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Thermal expansion and specific heat of mechanically milled FCC Fe72Pt28
Journal of Magnetism and Magnetic Materials 239 (2002) 60–62
Thermal expansion and specific heat of mechanically milled FCC Fe72Pt28 H. Takano*, S. Hikichi, J. Maeda, S. Murayama, K. Hoshi Department of Materials Science and Engineering, Muroran Institute of Technology, Muroran, Hokkaido 050-8585, Japan
Abstract Thermal expansion of mechanically milled FCC Fe72Pt28 was measured by X-ray diffractometry. For FCC Fe72Pt28 milled for 120 h the volume increased between 80 and 323 K with decreasing temperature. It was concluded that the volume expansion in such wide temperature range is related to the distribution of the Curie temperature TC suggested by specific heat measurement. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Invar alloy; Thermal expansion; Specific heat; Mechanical milling; Structural disorder
1. Introduction Mechanical milling of both ordered and disordered Fe72Pt28 Invar alloys [1] gives rise to martensitic transformation induced by stress. The structure of disordered Fe72Pt28 alloy after milling changes from FCC to BCC, and it changes again to FCC by heat treatment to 750 K. However, the structural disorder introduced by milling remains even after such heating. The degree of structural disorder depends on milling time and can be measured as the magnitude of strain of the structure by means of X-ray diffraction (XRD). The Curie temperature TC of the mechanically milled FCC Fe72Pt28, which is obtained from Arrott plots, and increases with increasing milling time. The temperature dependence of isothermal magnetic susceptibility dM=dHðH ¼ 10 kOeÞ shows a peak at TC and the width of the peak broadens with increasing milling time. This result suggests that TC distributes due to milling. On the other hand, TC shifts to higher temperature with increasing milling time. This means that the ferromagnetism of the disordered FCC Fe72Pt28 alloy is stabilized due to structural disorder. In this paper, we have investigated thermal properties of the disordered FCC *Corresponding author. Tel.: +81-143-46-5617; fax: +81143-46-5625. E-mail address: [email protected] (H. Takano).
Fe72Pt28 alloy, especially thermal expansion and specific heat, to make clear structural disorder effect on the Invar characteristics.
2. Experimental and analysis The samples were prepared in some steps. The detailed sample preparation is written in Ref. [1]. Thermal expansion is measured from 83 to 323 K by X-ray diffractometry. One accurate Bragg peak profile has been obtained at various temperatures. Since the Bragg peak profiles of mechanically milled samples are very broad due to the decrease of crystallite size and the increase of lattice strain, it is difficult to separate a component of Ka1 from a Ka doublet. We then propose that the profile of the Ka doublet can be fitted to an approximate function [1], ( fðD2yÞ ¼ S fV ðD2yÞ 1 1 lKa2 : sin yk þ fV 2 y sin lKa1 2 The first term in this function corresponds to the Ka1 line and the second the Ka2 line. Instead of using a Voigt function which is a convolution of the Lorentz function fL and the Gauss function fG ; each line is assumed to be approximated by a pseudo-Voigt function fV ðD2yÞ:
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 5 2 6 - 1
H. Takano et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 60–62
fV is given as follows and the detail is written in Ref. [2]. fV ðD2yÞ ¼ ZfL ðD2yÞ þ ð1 ZÞfG ðD2yÞ 2 D2y 1 1þ4 ¼Z pHk Hk pffiffiffiffiffiffiffiffi 2 ln 2 D2y : þ ð1 ZÞ pffiffiffi exp 4 ln 2 Hk pHk Here, D2y ¼ 2y 2yk ðyk : Bragg angle for the kth reflection). Z is the fraction of the Lorentz component. Hk is the full-width-at-half-maximum (FWHM) of fV : The FWHMs HkL and HkG for fL and fG of the original Voigt function, respectively, are given as functions of Z and Hk : The HkL and HkG correspond to crystallite size D and lattice strain e; respectively. The detailed definition is given in Ref. [1]. The thermal expansion Dl=l is obtained as change of the separation d of the (h k l) plane Dd=d: In these thermal expansion measurements, (1 1 1), (2 0 0) and (2 2 2) peaks of the unmilled reference and (2 0 0) peak of the FCC Fe72Pt28 milled for 120 h are used. We also estimate the crystallite size D and lattice strain e for the latter using yk ; HkL and HkG obtained from a profile fitting as described above. Specific heat Cp is measured between 80 and 800 K with a light-chopped AC calorimeter.
