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Magnetic property of a Zn–Mg–Sc icosahedral quasicrystal
Journal of Alloys and Compounds 342 (2002) 384–388
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Magnetic property of a Zn–Mg–Sc icosahedral quasicrystal Shiro Kashimoto a , Senni Motomura b , Hiroshi Nakano c , Yasushi Kaneko d , Tsutomu Ishimasa d , c, Susumu Matsuo * a b
Satellite Venture Business Laboratory, Utsunomiya University, Yoto, Utsunomiya 321 -8585, Japan Graduate School of Human Informatics, Nagoya University, Chikusa-ku, Nagoya 464 -8601, Japan c School of Informatics and Sciences, Nagoya University, Chikusa-ku, Nagoya 464 -8601, Japan d Graduate School of Engineering, Hokkaido University, Kita-ku, Sapporo 060 -8628, Japan
Abstract We have investigated the magnetism of a new Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal and a Zn 85.5 Sc 14.5 cubic phase, which is interpreted to be a 1 / 1 approximant of the new icosahedral quasicrystal, in the temperature region between 2 and 700 K. The magnetic susceptibility of the Zn 80 Mg 5 Sc 15 icosahedral quasicrystal shows an increase from 21.3310 27 to 20.8310 27 cgsemu / g with a rise in temperature from 90 to 700 K. The Zn 85.5 Sc 14.5 cubic phase shows also a rise from 21.8310 27 to 21.0310 27 cgsemu / g between 120 and 700 K. The increase in the susceptibility with a rise in temperature is accounted for by a temperature dependence of the Pauli paramagnetism. The experimental results strongly suggest a pseudogap in the electronic density of states at Fermi energy for the Zn 80 Mg 5 Sc 15 quasicrystal and the Zn 85.5 Sc 14.5 approximant, which has been observed in various stable icosahedral quasicrystals. 2002 Elsevier Science B.V. All rights reserved. Keywords: Quasicrystal; Magnetic measurements
1. Introduction Since the first report on the icosahedral phase in Al–Mn alloy which exhibited an icosahedral symmetry in electron diffraction patterns by Shechtman et al. [1], many studies have been made on the problem of why the unique structure with quasi-periodicity can stably exist. Although the first report by Shechtman et al. was carried out on the metastable icosahedral phase in a rapidly quenched alloy, until now many kinds of thermodynamically stable icosahedral quasicrystals have been discovered such as Al–Cu–Li [2], Al–Cu–Fe [3], Al–Pd–Mn [4], Zn–Mg–R (R5Ga, Y, Tb, Dy, Ho and Er) [5,6] and so on. When structural stability of quasicrystals is examined from the viewpoint of the electron theory, the Hume-Rothery rule [7] is theoretically and experimentally important. The rule can be explained by the stabilization mechanism on the basis of the interaction between the Fermi-sphere and Brillouin zone in the crystal alloy [8]. Friedel theoretically showed that the quasicrystal structure can be also stable because the electronic density states exhibit a minimum *Corresponding author. Tel.: 181-52-789-4762; fax: 181-52-7894804. E-mail address: [email protected] (S. Matsuo).
(pseudogap) at Fermi energy EF [9]. The pseudogap at EF was investigated experimentally by the ultraviolet photoelectron spectroscopy study of the electronic density of states [10], the electronic specific heat coefficient [11,12] and the temperature dependence of the Pauli paramagnetism [13–15]. The temperature dependence of the Pauli paramagnetism gives important information on the curvature of the electronic density of states at EF and affords a simple in situ method in a wide temperature region. Moreover, this method has an advantage that the measurement is possible even in a small amount of the sample in comparison with other methods. Recently a new type of icosahedral quasicrystal was found in the Zn–Mg–Sc alloy by Kaneko et al. [16]. The quasicrystal with the composition of Zn 80 Mg 5 Sc 15 has a primitive icosahedral quasilattice (P-type) with a 6-dimensional lattice parameter a 6D 50.7115 nm and shows a structural perfection in the sharpness of diffraction spots and a small deviation of the electron diffraction spots from the ideal icosahedral symmetric positions. This new quasicrystal is also expected to be a stable phase because of its presence in the annealed alloys. The Zn–Mg–Sc alloy includes two other crystalline phases as impurities; MgZn 2 -type Laves phase and Zn 17 Sc 3 -type cubic phase. The space group of the Zn 17 Sc 3 -type cubic phase is Im3¯
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 02 )00260-8
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[17], and can be interpreted as a 1 / 1 approximant crystal of the new quasicrystal [16]. One feature of the Zn 80 Mg 5 Sc 15 quasicrystal and the Zn 17 Sc 3 -type approximant is that it does not contain magnetic atoms like Fe, Mn and rare earth elements as in other stable quasicrystals known to date. Therefore, there is a possibility of detecting clearly the temperature dependence of the Pauli paramagnetism to lower temperatures without lurking in the temperature dependence of the Curie–Weiss paramagnetism arising from atoms with magnetic moments. In this paper, we present preliminary experimental observations of the temperature dependence of the Pauli paramagnetism suggesting a pseudogap in the electronic density of states at EF in the Zn 80 Mg 5 Sc 15 new P-type icosahedral quasicrystal and the Zn 17 Sc 3 -type cubic phase interpreted to be the 1 / 1 type approximant of the former.
