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Structural behavior and glass transition of bulk metallic glasses
Journal of Non-Crystalline Solids 345&346 (2004) 758–761 www.elsevier.com/locate/jnoncrysol
Structural behavior and glass transition of bulk metallic glasses Norbert Mattern a
a,*
, Jan Sakowski b, Uta Ku¨hn a, Hartmut Vinzelberg a, Ju¨rgen Eckert
c
Leibniz-Institute for Solid State and Materials Research, IFW Dresden, P.O. Box 270116, D-01171 Dresden, Germany b Department of Physics, Rostock University, D-18051 Rostock, Germany c Department for Material- and Geo-Sciences, Technical University Darmstadt, D-64287 Darmstadt, Germany Available online 12 October 2004
Abstract The thermal behavior of Pd40Cu30Ni10P20 and Zr60Ti2Cu20Ni8Al10 bulk metallic glasses has been investigated in situ through the glass transition by means of differential scanning calorimetry, high-temperature X-ray synchrotron diffraction, and electrical resistivity. The temperature dependence of the X-ray structure factor can be well described by the Debye theory within the glassy state with a Debye temperature of h = 296 K for Pd40Cu30Ni10P20, and h = 418 K for Zr60Ti2Cu20Ni8Al10, respectively. At the glass transition temperature the temperature dependence of the structure changes, pointing to a continuous development of structural changes in the liquid state with temperature. The electrical resistivity behaves similar to the structure factor in accordance with Ziman theory. Ó 2004 Elsevier B.V. All rights reserved. PACS: 61.43.Dq; 61.46.+w; 64.70.Nd
1. Introduction Bulk metallic glasses represent a new class of amorphous metallic alloys developed in recent years [1,2]. These multi-component metallic alloys can be obtained at low cooling rates, which allow the production of large-scale materials, by conventional casting processes [3]. Furthermore, bulk metallic glasses show a glass transition at the temperature Tg up to 120 K lower than the crystallization temperature Tx enabling hot deformation and shaping [3]. The transition of the glass into the supercooled liquid state upon constant rate heating is related to changes in thermodynamic properties e.g., the enthalpy, and in the thermal expansion coefficient [4]. A direct observation of the structural behavior at the calorimetric glass transition temperature is rather limited so far [5,6].
*
Corresponding author. Tel.:+49 351 4659 367; fax: +49 351 4659 452. E-mail address: [email protected] (N. Mattern). 0022-3093/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.08.197
The aim of this work is to study the reversible part of the temperature dependence of the structure of two different alloy types of bulk metallic glasses up to the supercooled liquid state by means of in situ by high-temperature synchrotron X-ray diffraction, and electrical resistivity measurements. To reduce the influence of relaxation the samples were preannealed at temperatures below the glass transition temperature Tg.
2. Experimental procedure Samples of Pd40Cu30Ni10P20 and Zr60Ti2Cu20Ni8Al10 bulk glasses were prepared in form of rods with 5 and 3 mm diameter and 50 mm length by copper mold casting of arc-melted prealloys. Discs of 1 mm height were cut from the rods for differential scanning calorimetry (DSC) and X-ray diffraction (XRD) experiments. Cylinders of 10 mm in length were used for the measurements of the electrical resistivity. To remove the influence of structural relaxation the samples were pre-annealed
N. Mattern et al. / Journal of Non-Crystalline Solids 345&346 (2004) 758–761
Tx
Heat flow endo up (a.u.)
Tg
Tx
Tg
Zr60Ti2Cu20Ni8Al10 Pd40Cu30Ni10P20
500
600
700
Temperature T ( K ) Fig. 1. DSC scans of Zr60Ti2Cu20Ni8Al10, and Pd40Cu30Ni10P10 bulk metallic glasses (heating rate 10 K/min).
