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Influence of atomic ordering on sigma phase precipitation of the Fe50Cr50 alloy
Journal of Alloys and Compounds 644 (2015) 1009–1012
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Influence of atomic ordering on sigma phase precipitation of the Fe50Cr50 alloy G.Y. Vélez a,b,⇑, G.A. Pérez Alcázar a a b
Universidad del Valle, Departamento de Física, A.A. 25360 Cali, Colombia Instituto de Física, Universidad Autónoma de San Luis Potosí, avenida Manuel Nava 6, zona universitaria, 78290 San Luis Potosí, SLP México, Mexico
a r t i c l e
i n f o
Article history: Received 11 December 2014 Received in revised form 14 April 2015 Accepted 2 May 2015 Available online 8 May 2015 Keywords: Fe–Cr alloys Sigma phase Atomic ordering Mössbauer spectroscopy
a b s t r a c t In this work we report a study of the kinetic of the formation of the r-Fe50Cr50 alloy which is obtained by heat treatment of a-FeCr samples with different atomic ordering. Two a-FeCr alloys were obtained, one by mechanical alloying and the other by arc-melting. Both alloys were heated at 925 K for 170 h and then quenched into ice water. Before heat treatment both alloys exhibit a-FeCr disordered structure with greater ferromagnetic behavior in the alloy obtained by mechanical alloying due to its higher atomic disorder. The sigma phase precipitation is influenced by the atomic ordering of the bcc samples: in the alloy obtained by mechanical alloying, the bcc phase is completely transformed into the r phase; in the alloy obtained by melted the a–r transformation is partial. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction The Fe–Cr binary system exhibits special interest in the materials industry mainly due its high corrosion resistance as well as its mechanical strength [1,2]. The majority of the studies related to this system are performed near to the equiatomic region since in this region the r-FeCr phase is precipitated which deteriorates the mechanical properties of the alloy [3]. Sigma structure is obtained at about 50% at. Cr and for temperatures between 800 and 1100 K. Above of this miscibility gap the alloy is solid and disordered, below, the alloy is composed of iron-rich as well as chromium-rich clusters, both with bcc A2 structure [4–6]. Sigma phase has tetrahedral structure with 30 atoms in its unitary cell, which are distributed among five crystallographically non-equivalent sites named A, B, C, D and E with occupancy numbers 2, 4, 8, 8 and 8, respectively. A and D sites are preferably occupied by iron atoms, while sites B, C and E are preferentially occupied by chromium atoms [6–9]. One of the main goals of stainless steels production based on Fe–Cr alloys with concentrations near to 50% at. Cr, is to retard the precipitation of sigma structure when the material is subjected to high temperatures. The occurrence of this structure is not immediate, experimental studies have shown that the heating time
⇑ Corresponding author at: Instituto de Física, Universidad Autónoma de San Luis Potosí, avenida Manuel Nava 6, zona universitaria, 78290 San Luis Potosí, SLP México, Mexico. Tel.: +52 444 8262362; fax: +52 444 8133874. E-mail address: [email protected] (G.Y. Vélez). http://dx.doi.org/10.1016/j.jallcom.2015.05.004 0925-8388/Ó 2015 Elsevier B.V. All rights reserved.