2. Experimental procedure Ingots with the nominal compositions, Zn 80 Mg 5 Sc 15 and Zn 86 Sc 14 , were prepared from the high-purity materials of Zn (Nilaco, 99.998%), Mg (Nilaco, 99.95%) and Sc (ShinEtsu Chemical, 99.9%; according to the analysis table of the material manufacturer, the Sc material includes some impurities; Al 44 ppm, Ca 16 ppm, Fe 360 ppm and W 86 ppm). The Zn 86 Sc 14 alloy was synthesized in a silica tube in an atmosphere of 200 Torr argon at 1112 K for 4 h and then quenched in water. The Zn 80 Mg 5 Sc 15 alloy was synthesized by adding zinc and magnesium to Zn 78 Sc 22 alloy prepared in advance. The Zn 78 Sc 22 alloy was synthesized in a silica tube in an argon atmosphere at 1068 K. Weighed materials of Zn, Mg and powdered Zn 78 Sc 22 alloy were enclosed in a package made of molybdenum foil (Nilaco, thickness 0.05 mm, 99.95%) in order to avoid the chemical reaction with a silica ampoule. The specimen was held at 1093 K for 3 h for melting and subsequently cooled to the annealing temperature at the rate of 58 K / h. The specimen was held at the annealing temperature 918 K for 15 h and then quenched in water. The weight loss during the heat treatment of the Zn 80 Mg 5 Sc 15 and the Zn 86 Sc 14 alloy were 0.4% and 2.11%, respectively. The nominal composition of the binary Zn–Sc alloy was estimated to be Zn 85.5 Sc 14.5 on the assumption that the weight loss of the specimen during the heat treatment was due to evaporation of zinc. Characterization of these specimens was carried out by precise analysis of powder X-ray diffraction patterns measured using Cu Ka radiation (Rigaku RINT-2000). Fig. 1a and b show X-ray powder diffraction patterns of the Zn 80 Mg 5 Sc 15 and the Zn 85.5 Sc 14.5 , respectively. The X-ray diffraction peaks of the Zn 80 Mg 5 Sc 15 icosahedral quasicrystal were analyzed by indexing method using six integers [18]. Fig. 1a indicates that a major part of the ingot is the Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal with 6-dimensional lattice parameter a 6D 50.7117 nm, and
Fig. 1. Powder X-ray diffraction patterns. (a) Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal. Reflections due to the icosahedral quasicrystal are indicated by Elser indices. Reflections due to the Zn 17 Sc 3 -type cubic phase and the MgZn 2 -type Laves phase are indicated by three indices written in bold and italic, respectively. (b) Zn 85.5 Sc 14.5 1 / 1 cubic-type approximant of the icosahedral phase. Reflections due to the Zn are denoted by arrowheads.
that the ingot includes a small amount of the Zn 17 Sc 3 -type cubic phase (a51.3864 nm) and the MgZn 2 -type Laves phase (a50.5256 nm, c50.8493 nm). Fig. 1b indicates that the major part of the Zn 85.5 Sc 14.5 ingot is the Zn 17 Sc 3 -type cubic phase (a51.3846 nm), and this ingot includes a small amount of the elementary substance of Zn as a secondary phase indicated by arrowheads in Fig. 1b. More details of the preparation and the characterization of these specimens by using selected-area electron diffraction and scanning electron microscopy are described in Ref. [16]. Samples for the experiment of magnetism were cut from the master ingots at a size suitable for the measurements weighing from 0.2 to 0.3 g. The magnetism in the lower temperature region between 2 and 300 K was measured using a SQUID magnetometer (Quantum Design MPMS-
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7) in a magnetic field of 5 T. Although the magnetization of these samples is linear following M 5 2 xdia H in most of the temperature region, the magnetization shows nonlinearity near the lowest temperature in the low magnetic field. It is probably caused by some magnetic impurity in the Sc material. Thus the Curie constants which were estimated on the data of magnetic susceptibility at the low temperatures (in Section 3) have a little error quantitatively. In the higher temperature region between 77 and 700 K, the temperature dependence of the magnetic susceptibility was measured using a magnetic balance with a standard electromagnet in a magnetic field 1 T. The sample was sealed in a quartz capsule with He atmosphere of 500 Torr in pressure in order to prevent oxidation.