(Pd40Cu30Ni10P20: 543 K for seven days; Zr60Ti2Cu20Ni8Al10: 653 K for 2 min). The DSC experiments were performed employing a Netzsch DSC 404 calorimeter (heating rate 10 K/min). In situ XRD measurements at elevated temperatures were conducted at the high-energy beam-line BW5 at the storage ring DORIS (HASYLAB, Hamburg) [7]. The sample was hold for 130 s at the corresponding temperature (20 s for exposure and additional 110 s for data read out time), and then heated up to the next temperature within 10 s. Immediately thereafter the measurement was started again. Standard four point geometry was applied to measure the electrical conductivity during continuous heating (heating rate 5 K/min). The mass density was determined by the Archimedes principle by weighing samples in air and in dodecan (C12H26).
3. Results The thermal behavior of Zr60Ti2Cu20Ni8Al10, Pd40Cu30Ni10P10 bulk metallic glasses is shown in Fig. 1 by the DSC measurement. The glass transition is indicated by to the endothermal event, which corresponds to
759
the increase Dcp of the specific heat of the supercooled liquid. The crystallization at the exothermal peak starts from the supercooled liquid region spreading over 70 K for both alloys. The calorimetric glass transition temperatures Tg and the crystallization temperatures Tx for the two investigated alloys are given in Table 1 (both characteristic temperatures are here defined as the onset temperatures of the respective endothermic and exothermic DSC heat flow events). The mass density of the bulk metallic glass is only 0.5% smaller than that of the corresponding crystallized material (Table 1), which indicates a high degree of dense packed atomic configuration in these materials. The structure factor S(q) was calculated from the measured intensities after radial integration of the image plate data and applying the usual corrections and normalization procedure to determine the coherent scattered intensity in absolute electron units. Fig. 2 shows some of the structure factors ST(q) of the Zr60Ti2Cu20Ni8Al10 alloy measured at room temperature and at elevated temperatures. The amorphous structure is preserved up to 733 K, which is 77 K above Tg. We find no indication of a general structural change between the glassy and the supercooled liquid state. The crystallization starts between 733 K and 753 K during our stepwise heating procedure. At T = 753 K several crystalline reflections become visible as the first step of crystallization starts. Cubic NiZr2 and tetragonal CuZr2 are formed by eutectic-type crystallization from the supercooled liquid. The diffraction curves of the amorphous state of the sample within the temperature range 293 K 6 T 6 733 K exhibit only small changes with increasing temperature. The same is observed for Pd40Cu30Ni10P20 bulk glass 293 K 6 T 6 670 K. Fig. 3 exhibits the normalized temperature dependence of the height of the structure factor S(q) at the positions of the first, second, third maximum S(qi) for Pd40Cu30Ni10P20 bulk glass, and of the first maximum for Zr60Ti2Cu20Ni8Al10. A linear decrease of S(q1) with increasing temperature is observed for the glass up to the corresponding glass transition temperature Tg. The temperature behavior of the structure factor is altered at the glass transition temperature and the slope of dS(q)/dT changes (Fig. 3). As long as no crystallization sets in,
Table 1 Glass transition temperature Tg, crystallization temperature Tx1 mass density r, position of the first maximum q1, electrical resistivity qel at 300 K, thermal coefficient of electrical resistivity aq, a: amorphous, l: supercooled liquid, and c: crystallized state Alloy composition
Tg (K)
Tx1 (K)
r (g cm3)
q1 (nm1)
q (300 K) (lX cm)
aq-measured (10–5/K)
aq-calculated (10–5/K)
Zr60Ti2Cu20Ni8Al10
656 ± 5
733 ± 5
a: 6.64 ± 0.01
25.9 ± 0.1
a: 140 ± 5
a: 7 ± 1 l: 13 ± 2 c: +85 ± 2
a: 6 l: 39
a: 11 ± 1 l: 33 ± 2 c: +69 ± 2
a: 13 l: 55
c: 6.66 ± 0.01 Pd40Cu30Ni10P20
569 ± 5
663 ± 5
a: 9.27 ± 0.01 c: 9.31 ± 0.01
c: 73 ± 5 29.0 ± 0.1
a: 150 ± 5 c: 80 ± 5
N. Mattern et al. / Journal of Non-Crystalline Solids 345&346 (2004) 758–761
Structure factor S(q)
T = 753 K T =733 K
10
T = 713 K T = 693 K T = 673 K T =653 K T = 633 K T = 613 K
5
T = 593 K T = 573 K T = 300 K
Electrical resistivity ρ / ρ300K
760
1.00 0.98 0.96 0.94 Zr60Ti2Cu20Al10Ni8 Pd40Cu30Ni10P20
0.92 0.90
300
400
500
600
700
800
Temperature ( K )
0 20
40
60
80
100 120 140
Scattering vector q ( nm-1 )
Fig. 4. Temperature dependence of the electrical resisitivity of Zr60Ti2Cu20Ni8Al10, and Pd40Cu30Ni10P10 bulk metallic glasses.