necessary to completely precipitate the structure may vary from a few days to several weeks depending of the heating temperature [6,8–11]. The purity of the alloy as well as the presence of carbon in small amounts retards the formation of the sigma phase [12]. In contrast, the addition of titanium favors its formation [13,14]. Considering that the sigma structure exhibits a substantial atomic order, it is possible that the kinetics in the formation of this structure depends on the degree of atomic order of bcc-FeCr alloy before heating. To test this hypothesis we obtained r-Fe50Cr50 samples which were precipitated from a-FeCr samples obtained by two different techniques, mechanical alloying (MA) and arc-melting. The investigation is performed by means of X-rays diffraction (XRD) and Mössbauer spectroscopy (MS). 2. Experimental procedure
a-Fe50Cr50 samples were initially synthesized by two different techniques, mechanical alloying and arc-melting. As precursor material was used in both cases, high-purity fine powder of iron and chromium. MA was carried out in a high energy planetary mill Fritsch-Pulverisette 5 with milling time of 10 h. The millings were realized at 280 rpm. Average vacuum inside of the jars was 4.5 105 bar, a ratio between balls and power mass of 20:1, and the ball diameter of 10 mm. Casting was carried out under argon atmosphere. Melted tablet was obtained by elemental mixture of the precursor powders (3 g in total) and compacted in a hydraulic press at 206 bars for 1 min. Both samples were heated at 925 K for 170 h and then quenched into ice water. The characterization of the samples before and after the heat treatment (HT) was performed by XRD and 57Fe MS. Diffraction measurements were performed in a powder diffractometer with Cu Ka radiation. The diffraction patterns were refined with the GSAS program using the Rietveld method. From the refinement of the XRD patterns it were explicitly obtained the structure of the samples, the
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G.Y. Vélez, G.A. Pérez Alcázar / Journal of Alloys and Compounds 644 (2015) 1009–1012
Fig. 1. XRD pattern of the Fe50Cr50 samples before HT.
values of their respective lattice parameter and average crystallite size in the perpendicular direction to the X-rays [15]. Mössbauer spectra were collected at room temperature in the transmission mode using a conventional spectrometer. The fit of the spectra were performed with the MOSFIT program [16]. The isomer shift (IS) of all components that constitute the different spectra are reported with reference to a-Fe.
3. Experimental results In Fig. 1 are illustrated the XRD patterns of the FeCr alloy obtained by MA and arc-melting. The refinement results show that both alloys exhibit only the bcc structure with similar lattice parameter (2.879 Å). In the patterns it can be observed that the background of the MA sample shows high dispersion compared with the melted sample, this fact can be attributed to the difference in the atomic ordering of both samples. This result is acceptable taking into account the nature of the preparation techniques, samples prepared by MA are normally disordered, inhomogeneous, even in some cases can reach an amorphous structure [17], while alloys prepared by arc-melting are more homogeneous. Crystallite size of the MA sample (16 nm) is significantly lower than that of the melted sample (72 nm). The difference between these two values is strictly a consequence of the preparation method. It is well known that in alloys produced by MA, the crystallite size decreases with the milling time due to the fragility which is induced by microstress inside the grains [11]. Mössbauer spectra of the FeCr alloys produced by MA and arc-melting are shown in Fig. 2 and the parameters of the hyperfine components used in the fit of these spectra are listed in Table 1. MA sample spectrum is composed of a non-magnetic site and a hyperfine magnetic field distribution (HMFD), while the
melted sample spectrum only present the HMFD. In the MA sample spectrum appears a singlet whose IS is 0.087 mm/s. Costa et al. have obtained this component in the Mössbauer spectra of Fe–Cr alloys with similar concentrations and they attributed it to bcc Fe–Cr amorphous grains [11,18,19]. Costa et al. prepared their alloys by MA samples of r-FeCr tetrahedral structure which was transformed into a bcc structure with milling time. In our study the kinetics of formation of the bcc structure is different and it is not conceivable that it can be obtained amorphous grains at 10 h when the milling starts with elemental powders; therefore, it is more feasible that the non-magnetic site of the Mossbauer spectrum is due to rich-chromium grains. By XRD it was determined that samples exhibit similar structural properties and there are few differences between both structures, the most important one is the grade of atomic order of the samples. The difference in atomic order is more noticeable through the shape adopted by the HMFD’s, and has an important effect on the magnetic behavior of the alloys. HMFD of the alloy obtained by MA is wide and the fields that comprise have a behavior quasi-discrete, that is, maximum probability fields surrounded by less probability fields; this behavior is due that for the 10 h of milling the homogeneity of the sample is not yet reached and iron sites exist in the structure with different neighborhoods. It appear peaks with a probability close to 30% compared with the maximum probability of distribution, which correspond to magnetic fields of 2.9 and 33.0 T. Iron sites with 6 or more chromium atoms as next nearest neighbors gives rise to the non-magnetic component present in the spectrum of MA sample [19], therefore the field of 2.9 T must corresponds to iron atoms with 5 chrome and 3 iron atoms as next nearest neighbors. The field of 33.0 T is associated with the a-Fe. The appearance of both the singlet and near fields to 33 T is also a proof of the low atomic diffusion reached with 10 h of milling. HMFD of the melted sample is narrower and practically is around 16.6 T, but also appears the maximum of small intensity corresponding to chromium-rich ferromagnetic sites. The high degree of homogeneity achieved during melting does not permit the formation of iron-rich sites, for this reason the MA sample exhibits higher ferromagnetic behavior than that the melted sample. The difference in the IS of the two HMFDs have a similar explanation (see Table 1), the IS of bcc Fe–Cr alloys decreases with the chromium content [20], therefore it is expected that the HMFD with the highest contribution of high fields is that which exhibits greater IS. Simultaneously, both samples were heated to 925 K for 7 days and then quenched into ice water. As seen in the XRD patterns of Fig. 3, for the heat treated samples, the bcc-FeCr structural phase of the MA sample is completely transformed into the r-FeCr phase whose space group is P42/mnm. With HT crystallite size of the
Fig. 2. Mössbauer spectrum of the Fe50Cr50 samples before HT.