3. Results and discussion Fig. 2 shows the magnetic susceptibility x as a function of temperature T measured by the SQUID magnetometer in the temperature region between 2 and 300 K at a magnetic field of 5 T. The two samples show diamagnetism at high temperatures and Curie–Weiss paramagnetism in low temperatures. A least-squares fitting of x to the following function was tried in the temperature region between 2 and 50 K
x 5 x0 1 C /(T 2 Q )
(1)
where x0 is a constant susceptibility, C is the Curie constant and Q is the Curie temperature. Fitted results are shown by solid curves in Fig. 2. The fitting gives parameters x0 as 21.50310 27 cgsemu / g and 22.06310 27 cgsemu / g, C as 1.04310 26 cgsemu K / g and 1.65310 26 cgsemu K / g, Q as 28.76 K and 217.6 K for Zn 80 Mg 5 Sc 15 and Zn 85.5 Sc 14.5 , respectively. The Curie– Weiss paramagnetism seems to be due to the effect of some impurity included in the sample ingots, because the Zn–Mg–Sc quasicrystal phase and the Zn–Sc approximant phase consisting of Zn, Mg and Sc must have no local magnetic moments. A candidate for the explanation of the Curie–Weiss paramagnetism is the effect of the local magnetic moments of the Fe impurity, since 360 ppm Fe atoms exist in the Sc material. Curie constant C by the Fe impurity is estimated from this Fe concentration by the use of a well-known formula, C 5 Np 2 mB 2 / 3k B , where p is the effective number of Bohr magneton mB (Fe 21 : p55.4, Fe 31 : p55.9) and N is the number of magnetic moments of Fe per gram in the sample. In the case of the Zn 80 Mg 5 Sc 15 quasicrystal, it gives C52.63310 26 cgsemu K / g and C53.14310 26 cgsemu K / g in the case of Fe 21 and Fe 31 , respectively. The values are of the same order as the one obtained by the Curie–Weiss fit, however, these values are not entirely in good agreement. Moreover, according to the theory of virtual bound state, local magnetic moment does not arise for Fe in divalent metals [19]. We must not jump to conclusions about the origin of
Fig. 2. Magnetic susceptibility as a function of temperature of (a) Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal and (b) Zn 85.5 Sc 14.5 1 / 1 cubic-type approximant under 5 T using a SQUID magnetometer. Solid curves indicate a least squares fit to Curie–Weiss law in the temperature region between 2 and 50 K. Insets are measurement results in higher temperatures, using the magnetic balance. The arrows denote the direction in the measurement process.
Curie–Weiss paramagnetism in low temperatures for the present. The magnetic susceptibility x of Zn 80 Mg 5 Sc 15 and Zn 85.5 Sc 14.5 distinctly increases with a rise in temperature in the higher temperature region as shown in Fig. 2. The insets in Fig. 2 are the results of measurements above room temperature region between 300 and 700 K using a magnetic balance. In the first half process with rising temperature, a rate of increase in the magnetic susceptibility changes around 550 K for both samples. After that the susceptibility once more increases with a clear positive gradient. However, in the cooling process, the susceptibility decreases monotonously. We continuously measured the susceptibility with the same process for these samples, then the results of the measurements did not show reappearance of hysteresis of the susceptibility; the susceptibility changed monotonously in both processes. It seems that the hysteresis is caused by some atomic relaxation, because the samples were prepared by quenching in water.
S. Kashimoto et al. / Journal of Alloys and Compounds 342 (2002) 384 – 388
The increase of x with a rise in temperature continues up to 700 K as shown in the insets of Fig. 2 for both the quasicrystal and the approximant. Such an increase in x has been reported for Zn–Mg–Ga [13], Al–Cu–Fe [14] and Al–Pd–Mn [15] and was interpreted by the temperature dependence of Pauli paramagnetism of conduction electrons which varies as AT 2 , where A is a constant. The present samples show also a straight line below 240 K in a x –T 2 plot as shown in Fig. 3. The coefficients A were obtained from the gradient in Fig. 3 as 3.01310 213 cgsemu / K 2 g and 4.40310 213 cgsemu / K 2 g for Zn 80 Mg 5 Sc 15 and Zn 85.5 Sc 14.5 , respectively. These values 213 2 are comparable to 2.0310 cgsemu / K g for Zn–Mg– Ga icosahedral quasicrystal [13]. The coefficient A is given by the following expression [14], A 5 (1 / 3)mB 2 N(EF )(p k)2 [h1 /N(E)jhd 2 N(E) / dE 2 j 2 h1 /N(E)j 2 hdN(E) / dEj 2 ] E 5E F
(2)
where N(EF ) is the electronic density of states and EF is the Fermi energy at 0 K. Now the coefficient A was obtained as positive, the second derivative of the density of
