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Superconductivity in a representative Zr-based bulk metallic glass
Journal of Non-Crystalline Solids 351 (2005) 2378–2382 www.elsevier.com/locate/jnoncrysol
Superconductivity in a representative Zr-based bulk metallic glass Yong Li, Hai Yang Bai
*
Key Laboratory of Extreme Conditions Physics, Institute of Physics, Chinese Academy of Sciences, 3rd South Street, Beijing 100080, People’s Republic of China Received 1 December 2004; received in revised form 23 June 2005
Abstract The Zr41Ti14Cu12.5Ni10Be22.5 bulk metallic glass (BMG) is investigated by means of electrical measurement. A superconducting transition was observed in the BMG which belongs to a typical type-II superconductor with a high Ginzburg–Landau parameter. The superconducting critical temperature Tc and the temperature gradient ðdH c2 =dT ÞT c of the upper critical field Hc2 near Tc is 1.62 K and 2.26 T/K, respectively. Some superconducting properties of the BMG are based on the electrical resistivity and critical field measurements. An analysis of the electron–phonon coupling constant k indicates that the Zr41Ti14Cu12.5Ni10Be22.5 BMG is a weak-coupling superconductor with k 0.49. The observed linearity of Hc2(t) and its extrapolated low-temperature limiting value are discussed and compared to predicted behavior for Hc2(t). 2005 Published by Elsevier B.V. PACS: 81.05.Kf; 72.15.Cz; 74.80.Bj
1. Introduction Metallic glasses present a unique opportunity for understanding how the basic low-temperature phonon and electron transport of metals are affected by structural disorder. It has been observed that the superconducting transition temperature Tc in glassy (or highly disordered) metals differs strongly from that of crystalline metals [1]. Amorphous superconductors were studied 50 years ago by Buchel and Hilsch [2] in the vapor-quenched films of alloys of simple metals. A particularly interesting and ambitious experiment was carried out by Collver and Hammond [1], who measured the superconducting transition temperature Tc of the highly disordered vapor-quenched metals and alloys of neighboring metals of the 4d and 5d transition series.
*
Corresponding author. E-mail address: [email protected] (H.Y. Bai).
0022-3093/$ - see front matter 2005 Published by Elsevier B.V. doi:10.1016/j.jnoncrysol.2005.07.006
Although the vapor-quenched amorphous films provide unique opportunities to study superconducting properties in non-crystalline solids, their thermal instability even at room temperature and the thickness limit (<0.1 lm) make these materials less practical in technical applications. Moreover, voids and gaseous inclusions inherent to vapor-deposited films make quantitative property studies difficult. Liquid-quenched amorphous metals, which are usually called metallic glasses, were first studied by Duwez and co-workers [3]. In the years since, a wide variety of amorphous metal have been found to exhibit superconductivity [4]. Unfortunately, the effects of low density, microcrystallinity, gaseous contamination, and large internal surface area may all play a significant role in the superconductivity of thin films. Thus results for thin films may not be comparable to those obtained for a bulk metallic glass (BMG) in which the density is close to that of the corresponding crystallized sample. Zr–Ti–Cu–Ni– Be alloy is a typical alloy that shows best glass forming ability and excellent mechanical and physical properties
2. Experimental details The Zr41Ti14Cu12.5Ni10Be22.5 ingots were prepared from Ti(99.99%), Zr(99.9%), Cu(99.999%), Ni(99.99%), and Be(99.99%) in an inductive levitation melting device under a Ti-gettered Ar atmosphere, and by quenching of the molten droplet. The BMG with the dimensions of 2 · 12 · 50 mm3 was prepared by sucking the remelted alloy into a copper mould. The details of the preparation procedure can be referred to Refs. [7–9]. The amorphous nature of the cast sample was verified using X-ray diffraction (XRD) with Cu Ka radiation and differential scanning calorimeter (DSC). Specimens with the dimensions of 1 · 2 · 10 mm3 used for the measurement were cut from the cast sample. Electrical resistivity as a function of temperature was measured by PPMS (Physical Property Measurement System, made by Quantum Design, USA) using a standard four-probe technique. The temperature can be stabilized to be better than 1 mK. The silver paints were used to establish electrical lead connection. The accuracy of the resistance measurement is better than 1 part in 104. Electrical resistivities are calculated from the measured resistance and the dimensions of the specimens. The uncertainties in the resistivity arise mainly from the uncertainties in the measurements of the sample geometry and are accurate to ±3%. The current densities used in the measurement were 250 mA/cm2. Mass density q was measured by the Archimedes principle and the accuracy was evaluated to be 0.005 g/cm3.
3. Results Fig. 1 shows the X-ray diffraction pattern from the transverse cross-section (the surface of 2 · 10 mm2) of the BMG. The pattern of Fig. 1 consists only of a broad peak and there are no diffraction peaks corresponding to crystalline phases.