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residual BCC structure is seen at 2y ¼ 43:51 for the milled sample. Therefore, the peak of (2 0 0) is chosen instead of (1 1 1). As mentioned above, the crystallite size D and the lattice strain e of the sample milled for 120 h are determined to be (10.871.5) nm is (0.6370.05)%, respectively. The crystallite size for the unmilled reference is estimated about 70 nm by Scherrer’s method. These are consistent with the previous results. Temperature dependence of the thermal expansion Dl=l is shown in Fig. 2. Figs. 2(a) and (b) are for the unmilled and milled samples, respectively. Fig. 2(c) is the results of Sumiyama et al. [5], which was obtained for bulk sample of a disordered Fe72Pt28 using a differential transformer type dilatometer. They observed negative thermal expansion between 280 and 385 K in the disordered Fe72Pt28 near and below TC : From Fig. 2(a) it is seen that the thermal expansion Dl=l for the unmilled sample has the maximum around 230 K. Though the maximum temperature of the unmilled sample is lower about 30 K than that for the disordered Fe72Pt28 in Fig. 2(c), both have a common behavior. The
3. Results and discussion Fig. 1 shows the XRD patterns of the FCC Fe72Pt28 unmilled sample and the sample milled for 120 h. Both XRD patterns show that these samples have a FCC structure. After mechanical milling the intensity of all peaks decreases and the width broadens in comparison with those of the unmilled reference as seen in other mechanically milled samples [3,4]. A small (1 1 0) peak of
Fig. 1. X-ray diffraction patterns of the unmilled sample and the sample milled for 120 h.
Fig. 2. Thermal expansion of (a) the unmilled sample and (b) the sample milled for 120 h. (c) is taken from Ref. [5].
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H. Takano et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 60–62
Fig. 3. Specific heat Cp of the unmilled sample and the sample milled for 120 h. The arrows indicate the Curie temperature TC ’s.
negative thermal expansion (from 240 to 340 K) was observed not only in the unmilled sample, but also in the milled sample. It is characteristic in the milled sample that the negative thermal expansion happens in lower and much wider temperature range between 80 and 323 K in Fig. 2(b). Fig. 3 shows the total specific heat Cp of the unmilled and the milled sample versus temperature. TC0h and TC120h are the Curie temperatures of the unmilled and milled samples, respectively, which are obtained from the previous investigation [1]. A broad and rounded maximum caused by the ferromagnetic transition is observed for the unmilled sample also by Rellinghaus et al. [6]. Such a specific peak of Cp is also seen for the milled sample. The peak temperature of the
milled sample shifts to higher temperature and the width is broader than that of the unmilled sample. These results indicate that the distribution of TC in the milled sample occur in the wide temperature range than in the unmilled sample observed in Ref. [1]. As described above, the anomalous negative thermal expansion in the disordered Fe72Pt28 occurs near and below TC : Ono et al. explained the negative thermal expansion in disordered Fe-Pt Invar alloys on the basis of the normal lattice contribution and the magnetovolume coupling with longitudinal spin fluctuation [7]. It is expected that similar magnetovolume effect occurs also in the milled sample with appearance of ferromagnetism. Since TC distributes in the milled sample, it is considered that the negative thermal expansion occurs in the wide range of temperature for the mechanically milled FCC Fe72Pt28.
References [1] H. Takano, N. Oba, S. Murayama, K. Hoshi, H. Bakker, F.R. de Boer, J. Alloys Compounds 287 (1999) 256. [2] P. Thompson, D.E. Cox, J.B. Hastings, J. Appl. Cryst. 20 (1987) 79. [3] L.M. Di, H. Bakker, Y. Tamminga, F.R. de Boer, Phys. Rev. B 44 (1991) 2444. [4] G.F. Zhou, H. Bakker, Acta Metall. Matter. 42 (1994) 3009. [5] K. Sumiyama, M. Shiga, M. Morioka, Y. Nakamura, J. Phys. F: Metal Phys. 9 (1979) 1665. [6] B. Rellinghaus, J. K.aestner, T. Schneider, E.W. Wassermann, P. Mohn, Phys. Rev. B 51 (1995) 2983. [7] F. Ono, H. Maeta, T. Kittaka, J. Magn. Magn. Mater. 31–34 (1983) 113.
