Self Diffusion along Dislocations in Ultra High Purity Iron

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(1)Materials Transactions, Vol. 43, No. 2 (2002) pp. 173 to 177 Special Issue on Ultra-High Purity Metals (II) c 2002 The Japan Institute of Metals. Self-Diffusion along Dislocations in Ultra High Purity Iron Yumiko Shima1, ∗1 , Yukio Ishikawa2, ∗2 , Hiroyuki Nitta1, ∗3 , Yoshihiro Yamazaki1 , Kouji Mimura2 , Minoru Isshiki2 and Yoshiaki Iijima1 1 2. Department of Materials Science, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan. Self-diffusion along dislocations in ultra high purity iron containing 0.5–1.2 mass ppm carbon, 0.1–1.0 mass ppm nitrogen and 1.8–4.0 mass ppm oxygen has been studied by the radioactive tracer method with the sputter-microsectioning technique. Below 700 K, the self-diffusion coefficient along dislocations has been determined directly from the type C kinetics classified by Harrison, whereas above 800 K it has been obtained by the type B kinetics assuming that the effective radius of dislocation pipe is equal to 5 × 10−10 m. The temperature dependence of the self-diffusion coefficient along dislocations does not show a linear Arrhenius relation. Below 900 K the Arrhenius plot shows slightly downward curvature. However, above 900 K the self-diffusion coefficient along dislocations increases remarkably with increasing temperature. The value at 900 K is 10−14 m2 s−1 , while it takes 10−10 m2 s−1 at the Curie temperature (1043 K). It seems that the steep increase of the self-diffusion coefficient along dislocations near the Curie temperature is related to the magnetic transformation in ultra high purity iron. (Received August 24, 2001; Accepted November 6, 2001) Keywords: ultra high purity iron, lattice self-diffusion, dislocation self-diffusion, impurity-free dislocation, carbon segregation, pipe diffusion, magnetic effect. 1. Introduction It has been recognized that atomic migration along dislocations in metals is more rapid than through the crystal lattice itself.1) Since all metal crystals contain dislocations, it follows that any measured bulk diffusion rate will in principle always contain a contribution from dislocation diffusion. However, this may be quite negligible for low dislocation densities, and especially so at high temperatures, but it can become important at lower temperatures because of the lower activation energy for dislocation diffusion relative to that for volume diffusion. The high diffusivity along dislocations represents in itself an interesting scientific phenomenon and it plays a role in several important technologies.2) However, our understanding of dislocation diffusion is still unsatisfactory.1, 2) Several experimental studies on the volume and grain boundary diffusion in iron and iron-base alloys have been carried out.3–5) However, experiment on dislocation diffusion in iron as well as other metals is seldom.6) So far, an experimental study on the self-diffusion along dislocations in iron was made by Mehrer and Lübbehusen7) in 1989. Nonmetallic impurities in the iron used in their work were O:25, C:16, S:6 and N:1 mass ppm. Taking into consideration the thermodynamic interaction between a dislocation and the interstitial impurities of the content, these interstitial impurities are supposed to be segregated to the dislocation cores in the iron at their diffusion temperatures. Thus, it can be said that self-diffusion along impurity-free dislocations in iron has not been measured. Recently, using a floating zone refining under reduced pressure with dynamic hydrogen flow, ultra high purity iron with RRRH,0 K :11000 was obtained.8) Using this ultra high purity ∗1 Graduate. Student, Tohoku University, Present address: Tanaka Kikinzoku Kogyo K.K., Atsugi 243-0213, Japan. ∗2 Present address: Sumitomo Electric Industries, Ltd., Itami 664-0016, Japan. ∗3 Graduate Student, Tohoku University.. iron, an experiment on the self-diffusion along impurity-free dislocations in iron has been attempted by the radioactive tracer method with the sputter-microsectioning technique. 