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G.Y. Vélez, G.A. Pérez Alcázar / Journal of Alloys and Compounds 644 (2015) 1009–1012 Table 1 Hyperfine parameters obtained by fitting the Mössbauer spectra of Fe50Cr50 samples before HT. Sample
Component
%
C ± 0.02 (mm/s)
IS ± 0.010 (mm/s)
DQ ± 0.05 (mm/s)
hBhfi ± 0.2 (T)
MA
HMFD Singlet HMFD
94 6 100
0.30 0.48 0.30
0.039 0.087 0.095
0.02 – 0.00
18.5 – 15.0
Melted
Fig. 3. XRD pattern of the Fe50Cr50 samples after HT.
Fig. 4. Mössbauer spectrum of the Fe50Cr50 samples after HT.
tetrahedral structure loses the nanometer range and grows until 126 nm, the lattice parameters obtained from the refinement of the diffractogram are a = 8.792 and c = 4.566 Å, very similar to those reported in the literature by various authors [21]. In the melted sample the effects are not the same, in this alloy the a–r transformation is partial and after the HT it still exists grains with
bcc-FeCr structure. Lattice parameters a and c of the sigma structure are similar to those of the MA sample but crystallite size only grows up to 31 nm. The lattice parameter of the bcc structure remains constant; however its crystallite size decreases from 72 to 16 nm. This result suggests that the a–r transformation and the decrease of crystallite size of the bcc grains are simultaneous phenomena, therefore, it is expected that the precipitation of the r-FeCr phase is delayed with the size of the bcc grains. Despite having similar structural properties, r-FeCr phase is only obtained when the alloy is produced by MA, the reason is due to: (1) the greater inertia in the process of sigma structure formation which favored by the greater atomic disorder and higher concentration microgradients; (2) the low value of the crystallite size of bcc structure, which is favored by the higher microstresses. Mössbauer spectra of both HT alloys are illustrated in Fig. 4. It can be seen that the results are in agreement with those obtained by XRD, the MA sample spectrum is the characteristic of the sigma phase, while in the melted sample spectrum additionally shows the magnetic component associated with the bcc grains that have not undergone the bcc-r transformation. While it is true that the Mössbauer spectrum of the sigma structure is well known, it is difficult to make a fit that consistently relates the spectral components with the crystallographic sites of its unit cell. The reason is that the number of free parameters involved in the adjustment (for example, IS, quadrupolar splitting (DQ), line width, intensity, etc.) increases with the number of subspectra. This problem has been solved recently by Cieslak et al. who through computational calculations obtained the IS and DQ of different crystallographic sites of the r-Fe53.8Cr46.2 alloy [9]. The difference between the nearest neighbors of the A, . . ., E sites of r-Fe50Cr50 and r-Fe53.8Cr46.2 alloys is not significant [8], therefore as a first approximation we can use DQ values reported in Ref. [9] in the adjustment of our spectra. Using only the DQ values obtained by Cies´lak, we have adjusting the MA sample Mössbauer spectrum by the composition of non-magnetic five sites which are related to the five non-equivalent crystallographic sites of the sigma structure. The hyperfine parameters obtained by fitting are listed in Table 2. From the percent area of the different sites it was determined that the iron occupation number of A, . . ., E sites are 1.41, 0.48, 3.97, 7.11, and 2.03, respectively. This adjustment model cannot be carried out in the melted sample spectrum because the number of variables increases notably with the HMFD related to a-phase, however, the adjustment can be simplified by
