Phase Diagrams, Springer-Verlag Berlin Heidelberg New York (198). [5]. Hansen, Constitution of Binary Alloys (1958). [6]. M. Takahashi, et al, Experimental Study on Flow Technology and Steel Corrosion of Lead-Bismuth, Proc. of 1 th International Conference on Nuclear Engineering. Counts 1 3 1 Ni 1 Pb 1 Bi 1 3 4 5 6 Distance (µm) Fig. 1 Result of SEM and EDX analyses for SUS316 Cr Fe 6. CONCLUSIONS Theoretically, Fe atoms in the perfect crystals don t dissolve into liquid Pb-Bi atoms. But Pb atoms may penetrate into the crystals due to the crystal defects such as lattice-defects, surface-defects and grain boundary. For SUS316, it is verified that the corrosions are mainly caused from the diffusions of Ni and Cr atoms and the penetrations of the Pb and Bi atoms from the analytical and experimental results.. REFERENCES [1]. J. B. Foresman and A. E. Frisch, Exploring Chemistry with Electronic Structure Methods: A Guide to Using Gaussian, Gaussian, Inc. (1993). []. F. Shimojo et al., J. Phys. Soc. of Japan 63, 141 (1994). 6 Copyright 3 by JSME