- Email: [email protected]
Stability of ferromagnetism in FCC Fe–Cu–Au alloys prepared by mechanical alloying
Materials Science and Engineering A312 (2001) 262– 266 www.elsevier.com/locate/msea
Stability of ferromagnetism in FCC Fe–Cu–Au alloys prepared by mechanical alloying H. Ino a,*, M. Kincho b, K. Oda c, K. Tokumitsu d b
a College of Engineering, Hosei Uni6ersity, Koganei, Tokyo 184 -8584, Japan Graduate student, College of Engineering, Hosei Uni6ersity, Koganei, Tokyo 184 -8584, Japan c Institute of Industrial Science, Uni6ersity of Tokyo, Minato-ku, Tokyo 106 -8558, Japan d Graduate School of Engineering, Uni6ersity of Tokyo, Bunkyo-ku, Tokyo 113 -8656, Japan
Received 26 May 2000; received in revised form 8 September 2000
Abstract We have studied the relation between the stability of ferromagnetism and the atomic volume of FCC Fe– Cu–Au alloys prepared by mechanical alloying by means of X-ray diffraction, magnetization measurement and Mossbauer effect. The atomic volume of the FCC Fe0.5Cu0.5 alloy increased almost linearly with the substitution of Au atoms for Cu from original 12.09 ×10 − 3 to 13.31 ×10 − 3 nm3 for 40% replacement. The Curie temperature of the alloy also increased in the same manner from 489 to 582 K. It is found that the increase in atomic volume stabilizes the ferromagnetic state of the FCC alloys. The values of magnetic moment of iron in Fe0.5Cu0.4Au0.1 and Fe0.5Cu0.3Au0.2 were estimated to be 2.34 and 2.44 mB, respectively, which are larger than that of a-iron (2.22 mB). The magnetic hyperfine field of iron in Fe0.5Cu0.4Au0.1 showed wide distribution from 22 to 38 T at 82 K, which is probably caused by the variation of species of surrounding atoms of iron. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Mechanical alloying; Iron–copper–gold alloy; Atomic volume; Ferromagnetism; Magnetic moment; Mossbaure effect
1. Introduction Iron and copper elements are partially soluble with each other in equilibrium (B 11 at.% Cu in Fe, B 4.8 at.% Fe in Cu). However, mechanical alloying method allows supersaturated solid solutions to be formed in the whole range of the Fe – Cu system [1 – 11]. The BCC structure is formed in the alloys containing more than about 65% of iron, whereas the FCC structure of the solution is formed in the alloys containing less than that percentage of iron [1,2,10,11]. The iron atoms in the FCC solution have a large magnetic moment comparable to that of the BCC iron [2,11]. We have concluded in previous papers [10,11] that the ferromagnetism of the FCC Fe – Cu alloys is stabilized by the expansion of the atomic volume of the lattice.
* Corresponding author. Fax: + 81-423-876121. E-mail address: [email protected] (H. Ino).
The purpose of the present work is to verify clearly the relation between the stability of ferromagnetism and the atomic volume of the FCC alloys. We prepared ternary Fe –Cu –Au alloys in which Cu atoms (atomic diameter 0.2556 nm) were partly replaced by Au atoms (0.2884 nm) in order to expand the FCC lattice.
2. Experimental procedure We prepared binary Fe1 − x Cux and ternary Fe1 − x(Cu1 − y Auy )x alloys (x= 0.3, 0.35, 0.5; y= 0, 0.1, 0.2, 0.4) by grinding mechanically powders of 99.9% pure Fe (B 300 meshes), Cu (B15 mm) and Au ( B100 meshes). Metal powders of 0.3 mol in total were put into a zirconia vial together with 30 zirconia balls with a diameter of 10 mm and a small amount (0.0002 mol) of stearic acid (CH3(CH2)16COOH) to prevent coagulation of the powders. A machine (Super-Misuni) was operated with a vibration frequency of 12 Hz and with standard milling time 120 or 240 h. To prevent the
0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 0 ) 0 1 8 6 8 - 2
H. Ino et al. / Materials Science and Engineering A312 (2001) 262–266
oxidization the mixing of metal powders was done in a globe box filled with nitrogen gas and the grinding of them in the airtight vial. X-ray diffraction step scanning method was used to measure the lattice parameters of the alloys precisely. The scanning speed was 1° h − 1 and the sampling interval 0.01°. To investigate the magnetic state of the alloys the samples were examined by a vibrating sample magnetometer (VSM) and Mossbauer effect spectrometer. The alloyed powders less than 50 mm was selected by a sieve of 300 meshes for effective detection of absorbed g-rays in the Mossbauer effect measurement.