Thermal expansion and specific heat of mechanically milled FCC Fe72Pt28 H. Takano*, S. Hikichi, J. Maeda, S. Murayama, K. Hoshi Department of Materials Science and Engineering, Muroran Institute of Technology, Muroran, Hokkaido 050-8585, Japan
Abstract Thermal expansion of mechanically milled FCC Fe72Pt28 was measured by X-ray diffractometry. For FCC Fe72Pt28 milled for 120 h the volume increased between 80 and 323 K with decreasing temperature. It was concluded that the volume expansion in such wide temperature range is related to the distribution of the Curie temperature TC suggested by specific heat measurement. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Invar alloy; Thermal expansion; Specific heat; Mechanical milling; Structural disorder
1. Introduction Mechanical milling of both ordered and disordered Fe72Pt28 Invar alloys [1] gives rise to martensitic transformation induced by stress. The structure of disordered Fe72Pt28 alloy after milling changes from FCC to BCC, and it changes again to FCC by heat treatment to 750 K. However, the structural disorder introduced by milling remains even after such heating. The degree of structural disorder depends on milling time and can be measured as the magnitude of strain of the structure by means of X-ray diffraction (XRD). The Curie temperature TC of the mechanically milled FCC Fe72Pt28, which is obtained from Arrott plots, and increases with increasing milling time. The temperature dependence of isothermal magnetic susceptibility dM=dHðH ¼ 10 kOeÞ shows a peak at TC and the width of the peak broadens with increasing milling time. This result suggests that TC distributes due to milling. On the other hand, TC shifts to higher temperature with increasing milling time. This means that the ferromagnetism of the disordered FCC Fe72Pt28 alloy is stabilized due to structural disorder. In this paper, we have investigated thermal properties of the disordered FCC *Corresponding author. Tel.: +81-143-46-5617; fax: +81143-46-5625. E-mail address: [email protected] (H. Takano).
Fe72Pt28 alloy, especially thermal expansion and specific heat, to make clear structural disorder effect on the Invar characteristics.
2. Experimental and analysis The samples were prepared in some steps. The detailed sample preparation is written in Ref. [1]. Thermal expansion is measured from 83 to 323 K by X-ray diffractometry. One accurate Bragg peak profile has been obtained at various temperatures. Since the Bragg peak profiles of mechanically milled samples are very broad due to the decrease of crystallite size and the increase of lattice strain, it is difficult to separate a component of Ka1 from a Ka doublet. We then propose that the profile of the Ka doublet can be fitted to an approximate function [1], ( fðD2yÞ ¼ S fV ðD2yÞ 1 1 lKa2 : sin yk þ fV 2 y sin lKa1 2 The first term in this function corresponds to the Ka1 line and the second the Ka2 line. Instead of using a Voigt function which is a convolution of the Lorentz function fL and the Gauss function fG ; each line is assumed to be approximated by a pseudo-Voigt function fV ðD2yÞ:
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 5 2 6 - 1
H. Takano et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 60–62
fV is given as follows and the detail is written in Ref. [2]. fV ðD2yÞ ¼ ZfL ðD2yÞ þ ð1 ZÞfG ðD2yÞ 2 D2y 1 1þ4 ¼Z pHk Hk pffiffiffiffiffiffiffiffi 2 ln 2 D2y : þ ð1 ZÞ pffiffiffi exp 4 ln 2 Hk pHk Here, D2y ¼ 2y 2yk ðyk : Bragg angle for the kth reflection). Z is the fraction of the Lorentz component. Hk is the full-width-at-half-maximum (FWHM) of fV : The FWHMs HkL and HkG for fL and fG of the original Voigt function, respectively, are given as functions of Z and Hk : The HkL and HkG correspond to crystallite size D and lattice strain e; respectively. The detailed definition is given in Ref. [1]. The thermal expansion Dl=l is obtained as change of the separation d of the (h k l) plane Dd=d: In these thermal expansion measurements, (1 1 1), (2 0 0) and (2 2 2) peaks of the unmilled reference and (2 0 0) peak of the FCC Fe72Pt28 milled for 120 h are used. We also estimate the crystallite size D and lattice strain e for the latter using yk ; HkL and HkG obtained from a profile fitting as described above. Specific heat Cp is measured between 80 and 800 K with a light-chopped AC calorimeter.