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states d 2 N(EF ) / dEF 2 must be positive because the second term in [ ] is always negative. Therefore the results strongly suggest a valley-like structure; i.e. pseudogap in the density of states at the Fermi energy for the present new Zn 80 Mg 5 Sc 15 quasicrystal and Zn 85.5 Sc 14.5 1 / 1 type approximant. There is a small difference between the values of A for Zn 80 Mg 5 Sc 15 quasicrystal and the one for Zn 85.5 Sc 14.5 approximant as aforesaid. However, we cannot immediately compare the pseudogap depths of the samples, because the coefficient A contains not only d 2 N(E) / dE 2 but also the square of derivative of N(E) with respect to E as shown in the second term in [ ] of Eq. (2). The pseudogap at Fermi energy EF may be mainly related to the strong diffraction spots. We compare the Fermi wave number k F with the diffraction spots obtained by the powder X-ray diffraction measurement. The Fermi wave number k F is expressed as the following relation k F 5 (1 / 2p )(3p 2 N /V )1 / 3
(3)
where N /V is the electron density per unit volume. The values of the mass density and e /a are necessary in order to estimate N /V. The mass densities of the Zn 80 Mg 5 Sc 15 measured by an Archimedes principle method (Mettler Toledo AG245) are given as 6.1760.03 g / cm 3 . The mass density of the Zn 85.5 Sc 14.5 cubic phase was estimated to be 6.23 g / cm 3 from the value of the unit-cell period a5 1.3852 nm and the atom number contained in the unit-cell (24Sc, 136Zn) which are reported [17] for Zn 17 Sc 3 cubic phase. The e /a are given as 2.15 for both Zn 80 Mg 5 Sc 15 and Zn 17 Sc 3 by assuming two valence electrons for Zn, Mg and three valence electrons for Sc. These values and the above relation give k F 52.51 nm 21 and 2.49 nm 21 for Zn 80 Mg 5 Sc 15 and Zn 17 Sc 3 , respectively. The values of k F yield 1 / 2k F 5 0.199 nm and 0.201 nm. The results nearly coincide with the relatively strong spots having indices 0 2 1¯ 2¯ 0 2 (d 5 0.1992 nm) and 6 3 1 (d 5 0.2042 nm) denoted by arrows in Fig. 1. Therefore, the structures of the quasicrystal and the cubic 1 / 1 approximant including Sc are considered to be stabilized by the mechanism of the Hume-Rothery rule.
4. Conclusion
Fig. 3. Magnetic susceptibility of (a) Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal and (b) Zn 85.5 Sc 14.5 1 / 1 cubic-type approximant as a function of square of temperature. Solid lines are obtained by least squares fit to a linear function in the temperature region between (a) 100 and 240 K, (b) 140 and 265 K, respectively.
We have shown in this study that the magnetic susceptibility x shows an increase with T 2 -dependence in the wide temperature region for the new Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal and the Zn 85.5 Sc 14.5 1 / 1 approximant of the quasicrystal. The temperature dependence of x is interpreted on the basis of the temperature dependence of Pauli paramagnetism of conduction electrons. The positive value of coefficient of the T 2 -term signifies that there is a pseudogap in the electronic density of states at the Fermi energy. The Fermi wave number k F , which is estimated by using the values of e /a and the mass density,
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nearly coincides with the relatively strong spots in the X-ray diffraction pattern. The results strongly suggest that the new P-type quasicrystal and its approximant including Sc exhibit the pseudogap inferred from the strong diffraction spots and are stabilized by the mechanism of the Hume-Rothery rule.
Acknowledgements Thanks are due to the Research Center for Molecular Materials, Institute for Molecular Science. The authors would like to thank M. Sakai of the Research Center for help in the use of the SQUID magnetometer.
References [1] D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53 (1984) 1951. [2] B. Dubost, J.M. Lang, M. Tanaka, P. Sainfort, M. Audier, Nature 324 (1986) 48.
[3] A.P. Tsai, A. Inoue, T. Masumoto, Jpn. J. Appl. Phys. 26 (1987) L1505. [4] A.P. Tsai, A. Inoue, Y. Yokoyama, T. Masumoto, Mater. Trans. JIM 31 (1990) 98. [5] W. Ohashi, F. Spaepen, Nature 330 (1987) 555. [6] Z. Luo, S. Zhang, Y. Tang, D. Zhao, Scripta Metall. Mater. 28 (1993) 1513. [7] W. Hume-Rothery, J. Inst. Metals 35 (1926) 295. [8] H. Jones, Proc. Phys. Soc. 49 (1937) 250. [9] J. Friedel, Helv. Phys. Acta 61 (1988) 538. [10] M. Mori, S. Matsuo, T. Ishimasa, T. Matsuura, K. Kamiya, H. Inokuchi, T. Matsukawa, J. Phys.: Condens. Matter 3 (1991) 767. [11] J.L. Wagner, K.M. Wong, J. Poon, Phys. Rev. B 39 (1989) 809. [12] J.L. Wagner, B.D. Biggs, J. Poon, Phys. Rev. Lett. 65 (1990) 203. [13] K. Saito, S. Matsuo, T. Ishimasa, J. Phys. Soc. Jpn. 62 (1993) 604. [14] S. Matsuo, H. Nakano, T. Ishimasa, Y. Fukano, J. Phys.: Condens. Matter 1 (1989) 6839. [15] K. Saito, S. Matsuo, H. Nakano, T. Ishimasa, M. Mori, J. Phys. Soc. Jpn. 63 (1994) 1940. [16] Y. Kaneko, Y. Arichika, T. Ishimasa, Phil. Mag. Lett. 81 (2001) 777. [17] R.I. Andrusyak, B.Ya. Kotur, V.E. Zavodnik, Soy. Phys. Crystallogr. 34 (1989) 996. [18] V. Elser, Acta Crystallogr. A 42 (1986) 36. [19] J. Friedel, private communication related to Ref. [14].