20
30
40 50 60 2θ (degree)
70
80
Fig. 1. The X-ray diffraction patterns of the Zr41Ti14Cu12.5Ni10Be22.5 BMG.
Resistivity of the BMG was measured from room temperature down to 0.45 K. Fig. 2 shows the temperature dependence of the electrical resistivity q. The temperature dependence of resistivity is semiconductor-like with dq/dT < 0 for the amorphous sample. Between 4.2 K and 300 K, the total variations jq(4.2 K)/ p(300 K)j are 1.05 for the BMG. Superconductivity phenomenon was observed in the Zr41Ti14Cu12.5Ni10Be22.5 BMG. Superconducting transition as measured from resistivity at different applied magnetic fields are plotted in Fig. 3. As shown in Figs. 2 and 3 the Zr41Ti14Cu12.5Ni10Be22.5 BMG passes the superconducting transition at low temperature. The critical temperature Tc is defined at the point at which the resistivity reaches half of its normal-state value. A sharp resistive transition with Tc = 1.62 K is observed for the amorphous sample. The transition width in zero field, DTc, taken as the temperature interval where the resistivity changes from 10% to 90% of the normal-state value, were 137 mK. The sharp resistive transition (transition width DTc = 137 mK), indicative of a single phase, hints at rather good homogeneity of the BMG. The measurement of the field-dependent resistivity was carried out in two ways. In the first, applying a constant magnetic field, the resistivity of the Zr41Ti14Cu12.5Ni10Be22.5 BMG as a function of temperature was
150
ρ ( µΩ cm)
in the family of BMGs, which offers excellent opportunities for the understanding of metallic glassy state and the investigation of physical properties of metallic glasses by various physical methods. Up to now, only a few studies have been carried out on the low temperature properties of the novel metallic glasses [5,6], and not much information is known so far on the superconductivity in BMGs. In this paper, we report the results of X-ray diffraction analysis, electrical resistivity measurements, and critical magnetic field measurements for superconducting Zr41Ti14Cu12.5Ni10Be22.5 BMG. Based on these experimental results, estimation of several intrinsic parameters characteristic of the superconducting state is presented and discussed in conjunction with the observed behavior of the upper critical field Hc2(T).
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100 50 0 0
100
200 T (K)
300
Fig. 2. Resistivity as a function of temperature for the Zr41Ti14Cu12.5Ni10Be22.5 BMG.
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behavior is commonly observed in amorphous superconductors. The temperature gradient ðdH c2 =dT ÞT c near Tc is about 2.26 T/K.
ρ ( µΩ cm)
200 (a) 150 0T 0.5 T 1.0 T 1.5 T 2.0 T 2.5 T
100 50 0 0.5
1.0
1.5
2.0
T (K)
ρ ( µΩ cm)
200 (b)
4. Discussion To gain some insight into the intrinsic properties of the Zr41Ti14Cu12.5Ni10Be22.5 BMG, the following estimations of several important quantities for superconducting properties are made. 4.1. The electron–phonon coupling constant
150 0.45K 0.6K 0.9K 1.2K 1.5K 2.0K
100 50
One of the most important parameters in the theory of superconductivity is the electron–phonon coupling constant k. For a Tc calculation the numerical solution of the Eliashberg equations by McMillan [10] is commonly accepted:
0 0
10
20 H (kOe)
30
k¼
Fig. 3. (a) Superconducting transition as measured from resistivity at different applied magnetic fields, and (b) resistivity as a function of magnetic field at different temperatures of the Zr41Ti14Cu12.5Ni10Be22.5 BMG.
measured. In the second, the temperature is fixed and the field is varied from H = 0 up to H = 50 kOe. The results of the two sets of measurements are all shown in Fig. 3. It is clear that the superconducting transition width DTc is broadened by the applied magnetic field. The resistive transition as a function of applied field as measured at constant temperature with the applied field perpendicular to the direction of current flow is shown in Fig. 3(b). The upper critical field Hc2 defined as a midpoint of the transition is plotted in Fig. 4 as a function of temperature. Linear behavior of the upper critical field Hc2(T) curve is observed in the vicinity of Tc. This
Hc2 (Tesla)
3
2
1
0 0.0
0.5
1.0
1.5
T(K) Fig. 4. Upper critical field Hc2 as a function of temperature for the Zr41Ti14Cu12.5Ni10Be22.5 BMG. The dashed line is obtained using the Maki expression given in Eq. (4).