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residual BCC structure is seen at 2y ¼ 43:51 for the milled sample. Therefore, the peak of (2 0 0) is chosen instead of (1 1 1). As mentioned above, the crystallite size D and the lattice strain e of the sample milled for 120 h are determined to be (10.871.5) nm is (0.6370.05)%, respectively. The crystallite size for the unmilled reference is estimated about 70 nm by Scherrer’s method. These are consistent with the previous results. Temperature dependence of the thermal expansion Dl=l is shown in Fig. 2. Figs. 2(a) and (b) are for the unmilled and milled samples, respectively. Fig. 2(c) is the results of Sumiyama et al. [5], which was obtained for bulk sample of a disordered Fe72Pt28 using a differential transformer type dilatometer. They observed negative thermal expansion between 280 and 385 K in the disordered Fe72Pt28 near and below TC : From Fig. 2(a) it is seen that the thermal expansion Dl=l for the unmilled sample has the maximum around 230 K. Though the maximum temperature of the unmilled sample is lower about 30 K than that for the disordered Fe72Pt28 in Fig. 2(c), both have a common behavior. The
3. Results and discussion Fig. 1 shows the XRD patterns of the FCC Fe72Pt28 unmilled sample and the sample milled for 120 h. Both XRD patterns show that these samples have a FCC structure. After mechanical milling the intensity of all peaks decreases and the width broadens in comparison with those of the unmilled reference as seen in other mechanically milled samples [3,4]. A small (1 1 0) peak of
Fig. 1. X-ray diffraction patterns of the unmilled sample and the sample milled for 120 h.
Fig. 2. Thermal expansion of (a) the unmilled sample and (b) the sample milled for 120 h. (c) is taken from Ref. [5].
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H. Takano et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 60–62
Fig. 3. Specific heat Cp of the unmilled sample and the sample milled for 120 h. The arrows indicate the Curie temperature TC ’s.
negative thermal expansion (from 240 to 340 K) was observed not only in the unmilled sample, but also in the milled sample. It is characteristic in the milled sample that the negative thermal expansion happens in lower and much wider temperature range between 80 and 323 K in Fig. 2(b). Fig. 3 shows the total specific heat Cp of the unmilled and the milled sample versus temperature. TC0h and TC120h are the Curie temperatures of the unmilled and milled samples, respectively, which are obtained from the previous investigation [1]. A broad and rounded maximum caused by the ferromagnetic transition is observed for the unmilled sample also by Rellinghaus et al. [6]. Such a specific peak of Cp is also seen for the milled sample. The peak temperature of the
milled sample shifts to higher temperature and the width is broader than that of the unmilled sample. These results indicate that the distribution of TC in the milled sample occur in the wide temperature range than in the unmilled sample observed in Ref. [1]. As described above, the anomalous negative thermal expansion in the disordered Fe72Pt28 occurs near and below TC : Ono et al. explained the negative thermal expansion in disordered Fe-Pt Invar alloys on the basis of the normal lattice contribution and the magnetovolume coupling with longitudinal spin fluctuation [7]. It is expected that similar magnetovolume effect occurs also in the milled sample with appearance of ferromagnetism. Since TC distributes in the milled sample, it is considered that the negative thermal expansion occurs in the wide range of temperature for the mechanically milled FCC Fe72Pt28.
References [1] H. Takano, N. Oba, S. Murayama, K. Hoshi, H. Bakker, F.R. de Boer, J. Alloys Compounds 287 (1999) 256. [2] P. Thompson, D.E. Cox, J.B. Hastings, J. Appl. Cryst. 20 (1987) 79. [3] L.M. Di, H. Bakker, Y. Tamminga, F.R. de Boer, Phys. Rev. B 44 (1991) 2444. [4] G.F. Zhou, H. Bakker, Acta Metall. Matter. 42 (1994) 3009. [5] K. Sumiyama, M. Shiga, M. Morioka, Y. Nakamura, J. Phys. F: Metal Phys. 9 (1979) 1665. [6] B. Rellinghaus, J. K.aestner, T. Schneider, E.W. Wassermann, P. Mohn, Phys. Rev. B 51 (1995) 2983. [7] F. Ono, H. Maeta, T. Kittaka, J. Magn. Magn. Mater. 31–34 (1983) 113.