2. Experimental Procedure 2.1 Specimen preparation A rod of ultra high purity iron with RRRH,0 K :11000 was obtained by the following way.8) Commercial high purity iron with nominal purity of 99.999 mass% was used as a starting material for floating zone refining. The sample rod of 7 mm in diameter was electrochemically polished prior to floating zone refining. Hydrogen pressure was kept at 0.2 Pa for the 1st to the 5th passes, and furthermore the zone was refined under vacuum at 10−5 Pa for the 6th to the 10th passes. After the zone refining a rod of 5 mm in diameter was obtained. Glow discharge mass spectrometry was used for analysis of metallic impurities. Infrared absorption technique after oxygen combustion method was used to analysis of carbon, while inert gas fusion method was used to analysis of oxygen and nitrogen. The contents of the nonmetallic impurities in the top side of the zone refined iron rod were O:1.8, C:1.2 and N:0.1 mass ppm, and those in the end side of it were O:4.0, C:0.5 and N:1.0 mass ppm. Specimens of 5 mm in diameter and 1 mm in thickness were machined from the rod. The flat face of the specimens was ground on abrasive papers and electropolished at 273 K in an aqueous solution containing 77 vol% acetic acid and 18 vol% perchloric acid. To cause grain growth and to obtain a stress-free surface, the specimens were annealed at 973 K for 86.4 ks in a stream of hydrogen gas purified by permeation through a palladium alloy tube at 700 K. The resultant grain size was about 1 mm. After the grain growth, the specimens were mechanically polished, and some of them were used for diffusion of the type C kinetics. Others were used for diffusion of the type B kinetics after annealing again at 973 K for 14.4 ks in a stream of hydrogen gas.

(2) 174. Y. Shima et al.. and electropolishing in the same conditions mentioned above. 2.2 Diffusion annealing and analysis The radioisotope 59 Fe (γ -rays, 1.095 and 1.292 MeV; half-life, 45.6 d) in a form of FeCl3 in 0.5 kmol m−3 HCl solution was supplied from New England Nuclear Corporation, U.S.A. A few drops of the solution containing the radioisotope was deposited on the mirror-like surface of the specimen and dried under a heating lamp. Then the specimen was diffused at temperatures in the range 623–1053 K for 2.7–328.3 ks in a stream of the purified hydrogen gas in furnaces controlled within ±1 K. To measure the penetration profiles of the radioisotope in the specimen, two types of the serial sputter-microsectioning apparatus were used; the radio-frequency type for long penetration profiles diffused at high temperatures and the ion-beam type for short penetration profiles diffused at low temperatures. The details of the methods were described elsewhere.9, 10) For each specimen 15–40 successive sections were sputtered. A constant fraction more than 60% of the sputtered-off material was collected on an aluminum foil. The intensity of the radioactivity of the isotope in each section was measured by a well-type Tl-activated NaI detector with a 1024-channels pulse height analyzer.. Fig. 1 Examples of penetration profiles for volume self-diffusion in α-Fe.. 3. Results and Discussion 3.1 Volume self-diffusion in ultra high purity iron Firstly, volume diffusion coefficient in ultra high purity iron has been determined. For one-dimensional volume diffusion of a tracer from an infinitesimally thin surface layer into a sufficiently long rod, the solution of the Fick’s second law is given by I (X, t) ∝ C(X, t) = M/ π DV t exp(−X 2 /4DV t), (1) where I (X, t) and C(X, t) are the intensity and the concentration of the radioactivity, respectively, of the tracer at a distance X from the original surface after a diffusion time t. DV is the volume diffusion coefficient of the tracer and M is the total amount of the tracer deposited on the surface before diffusion. Figure 1 shows typical penetration profiles of ln I (X, t) vs. X 2 for the diffusion of 59 Fe in the iron. The linearity observed in Fig. 1 proves that eq. (1) holds, and thus the volume diffusion coefficient was calculated from the slope of the plot. The Arrhenius plot of the diffusion coefficients is shown in Fig. 2, where the open circles show the volume self-diffusion coefficients obtained previously by Iijima et al.11) Their specimen was made by the following way. High purity electrolytic iron was vacuum-melted in an alumina crucible and refined in a hydrogen gas atmosphere of 101 kPa for 900 s and cast into a steel mold 25 mm in diameter after substitution of hydrogen by argon. The ingot was hot-forged and machined to 12 mm in diameter. To cause grain growth and reduce the contents of carbon, nitrogen and oxygen, the rod was annealed in the δ-iron phase region at 1753 k for 86.5 ks in a stream of hydrogen gas purified by permeation through a palladium tube at 700 K and passed through a liquid nitrogen trap. Therefore, the specimens used by Iijima et al. were carefully prepared to reduce the content of impurities at that. Fig. 2 Arrhenius plot of self-diffusion coefficients in α-Fe.. time. The self-diffusion coefficients in α-iron obtained by Iijima et al.11) are well in agreement with those by Hettich et al.12) and by Lübbehusen and Mehrer,13) although their experimental points are not shown in Fig. 2 to avoid intricate plots. As seen in Fig. 2, the diffusion coefficients measured by the present work are in agreement with that by Iijima et al. However, it seems that at lower temperatures the former is.