1.04 þ l lnðHD =1.45T c Þ ; ð1 0.62l Þ lnðHD =1.45T c Þ 1.04
ð1Þ
where l* is the effective Coulomb coupling constant which is usually set up to l* = 0.13, and HD is Debye temperature evaluated from the cubic term in the specific-heat, HD = 285.7 K for the amorphous sample [11]. The electron–phonon coupling constant k is estimated to be 0.49. The magnitude of k indicates that the Zr41Ti14Cu12.5Ni10Be22.5 BMG is a weak-coupling superconductor and is significantly smaller than the value observed for the simple (non-transition) amorphous superconductors (k 2). 4.2. The bare density of states Nb(EF) Since there is no any measurement of the bare density of states (e.g., ultraviolet photoemission spectroscopy experiment) in the Zr41Ti14Cu12.5Ni10Be22.5 BMG, we try to give the value of the bare density of states from the dressed density of states that obtained from experimental measurement of Hc2. An extended Ginzburg– Landau–Abrikosov–Gorkov (GLAG) theory [12] gives dH c2 ðT Þ ¼ gð4k B e=pÞqN H c2 ðEF Þ; ð2Þ dT T !T c where N H c2 ðEF Þ is the dressed density of states at the Fermi surface and q is the electrical resistivity. The g is an enhancement factor, taking the value of 1 for weak-coupling superconductors [13]. The value for N H c2 ðEF Þ determined from Eq. (2) is about 1.2 eV1 atom1. The quantity N H c2 ðEF Þ is related to the bare density of states at Fermi level Nb(EF) through the electron–phonon coupling parameter k by N H c2 ðEF Þ ¼ ð1 þ kÞN b ðEF Þ. For a comparison with the measurement of the density of states which do not include
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˚ . The relatively small values of the NND reflect d 2.9 A the high density (6.125 g/cm3) of the Zr41Ti14Cu12.5Ni10Be22.5 BMG as compared to values of the amorphous films. Crudely speaking, d is a rough estimate of the typical NND in amorphous alloys. Some of the parameters and results are listed in Table 1.
electron–phonon interactions, the value of the bare density of states Nb(EF) is determined from the ratio of N H c2 ðEF Þ=ð1 þ kÞ to be 0.78 eV1 atom1. 4.3. The Ginzburg–Landau (GL) parameter j The residual resistivity at 10 K may give the value of the electronic mean free path l. By assuming that Zr, Ti, Cu, Ni and Be contribute 2, 2, 1, 1 and 2 conduction electrons [14–16], respectively, vF = 1.7 · 106 m/s is used. From the measured value of q(10 K)=179 lX cm for the Zr41Ti14Cu12.5Ni10Be22.5 BMG, the electronic ˚ . Thus j, mean free path is estimated to be about 3 A the Ginzburg–Landau (GL) parameter, can be estimated using jðtÞ ¼ 0.725 kLlð0Þ [17,18], where kL(0) is the London penetration depth. In the Zr41Ti14Cu12.5Ni10Be22.5 BMG superconductor, the small value of l yields a large j 40. The j can also be estimated with the Gorkov relation: j = 7.5 · 103qc1/2, where q is the electric resistivity in X cm and c is the Sommerfeld constant in erg/ cm3 K2. The measured mass density of the Zr41Ti14Cu12.5Ni10Be22.5 BMG is 6.125 g/cm3. The value of c is obtained from the results of the specific-heat measurement [11], thus we estimated the GL parameter j = 82. Summarizing, a type-II behavior characterized by a large GL parameter is observed.
4.5. Discussion on Hc2(t) For a severely disordered crystal lattice, in particular for an amorphous material where the electronic mean free path is the order of the interatomic distance, an extremely large upper critical field Hc2 is expected. Gorkov [23] estimated the maximum critical field attainable for a 4 given Tc to be H max c2 10 T c G. In our case, Tc = 1.62 K, max H c2 16.2 kG. The zero-temperature upper critical field can be given by ClogstonÕs equation [24], H max c2 1.84 104 T c G, by considering the paramagnetic contribution to the free energy of the normal state. By ignoring the paramagnetic and spin–orbit effects, the upper critical field of weak-coupling superconductors with small mean free path has been calculated for all temperature by Maki [19] and de Gennes [20] which related Hc2(t) and t throughout the range 0 < t < 1 in the dirty limit. They found 4gk B T c 1 28 4 fð3Þ ð1 tÞ H c2 ðtÞ ¼ ð1 tÞ 1 2 p peD
4.4. The nearest-neighbor distance of atoms
ð4aÞ In the framework of the free-electron model, Eq. (2) can be rewritten as [19,20] dH c2 ðT Þ ¼ gð4k B Þ=peD ; ð3Þ dT
for the limiting case t ! 1 and 0.87gk B T c 2 pt 2 H c2 ðtÞ ¼ 1 3 1.75 eD
where D ¼ vF l=3 is the dressed diffusivity. The value of D* is determined from the data of Fig. 4. In a study of several non-crystalline superconductors obtained by liquid quenching, Johnson and Poon [21] have obtained an empirical relation, D* = 0.134d0.014, between D* and the nearest-neighbor distance (NND) d. The result ˚. of NND obtained through this formula is about 3.6 A On the other hand, one can also obtain a rough estimate of the typical NND d in an amorphous alloy from the position kp (kp is the wave number of the first maximum in the structure factor) by the Debye formula [22]: .23k ¼ 1.232p, where 2h is the Bragg diffraction d 21sin p hp kp angle corresponding to the first peak in the structure factor S(k). Using the kp values from X-ray diffraction gives