Fig. 1. Change in atomic volume of FCC Fe0.5(Cu1 − y Auy )0.5 alloys and BCC Fe0.7(Cu1 − y Auy )0.3 alloys.
Fig. 2. Magnetization vs. temperature curve for the Fe0.5Cu0.4Au0.1 alloy. The arrow denoted as Tc indicates the Curie temperature of the FCC solid solution and Tx shows the starting point of the decomposition of the solution.
263
3. Results The FCC supersaturated solutions were obtained in the alloys containing less than 60% of iron, whereas the BCC solutions were formed in the alloys containing more than 70% of iron. The mixture of FCC and BCC phases was obtained at 65% of iron. Similar results were also obtained in the ternary alloys substituting 10–40% gold for copper. The substitution of gold for copper showed a trend favorable to form the BCC phase but the effect was not significant. The measurements of X-ray diffraction showed that the lattice parameters, and thus the atomic volumes of both FCC and BCC alloys increased with increasing substitution of Au atoms for Cu. Fig. 1 shows the change in atomic volumes of the FCC Fe0.5(Cu1 − yAuy )0.5 alloys (y= 0, 0.1, 0.2, 0.4) and the BCC Fe0.7(Cu1 − y Auy )0.3 alloys (y= 0, 0.2, 0.4) as functions of Au substitution for Cu. The values for pure Cu, BCC a-iron and FCC g-iron are also included in the figure. In the alloys of Fe0.65Cu0.35 − y Auy the mixture of FCC and BCC phases were observed. Reliable data on the values of atomic volume of the FCC phase were not obtained, although the trend of increase with increasing Au substitution was observed. The atomic volume of the FCC Fe0.5(Cul − y Auy )0.5 alloys reaches 13.3× 10 − 3 nM3 at y= 0.4, which is about 10% expansion from Fe0.5Cu0.5 and 17% expansion from g-iron. The atomic volume of the FCC alloys increases linearly with increasing Au concentration at a rate (atomic volume per substitution, y, of Au atoms) of 3.0× 10 − 3 nM3 or 25% for full substitution of Au (Fe0.5Au0.5. This rate is consistent with the value (2.6× 10 − 3 nM3 or 22%) expected from the difference in atomic volume between Cu and Au. In the BCC alloys of Fe0.7Cu0.3 − y Auy the atomic volume also increased almost linearly at a rate of 1.6× 10 − 3 nM3 or 13% for full substitution of Au (Fe0.7Au0.3). The rate is in good agreement with the value (1.5× 10 − 3 nM3 or 13%) expected from the size difference between Cu and Au. Fig. 2 shows the magnetization versus temperature curve for the alloy of Fe0.5Cu0.4Au0.1 measured at a constant heating rate of 0.1 K s − 1 in a weak external magnetic field of 0.5 kOe. The arrow denoted as Tc points the Curie temperature of the FCC solid solution and Tx indicate the starting point of the decomposition of the solution into BCC iron rich and FCC copper rich phases. Fig. 3 shows the changes of Tc and Tx for the FCC alloys of Fe0.5Cu0.5 − y Auy as a function of Au substitution. The Curie temperature of the alloys increases with the concentration of Au atoms. It is, therefore, concluded that the substitution of Au for Cu stabilizes the ferromagnetism of the FCC alloys. Furthermore, the increased substitution of Au for Cu tends to increase the stability of the supersaturated FCC solid solutions.
264
H. Ino et al. / Materials Science and Engineering A312 (2001) 262–266
Fig. 3. Changes in Curie temperature, Tc, and decomposition temperature, Tx, of FCC Fe0.5(Cu1 − y Auy )0.5 alloys.
Fig. 4. Mossbauer spectrum for the FCC Fe0.5Cu0.4Au0.1 alloy measured at 82 K (a) and analyzed magnetic hyperfine field distribution (b).
Fig. 4a shows a Mossbauer spectrum of Fe0.5Cu0.40Au0.1 measured at 82 K. The spectrum consists of a broad sextet, indicating the magnetic hyperfine splitting of energy level of iron nuclei. The distribution profile of the magnetic hyperfine field derived from the Mossbauer spectrum is shown in Fig. 4b. The average magnetic field of 57Fe in the alloy is estimated to be about 32 T, which is about 0.94 of that in pure a-iron. Fig. 5 shows the Mossbauer spectrum of the same alloy measured at 292 K, together with the distribution profile of the magnetic hyperfine field. The average value of the magnetic field is about 26 T. The sharp decrease in the magnetic field from 32 to 26 T (81%) is due to the relatively low Curie temperature of the alloy ( 530 K) as compared with a-iron (1043 K). The magnetization measurement of the same alloy showed that the values of saturation magnetization were 89.3 emu g − 1 at 77 K and 75.5 emu g − 1 at 293 K, which means 234 emu g − 1 Fe and 198 emu g − 1 Fe, respectively, by taking into account the iron mass fraction (0.382) of the alloy. The measurements of magnetization of Fe0.5Cu0.3Au0.2 show 79.0 emu g − 1, i.e. 244 emu g − 1 Fe at 77 K and 68.4 emu g − 1, i.e. 212 emu g − 1 Fe at 293 K.