(3) Self-Diffusion along Dislocations in Ultra High Purity Iron. 175. somewhat smaller than the latter. Further discussion on the effect of purification on the temperature dependence of the volume diffusion coefficient in α-iron should be hold until experimental data on the low temperature region are fully obtained. 3.2 Self-diffusion along dislocations in ultra high purity iron Mathematical analysis of penetration curves for dislocation diffusion is given by LeClaire and Rabinovich.1) This description is based on Smoluchowski’s model, where the average dislocation distance is 2R, and the dislocation cores are represented by cylindrical pipes of radius a, embedded in a matrix with lower diffusivity. Inside the pipes the diffusion coefficient is Dd . Outside the pipes it is assumed that the diffusion coefficient is equal to DV , the value in the crystal lattice. Any influence far from the strain field of the dislocation is neglected in this model. Following Harrison,14) the microstructural quantities R, a, and the average diffusion length √ DV t determine the types of the diffusion kinetics A, B and C. (i) In the type A kinetics, the lattice diffusion distance is much longer than R. In this type, distinct separation of the contribution of dislocation diffusion from the profile is not easy. (ii) In the type B kinetics, diffusion takes place simultaneously from the surface into the bulk and down and out of dislocations √ into the surrounding lattice. When the diffusion length DV t is sufficiently smaller than R, the lateral diffusion zones surrounding the dislocations are not influenced by neighboring dislocations. The penetration profile consists of a nearly Gaussian portion in the near surface region and a tail region. From the slope ∂ ln C/∂ X of the tail region in the penetration profile the product a 2 Dd can be determined in the equation 2 A(α) a 2 Dd = DV − (2) ∂ ln C/∂ X √ where α = a/ DV t and ∞ 2 e−z dz 8 2 A (α) = 2 (3) π 0 z[J02 (zα) + Y02 (zα)] J0 and Y0 being Bessel functions of the first and second kind respectively, of order zero. According to LeClaire and Rabinovitch,1) A(α) depends very weakly on α but that for most practical purposes lies between 0.5–0.8. Numerical values of A(α) has been plotted against α in Ref. 1. In the present experimental conditions of α, A(α) lies in the range from 0.55 to 0.64. Equation (2) also implies that the slope of the tail is practically independent of time as long as the type B kinetics conditions are fulfilled. (iii) In the type C kinetics, lattice diffusion is negligible and a significant transport of matter occurs only within the dislocation pipes. The tail region will vary linearly with the penetration distance squared and the slope yields Dd itself. Figure 3 shows the penetration profiles of ln I (X, t) vs. X for the diffusion at 973, 1033 and 1053 K. The profiles consist of a nearly Gaussian portion in the near surface region and a linear tail region of the type B kinetics. As shown in Fig. 4, in the profiles diffused at 973 K for 1.68 and 67.5 ks, the slope of the tail region is independent of time. Thus, it is confirmed. Fig. 3 Examples of penetration profiles for self-diffusion along dislocations of in α-Fe (type B kinetics).. Fig. 4 Tail slope of the profiles diffused at 973 K for 1.68 and 67.5 ks.. that the conditions for the type B kinetics are satisfied. Furthermore, it can be said that the tails are due to randomly dispersed dislocations and not due to dislocations arranged in small angle grain boundaries.1, 7) The third deeper region observed in Fig. 3 may be due to the grain boundary diffusion, because polycrystal specimens are used in the present experiments. Figure 5 shows the penetration profiles of ln I (X, t) vs. X 2 for the diffusion below 753 K. The linear tail region represents that the profile obeys the type C kinetics. The self-diffusion coefficients along dislocations are calculated from the slope in the tail region in Figs. 3 and 5. For the type B kinetics, the effective radius of dislocation pipe a is assumed to be 5 × 10−10 m which is often used.1, 7) Finally, the.