Table 2 Hyperfine parameters obtained by fitting the Mössbauer spectra of Fe50Cr50 samples after HT. Sample
Component
% Area ± 0.5
C ± 0.02 (mm/s)
IS ± 0.01 (mm/s)
DQ ± 0.05 (mm/s)
hBhfi ± 0.2 (T)
MA + HT
Site Site Site Site Site
A B C D E
9.4 3.2 26.4 47.4 13.6
0.28 0.28 0.28 0.28 0.28
0.27 0.08 0.00 0.27 0.15
0.34 0.24 0.18 0.21 0.45
– – – – –
Melted + HT
Sites A y D Site B Site C Site E HMFD
47.2 1.5 18.0 10.1 23.2
0.32 0.28 0.28 0.28 0.30
0.19 0.08 0.00 0.15 0.10
0.24 0.24 0.18 0.45 0.0
– – – – 14.9
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G.Y. Vélez, G.A. Pérez Alcázar / Journal of Alloys and Compounds 644 (2015) 1009–1012
fixing DQ and IS values of the B, C, and E sites with respect to those obtained for MA sample, and fusing the sites A and D because they exhibit similar symmetry (see Table 2). The insert of Fig. 4 shows the HMFD related to the bcc structure, clearly is noted that there are no fields associated with iron-rich and chromium-rich sites; practically, HMFD consists of the fields of 13.3 and 17.2 T which should correspond to the most probable atomic configurations, that is, iron sites with 4 and 3 chromium atoms as nearest neighbors, respectively. The contribution of the second neighbors gives rise to probabilities around the two most probable magnetic fields. 4. Conclusions Precipitation kinetics of sigma structure from bcc-FeCr samples with different atomic order was studied by means of XRD and MS. The results have shown that the formation of the sigma structure can be accelerated when the bcc structure exhibits higher atomic disorder and its crystallite size is small, the reason is attributed to the greater number of concentration microgradients present in the disordered sample and to the higher microstresses of its grains, respectively. It was possible to perform the adjustment of the sigma structure Mössbauer spectrum by the composition of five non-magnetic sites which are related to the five non-equivalent crystallographic sites of its unit cell, and through this adjustment it was explicitly determined the iron occupation number for each of them. Acknowledgements This work was financed by COLCIENCIAS (Colombian agency) in cooperation with the Universidad del Valle through the project
‘‘Experimental and theoretical study of nanostructured magnetic systems Fe1xMx type, with M = Ni, Si and Nb’’, ascribed to the University with the internal Code No. 785. References [1] A. Hishinuma, S. Isozaki, S. Takaki, K. Abiko, Phys. Status Solidi (A) 160 (1997) 431. [2] K.H. Lo, C.H. Shek, J.K.L. Lai, Mater. Sci. Eng. R: Rep. 65 (2009) 39. [3] S.M. Dubiel, Hyperfine Interact. 189 (2009) 53. [4] O. Kubachewski, Iron-Binary Phase Diagrams, Springer, Berlin, 1982, p. 185. [5] T.B. Massalski, Binary Alloy Phase Diagrams, vol. 1, ASM International, Metal Park, OH, 1990. [6] S.M. Dubiel, J. Cieslak, Crit. Rev. Solid State Mater. Sci. 36 (2011) 191. [7] S.M. Dubiel, J. Cieslak, W. Sturhahn, M. Sternik, P. Piekarz, S. Stankov, K. Parlinski, Phys. Rev. Lett. 104 (2010) 155503. [8] J. Ciéslak, M. Reissner, S.M. Dubiel, J. Wernisch, W. Steiner, J. Alloys Comp. 460 (2008) 20. [9] J. Ciéslak, J. Tobola, S.M. Dubiel, S. Kaprzyk, W. Steiner, M. Reissner, J. Phys.: Condens. Matter 20 (2008) 235234. [10] Ajay Gupta, G. Principi, G.M. Paolucci, Hyperfine Interact. 54 (1990) 805. [11] B.F.O. Costa, J.M. Loureiro, G. Le Caër, Hyperfine Interact. 165 (2005) 107. [12] K. Yano, K. Abiko, Phys. Status Solidi (A) 160 (1997) 449. [13] J. Ciéslak, S.M. Dubiel, B. Sepiol, Solid State Commun. 