Fig. 5. Mossbouer spectrum for the same alloy measured at 291 K (a) and the analyzed magnetic hyperfine field distribution (b).
H. Ino et al. / Materials Science and Engineering A312 (2001) 262–266
4. Discussion It is known that the stability of ferromagnetism in the transition metal alloys is strongly dependent on the atomic distance of the alloys conceptionally shown as Bethe –Slater curve [12]. We have suggested in a previous paper that the atomic volume is a much more essential parameter than the atomic distance, irrespective of crystal structure, to consider the conditions for the appearance of ferromagnetism [11]. The FCC giron, of which the atomic volume is estimated to be 11.4× 10 − 3 nM3 [13], is known as an antiferromagnetic substance with a small magnetic moment (− 0.1 mB) and low Neel temperature (67 K) [14]. In contrast, the BCC g-iron with the atomic volume of 11.77×10 − 3 nM3 is ferromagnetic, although it has a shorter atomic distance (0.248 nm) than that of g-iron (0.252 nm). Previous studies on Fe– Cu alloys prepared by mechanical alloying revealed that these alloys are ferromagnetic and have larger atomic volumes than that of a-iron [2,10,11]. The present experiment clearly shows that the substitution of Au for Cu expands the atomic volumes of the alloys and enhances their ferromagnetic behavior. In the Fe0.5(Cu1 − y Auy )0.5 alloys the Curie temperature, the magnetic moment of iron and the magnetic hyperfine filed of iron nuclei increase with increasing Au substitution for Cu. The magnetic moment of iron in the Fe0.5Cu0.4Au0.1 is estimated to be about 2.34 mB from the magnetization measurements. It should be noted that this value is 5% larger than that of a-iron (2.22 mB). The enhancement of the magnetic moment is even larger in the Fe0.5Cu0.3Au0.2 alloy (2.44 mB). The FCC structure of the alloys is presumably responsible for such a high magnetic moment. The magnetic hyperfine field Hmhf of iron in alloys is expressed in general as
265
perhaps corresponds to the iron atoms which are surrounded mainly by magnetic ions, and have magnetic moment larger than a-iron. Iron atoms having the same magnetic moment but surrounded mainly by non-magnetic ions will show lower values of magnetic field. This consideration well explains the discrepancy between the measured magnetic moment of iron (2.34 mB) and the average magnetic hyperfine field of the alloy at 82 K (32 T). The former is larger than that of a-iron (2.22 mB) and the latter is smaller than that of a-iron (34 T). It is considered that the decrease in Hmhf is mainly caused by the decrease in v¯ nn. Another possibility is that changes in the coefficient, due to expansion of the volume of the alloy, cause the decrease in Hmhf. Next, we discuss the ferromagnetic to paramagnetic transition of the FCC Fe–Cu –Au alloys. The Curie temperature of the Fe0.5(Cu1 − y Auy )0.5 alloy increases with Au substitution, as shown in Fig. 3. The Curie temperature of Fe0.5Cu0.3Au0.2 reaches 585 K. This value is highest among Fe–Cu based FCC alloys prepared by mechanical alloying [2]. However, the value is far below the Curie temperature of BCC a-iron (1043 K). The Curie temperature Tc of a ferromagnet is given by the relation within a mean field approximation Tc = zJ/2k, where z is the number of nearest neighboring ferromagnetic atoms, J the exchange interaction energy and k is the Boltzmann constant. For the BCC a-iron z= 8 and for the FCC Fe0.5(Cu1 − y Auy )0.5 alloys z = 6 in average. Then the ratio of exchange energy J of the FCC Fe0.5Cu0.3Au0.2 alloy to a-iron is estimated to be about 0.75. It is, therefore, concluded that the magnetic moment of iron in the Fe0.5Cu0.3Au0.2 alloy is larger than a-iron but the exchange interaction between iron atoms is less than that of a-iron.