for the limiting case t ! 0. The dashed line in Fig. 4 is calculated according to Eq. (4), and thus it gives a value of H c2 ð0Þ of 29.9 kG. Therefore the dashed line in Fig. 4 gives an upper limit for the theoretical Hc2 values. It is seen in Fig. 4 that the initial slope at Tc is fitted to the experimental points and the exact shape of the observed Hc2(t) curve at low temperature deviates from the shape predicted by Eq. (4). The observed linearity of Hc2(t) extends to lower temperatures than predicted by Eq. (4). Eq. (4) has been extended by Werthamer and co-worker [25] to include both the paramagnetic effect and the effect of spin–orbit scattering. They showed that the initial slope at Tc is not changed by the inclusion of the electron–spin and the spin–orbit coupling. But the paramag-
T !T c
ð4bÞ
Table 1 The room temperature resistivity q(300 K), superconducting transition temperature Tc, temperature gradient ðdH c2 =dT ÞT c near Tc, electron– phonon coupling constant k, dressed density of states N H c2 ðEF Þ, bare density of states Nb(EF), Ginzburg–Landau parameter j, and the nearestneighbor distance d of the Zr41Ti14Cu12.5Ni10Be22.5 BMG ˚) q(300 K) (lX cm) Tc (K) ðdH c2 =dT Þ (T/K) k N H ðEF Þ (eV1 atom1) Nb(EF) (eV1 atom1) j (Gorkov) d (A Tc
171
1.62
2.26
c2
0.49
1.2
0.78
82
2.9
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netic effect tends to suppress Hc2(t) at low temperatures. The spin–orbit scattering effect, however, tends to compensate for the paramagnetic suppression and tends to restore the linearity of Hc2(t). The linearity of Hc2(t) over a large temperature range observed for the Zr41Ti14Cu12.5Ni10Be22.5 BMG can been explained by the presence of a large spin–orbit scattering effect [26]. We find, however, that the Zr41Ti14Cu12.5Ni10Be22.5 BMG with extremely small mean free path show an upper critical field which exceeds the theoretical limit at low temperature by about 10%.
Natural Science Foundation of China (Grant numbers 50225101 and 50171075).
References [1] [2] [3] [4]
5. Conclusions
[5]
Based on the data presented here, several concluding remarks can be made. The Zr41Ti14Cu12.5Ni10Be22.5 BMG is classified as a typical type-II superconductor with a large Ginzburg–Landau parameter. The electron–phonon coupling constant k = 0.49 as determined from Tc and HD indicates that the BMG is weak-coupling superconductor. This differs from the case of the non-transition-metal amorphous alloys which have been identified as strong-coupling superconductors with k in the vicinity of 2. The present results suggest that the most critical need to further understanding of the superconducting amorphous alloys is information on charge transfer, Fermisurface diameter, and electronic structure in general. Measurements such as positron annihilation, soft X-ray spectroscopy, and photoemission should be of great interest for this class of materials. It is hoped that these results will stimulate theoretical interest in the superconducting BMGs.
[6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
[23]
Acknowledgments The authors are grateful to W.H. Wang for the sample preparation and financial support of the National
[24] [25] [26]
M.M. Collver, R.H. Hammond, Phys. Rev. Lett. 30 (1973) 92. W. Buckel, R. Hilsch, Phys. Verh. 2 (1951) 102. W. Klement, R.H. Willems, P. Duwez, Nature 187 (1960) 869. G. Bergmann, Phys. Rep. 27 (1976) 159; K. Samwer, H.v. Lohneysen, Phys. Rev. B 26 (1982) 107; W.L. Johnson, S.J. Poon, P. Duwez, Phys. Rev. B 11 (1975) 150; W.L. Johnson, in: Proceedings of the 3rd International Conference on Rapidly Quenched Metals, 1978, p. 1. A. Gerber, A. Milner, A. Voronel, A. Rubstein, Yu. Rosenberg, M.P. Macht, Physica C 275 (1997) 333. Y. Li, H.Y. Bai, P. Wen, Z.X. Liu, Z.F. Zhao, J. Phys.: Condens. Matter. 15 (2003) 4809. W.H. Wang, R.J. Wang, Appl. Phys. Lett. 74 (1999) 1803. W.H. Wang, H.Y. Bai, J. Appl. Phys. 84 (1998) 5961. W.H. Wang, Mater. Sci. Eng. R 44 (2004) 45; W.H. Wang, Q. Wei, H.Y. Bai, Appl. Phys. Lett. 71 (1997) 58. W.L. McMillan, Phys. Rev. 167 (1968) 331. H.Y. Bai, J.L. Luo, Z.J. Chen, W.H. Wang, Appl. Phys. Lett. 78 (2001) 2697. G. Eilenberger, V. Ambegaokar, Phys. Rev. 158 (1967) 332. D. Rainer, G. Bergmann, J. Low Temp. Phys. 14 (1974) 501. R. Hasegawa, L.E. Tanner, Phys. Rev. B 16 (1977) 3925. P.J. Cote, Solid State Commun. 18 (1976) 1311. G. Busch, H.-J. Guntherodt, Solid State Phys. 29 (1974) 235. P.G. De Gennes, Superconductivity of Metals and Alloys, Benjamin, New York, 1966. D. Saint-James, G. Sarma, E.J. Thomas, Theory of Type II Superconductivity, Pergamon, Oxford, 1969. K. Maki, Physics 1 (1964) 127. P.D. de Gennes, Phys. Kond. Mater. 2 (1964) 79. W.L. Johnson, S.J. Poon, J. Appl. Phys. 46 (1975) 1787. A. Guinier, X-ray Diffraction, Freeman, San Francisco, 1963, p. 72 (Chapter 3); G.S. Cargill III, Solid State Phys. 30 (1975) 227. L.P. Gorkov, Zh. Eksp. Teor. Fiz. 37 (1959) 833 [English transl.: Soviet Phys.-JETP 10 (1960) 593. A.M. Clogston, Phys. Rev. Lett. 9 (1962) 266. E. Helfand, N.R. Werthamer, Phys. Rev. 147 (1966) 288. M. Ashkin, D.W. Deis, J.R. Gavaler, C.K. Jones, AIP Conf. Proc. 4 (1972) 204.