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Magnetic property of a Zn–Mg–Sc icosahedral quasicrystal Shiro Kashimoto a , Senni Motomura b , Hiroshi Nakano c , Yasushi Kaneko d , Tsutomu Ishimasa d , c, Susumu Matsuo * a b
Satellite Venture Business Laboratory, Utsunomiya University, Yoto, Utsunomiya 321 -8585, Japan Graduate School of Human Informatics, Nagoya University, Chikusa-ku, Nagoya 464 -8601, Japan c School of Informatics and Sciences, Nagoya University, Chikusa-ku, Nagoya 464 -8601, Japan d Graduate School of Engineering, Hokkaido University, Kita-ku, Sapporo 060 -8628, Japan
Abstract We have investigated the magnetism of a new Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal and a Zn 85.5 Sc 14.5 cubic phase, which is interpreted to be a 1 / 1 approximant of the new icosahedral quasicrystal, in the temperature region between 2 and 700 K. The magnetic susceptibility of the Zn 80 Mg 5 Sc 15 icosahedral quasicrystal shows an increase from 21.3310 27 to 20.8310 27 cgsemu / g with a rise in temperature from 90 to 700 K. The Zn 85.5 Sc 14.5 cubic phase shows also a rise from 21.8310 27 to 21.0310 27 cgsemu / g between 120 and 700 K. The increase in the susceptibility with a rise in temperature is accounted for by a temperature dependence of the Pauli paramagnetism. The experimental results strongly suggest a pseudogap in the electronic density of states at Fermi energy for the Zn 80 Mg 5 Sc 15 quasicrystal and the Zn 85.5 Sc 14.5 approximant, which has been observed in various stable icosahedral quasicrystals. 2002 Elsevier Science B.V. All rights reserved. Keywords: Quasicrystal; Magnetic measurements
1. Introduction Since the first report on the icosahedral phase in Al–Mn alloy which exhibited an icosahedral symmetry in electron diffraction patterns by Shechtman et al. [1], many studies have been made on the problem of why the unique structure with quasi-periodicity can stably exist. Although the first report by Shechtman et al. was carried out on the metastable icosahedral phase in a rapidly quenched alloy, until now many kinds of thermodynamically stable icosahedral quasicrystals have been discovered such as Al–Cu–Li [2], Al–Cu–Fe [3], Al–Pd–Mn [4], Zn–Mg–R (R5Ga, Y, Tb, Dy, Ho and Er) [5,6] and so on. When structural stability of quasicrystals is examined from the viewpoint of the electron theory, the Hume-Rothery rule [7] is theoretically and experimentally important. The rule can be explained by the stabilization mechanism on the basis of the interaction between the Fermi-sphere and Brillouin zone in the crystal alloy [8]. Friedel theoretically showed that the quasicrystal structure can be also stable because the electronic density states exhibit a minimum *Corresponding author. Tel.: 181-52-789-4762; fax: 181-52-7894804. E-mail address: [email protected] (S. Matsuo).
(pseudogap) at Fermi energy EF [9]. The pseudogap at EF was investigated experimentally by the ultraviolet photoelectron spectroscopy study of the electronic density of states [10], the electronic specific heat coefficient [11,12] and the temperature dependence of the Pauli paramagnetism [13–15]. The temperature dependence of the Pauli paramagnetism gives important information on the curvature of the electronic density of states at EF and affords a simple in situ method in a wide temperature region. Moreover, this method has an advantage that the measurement is possible even in a small amount of the sample in comparison with other methods. Recently a new type of icosahedral quasicrystal was found in the Zn–Mg–Sc alloy by Kaneko et al. [16]. The quasicrystal with the composition of Zn 80 Mg 5 Sc 15 has a primitive icosahedral quasilattice (P-type) with a 6-dimensional lattice parameter a 6D 50.7115 nm and shows a structural perfection in the sharpness of diffraction spots and a small deviation of the electron diffraction spots from the ideal icosahedral symmetric positions. This new quasicrystal is also expected to be a stable phase because of its presence in the annealed alloys. The Zn–Mg–Sc alloy includes two other crystalline phases as impurities; MgZn 2 -type Laves phase and Zn 17 Sc 3 -type cubic phase. The space group of the Zn 17 Sc 3 -type cubic phase is Im3¯
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 02 )00260-8
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[17], and can be interpreted as a 1 / 1 approximant crystal of the new quasicrystal [16]. One feature of the Zn 80 Mg 5 Sc 15 quasicrystal and the Zn 17 Sc 3 -type approximant is that it does not contain magnetic atoms like Fe, Mn and rare earth elements as in other stable quasicrystals known to date. Therefore, there is a possibility of detecting clearly the temperature dependence of the Pauli paramagnetism to lower temperatures without lurking in the temperature dependence of the Curie–Weiss paramagnetism arising from atoms with magnetic moments. In this paper, we present preliminary experimental observations of the temperature dependence of the Pauli paramagnetism suggesting a pseudogap in the electronic density of states at EF in the Zn 80 Mg 5 Sc 15 new P-type icosahedral quasicrystal and the Zn 17 Sc 3 -type cubic phase interpreted to be the 1 / 1 type approximant of the former.