Hmhf =avFe +bv¯ nn
5. Conclusion
where vFe is the magnetic moment of the iron atom and v¯ nn is the averaged value of magnetic moment of surrounding atoms. Both vFe and v¯ nn depend in general on the environments of the iron atom. In the present case, vFe is probably determined only by the atomic volume of iron, namely, by the average atomic distances between the centered iron atom and the nearest neighboring atoms. v¯ nn Depends directly on the species of nearest neighboring atoms, that is, on the number of magnetic ions (iron atoms). The magnetic hyperfine field of 57Fe in the Fe0.5Cu0.4Au0.1 alloy widely distributes from 22 to 38 T at 82 K and from 17 to 31 T at 291 K as shown in Figs. 4 and 5. This wide distribution is probably arising from the variation in v¯ nn, namely, the difference in the species of nearest neighboring atoms. The uppermost value of the distribution of magnetic field (\ 35 T)
The atomic volume of the FCC Fe0.5(Cu1 − y Auy )0.5 alloys (y= 0, 0.1, 0.2, 0.4) expands in proportion to the amount of Au substitution for Cu, from 12.09×10 − 3 to 13.13× 10 − 3 nM3. The Curie temperature of the alloys rises almost linearly with the substitution of Au from 216 to 309°C for 40% replacement. The magnetic moment of iron in the alloys increases with the substitution of Au. The value in Fe0.5Cu0.4Au0.1 is estimated to be 2.34 mB and that in Fe0.5Cu0.3Au0.2 is 2.44 mB. These values are larger than the magnetic moment of a-iron (2.22 mB). The magnetic hyperfine field of 57Fe nuclei in the Fe0.5Cu0.4Au0.1 alloy shows wide distribution from 22 to 38 and 17–31 T at 82 and 292 K, respectively. The wide distribution is probably caused by the variation of
266
H. Ino et al. / Materials Science and Engineering A312 (2001) 262–266
species of surrounding atoms of iron. Non-magnetic surrounding atoms (Cu, Au) cause the reduction of magnetic hyperfine field, even when the magnetic moment of iron is unchanged. The Curie temperature of the Fe0.5(Cu1 − y Auy )0.5 alloys is very low compared with the BCC a-iron, which suggests that the exchange interaction energy between iron atoms is smaller in the FCC alloys. The exchange energy J for Fe0.5Cu0.3Au0.2 is estimated to be about 0.74 of a-iron.
Acknowledgements The present work was support by a grant-in-aid for Research on Priority Area of Phase Transformations (1997–1999) from the Ministry of Education, Science and Culture of Japan.
References [1] K. Uenishi, K.F. Kobayashi, S. Nasu, H. Hatano, K.N. Ishihara, P.H. Shingu, Z. Metallkd. 83 (1992) 132 –135.
.
[2] E. Ma, M. Atzmon, E.E. Pinkerton, J. Appl. Phys. 74 (1993) 955 – 962. [3] J.Z. Jiang, U. Gonser, C. Gente, R. Bormann, Appl. Phys. Lett. 63 (1993) 1056 – 1058. [4] P.P. Macri, P. Rose, R. Frattini, S. Enzo, G. Principi, W.X. Hu, N. Cowlam, J. Appl. Phys. 76 (1994) 4061 – 4067. [5] O. Drbohlav, A.R. Yavari, J. Magn. Magn. Mater. 137 (1994) 243 – 248. [6] O. Drbohlav, A.R. Yavari, Acta Metall. Mater. 43 (1995) 1799 – 1809. [7] B. Mazumdar, M.M. Raja, A. Naraganasamy, K. Chattopadhyay, J. Alloys Compounds 248 (1997) 192 – 200. [8] K. Tokumitsu, Mater. Sci. Forum 269 (1998) 467 – 472. [9] K. Tokumitsu, Mater. Sci. Forum 312 – 314 (1999) 405 –410, 557 – 562. [10] H. Ino, K. Tokumitsu, in: M. Koiwa, K. Otsuka, T. Miyazaki (Eds.), Solid – Solid Phase Transformations PTM’99, Japan Institute of Metals Proceedings (JIMIC-3), vol. 12, 1999, pp. 1255 – 1258. [11] H. Ino, K. Hayasi, T. Otsuka, D. Isobe, K. Tokumitsu, K. Oda, in: Proceedings of the Tenth International Conference on Rapidly Quenches and Metastable Materials, Bangalore, August 1999, in press. [12] L. Neel, ‘Le Magnetism’, vol. 2, 1940, quoted from K. Ohta, ‘Jikikougaku no Kiso’, 1973. [13] K. Oda, H. Fujimura, H. Ino, J. Phys.: Condens. Matter 6 (1994) 679 – 692. [14] U. Gonser, C.J. Meechan, A.H. Muir, H. Wiedersich, J. Appl. Phys. 34 (1963) 2373 – 2378.