111 (1999) 613. [14] A. Blachowski, J. Cieslak, S.M. Dubiel, J. Zukrowski, J. Alloys Comp. 308 (2000) 189. [15] A.C. Larson, R.B. Von Dreele, General Structure Analysis System (GSAS), Los Alamos National Laboratory Report LAUR, 2004. pp. 86. [16] F. Varret, J. Teillet, Unpublished MOSFIT Program. [17] C. Surnayarayana, Prog. Mater. Sci. 46 (2001) 1. [18] B.F.O. Costa, G. Le Caër, J.M. Loureiro, V.S. Amaral, J. Alloys Comp. 424 (2006) 131. [19] J.M. Loureiro, B.F.O. Costa, G. Le Caër, P. Delcroix, Hyperfine Interact. 183 (2008) 109. [20] J.M.D. Yu Boliang, M.Olivier. Coey, J.O. Strom-Olsen, J. Appl. Phys. 55 (1984) 1748. [21] M. Hansen, K. Ardenko, Constitution of Binary Alloys, McGraw-Hill, New York, 1958.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Influence of atomic ordering on sigma phase precipitation of the Fe50Cr50 alloy G.Y. Vélez a,b,⇑, G.A. Pérez Alcázar a a b
Universidad del Valle, Departamento de Física, A.A. 25360 Cali, Colombia Instituto de Física, Universidad Autónoma de San Luis Potosí, avenida Manuel Nava 6, zona universitaria, 78290 San Luis Potosí, SLP México, Mexico
a r t i c l e
i n f o
Article history: Received 11 December 2014 Received in revised form 14 April 2015 Accepted 2 May 2015 Available online 8 May 2015 Keywords: Fe–Cr alloys Sigma phase Atomic ordering Mössbauer spectroscopy
a b s t r a c t In this work we report a study of the kinetic of the formation of the r-Fe50Cr50 alloy which is obtained by heat treatment of a-FeCr samples with different atomic ordering. Two a-FeCr alloys were obtained, one by mechanical alloying and the other by arc-melting. Both alloys were heated at 925 K for 170 h and then quenched into ice water. Before heat treatment both alloys exhibit a-FeCr disordered structure with greater ferromagnetic behavior in the alloy obtained by mechanical alloying due to its higher atomic disorder. The sigma phase precipitation is influenced by the atomic ordering of the bcc samples: in the alloy obtained by mechanical alloying, the bcc phase is completely transformed into the r phase; in the alloy obtained by melted the a–r transformation is partial. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction The Fe–Cr binary system exhibits special interest in the materials industry mainly due its high corrosion resistance as well as its mechanical strength [1,2]. The majority of the studies related to this system are performed near to the equiatomic region since in this region the r-FeCr phase is precipitated which deteriorates the mechanical properties of the alloy [3]. Sigma structure is obtained at about 50% at. Cr and for temperatures between 800 and 1100 K. Above of this miscibility gap the alloy is solid and disordered, below, the alloy is composed of iron-rich as well as chromium-rich clusters, both with bcc A2 structure [4–6]. Sigma phase has tetrahedral structure with 30 atoms in its unitary cell, which are distributed among five crystallographically non-equivalent sites named A, B, C, D and E with occupancy numbers 2, 4, 8, 8 and 8, respectively. A and D sites are preferably occupied by iron atoms, while sites B, C and E are preferentially occupied by chromium atoms [6–9]. One of the main goals of stainless steels production based on Fe–Cr alloys with concentrations near to 50% at. Cr, is to retard the precipitation of sigma structure when the material is subjected to high temperatures. The occurrence of this structure is not immediate, experimental studies have shown that the heating time
⇑ Corresponding author at: Instituto de Física, Universidad Autónoma de San Luis Potosí, avenida Manuel Nava 6, zona universitaria, 78290 San Luis Potosí, SLP México, Mexico. Tel.: +52 444 8262362; fax: +52 444 8133874. E-mail address: [email protected] (G.Y. Vélez). http://dx.doi.org/10.1016/j.jallcom.2015.05.004 0925-8388/Ó 2015 Elsevier B.V. All rights reserved.