2. Experimental procedure Ingots with the nominal compositions, Zn 80 Mg 5 Sc 15 and Zn 86 Sc 14 , were prepared from the high-purity materials of Zn (Nilaco, 99.998%), Mg (Nilaco, 99.95%) and Sc (ShinEtsu Chemical, 99.9%; according to the analysis table of the material manufacturer, the Sc material includes some impurities; Al 44 ppm, Ca 16 ppm, Fe 360 ppm and W 86 ppm). The Zn 86 Sc 14 alloy was synthesized in a silica tube in an atmosphere of 200 Torr argon at 1112 K for 4 h and then quenched in water. The Zn 80 Mg 5 Sc 15 alloy was synthesized by adding zinc and magnesium to Zn 78 Sc 22 alloy prepared in advance. The Zn 78 Sc 22 alloy was synthesized in a silica tube in an argon atmosphere at 1068 K. Weighed materials of Zn, Mg and powdered Zn 78 Sc 22 alloy were enclosed in a package made of molybdenum foil (Nilaco, thickness 0.05 mm, 99.95%) in order to avoid the chemical reaction with a silica ampoule. The specimen was held at 1093 K for 3 h for melting and subsequently cooled to the annealing temperature at the rate of 58 K / h. The specimen was held at the annealing temperature 918 K for 15 h and then quenched in water. The weight loss during the heat treatment of the Zn 80 Mg 5 Sc 15 and the Zn 86 Sc 14 alloy were 0.4% and 2.11%, respectively. The nominal composition of the binary Zn–Sc alloy was estimated to be Zn 85.5 Sc 14.5 on the assumption that the weight loss of the specimen during the heat treatment was due to evaporation of zinc. Characterization of these specimens was carried out by precise analysis of powder X-ray diffraction patterns measured using Cu Ka radiation (Rigaku RINT-2000). Fig. 1a and b show X-ray powder diffraction patterns of the Zn 80 Mg 5 Sc 15 and the Zn 85.5 Sc 14.5 , respectively. The X-ray diffraction peaks of the Zn 80 Mg 5 Sc 15 icosahedral quasicrystal were analyzed by indexing method using six integers [18]. Fig. 1a indicates that a major part of the ingot is the Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal with 6-dimensional lattice parameter a 6D 50.7117 nm, and
Fig. 1. Powder X-ray diffraction patterns. (a) Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal. Reflections due to the icosahedral quasicrystal are indicated by Elser indices. Reflections due to the Zn 17 Sc 3 -type cubic phase and the MgZn 2 -type Laves phase are indicated by three indices written in bold and italic, respectively. (b) Zn 85.5 Sc 14.5 1 / 1 cubic-type approximant of the icosahedral phase. Reflections due to the Zn are denoted by arrowheads.
that the ingot includes a small amount of the Zn 17 Sc 3 -type cubic phase (a51.3864 nm) and the MgZn 2 -type Laves phase (a50.5256 nm, c50.8493 nm). Fig. 1b indicates that the major part of the Zn 85.5 Sc 14.5 ingot is the Zn 17 Sc 3 -type cubic phase (a51.3846 nm), and this ingot includes a small amount of the elementary substance of Zn as a secondary phase indicated by arrowheads in Fig. 1b. More details of the preparation and the characterization of these specimens by using selected-area electron diffraction and scanning electron microscopy are described in Ref. [16]. Samples for the experiment of magnetism were cut from the master ingots at a size suitable for the measurements weighing from 0.2 to 0.3 g. The magnetism in the lower temperature region between 2 and 300 K was measured using a SQUID magnetometer (Quantum Design MPMS-
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S. Kashimoto et al. / Journal of Alloys and Compounds 342 (2002) 384 – 388
7) in a magnetic field of 5 T. Although the magnetization of these samples is linear following M 5 2 xdia H in most of the temperature region, the magnetization shows nonlinearity near the lowest temperature in the low magnetic field. It is probably caused by some magnetic impurity in the Sc material. Thus the Curie constants which were estimated on the data of magnetic susceptibility at the low temperatures (in Section 3) have a little error quantitatively. In the higher temperature region between 77 and 700 K, the temperature dependence of the magnetic susceptibility was measured using a magnetic balance with a standard electromagnet in a magnetic field 1 T. The sample was sealed in a quartz capsule with He atmosphere of 500 Torr in pressure in order to prevent oxidation.
