PERGAMON Solid State Communications 111 (1999) 613–618 In situ Mössbauer-effect study of the kinetics of the s-phase formation J. Cieślak a, S.M. Dubiel a,*, B. Sepiol b a Faculty of Physics and Nuclear Techniques, The University of Mining and Metallurgy (AGH), al. Mickiewicza 30, PL-30-059 Kraków, Poland b Institut für Materialphysik, Universität Wien, Strudlhofgasse 4, A-1090 Vienna, Austria Received 1 March 1999; received in revised form 6 April 1999; accepted 20 May 1999 by M. Grynberg Abstract Kinetics of the s-phase formation promoted by an isothermal annealing at T ˆ 600 and 7008C was investigated in a polycrystalline alloy of Fe53.8Cr46.2 –0.1 at.%Ti by means of the in situ 57Fe Mössbauer-effect measurements. It is demonstrated that the kinetics can be obtained from the temperature dependence of the average isomer shift. Using this new approach, the activation energy was evaluated as equal to 109.8 kJ/mol. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Magnetically ordered materials; D. Phase transitions; E. Nuclear resonances The s-phase was found in over 50 binary transitionmetal alloys [1]. It is of great interest for both scientific and technological purposes. The former is related to gathering knowledge of physical properties of the phase, and, in particular those involved in the mechanisms of its formation. The latter originates from the fact that the s-phase often occurs in materials that are technologically important and its presence drastically deteriorates their properties. One class of such materials is high-chromium steels, which have superior creep- and heat-resistant properties and, consequently, they have found a wide application in various branches of industry, e.g. in oil refineries and nuclear power plants. The steels are composed of over 95% of Fe–Cr alloy, hence the alloy has been regarded as a model system for the investigation of the s-phase [2–5]. It can be 100% transformed into the s-phase by annealing, provided the chromium * Corresponding author. Tel.: 1 48-12-33-37-40; fax: 1 48-1234-00-10. E-mail address: dubiel@novell.ftj.agh.edu.pl (S.M. Dubiel) content lies within the range of 45–50 at.% and the annealing temperature, T, 773 K # T # 1110 K [6]. In this communication we report a new approach to the investigation of the kinetics of the s-phase formation. The approach will be presented in the context of the in situ Mössbauer-effect study of an alloy of Fe53.8Cr46.2 –0.1 at.%Ti. The alloy was prepared by melting appropriate amounts of iron (99.95% purity), chromium (99.5% purity) and titanium (99.9% purity) in a vacuum induction furnace. The ingot received was next cut into cubes of 5 × 5 × 5 mm 3 size, which were then homogenized by vacuum annealing for 24 h at T ˆ 12008C followed by water quenching. Chemical composition was measured on the homogenized sample by an electron probe microanalysis (EPMA) as well as by chemical analysis (CHA). The former yielded for the concentration of Ti the value of 0.1 at.% (as the average over five values found in various places across the sample), while the value of 0.4 at.%Ti was obtained by CHA. The difference may be due to the fact that CHA gives the total Ti content 0038-1098/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00259-8 614 J. Cieślak et al. / Solid State Communications 111 (1999) 613–618 Fig. 1. 57Fe Mössbauer spectra recorded in situ at T ˆ 7008C on an Fe53.8Cr46.2 –0.1 at.%Ti sample: (a) (100% a); (b) s 1 a†;and (c) (100% s). The solid lines represent the best-fits to the data. irrespective of its form, while EPMA supplies the information on Ti in solution. For the in situ Mössbauer-effect measurements the sample was first rolled down to a thickness of ca. 30 mm and then it was vacuum annealed at 9008C for an hour to remove the strain. The measurements themselves were carried out in a vacuum furnace at two different temperatures, T ˆ 600 and 7008C. The spectra were automatically recorded every 15 min. After the measurements at 7008C were completed, a Mössbauer spectrum was recorded at room temperature. Its shape and the values of the spectral parameters gave evidence that it was 100% due to the s-phase. A typical spectrum characteristic of the a-phase as recorded at 7008C is shown in Fig. 