necessary to completely precipitate the structure may vary from a few days to several weeks depending of the heating temperature [6,8–11]. The purity of the alloy as well as the presence of carbon in small amounts retards the formation of the sigma phase [12]. In contrast, the addition of titanium favors its formation [13,14]. Considering that the sigma structure exhibits a substantial atomic order, it is possible that the kinetics in the formation of this structure depends on the degree of atomic order of bcc-FeCr alloy before heating. To test this hypothesis we obtained r-Fe50Cr50 samples which were precipitated from a-FeCr samples obtained by two different techniques, mechanical alloying (MA) and arc-melting. The investigation is performed by means of X-rays diffraction (XRD) and Mössbauer spectroscopy (MS). 2. Experimental procedure
a-Fe50Cr50 samples were initially synthesized by two different techniques, mechanical alloying and arc-melting. As precursor material was used in both cases, high-purity fine powder of iron and chromium. MA was carried out in a high energy planetary mill Fritsch-Pulverisette 5 with milling time of 10 h. The millings were realized at 280 rpm. Average vacuum inside of the jars was 4.5 105 bar, a ratio between balls and power mass of 20:1, and the ball diameter of 10 mm. Casting was carried out under argon atmosphere. Melted tablet was obtained by elemental mixture of the precursor powders (3 g in total) and compacted in a hydraulic press at 206 bars for 1 min. Both samples were heated at 925 K for 170 h and then quenched into ice water. The characterization of the samples before and after the heat treatment (HT) was performed by XRD and 57Fe MS. Diffraction measurements were performed in a powder diffractometer with Cu Ka radiation. The diffraction patterns were refined with the GSAS program using the Rietveld method. From the refinement of the XRD patterns it were explicitly obtained the structure of the samples, the
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G.Y. Vélez, G.A. Pérez Alcázar / Journal of Alloys and Compounds 644 (2015) 1009–1012
Fig. 1. XRD pattern of the Fe50Cr50 samples before HT.
values of their respective lattice parameter and average crystallite size in the perpendicular direction to the X-rays [15]. Mössbauer spectra were collected at room temperature in the transmission mode using a conventional spectrometer. The fit of the spectra were performed with the MOSFIT program [16]. The isomer shift (IS) of all components that constitute the different spectra are reported with reference to a-Fe.
3. Experimental results In Fig. 1 are illustrated the XRD patterns of the FeCr alloy obtained by MA and arc-melting. The refinement results show that both alloys exhibit only the bcc structure with similar lattice parameter (2.879 Å). In the patterns it can be observed that the background of the MA sample shows high dispersion compared with the melted sample, this fact can be attributed to the difference in the atomic ordering of both samples. This result is acceptable taking into account the nature of the preparation techniques, samples prepared by MA are normally disordered, inhomogeneous, even in some cases can reach an amorphous structure [17], while alloys prepared by arc-melting are more homogeneous. Crystallite size of the MA sample (16 nm) is significantly lower than that of the melted sample (72 nm). The difference between these two values is strictly a consequence of the preparation method. It is well known that in alloys produced by MA, the crystallite size decreases with the milling time due to the fragility which is induced by microstress inside the grains [11]. Mössbauer spectra of the FeCr alloys produced by MA and arc-melting are shown in Fig. 2 and the parameters of the hyperfine components used in the fit of these spectra are listed in Table 1. MA sample spectrum is composed of a non-magnetic site and a hyperfine magnetic field distribution (HMFD), while the