3. Results and discussion Fig. 2 shows the magnetic susceptibility x as a function of temperature T measured by the SQUID magnetometer in the temperature region between 2 and 300 K at a magnetic field of 5 T. The two samples show diamagnetism at high temperatures and Curie–Weiss paramagnetism in low temperatures. A least-squares fitting of x to the following function was tried in the temperature region between 2 and 50 K
x 5 x0 1 C /(T 2 Q )
(1)
where x0 is a constant susceptibility, C is the Curie constant and Q is the Curie temperature. Fitted results are shown by solid curves in Fig. 2. The fitting gives parameters x0 as 21.50310 27 cgsemu / g and 22.06310 27 cgsemu / g, C as 1.04310 26 cgsemu K / g and 1.65310 26 cgsemu K / g, Q as 28.76 K and 217.6 K for Zn 80 Mg 5 Sc 15 and Zn 85.5 Sc 14.5 , respectively. The Curie– Weiss paramagnetism seems to be due to the effect of some impurity included in the sample ingots, because the Zn–Mg–Sc quasicrystal phase and the Zn–Sc approximant phase consisting of Zn, Mg and Sc must have no local magnetic moments. A candidate for the explanation of the Curie–Weiss paramagnetism is the effect of the local magnetic moments of the Fe impurity, since 360 ppm Fe atoms exist in the Sc material. Curie constant C by the Fe impurity is estimated from this Fe concentration by the use of a well-known formula, C 5 Np 2 mB 2 / 3k B , where p is the effective number of Bohr magneton mB (Fe 21 : p55.4, Fe 31 : p55.9) and N is the number of magnetic moments of Fe per gram in the sample. In the case of the Zn 80 Mg 5 Sc 15 quasicrystal, it gives C52.63310 26 cgsemu K / g and C53.14310 26 cgsemu K / g in the case of Fe 21 and Fe 31 , respectively. The values are of the same order as the one obtained by the Curie–Weiss fit, however, these values are not entirely in good agreement. Moreover, according to the theory of virtual bound state, local magnetic moment does not arise for Fe in divalent metals [19]. We must not jump to conclusions about the origin of
Fig. 2. Magnetic susceptibility as a function of temperature of (a) Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal and (b) Zn 85.5 Sc 14.5 1 / 1 cubic-type approximant under 5 T using a SQUID magnetometer. Solid curves indicate a least squares fit to Curie–Weiss law in the temperature region between 2 and 50 K. Insets are measurement results in higher temperatures, using the magnetic balance. The arrows denote the direction in the measurement process.
Curie–Weiss paramagnetism in low temperatures for the present. The magnetic susceptibility x of Zn 80 Mg 5 Sc 15 and Zn 85.5 Sc 14.5 distinctly increases with a rise in temperature in the higher temperature region as shown in Fig. 2. The insets in Fig. 2 are the results of measurements above room temperature region between 300 and 700 K using a magnetic balance. In the first half process with rising temperature, a rate of increase in the magnetic susceptibility changes around 550 K for both samples. After that the susceptibility once more increases with a clear positive gradient. However, in the cooling process, the susceptibility decreases monotonously. We continuously measured the susceptibility with the same process for these samples, then the results of the measurements did not show reappearance of hysteresis of the susceptibility; the susceptibility changed monotonously in both processes. It seems that the hysteresis is caused by some atomic relaxation, because the samples were prepared by quenching in water.
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The increase of x with a rise in temperature continues up to 700 K as shown in the insets of Fig. 2 for both the quasicrystal and the approximant. Such an increase in x has been reported for Zn–Mg–Ga [13], Al–Cu–Fe [14] and Al–Pd–Mn [15] and was interpreted by the temperature dependence of Pauli paramagnetism of conduction electrons which varies as AT 2 , where A is a constant. The present samples show also a straight line below 240 K in a x –T 2 plot as shown in Fig. 3. The coefficients A were obtained from the gradient in Fig. 3 as 3.01310 213 cgsemu / K 2 g and 4.40310 213 cgsemu / K 2 g for Zn 80 Mg 5 Sc 15 and Zn 85.5 Sc 14.5 , respectively. These values 213 2 are comparable to 2.0310 cgsemu / K g for Zn–Mg– Ga icosahedral quasicrystal [13]. The coefficient A is given by the following expression [14], A 5 (1 / 3)mB 2 N(EF )(p k)2 [h1 /N(E)jhd 2 N(E) / dE 2 j 2 h1 /N(E)j 2 hdN(E) / dEj 2 ] E 5E F
(2)
where N(EF ) is the electronic density of states and EF is the Fermi energy at 0 K. Now the coefficient A was obtained as positive, the second derivative of the density of
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states d 2 N(EF ) / dEF 2 must be positive because the second term in [ ] is always negative. Therefore the results strongly suggest a valley-like structure; i.e. pseudogap in the density of states at the Fermi energy for the present new Zn 80 Mg 5 Sc 15 quasicrystal and Zn 85.5 Sc 14.5 1 / 1 type approximant. There is a small difference between the values of A for Zn 80 Mg 5 Sc 15 quasicrystal and the one for Zn 85.5 Sc 14.5 approximant as aforesaid. However, we cannot immediately compare the pseudogap depths of the samples, because the coefficient A contains not only d 2 N(E) / dE 2 but also the square of derivative of N(E) with respect to E as shown in the second term in [ ] of Eq. (2). The pseudogap at Fermi energy EF may be mainly related to the strong diffraction spots. We compare the Fermi wave number k F with the diffraction spots obtained by the powder X-ray diffraction measurement. The Fermi wave number k F is expressed as the following relation k F 5 (1 / 2p )(3p 2 N /V )1 / 3
(3)
where N /V is the electron density per unit volume. The values of the mass density and e /a are necessary in order to estimate N /V. The mass densities of the Zn 80 Mg 5 Sc 15 measured by an Archimedes principle method (Mettler Toledo AG245) are given as 6.1760.03 g / cm 3 . The mass density of the Zn 85.5 Sc 14.5 cubic phase was estimated to be 6.23 g / cm 3 from the value of the unit-cell period a5 1.3852 nm and the atom number contained in the unit-cell (24Sc, 136Zn) which are reported [17] for Zn 17 Sc 3 cubic phase. The e /a are given as 2.15 for both Zn 80 Mg 5 Sc 15 and Zn 17 Sc 3 by assuming two valence electrons for Zn, Mg and three valence electrons for Sc. These values and the above relation give k F 52.51 nm 21 and 2.49 nm 21 for Zn 80 Mg 5 Sc 15 and Zn 17 Sc 3 , respectively. The values of k F yield 1 / 2k F 5 0.199 nm and 0.201 nm. The results nearly coincide with the relatively strong spots having indices 0 2 1¯ 2¯ 0 2 (d 5 0.1992 nm) and 6 3 1 (d 5 0.2042 nm) denoted by arrows in Fig. 1. Therefore, the structures of the quasicrystal and the cubic 1 / 1 approximant including Sc are considered to be stabilized by the mechanism of the Hume-Rothery rule.