Stability of ferromagnetism in FCC Fe–Cu–Au alloys prepared by mechanical alloying H. Ino a,*, M. Kincho b, K. Oda c, K. Tokumitsu d b
a College of Engineering, Hosei Uni6ersity, Koganei, Tokyo 184 -8584, Japan Graduate student, College of Engineering, Hosei Uni6ersity, Koganei, Tokyo 184 -8584, Japan c Institute of Industrial Science, Uni6ersity of Tokyo, Minato-ku, Tokyo 106 -8558, Japan d Graduate School of Engineering, Uni6ersity of Tokyo, Bunkyo-ku, Tokyo 113 -8656, Japan
Received 26 May 2000; received in revised form 8 September 2000
Abstract We have studied the relation between the stability of ferromagnetism and the atomic volume of FCC Fe– Cu–Au alloys prepared by mechanical alloying by means of X-ray diffraction, magnetization measurement and Mossbauer effect. The atomic volume of the FCC Fe0.5Cu0.5 alloy increased almost linearly with the substitution of Au atoms for Cu from original 12.09 ×10 − 3 to 13.31 ×10 − 3 nm3 for 40% replacement. The Curie temperature of the alloy also increased in the same manner from 489 to 582 K. It is found that the increase in atomic volume stabilizes the ferromagnetic state of the FCC alloys. The values of magnetic moment of iron in Fe0.5Cu0.4Au0.1 and Fe0.5Cu0.3Au0.2 were estimated to be 2.34 and 2.44 mB, respectively, which are larger than that of a-iron (2.22 mB). The magnetic hyperfine field of iron in Fe0.5Cu0.4Au0.1 showed wide distribution from 22 to 38 T at 82 K, which is probably caused by the variation of species of surrounding atoms of iron. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Mechanical alloying; Iron–copper–gold alloy; Atomic volume; Ferromagnetism; Magnetic moment; Mossbaure effect
1. Introduction Iron and copper elements are partially soluble with each other in equilibrium (B 11 at.% Cu in Fe, B 4.8 at.% Fe in Cu). However, mechanical alloying method allows supersaturated solid solutions to be formed in the whole range of the Fe – Cu system [1 – 11]. The BCC structure is formed in the alloys containing more than about 65% of iron, whereas the FCC structure of the solution is formed in the alloys containing less than that percentage of iron [1,2,10,11]. The iron atoms in the FCC solution have a large magnetic moment comparable to that of the BCC iron [2,11]. We have concluded in previous papers [10,11] that the ferromagnetism of the FCC Fe – Cu alloys is stabilized by the expansion of the atomic volume of the lattice.
* Corresponding author. Fax: + 81-423-876121. E-mail address: [email protected] (H. Ino).
The purpose of the present work is to verify clearly the relation between the stability of ferromagnetism and the atomic volume of the FCC alloys. We prepared ternary Fe –Cu –Au alloys in which Cu atoms (atomic diameter 0.2556 nm) were partly replaced by Au atoms (0.2884 nm) in order to expand the FCC lattice.
2. Experimental procedure We prepared binary Fe1 − x Cux and ternary Fe1 − x(Cu1 − y Auy )x alloys (x= 0.3, 0.35, 0.5; y= 0, 0.1, 0.2, 0.4) by grinding mechanically powders of 99.9% pure Fe (B 300 meshes), Cu (B15 mm) and Au ( B100 meshes). Metal powders of 0.3 mol in total were put into a zirconia vial together with 30 zirconia balls with a diameter of 10 mm and a small amount (0.0002 mol) of stearic acid (CH3(CH2)16COOH) to prevent coagulation of the powders. A machine (Super-Misuni) was operated with a vibration frequency of 12 Hz and with standard milling time 120 or 240 h. To prevent the
0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 0 ) 0 1 8 6 8 - 2
H. Ino et al. / Materials Science and Engineering A312 (2001) 262–266
oxidization the mixing of metal powders was done in a globe box filled with nitrogen gas and the grinding of them in the airtight vial. X-ray diffraction step scanning method was used to measure the lattice parameters of the alloys precisely. The scanning speed was 1° h − 1 and the sampling interval 0.01°. To investigate the magnetic state of the alloys the samples were examined by a vibrating sample magnetometer (VSM) and Mossbauer effect spectrometer. The alloyed powders less than 50 mm was selected by a sieve of 300 meshes for effective detection of absorbed g-rays in the Mossbauer effect measurement.