1(a). As can be seen it has a shape of a single line because the sample is in the paramagnetic state, has a cubic symmetry and there is one Fe site only. The spectrum characteristic of the s-phase is illustrated in Fig. 1(c). Although the sample is also in the paramagnetic state, its spectrum exhibits in this case some structure because the symmetry of the sample is lower than cubic (tetrahedral) and there are five different Fe sites. The spectrum shown in Fig. 1(b) reflects a two-phase state of the sample and it has features characteristic of the spectra recorded for the pure phases. All the spectra were analyzed in terms of the distribution of the isomer shift, IS. Those derived from the spectra shown in Fig. 1 are displayed in Fig. 2. By integration of the P(IS)-curves, the average isomer shift, kISl was derived kISl ˆ Z P IS† dIS: 1† The kISl-values obtained in this way from the spectra recorded at 7008C are plotted in Fig. 3. As can be clearly seen they reproduce the behavior expected for the Arrhenius-like law, so they were fitted in terms of the Johnson–Avrami–Mehl (JAM) approach kISl ˆ ISa 2 ISs †exp 2 kt†n † 1 ISs ; 2† Table 1 The best-fit values for k and n parameters in the Johnson–Avrami– Mehl equation Fig. 2. The distributions of the isomer shift derived from the spectra shown in Fig. 1. The labels correspond with those in Fig. 1. Method k × 103 (min 21) n Isomer shift Spectral area 2.71 2.59 2.67 2.58 J. Cieślak et al. / Solid State Communications 111 (1999) 613–618 615 Fig. 3. The average isomer shift (relative to the 57Co/Rh source), kISl; vs. measuring time, t, as obtained from Eq. (1). The solid line represents the best-fit in terms of Eq. (2). where k is a time constant, n is the form factor and ISa, ISs are isomer shifts for a- and s-phases, respectively. The best-fit to the data is represented by a solid line in Fig. 3, and the best-fit values of the parameters obtained are displayed in Table 1. To verify whether or not there is one-to-one correspondence between the kinetics of the a–s-phase transformation as yielded by the above-presented approach and the traditional one, i.e. in terms of the spectral area, the spectra were analyzed in the latter way, too. It was assumed here that the amount of the s-phase precipitated, As, was equal to the relative spectral area ascribed to that phase As ˆ Ss 100 ˆ 100 1 2 exp 2 kt†n ††; S a 1 Ss 3† where Sa is a spectral area due to the a-phase, and Ss the one due to the s-phase. The As-values obtained from Eq. (3) are presented in Fig. 4 together with the best-fit curve. The best-fit values of k and n yielded are shown in Table 1, too. It is obvious that the results obtained with both approaches agree well with each other which proves that there is one-to-one correspondence between the average isomer shift and the Fig. 4. The relative amount of the s-phase, As, as obtained from the spectral area vs. the measuring time, t. The solid line represents the best-fit in terms of Eq. (3). 616 J. Cieślak et al. / Solid State Communications 111 (1999) 613–618 Fig. 5. The average isomer shift, kISl, vs. measuring time, t, derived from Eq. (1) for the spectra measured at T ˆ 7008C (open squares) and at T ˆ 6008C (open circles). The solid lines represent the best-fits in terms of Eq. (2). Fig. 6. The fraction of the s-phase, As, vs. measuring time, t, as determined from the spectral area of the spectra measured at T ˆ 7008C (open squares) and at T ˆ 6008C (open circles). The full circle represents the value of As found from the spectrum recorded at room temperature. spectral area of the s-phase. The advantage of the approach proposed here, in terms of the average isomer shift used to investigate the kinetics of phase transformation, stems from the fact that it is a much Table 2 The best-fit values for k and n parameters in the Johnson–Avrami– Mehl equation Method T (8C) k × 103 (min 21) n Isomer shift Spectral area Isomer shift Spectral area 700 700 600 600 2.71 2.59 0.57 0.55 2.67 2.58 2.53 2.76 more reliable way of spectral analysis, especially in cases like the present one when the spectral parameters of the subspectra are similar. In order to get information on the activation energy, E, a second series of in situ measurements was performed