Fig. 2. Structure factor S(q) of Zr60Ti2Cu20Ni8Al10 bulk metallic glass at elevated temperatures.
Height of structure factor ST / ST=290K
300 K to 773 K, and the room-temperature resistivity is about 50% of the value of the glassy phase (Table 1). 1.0
4. Discussion The temperature dependence of the X-ray intensities can be described within the framework of the Debye theory [8]. The structure factor at a temperature T2 can be calculated from any temperature T1 by the relation
0.9
0.8
S T 2 ðqÞ 1 ¼ expf2½W T 2 ðqÞ W T 1 ðqÞg; S T 1 ðqÞ 1 2 Z H=T 3h2 q2 T 1 1 þ z WT ¼ z dz; 2 e 1 2ma k B H H 0
Zr-based S(q ) 1 Pd-based S(q ) 1
Pd-based S(q ) 2 Pd-based S(q )
0.7
3
300
400
500
600
700
Temperature T ( K ) Fig. 3. Temperature dependence of the normalized heights of maxima of the structure factor S(q) of Zr60Ti2Cu20Ni8Al10, and Pd40Cu30Ni10P10 bulk metallic glasses.
the temperature dependence of the structure factor is reversible within an error limit of about 0.1% (relative changes) for the determination of S(q1). The beginning crystallization is detected sensitively by an increase of S(q1) (not shown here). The measured dependence of the electrical resistivity is shown in Fig. 4. The resistivity of both glassy alloys decreases with temperature. At Tg, the slope of the curves changes. The experimental curves are qualitatively in accordance with the behavior of the structure factor. The values specific electrical resistiviy and the temperature coefficients are given in Table 1. The onset of crystallization is followed by a rapid decrease of the resistivity (not shown here). The crystallized alloy has a positive temperature coefficient in the range from
ð1Þ
where exp(2WT) denotes the Debye–Waller factor, ⁄ is the PlanckÕs constant, kB is the BoltzmannÕs constant, ma is the atomic mass, and h is the Debye temperature. The latter one can be calculated by a least squares fit of Eq. (1) to the data for the temperature dependence of the height of the first maximum of I(q). One obtains h = (296 ± 12) K for the Pd40Cu30Ni10P20 bulk glass, and h = (418 ± 10) K for the Zr60Ti2Cu20Ni8Al10 bulk glass, respectively. Using Eq. (1) choosing T1 = 293 K, the theoretical structure factor of any high temperature T2 can be calculated from the experimental curve measured at room temperature T1. Within the temperature range of the glassy state the calculated interference functions and the experimental curves agree well for both alloys. This confirms the conclusion that only effects of atomic thermal vibrations but no structural changes appear within the temperature range from room temperature up to the glass transition temperature. The temperature dependence of S(q1) in the supercooled liquid state gives a fictive lower Debye temperature. The calculations of S(q) in the supercooled liquid state differ from the measured S(q) curves clearly. This behavior is also expressed by the different slopes of dS(qi)/dT
N. Mattern et al. / Journal of Non-Crystalline Solids 345&346 (2004) 758–761
(i = 1, 2, 3) for the Pd40Cu30Ni10P20 bulk glass as shown in Fig. 3. The differences of the slopes of in the glassy state is due to the q-dependence of the structure factor. In the supercooled liquid state the slope dS(qi)/dT is rather similar for the different maxima. This means that the temperature dependence of the structure of the liquid state cannot be described by a temperature factor only. From this follows, starting at Tg a continuous development of structural changes appears with temperature. The electrical conductivity of liquid and amorphous metals is semi-quantitatively described within the framework of the extended Ziman theory [9–11]. For temperatures T P h the temperature coefficient of the electrical resistivity aq is related to the value of the structure factor ST(q) at q = 2kFwhere kF is the Fermi wave vector [10]: aq ¼
1 oq 1 S T ð2k F Þ oW ðT Þ 2 q oT S T ð2k F Þ oT 2
k F ¼ ð3p q0 ZÞ
quantitative numbers differ for the liquid state probably to the structural changes with temperature. 5. Conclusions The temperature dependence of the structure of the glassy state and the structural behavior at the glass transition of two different bulk metallic alloys could be studied by means of in situ by high-temperature synchrotron XRD, and by electrical resistivity measurements. Up to the glass transition temperature Tg, the changes of the structure factor are determined by the Debye-Waller temperature factor. Above Tg structural changes develop continuously in the supercooled liquid state with temperature. The temperature dependence of the electrical resistivity corresponds to the behavior of the structure factor.