(4) 176. Y. Shima et al.. Fig. 5 Examples of penetration profiles for self-diffusion along dislocations of in α-Fe (type C kinetics).. self-diffusion coefficient along dislocations Dd is plotted in Fig. 6 along with that obtained by Mehrer and Lübbehusen.7) The volume self-diffusion coefficient of iron is also plotted for comparison. As seen in Fig. 6, the temperature dependence of the self-diffusion coefficient along dislocations does not show a linear Arrhenius relation. Below 900 K the Arrhenius plot shows a slightly downward curvature in contrast to the curvature of the volume diffusion coefficients. Furthermore, in Fig. 6 it is noticed that Dd obtained by the type B kinetics above 853 K links smoothly with Dd obtained by the type C kinetics below 753 K, suggesting that the assumption of a = 5 × 10−10 m is suitable. The self-diffusion coefficient along dislocations obtained by Mehrer and Lübbehusen7) is smaller than that by the present work. The difference between them is only twice at about 900 K. However, it increases up to about two orders of magnitude with decreasing temperature. In the present work, the ultra high purity iron containing gas impurities of 0.5–1.2 mass ppm carbon, 0.1–1.0 mass ppm nitrogen and 1.8–4.0 mass ppm oxygen was used, whereas Mehrer and Lübbehusen7) used also the high purity iron containing gas impurities of 16 mass ppm carbon, 1 mass ppm nitrogen and 25 mass ppm oxygen. Among these impurities, it is known that carbon has relatively strong interaction with dislocation.15) The concentration of carbon C segregated to the dislocation core can be represented by the following equation:15) C=. C 0 exp(w/RT ) [1 + C 0 exp(w/RT )]. (4). where C 0 is the average concentration of carbon in the matrix, w the interaction energy between carbon and dislocation. Fig. 6 Arrhenius plots of self-diffusion coefficients along dislocations in α-Fe.. Fig. 7 Segregation of carbon to dislocation core in α-iron containing 0.5 and 16 mass ppm C.. core. Putting 1×10−19 J/(1 carbon atom)15) into w and 0.5 and 16 mass ppm into C 0 , the concentration of carbon segregated to dislocation core is calculated and the temperature dependence of it is shown in Fig. 7. In the ultra high purity iron used in the present work the segregation of carbon is negligible at high temperatures and even at 600 K it is about 0.2. Therefore, it is recognized that the dislocations in the iron are in a state of impurity-free at least above 700 K. On the other hand,.