at 6008C. The spectra were analyzed both in terms of the average isomer shift as well as in terms of the spectral area. Fig. 5 illustrates the results obtained with the former method and Fig. 6 those with the latter. In addition, the data derived from the room temperature spectrum measured on the sample annealed at 6008C (full circle) were added for comparison. It is clear that they agree well with those J. Cieślak et al. / Solid State Communications 111 (1999) 613–618 617 Fig. 7. The fraction of the s-phase, As, determined from the spectral area of the spectra recorded at T ˆ 7008C as a function of measuring time, t. Open symbols represent the data obtained assuming fs ˆ fa , while full symbols stand for the data obtained assuming fs ˆ 1:15fa . The full lines illustrate the best-fits in terms of the JAM-equation. derived from the corresponding in situ spectrum. The best-fit parameters are shown in Table 2. Assuming the phase transformation follows the Arrhenius law, i.e.   E ; 4† k ˆ k0 exp 2 RT where R is the gas constant, and using for k the values from Table 2, the activation energy E ˆ 109:8 kJ/mol was derived from the isomer shift approach, and E ˆ 109:6 kJ/mol from the spectral area. For comparison, E ˆ 137 kJ/mol was reported in Ref. [7] and E ˆ 193 kJ/mol in Ref. [8], both for undoped Fe–Cr alloys. As we have recently found [9], addition of 0.1 at.%Ti to Fe–Cr decreases E by 14 kJ/mol. In addition, the activation energy strongly depends on the size of grains [10], so the difference between the presently found value of E and those reported in literature may be accounted for by the various microstructures of the samples. Finally, it should be mentioned that the present study gives us a chance to verify whether or not the Mössbauer–Lamb factor, f, at elevated temperatures, Table 3 The best-fit values of k and n parameters in the JAM-equation Method k × 103 (min 21) n No correction With correction 2.59 2.50 2.58 2.61 the same for the s- and the a-phase. The spectral area is proportional to f, so if fs ˆ fa ; the spectral area of the spectrum shown in Fig. 1(a), Sa, should be the same as the one of that shown in Fig. 1(c), Ss. The analysis of the two spectra yielded Ss =Sa ˆ 1:15: This means that fs ˆ 1:15fa : The result seems to be reasonable as Fe atoms in the s-phase are more closely packed than those in the a-phase (the packing factor for the former is 0.69 against 0.68 for the latter). Consequently, the amount of the s-phase determined from the Mössbauer spectra at 7008C is overestimated by ca.15%. In studying the a–s-phase transformation one should then correct for that factor. To see how much it influences the present case, we compare in Fig. 7 the data obtained without (open circles) and with the correction (full circles). The best-fit parameters obtained—see Table 3—give evidence that the correction in this case can be neglected. In conclusion, we would like to stress that in situ Mössbauer-effect measurements are advantageous in comparison with the traditional measurements performed at RT, when investigating the kinetics of phase transformations. The main advantage follows from the fact that the former is much quicker and more economic (it requires only one sample for one T). We have also demonstrated that the analysis of the spectra in terms of the average isomer shift instead of the spectral area can be well used in such studies. 618 J. Cieślak et al. / Solid State Communications 111 (1999) 613–618 Acknowledgements One of us (SMD) wishes to thank the State Research Committee (KBN), Warsaw for a financial support. References [1] E.O. Hall, S.H. Algie, Metall. Rev. 11 (1966) 61. [2] Ying-Yu Chuang, Jen-Chwen Lin, Y. Austin Chang, Calphad 11 (1987) 57. [3] A. Gupta, G. Principi, G.M. Paolucci, Hyperf. Inter. 54 (1990) 805. [4] B.F.O. Costa, S.M. Dubiel, Phys. Stat. Sol. (a) 139 (1993) 83. [5] M.H.F. Sluiter, K. Esfarjani, Y. Kawazoe, Phys. Rev. Lett. 75 (1995) 3142. [6] O. Kubaschewski, Iron Binary Phase Diagrams, Springer, Berlin, 1982. [7] W.A. Dench, Trans. Faraday Soc. 59 (1963) 1279. [8] H. Kuwano, Trans. Jpn. Inst. Met. 26 (1985) 482. [9] A. Blachowski, J. Cieslak, S.M. Dubiel, B. Sepiol, Phil. Mag. Lett. 79 (1999) 87. [10] A. Chiba, Trans. Jpn. Inst. Met. 25 (1984) 523.