Fig. 1. Change in atomic volume of FCC Fe0.5(Cu1 − y Auy )0.5 alloys and BCC Fe0.7(Cu1 − y Auy )0.3 alloys.
Fig. 2. Magnetization vs. temperature curve for the Fe0.5Cu0.4Au0.1 alloy. The arrow denoted as Tc indicates the Curie temperature of the FCC solid solution and Tx shows the starting point of the decomposition of the solution.
263
3. Results The FCC supersaturated solutions were obtained in the alloys containing less than 60% of iron, whereas the BCC solutions were formed in the alloys containing more than 70% of iron. The mixture of FCC and BCC phases was obtained at 65% of iron. Similar results were also obtained in the ternary alloys substituting 10–40% gold for copper. The substitution of gold for copper showed a trend favorable to form the BCC phase but the effect was not significant. The measurements of X-ray diffraction showed that the lattice parameters, and thus the atomic volumes of both FCC and BCC alloys increased with increasing substitution of Au atoms for Cu. Fig. 1 shows the change in atomic volumes of the FCC Fe0.5(Cu1 − yAuy )0.5 alloys (y= 0, 0.1, 0.2, 0.4) and the BCC Fe0.7(Cu1 − y Auy )0.3 alloys (y= 0, 0.2, 0.4) as functions of Au substitution for Cu. The values for pure Cu, BCC a-iron and FCC g-iron are also included in the figure. In the alloys of Fe0.65Cu0.35 − y Auy the mixture of FCC and BCC phases were observed. Reliable data on the values of atomic volume of the FCC phase were not obtained, although the trend of increase with increasing Au substitution was observed. The atomic volume of the FCC Fe0.5(Cul − y Auy )0.5 alloys reaches 13.3× 10 − 3 nM3 at y= 0.4, which is about 10% expansion from Fe0.5Cu0.5 and 17% expansion from g-iron. The atomic volume of the FCC alloys increases linearly with increasing Au concentration at a rate (atomic volume per substitution, y, of Au atoms) of 3.0× 10 − 3 nM3 or 25% for full substitution of Au (Fe0.5Au0.5. This rate is consistent with the value (2.6× 10 − 3 nM3 or 22%) expected from the difference in atomic volume between Cu and Au. In the BCC alloys of Fe0.7Cu0.3 − y Auy the atomic volume also increased almost linearly at a rate of 1.6× 10 − 3 nM3 or 13% for full substitution of Au (Fe0.7Au0.3). The rate is in good agreement with the value (1.5× 10 − 3 nM3 or 13%) expected from the size difference between Cu and Au. Fig. 2 shows the magnetization versus temperature curve for the alloy of Fe0.5Cu0.4Au0.1 measured at a constant heating rate of 0.1 K s − 1 in a weak external magnetic field of 0.5 kOe. The arrow denoted as Tc points the Curie temperature of the FCC solid solution and Tx indicate the starting point of the decomposition of the solution into BCC iron rich and FCC copper rich phases. Fig. 3 shows the changes of Tc and Tx for the FCC alloys of Fe0.5Cu0.5 − y Auy as a function of Au substitution. The Curie temperature of the alloys increases with the concentration of Au atoms. It is, therefore, concluded that the substitution of Au for Cu stabilizes the ferromagnetism of the FCC alloys. Furthermore, the increased substitution of Au for Cu tends to increase the stability of the supersaturated FCC solid solutions.
264
H. Ino et al. / Materials Science and Engineering A312 (2001) 262–266
Fig. 3. Changes in Curie temperature, Tc, and decomposition temperature, Tx, of FCC Fe0.5(Cu1 − y Auy )0.5 alloys.
Fig. 4. Mossbauer spectrum for the FCC Fe0.5Cu0.4Au0.1 alloy measured at 82 K (a) and analyzed magnetic hyperfine field distribution (b).
Fig. 4a shows a Mossbauer spectrum of Fe0.5Cu0.40Au0.1 measured at 82 K. The spectrum consists of a broad sextet, indicating the magnetic hyperfine splitting of energy level of iron nuclei. The distribution profile of the magnetic hyperfine field derived from the Mossbauer spectrum is shown in Fig. 4b. The average magnetic field of 57Fe in the alloy is estimated to be about 32 T, which is about 0.94 of that in pure a-iron. Fig. 5 shows the Mossbauer spectrum of the same alloy measured at 292 K, together with the distribution profile of the magnetic hyperfine field. The average value of the magnetic field is about 26 T. The sharp decrease in the magnetic field from 32 to 26 T (81%) is due to the relatively low Curie temperature of the alloy ( 530 K) as compared with a-iron (1043 K). The magnetization measurement of the same alloy showed that the values of saturation magnetization were 89.3 emu g − 1 at 77 K and 75.5 emu g − 1 at 293 K, which means 234 emu g − 1 Fe and 198 emu g − 1 Fe, respectively, by taking into account the iron mass fraction (0.382) of the alloy. The measurements of magnetization of Fe0.5Cu0.3Au0.2 show 79.0 emu g − 1, i.e. 244 emu g − 1 Fe at 77 K and 68.4 emu g − 1, i.e. 212 emu g − 1 Fe at 293 K.