(5) Self-Diffusion along Dislocations in Ultra High Purity Iron. in the iron containing 16 mass ppm carbon the segregation of carbon is visible in the whole temperature range of the diffusion experiments by Mehrer and Lübbehusen.7) As shown in Fig. 6, the segregation of carbon retards the self-diffusion along dislocations in iron. Since the segregation of carbon to the dislocation core depends on temperature, as shown in Fig. 7, the surroundings of jumping iron atoms in the dislocation core varies with temperature. Highly segregated state requires higher activation energy for self-diffusion along dislocations. Thus, downward curvature of the Arrhenius plot is observed, especially when carbon starts to segregate very weakly at lower temperatures. Above 900 K the self-diffusion coefficient along dislocations increases remarkably with increasing temperature. The value is 10−14 m2 s−1 , whereas it takes 10−19 m2 s−1 at the Curie temperature (1043 K). This increase near the Curie temperature is anomalously large in comparison with the increase of the volume diffusion coefficient in Fig. 6. It seems that the very large increase of the diffusion coefficient is caused by disappearance of the magnetic moment of iron atoms located at the dislocation core near the Curie temperature. The magnetic moment of atoms is sensitive to the atomic distance. Then, it appears that atoms located at the dislocation core have a large magnetic moment in the ferromagnetic state because the atoms are in a strong compressive strain field. 4. Conclusion Using ultra high purity iron, experiments on the selfdiffusion along impurity-free dislocations in iron have been carried out by radioactive tracer method with the sputter-microsectioning technique. The Arrhenius plot of the self-diffusion coefficient along dislocations below 900 K shows slightly downward curvature. However, above 900 K the self-diffusion coefficient along dislocations increases remarkably with increasing temperature.. 177. Acknowledgements This work was supported by the Iketani Science and Technology Foundation and by the Sasakawa Scientific Research Grant from the Japan Science Society. REFERENCES 1) A. D. LeClaire and A. Rabinovitch: Diffusion in Crystalline Solids, ed. by G. E. Murch and A. S. Nowick (Academic Press, Inc., Orland, 1984) pp. 257–318. 2) P. Shewmon: Diffusion in Solids, 2nd Edition, (TMS, Pennsylvania, 1989) pp. 189–222. 3) Y. Iijima and K. Hirano: Diffusion Processes in Nuclear Materials, ed. by R. P. Agarwala (Elsevier Science Publishers B.V., 1992) pp. 169–200. 4) I. Kaur and W. Gust: in Diffusion in Solid Metals and Alloys, ed. by H. Mehrer, Landolt-Bornstein, New Series, Group 3, Vol. 26, (Springer, Berlin, 1990) pp. 630–716. 5) I. Kaur, W. Gust and L. Kozma: Handbook of Grain and Interface Boundary Diffusion Data, (Zeigler Press, Stuttgart, 1989). 6) A. D. LeClaire: in Diffusion in Solid Metals and Alloys, ed. by H. Mehrer, Landolt-Bornstein, New Series, Group 3, Vol. 26, (Springer, Berlin, 1990) pp. 626–629. 7) H. Mehrer and M. Lübbehusen: Defect and Diffusion Forum 66–69 (1989) 591–604. 8) Y. Ishikawa, K. Mimura and M. Isshiki: Mater. Trans., JIM 41 (2000) 420–424. 9) Y. Iijima, K. Kimura and K. Hirano: Proc. 10th Symp. Ion Sources and Ion-Assisted Technology, ed. by T. Takagi, (Ionics, Tokyo, 1986) pp. 297–302. 10) Y. Iijima, K. Yamada, H. Katoh, J.-K. Kim and K. Hirano: Proc. 13th Symp. Ion Sources and Ion-Assisted Technology, ed. by T. Takagi (Ionics, Tokyo, 1990) pp. 179–182. 11) Y. Iijima, K. Kimura and K. Hirano: Acta Metall. 36 (1988) 2811–2820. 12) G. Hettich, H. Mehrer and K. Maier: Scr. Metall. 11 (1977) 795–802. 13) M. Lübbehusen and H. Mehrer: Acta Metall. Mater. 38 (1990) 283–292. 14) L. G. Harrison: Trans. Faraday Soc. 57 (1961) 1191–1199. 15) H. Kimura: Zairyo Kyodo no Kangaekata (in Japanese), (Agune Gijutu Center, Tokyo, 1998) pp. 157..

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