Superconductivity in a representative Zr-based bulk metallic glass Yong Li, Hai Yang Bai
*
Key Laboratory of Extreme Conditions Physics, Institute of Physics, Chinese Academy of Sciences, 3rd South Street, Beijing 100080, People’s Republic of China Received 1 December 2004; received in revised form 23 June 2005
Abstract The Zr41Ti14Cu12.5Ni10Be22.5 bulk metallic glass (BMG) is investigated by means of electrical measurement. A superconducting transition was observed in the BMG which belongs to a typical type-II superconductor with a high Ginzburg–Landau parameter. The superconducting critical temperature Tc and the temperature gradient ðdH c2 =dT ÞT c of the upper critical field Hc2 near Tc is 1.62 K and 2.26 T/K, respectively. Some superconducting properties of the BMG are based on the electrical resistivity and critical field measurements. An analysis of the electron–phonon coupling constant k indicates that the Zr41Ti14Cu12.5Ni10Be22.5 BMG is a weak-coupling superconductor with k 0.49. The observed linearity of Hc2(t) and its extrapolated low-temperature limiting value are discussed and compared to predicted behavior for Hc2(t). 2005 Published by Elsevier B.V. PACS: 81.05.Kf; 72.15.Cz; 74.80.Bj
1. Introduction Metallic glasses present a unique opportunity for understanding how the basic low-temperature phonon and electron transport of metals are affected by structural disorder. It has been observed that the superconducting transition temperature Tc in glassy (or highly disordered) metals differs strongly from that of crystalline metals [1]. Amorphous superconductors were studied 50 years ago by Buchel and Hilsch [2] in the vapor-quenched films of alloys of simple metals. A particularly interesting and ambitious experiment was carried out by Collver and Hammond [1], who measured the superconducting transition temperature Tc of the highly disordered vapor-quenched metals and alloys of neighboring metals of the 4d and 5d transition series.
*
Corresponding author. E-mail address: [email protected] (H.Y. Bai).
0022-3093/$ - see front matter 2005 Published by Elsevier B.V. doi:10.1016/j.jnoncrysol.2005.07.006
Although the vapor-quenched amorphous films provide unique opportunities to study superconducting properties in non-crystalline solids, their thermal instability even at room temperature and the thickness limit (<0.1 lm) make these materials less practical in technical applications. Moreover, voids and gaseous inclusions inherent to vapor-deposited films make quantitative property studies difficult. Liquid-quenched amorphous metals, which are usually called metallic glasses, were first studied by Duwez and co-workers [3]. In the years since, a wide variety of amorphous metal have been found to exhibit superconductivity [4]. Unfortunately, the effects of low density, microcrystallinity, gaseous contamination, and large internal surface area may all play a significant role in the superconductivity of thin films. Thus results for thin films may not be comparable to those obtained for a bulk metallic glass (BMG) in which the density is close to that of the corresponding crystallized sample. Zr–Ti–Cu–Ni– Be alloy is a typical alloy that shows best glass forming ability and excellent mechanical and physical properties
2. Experimental details The Zr41Ti14Cu12.5Ni10Be22.5 ingots were prepared from Ti(99.99%), Zr(99.9%), Cu(99.999%), Ni(99.99%), and Be(99.99%) in an inductive levitation melting device under a Ti-gettered Ar atmosphere, and by quenching of the molten droplet. The BMG with the dimensions of 2 · 12 · 50 mm3 was prepared by sucking the remelted alloy into a copper mould. The details of the preparation procedure can be referred to Refs. [7–9]. The amorphous nature of the cast sample was verified using X-ray diffraction (XRD) with Cu Ka radiation and differential scanning calorimeter (DSC). Specimens with the dimensions of 1 · 2 · 10 mm3 used for the measurement were cut from the cast sample. Electrical resistivity as a function of temperature was measured by PPMS (Physical Property Measurement System, made by Quantum Design, USA) using a standard four-probe technique. The temperature can be stabilized to be better than 1 mK. The silver paints were used to establish electrical lead connection. The accuracy of the resistance measurement is better than 1 part in 104. Electrical resistivities are calculated from the measured resistance and the dimensions of the specimens. The uncertainties in the resistivity arise mainly from the uncertainties in the measurements of the sample geometry and are accurate to ±3%. The current densities used in the measurement were 250 mA/cm2. Mass density q was measured by the Archimedes principle and the accuracy was evaluated to be 0.005 g/cm3.