4. Conclusion
Fig. 3. Magnetic susceptibility of (a) Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal and (b) Zn 85.5 Sc 14.5 1 / 1 cubic-type approximant as a function of square of temperature. Solid lines are obtained by least squares fit to a linear function in the temperature region between (a) 100 and 240 K, (b) 140 and 265 K, respectively.
We have shown in this study that the magnetic susceptibility x shows an increase with T 2 -dependence in the wide temperature region for the new Zn 80 Mg 5 Sc 15 P-type icosahedral quasicrystal and the Zn 85.5 Sc 14.5 1 / 1 approximant of the quasicrystal. The temperature dependence of x is interpreted on the basis of the temperature dependence of Pauli paramagnetism of conduction electrons. The positive value of coefficient of the T 2 -term signifies that there is a pseudogap in the electronic density of states at the Fermi energy. The Fermi wave number k F , which is estimated by using the values of e /a and the mass density,
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nearly coincides with the relatively strong spots in the X-ray diffraction pattern. The results strongly suggest that the new P-type quasicrystal and its approximant including Sc exhibit the pseudogap inferred from the strong diffraction spots and are stabilized by the mechanism of the Hume-Rothery rule.
Acknowledgements Thanks are due to the Research Center for Molecular Materials, Institute for Molecular Science. The authors would like to thank M. Sakai of the Research Center for help in the use of the SQUID magnetometer.
References [1] D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53 (1984) 1951. [2] B. Dubost, J.M. Lang, M. Tanaka, P. Sainfort, M. Audier, Nature 324 (1986) 48.
[3] A.P. Tsai, A. Inoue, T. Masumoto, Jpn. J. Appl. Phys. 26 (1987) L1505. [4] A.P. Tsai, A. Inoue, Y. Yokoyama, T. Masumoto, Mater. Trans. JIM 31 (1990) 98. [5] W. Ohashi, F. Spaepen, Nature 330 (1987) 555. [6] Z. Luo, S. Zhang, Y. Tang, D. Zhao, Scripta Metall. Mater. 28 (1993) 1513. [7] W. Hume-Rothery, J. Inst. Metals 35 (1926) 295. [8] H. Jones, Proc. Phys. Soc. 49 (1937) 250. [9] J. Friedel, Helv. Phys. Acta 61 (1988) 538. [10] M. Mori, S. Matsuo, T. Ishimasa, T. Matsuura, K. Kamiya, H. Inokuchi, T. Matsukawa, J. Phys.: Condens. Matter 3 (1991) 767. [11] J.L. Wagner, K.M. Wong, J. Poon, Phys. Rev. B 39 (1989) 809. [12] J.L. Wagner, B.D. Biggs, J. Poon, Phys. Rev. Lett. 65 (1990) 203. [13] K. Saito, S. Matsuo, T. Ishimasa, J. Phys. Soc. Jpn. 62 (1993) 604. [14] S. Matsuo, H. Nakano, T. Ishimasa, Y. Fukano, J. Phys.: Condens. Matter 1 (1989) 6839. [15] K. Saito, S. Matsuo, H. Nakano, T. Ishimasa, M. Mori, J. Phys. Soc. Jpn. 63 (1994) 1940. [16] Y. Kaneko, Y. Arichika, T. Ishimasa, Phil. Mag. Lett. 81 (2001) 777. [17] R.I. Andrusyak, B.Ya. Kotur, V.E. Zavodnik, Soy. Phys. Crystallogr. 34 (1989) 996. [18] V. Elser, Acta Crystallogr. A 42 (1986) 36. [19] J. Friedel, private communication related to Ref. [14].