melted sample spectrum only present the HMFD. In the MA sample spectrum appears a singlet whose IS is 0.087 mm/s. Costa et al. have obtained this component in the Mössbauer spectra of Fe–Cr alloys with similar concentrations and they attributed it to bcc Fe–Cr amorphous grains [11,18,19]. Costa et al. prepared their alloys by MA samples of r-FeCr tetrahedral structure which was transformed into a bcc structure with milling time. In our study the kinetics of formation of the bcc structure is different and it is not conceivable that it can be obtained amorphous grains at 10 h when the milling starts with elemental powders; therefore, it is more feasible that the non-magnetic site of the Mossbauer spectrum is due to rich-chromium grains. By XRD it was determined that samples exhibit similar structural properties and there are few differences between both structures, the most important one is the grade of atomic order of the samples. The difference in atomic order is more noticeable through the shape adopted by the HMFD’s, and has an important effect on the magnetic behavior of the alloys. HMFD of the alloy obtained by MA is wide and the fields that comprise have a behavior quasi-discrete, that is, maximum probability fields surrounded by less probability fields; this behavior is due that for the 10 h of milling the homogeneity of the sample is not yet reached and iron sites exist in the structure with different neighborhoods. It appear peaks with a probability close to 30% compared with the maximum probability of distribution, which correspond to magnetic fields of 2.9 and 33.0 T. Iron sites with 6 or more chromium atoms as next nearest neighbors gives rise to the non-magnetic component present in the spectrum of MA sample [19], therefore the field of 2.9 T must corresponds to iron atoms with 5 chrome and 3 iron atoms as next nearest neighbors. The field of 33.0 T is associated with the a-Fe. The appearance of both the singlet and near fields to 33 T is also a proof of the low atomic diffusion reached with 10 h of milling. HMFD of the melted sample is narrower and practically is around 16.6 T, but also appears the maximum of small intensity corresponding to chromium-rich ferromagnetic sites. The high degree of homogeneity achieved during melting does not permit the formation of iron-rich sites, for this reason the MA sample exhibits higher ferromagnetic behavior than that the melted sample. The difference in the IS of the two HMFDs have a similar explanation (see Table 1), the IS of bcc Fe–Cr alloys decreases with the chromium content [20], therefore it is expected that the HMFD with the highest contribution of high fields is that which exhibits greater IS. Simultaneously, both samples were heated to 925 K for 7 days and then quenched into ice water. As seen in the XRD patterns of Fig. 3, for the heat treated samples, the bcc-FeCr structural phase of the MA sample is completely transformed into the r-FeCr phase whose space group is P42/mnm. With HT crystallite size of the
Fig. 2. Mössbauer spectrum of the Fe50Cr50 samples before HT.
1011
G.Y. Vélez, G.A. Pérez Alcázar / Journal of Alloys and Compounds 644 (2015) 1009–1012 Table 1 Hyperfine parameters obtained by fitting the Mössbauer spectra of Fe50Cr50 samples before HT. Sample
Component
%
C ± 0.02 (mm/s)
IS ± 0.010 (mm/s)
DQ ± 0.05 (mm/s)
hBhfi ± 0.2 (T)
MA
HMFD Singlet HMFD
94 6 100
0.30 0.48 0.30
0.039 0.087 0.095
0.02 – 0.00
18.5 – 15.0
Melted
Fig. 3. XRD pattern of the Fe50Cr50 samples after HT.
Fig. 4. Mössbauer spectrum of the Fe50Cr50 samples after HT.