3. Results Fig. 1 shows the X-ray diffraction pattern from the transverse cross-section (the surface of 2 · 10 mm2) of the BMG. The pattern of Fig. 1 consists only of a broad peak and there are no diffraction peaks corresponding to crystalline phases.
20
30
40 50 60 2θ (degree)
70
80
Fig. 1. The X-ray diffraction patterns of the Zr41Ti14Cu12.5Ni10Be22.5 BMG.
Resistivity of the BMG was measured from room temperature down to 0.45 K. Fig. 2 shows the temperature dependence of the electrical resistivity q. The temperature dependence of resistivity is semiconductor-like with dq/dT < 0 for the amorphous sample. Between 4.2 K and 300 K, the total variations jq(4.2 K)/ p(300 K)j are 1.05 for the BMG. Superconductivity phenomenon was observed in the Zr41Ti14Cu12.5Ni10Be22.5 BMG. Superconducting transition as measured from resistivity at different applied magnetic fields are plotted in Fig. 3. As shown in Figs. 2 and 3 the Zr41Ti14Cu12.5Ni10Be22.5 BMG passes the superconducting transition at low temperature. The critical temperature Tc is defined at the point at which the resistivity reaches half of its normal-state value. A sharp resistive transition with Tc = 1.62 K is observed for the amorphous sample. The transition width in zero field, DTc, taken as the temperature interval where the resistivity changes from 10% to 90% of the normal-state value, were 137 mK. The sharp resistive transition (transition width DTc = 137 mK), indicative of a single phase, hints at rather good homogeneity of the BMG. The measurement of the field-dependent resistivity was carried out in two ways. In the first, applying a constant magnetic field, the resistivity of the Zr41Ti14Cu12.5Ni10Be22.5 BMG as a function of temperature was
150
ρ ( µΩ cm)
in the family of BMGs, which offers excellent opportunities for the understanding of metallic glassy state and the investigation of physical properties of metallic glasses by various physical methods. Up to now, only a few studies have been carried out on the low temperature properties of the novel metallic glasses [5,6], and not much information is known so far on the superconductivity in BMGs. In this paper, we report the results of X-ray diffraction analysis, electrical resistivity measurements, and critical magnetic field measurements for superconducting Zr41Ti14Cu12.5Ni10Be22.5 BMG. Based on these experimental results, estimation of several intrinsic parameters characteristic of the superconducting state is presented and discussed in conjunction with the observed behavior of the upper critical field Hc2(T).
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100 50 0 0
100
200 T (K)
300
Fig. 2. Resistivity as a function of temperature for the Zr41Ti14Cu12.5Ni10Be22.5 BMG.
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behavior is commonly observed in amorphous superconductors. The temperature gradient ðdH c2 =dT ÞT c near Tc is about 2.26 T/K.
ρ ( µΩ cm)
200 (a) 150 0T 0.5 T 1.0 T 1.5 T 2.0 T 2.5 T
100 50 0 0.5
1.0
1.5
2.0
T (K)
ρ ( µΩ cm)
200 (b)
4. Discussion To gain some insight into the intrinsic properties of the Zr41Ti14Cu12.5Ni10Be22.5 BMG, the following estimations of several important quantities for superconducting properties are made. 4.1. The electron–phonon coupling constant
150 0.45K 0.6K 0.9K 1.2K 1.5K 2.0K
100 50
One of the most important parameters in the theory of superconductivity is the electron–phonon coupling constant k. For a Tc calculation the numerical solution of the Eliashberg equations by McMillan [10] is commonly accepted:
0 0
10
20 H (kOe)
30
k¼
Fig. 3. (a) Superconducting transition as measured from resistivity at different applied magnetic fields, and (b) resistivity as a function of magnetic field at different temperatures of the Zr41Ti14Cu12.5Ni10Be22.5 BMG.