Fig. 5. Mossbouer spectrum for the same alloy measured at 291 K (a) and the analyzed magnetic hyperfine field distribution (b).
H. Ino et al. / Materials Science and Engineering A312 (2001) 262–266
4. Discussion It is known that the stability of ferromagnetism in the transition metal alloys is strongly dependent on the atomic distance of the alloys conceptionally shown as Bethe –Slater curve [12]. We have suggested in a previous paper that the atomic volume is a much more essential parameter than the atomic distance, irrespective of crystal structure, to consider the conditions for the appearance of ferromagnetism [11]. The FCC giron, of which the atomic volume is estimated to be 11.4× 10 − 3 nM3 [13], is known as an antiferromagnetic substance with a small magnetic moment (− 0.1 mB) and low Neel temperature (67 K) [14]. In contrast, the BCC g-iron with the atomic volume of 11.77×10 − 3 nM3 is ferromagnetic, although it has a shorter atomic distance (0.248 nm) than that of g-iron (0.252 nm). Previous studies on Fe– Cu alloys prepared by mechanical alloying revealed that these alloys are ferromagnetic and have larger atomic volumes than that of a-iron [2,10,11]. The present experiment clearly shows that the substitution of Au for Cu expands the atomic volumes of the alloys and enhances their ferromagnetic behavior. In the Fe0.5(Cu1 − y Auy )0.5 alloys the Curie temperature, the magnetic moment of iron and the magnetic hyperfine filed of iron nuclei increase with increasing Au substitution for Cu. The magnetic moment of iron in the Fe0.5Cu0.4Au0.1 is estimated to be about 2.34 mB from the magnetization measurements. It should be noted that this value is 5% larger than that of a-iron (2.22 mB). The enhancement of the magnetic moment is even larger in the Fe0.5Cu0.3Au0.2 alloy (2.44 mB). The FCC structure of the alloys is presumably responsible for such a high magnetic moment. The magnetic hyperfine field Hmhf of iron in alloys is expressed in general as
265
perhaps corresponds to the iron atoms which are surrounded mainly by magnetic ions, and have magnetic moment larger than a-iron. Iron atoms having the same magnetic moment but surrounded mainly by non-magnetic ions will show lower values of magnetic field. This consideration well explains the discrepancy between the measured magnetic moment of iron (2.34 mB) and the average magnetic hyperfine field of the alloy at 82 K (32 T). The former is larger than that of a-iron (2.22 mB) and the latter is smaller than that of a-iron (34 T). It is considered that the decrease in Hmhf is mainly caused by the decrease in v¯ nn. Another possibility is that changes in the coefficient, due to expansion of the volume of the alloy, cause the decrease in Hmhf. Next, we discuss the ferromagnetic to paramagnetic transition of the FCC Fe–Cu –Au alloys. The Curie temperature of the Fe0.5(Cu1 − y Auy )0.5 alloy increases with Au substitution, as shown in Fig. 3. The Curie temperature of Fe0.5Cu0.3Au0.2 reaches 585 K. This value is highest among Fe–Cu based FCC alloys prepared by mechanical alloying [2]. However, the value is far below the Curie temperature of BCC a-iron (1043 K). The Curie temperature Tc of a ferromagnet is given by the relation within a mean field approximation Tc = zJ/2k, where z is the number of nearest neighboring ferromagnetic atoms, J the exchange interaction energy and k is the Boltzmann constant. For the BCC a-iron z= 8 and for the FCC Fe0.5(Cu1 − y Auy )0.5 alloys z = 6 in average. Then the ratio of exchange energy J of the FCC Fe0.5Cu0.3Au0.2 alloy to a-iron is estimated to be about 0.75. It is, therefore, concluded that the magnetic moment of iron in the Fe0.5Cu0.3Au0.2 alloy is larger than a-iron but the exchange interaction between iron atoms is less than that of a-iron.