tetrahedral structure loses the nanometer range and grows until 126 nm, the lattice parameters obtained from the refinement of the diffractogram are a = 8.792 and c = 4.566 Å, very similar to those reported in the literature by various authors [21]. In the melted sample the effects are not the same, in this alloy the a–r transformation is partial and after the HT it still exists grains with
bcc-FeCr structure. Lattice parameters a and c of the sigma structure are similar to those of the MA sample but crystallite size only grows up to 31 nm. The lattice parameter of the bcc structure remains constant; however its crystallite size decreases from 72 to 16 nm. This result suggests that the a–r transformation and the decrease of crystallite size of the bcc grains are simultaneous phenomena, therefore, it is expected that the precipitation of the r-FeCr phase is delayed with the size of the bcc grains. Despite having similar structural properties, r-FeCr phase is only obtained when the alloy is produced by MA, the reason is due to: (1) the greater inertia in the process of sigma structure formation which favored by the greater atomic disorder and higher concentration microgradients; (2) the low value of the crystallite size of bcc structure, which is favored by the higher microstresses. Mössbauer spectra of both HT alloys are illustrated in Fig. 4. It can be seen that the results are in agreement with those obtained by XRD, the MA sample spectrum is the characteristic of the sigma phase, while in the melted sample spectrum additionally shows the magnetic component associated with the bcc grains that have not undergone the bcc-r transformation. While it is true that the Mössbauer spectrum of the sigma structure is well known, it is difficult to make a fit that consistently relates the spectral components with the crystallographic sites of its unit cell. The reason is that the number of free parameters involved in the adjustment (for example, IS, quadrupolar splitting (DQ), line width, intensity, etc.) increases with the number of subspectra. This problem has been solved recently by Cieslak et al. who through computational calculations obtained the IS and DQ of different crystallographic sites of the r-Fe53.8Cr46.2 alloy [9]. The difference between the nearest neighbors of the A, . . ., E sites of r-Fe50Cr50 and r-Fe53.8Cr46.2 alloys is not significant [8], therefore as a first approximation we can use DQ values reported in Ref. [9] in the adjustment of our spectra. Using only the DQ values obtained by Cies´lak, we have adjusting the MA sample Mössbauer spectrum by the composition of non-magnetic five sites which are related to the five non-equivalent crystallographic sites of the sigma structure. The hyperfine parameters obtained by fitting are listed in Table 2. From the percent area of the different sites it was determined that the iron occupation number of A, . . ., E sites are 1.41, 0.48, 3.97, 7.11, and 2.03, respectively. This adjustment model cannot be carried out in the melted sample spectrum because the number of variables increases notably with the HMFD related to a-phase, however, the adjustment can be simplified by
Table 2 Hyperfine parameters obtained by fitting the Mössbauer spectra of Fe50Cr50 samples after HT. Sample
Component
% Area ± 0.5
C ± 0.02 (mm/s)
IS ± 0.01 (mm/s)
DQ ± 0.05 (mm/s)
hBhfi ± 0.2 (T)
MA + HT
Site Site Site Site Site
A B C D E
9.4 3.2 26.4 47.4 13.6
0.28 0.28 0.28 0.28 0.28
0.27 0.08 0.00 0.27 0.15
0.34 0.24 0.18 0.21 0.45
– – – – –
Melted + HT
Sites A y D Site B Site C Site E HMFD
47.2 1.5 18.0 10.1 23.2
0.32 0.28 0.28 0.28 0.30
0.19 0.08 0.00 0.15 0.10
0.24 0.24 0.18 0.45 0.0
– – – – 14.9
1012
G.Y. Vélez, G.A. Pérez Alcázar / Journal of Alloys and Compounds 644 (2015) 1009–1012
fixing DQ and IS values of the B, C, and E sites with respect to those obtained for MA sample, and fusing the sites A and D because they exhibit similar symmetry (see Table 2). The insert of Fig. 4 shows the HMFD related to the bcc structure, clearly is noted that there are no fields associated with iron-rich and chromium-rich sites; practically, HMFD consists of the fields of 13.3 and 17.2 T which should correspond to the most probable atomic configurations, that is, iron sites with 4 and 3 chromium atoms as nearest neighbors, respectively. The contribution of the second neighbors gives rise to probabilities around the two most probable magnetic fields. 4. Conclusions Precipitation kinetics of sigma structure from bcc-FeCr samples with different atomic order was studied by means of XRD and MS. The results have shown that the formation of the sigma structure can be accelerated when the bcc structure exhibits higher atomic disorder and its crystallite size is small, the reason is attributed to the greater number of concentration microgradients present in the disordered sample and to the higher microstresses of its grains, respectively. It was possible to perform the adjustment of the sigma structure Mössbauer spectrum by the composition of five non-magnetic sites which are related to the five non-equivalent crystallographic sites of its unit cell, and through this adjustment it was explicitly determined the iron occupation number for each of them. Acknowledgements This work was financed by COLCIENCIAS (Colombian agency) in cooperation with the Universidad del Valle through the project
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