measured. In the second, the temperature is fixed and the field is varied from H = 0 up to H = 50 kOe. The results of the two sets of measurements are all shown in Fig. 3. It is clear that the superconducting transition width DTc is broadened by the applied magnetic field. The resistive transition as a function of applied field as measured at constant temperature with the applied field perpendicular to the direction of current flow is shown in Fig. 3(b). The upper critical field Hc2 defined as a midpoint of the transition is plotted in Fig. 4 as a function of temperature. Linear behavior of the upper critical field Hc2(T) curve is observed in the vicinity of Tc. This
Hc2 (Tesla)
3
2
1
0 0.0
0.5
1.0
1.5
T(K) Fig. 4. Upper critical field Hc2 as a function of temperature for the Zr41Ti14Cu12.5Ni10Be22.5 BMG. The dashed line is obtained using the Maki expression given in Eq. (4).
1.04 þ l lnðHD =1.45T c Þ ; ð1 0.62l Þ lnðHD =1.45T c Þ 1.04
ð1Þ
where l* is the effective Coulomb coupling constant which is usually set up to l* = 0.13, and HD is Debye temperature evaluated from the cubic term in the specific-heat, HD = 285.7 K for the amorphous sample [11]. The electron–phonon coupling constant k is estimated to be 0.49. The magnitude of k indicates that the Zr41Ti14Cu12.5Ni10Be22.5 BMG is a weak-coupling superconductor and is significantly smaller than the value observed for the simple (non-transition) amorphous superconductors (k 2). 4.2. The bare density of states Nb(EF) Since there is no any measurement of the bare density of states (e.g., ultraviolet photoemission spectroscopy experiment) in the Zr41Ti14Cu12.5Ni10Be22.5 BMG, we try to give the value of the bare density of states from the dressed density of states that obtained from experimental measurement of Hc2. An extended Ginzburg– Landau–Abrikosov–Gorkov (GLAG) theory [12] gives dH c2 ðT Þ ¼ gð4k B e=pÞqN H c2 ðEF Þ; ð2Þ dT T !T c where N H c2 ðEF Þ is the dressed density of states at the Fermi surface and q is the electrical resistivity. The g is an enhancement factor, taking the value of 1 for weak-coupling superconductors [13]. The value for N H c2 ðEF Þ determined from Eq. (2) is about 1.2 eV1 atom1. The quantity N H c2 ðEF Þ is related to the bare density of states at Fermi level Nb(EF) through the electron–phonon coupling parameter k by N H c2 ðEF Þ ¼ ð1 þ kÞN b ðEF Þ. For a comparison with the measurement of the density of states which do not include
Y. Li, H.Y. Bai / Journal of Non-Crystalline Solids 351 (2005) 2378–2382
2381
˚ . The relatively small values of the NND reflect d 2.9 A the high density (6.125 g/cm3) of the Zr41Ti14Cu12.5Ni10Be22.5 BMG as compared to values of the amorphous films. Crudely speaking, d is a rough estimate of the typical NND in amorphous alloys. Some of the parameters and results are listed in Table 1.
electron–phonon interactions, the value of the bare density of states Nb(EF) is determined from the ratio of N H c2 ðEF Þ=ð1 þ kÞ to be 0.78 eV1 atom1. 4.3. The Ginzburg–Landau (GL) parameter j The residual resistivity at 10 K may give the value of the electronic mean free path l. By assuming that Zr, Ti, Cu, Ni and Be contribute 2, 2, 1, 1 and 2 conduction electrons [14–16], respectively, vF = 1.7 · 106 m/s is used. From the measured value of q(10 K)=179 lX cm for the Zr41Ti14Cu12.5Ni10Be22.5 BMG, the electronic ˚ . Thus j, mean free path is estimated to be about 3 A the Ginzburg–Landau (GL) parameter, can be estimated using jðtÞ ¼ 0.725 kLlð0Þ [17,18], where kL(0) is the London penetration depth. In the Zr41Ti14Cu12.5Ni10Be22.5 BMG superconductor, the small value of l yields a large j 40. The j can also be estimated with the Gorkov relation: j = 7.5 · 103qc1/2, where q is the electric resistivity in X cm and c is the Sommerfeld constant in erg/ cm3 K2. The measured mass density of the Zr41Ti14Cu12.5Ni10Be22.5 BMG is 6.125 g/cm3. The value of c is obtained from the results of the specific-heat measurement [11], thus we estimated the GL parameter j = 82. Summarizing, a type-II behavior characterized by a large GL parameter is observed.