Hmhf =avFe +bv¯ nn
5. Conclusion
where vFe is the magnetic moment of the iron atom and v¯ nn is the averaged value of magnetic moment of surrounding atoms. Both vFe and v¯ nn depend in general on the environments of the iron atom. In the present case, vFe is probably determined only by the atomic volume of iron, namely, by the average atomic distances between the centered iron atom and the nearest neighboring atoms. v¯ nn Depends directly on the species of nearest neighboring atoms, that is, on the number of magnetic ions (iron atoms). The magnetic hyperfine field of 57Fe in the Fe0.5Cu0.4Au0.1 alloy widely distributes from 22 to 38 T at 82 K and from 17 to 31 T at 291 K as shown in Figs. 4 and 5. This wide distribution is probably arising from the variation in v¯ nn, namely, the difference in the species of nearest neighboring atoms. The uppermost value of the distribution of magnetic field (\ 35 T)
The atomic volume of the FCC Fe0.5(Cu1 − y Auy )0.5 alloys (y= 0, 0.1, 0.2, 0.4) expands in proportion to the amount of Au substitution for Cu, from 12.09×10 − 3 to 13.13× 10 − 3 nM3. The Curie temperature of the alloys rises almost linearly with the substitution of Au from 216 to 309°C for 40% replacement. The magnetic moment of iron in the alloys increases with the substitution of Au. The value in Fe0.5Cu0.4Au0.1 is estimated to be 2.34 mB and that in Fe0.5Cu0.3Au0.2 is 2.44 mB. These values are larger than the magnetic moment of a-iron (2.22 mB). The magnetic hyperfine field of 57Fe nuclei in the Fe0.5Cu0.4Au0.1 alloy shows wide distribution from 22 to 38 and 17–31 T at 82 and 292 K, respectively. The wide distribution is probably caused by the variation of
266
H. Ino et al. / Materials Science and Engineering A312 (2001) 262–266
species of surrounding atoms of iron. Non-magnetic surrounding atoms (Cu, Au) cause the reduction of magnetic hyperfine field, even when the magnetic moment of iron is unchanged. The Curie temperature of the Fe0.5(Cu1 − y Auy )0.5 alloys is very low compared with the BCC a-iron, which suggests that the exchange interaction energy between iron atoms is smaller in the FCC alloys. The exchange energy J for Fe0.5Cu0.3Au0.2 is estimated to be about 0.74 of a-iron.
Acknowledgements The present work was support by a grant-in-aid for Research on Priority Area of Phase Transformations (1997–1999) from the Ministry of Education, Science and Culture of Japan.
References [1] K. Uenishi, K.F. Kobayashi, S. Nasu, H. Hatano, K.N. Ishihara, P.H. Shingu, Z. Metallkd. 83 (1992) 132 –135.
.
[2] E. Ma, M. Atzmon, E.E. Pinkerton, J. Appl. Phys. 74 (1993) 955 – 962. [3] J.Z. Jiang, U. Gonser, C. Gente, R. Bormann, Appl. Phys. Lett. 63 (1993) 1056 – 1058. [4] P.P. Macri, P. Rose, R. Frattini, S. Enzo, G. Principi, W.X. Hu, N. Cowlam, J. Appl. Phys. 76 (1994) 4061 – 4067. [5] O. Drbohlav, A.R. Yavari, J. Magn. Magn. Mater. 137 (1994) 243 – 248. [6] O. Drbohlav, A.R. Yavari, Acta Metall. Mater. 43 (1995) 1799 – 1809. [7] B. Mazumdar, M.M. Raja, A. Naraganasamy, K. Chattopadhyay, J. Alloys Compounds 248 (1997) 192 – 200. [8] K. Tokumitsu, Mater. Sci. Forum 269 (1998) 467 – 472. [9] K. Tokumitsu, Mater. Sci. Forum 312 – 314 (1999) 405 –410, 557 – 562. [10] H. Ino, K. Tokumitsu, in: M. Koiwa, K. Otsuka, T. Miyazaki (Eds.), Solid – Solid Phase Transformations PTM’99, Japan Institute of Metals Proceedings (JIMIC-3), vol. 12, 1999, pp. 1255 – 1258. [11] H. Ino, K. Hayasi, T. Otsuka, D. Isobe, K. Tokumitsu, K. Oda, in: Proceedings of the Tenth International Conference on Rapidly Quenches and Metastable Materials, Bangalore, August 1999, in press. [12] L. Neel, ‘Le Magnetism’, vol. 2, 1940, quoted from K. Ohta, ‘Jikikougaku no Kiso’, 1973. [13] K. Oda, H. Fujimura, H. Ino, J. Phys.: Condens. Matter 6 (1994) 679 – 692. [14] U. Gonser, C.J. Meechan, A.H. Muir, H. Wiedersich, J. Appl. Phys. 34 (1963) 2373 – 2378.