4.5. Discussion on Hc2(t) For a severely disordered crystal lattice, in particular for an amorphous material where the electronic mean free path is the order of the interatomic distance, an extremely large upper critical field Hc2 is expected. Gorkov [23] estimated the maximum critical field attainable for a 4 given Tc to be H max c2 10 T c G. In our case, Tc = 1.62 K, max H c2 16.2 kG. The zero-temperature upper critical field can be given by ClogstonÕs equation [24], H max c2 1.84 104 T c G, by considering the paramagnetic contribution to the free energy of the normal state. By ignoring the paramagnetic and spin–orbit effects, the upper critical field of weak-coupling superconductors with small mean free path has been calculated for all temperature by Maki [19] and de Gennes [20] which related Hc2(t) and t throughout the range 0 < t < 1 in the dirty limit. They found 4gk B T c 1 28 4 fð3Þ ð1 tÞ H c2 ðtÞ ¼ ð1 tÞ 1 2 p peD
4.4. The nearest-neighbor distance of atoms
ð4aÞ In the framework of the free-electron model, Eq. (2) can be rewritten as [19,20] dH c2 ðT Þ ¼ gð4k B Þ=peD ; ð3Þ dT
for the limiting case t ! 1 and 0.87gk B T c 2 pt 2 H c2 ðtÞ ¼ 1 3 1.75 eD
where D ¼ vF l=3 is the dressed diffusivity. The value of D* is determined from the data of Fig. 4. In a study of several non-crystalline superconductors obtained by liquid quenching, Johnson and Poon [21] have obtained an empirical relation, D* = 0.134d0.014, between D* and the nearest-neighbor distance (NND) d. The result ˚. of NND obtained through this formula is about 3.6 A On the other hand, one can also obtain a rough estimate of the typical NND d in an amorphous alloy from the position kp (kp is the wave number of the first maximum in the structure factor) by the Debye formula [22]: .23k ¼ 1.232p, where 2h is the Bragg diffraction d 21sin p hp kp angle corresponding to the first peak in the structure factor S(k). Using the kp values from X-ray diffraction gives
for the limiting case t ! 0. The dashed line in Fig. 4 is calculated according to Eq. (4), and thus it gives a value of H c2 ð0Þ of 29.9 kG. Therefore the dashed line in Fig. 4 gives an upper limit for the theoretical Hc2 values. It is seen in Fig. 4 that the initial slope at Tc is fitted to the experimental points and the exact shape of the observed Hc2(t) curve at low temperature deviates from the shape predicted by Eq. (4). The observed linearity of Hc2(t) extends to lower temperatures than predicted by Eq. (4). Eq. (4) has been extended by Werthamer and co-worker [25] to include both the paramagnetic effect and the effect of spin–orbit scattering. They showed that the initial slope at Tc is not changed by the inclusion of the electron–spin and the spin–orbit coupling. But the paramag-
T !T c
ð4bÞ
Table 1 The room temperature resistivity q(300 K), superconducting transition temperature Tc, temperature gradient ðdH c2 =dT ÞT c near Tc, electron– phonon coupling constant k, dressed density of states N H c2 ðEF Þ, bare density of states Nb(EF), Ginzburg–Landau parameter j, and the nearestneighbor distance d of the Zr41Ti14Cu12.5Ni10Be22.5 BMG ˚) q(300 K) (lX cm) Tc (K) ðdH c2 =dT Þ (T/K) k N H ðEF Þ (eV1 atom1) Nb(EF) (eV1 atom1) j (Gorkov) d (A Tc
171
1.62
2.26
c2
0.49
1.2
0.78
82
2.9
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netic effect tends to suppress Hc2(t) at low temperatures. The spin–orbit scattering effect, however, tends to compensate for the paramagnetic suppression and tends to restore the linearity of Hc2(t). The linearity of Hc2(t) over a large temperature range observed for the Zr41Ti14Cu12.5Ni10Be22.5 BMG can been explained by the presence of a large spin–orbit scattering effect [26]. We find, however, that the Zr41Ti14Cu12.5Ni10Be22.5 BMG with extremely small mean free path show an upper critical field which exceeds the theoretical limit at low temperature by about 10%.
Natural Science Foundation of China (Grant numbers 50225101 and 50171075).
References [1] [2] [3] [4]
5. Conclusions
[5]
Based on the data presented here, several concluding remarks can be made. The Zr41Ti14Cu12.5Ni10Be22.5 BMG is classified as a typical type-II superconductor with a large Ginzburg–Landau parameter. The electron–phonon coupling constant k = 0.49 as determined from Tc and HD indicates that the BMG is weak-coupling superconductor. This differs from the case of the non-transition-metal amorphous alloys which have been identified as strong-coupling superconductors with k in the vicinity of 2. The present results suggest that the most critical need to further understanding of the superconducting amorphous alloys is information on charge transfer, Fermisurface diameter, and electronic structure in general. Measurements such as positron annihilation, soft X-ray spectroscopy, and photoemission should be of great interest for this class of materials. It is hoped that these results will stimulate theoretical interest in the superconducting BMGs.
[6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
[23]
Acknowledgments The authors are grateful to W.H. Wang for the sample preparation and financial support of the National
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