ð2Þ
2
oW ðT Þ 3 h2 ð2k F Þ ¼ ; oT 2M k B h2
761
1=3
:
Here, q0 is the average number density of atoms (Pd40Cu30Ni10P20: q0 = 76 nm3; Zr60Ti2Cu20Ni8Al10: q0 = 52 nm3 – from mass density in Table 1) and Z is the mean number of valence electrons per atom. Assuming Z = 1.5, 2kF = 30.0 nm1 is estimated for Pd40Cu30Ni10P20, and 2kF = 26.4 nm1 for Zr60Ti2Cu20Ni8Al10. The values of the Fermi wave vector corresponds to the position of the first maximum of the structure factor giving a negative sign for the temperature coefficient of the electrical resistivity aq. Taking into account the data from the temperature dependence of the structure factor one obtains the calculated values of aq given in Table 1. The experimental values for aq (Table 1) agree well with the calculated values for the glassy state. The decrease of aq at temperatures above Tg is reproduced, but the
References [1] T. Zang, A. Inoue, T. Masumoto, Mater. Trans. JIM 32 (1991) 1005. [2] A. Peker, W.L. Johnson, Appl. Phys. Lett. 63 (1993) 2342. [3] A. Inoue, A. Takeuchi, Mater. Trans. JIM 43 (2002) 1892. [4] I.-R. Lu, G.P. Go¨rler, H.-J. Fecht, R. Willnecker, J. Non-Cryst. Solids 274 (2000) 294. [5] H. Schumacher, U. Herr, D. Oelschlaeger, A. Traverse, K. Samwer, J. Appl. Phys. 82 (1997) 155. [6] N. Mattern, J. Eckert, U. Kuehn, H. Hermann, J. Sakowski, G. Herms, J. Neuefeind, Appl. Phys. Lett. 80 (2002) 4525. [7] J. Sakowski, G. Herms, Hasylab Annual Report, Part 1, 985, 2000. [8] S. Sinha, P.L. Srivastava, R.N. Singh, J. Phys.: Condens. Matter 1 (1989) 1695. [9] J.M. Ziman, Philos. Mag. 6 (1961) 1013. [10] S.R. Nagel, Phys. Rev. B 16 (1977) 1694. [11] O. Dreirach, R. Evans, H.-J. Gu¨nthherrodt, A.-U. Ku¨nzi, J. Phys. F: Met. Phys. 2 (1972) 709.
Structural behavior and glass transition of bulk metallic glasses Norbert Mattern a
a,*
, Jan Sakowski b, Uta Ku¨hn a, Hartmut Vinzelberg a, Ju¨rgen Eckert
c
Leibniz-Institute for Solid State and Materials Research, IFW Dresden, P.O. Box 270116, D-01171 Dresden, Germany b Department of Physics, Rostock University, D-18051 Rostock, Germany c Department for Material- and Geo-Sciences, Technical University Darmstadt, D-64287 Darmstadt, Germany Available online 12 October 2004
Abstract The thermal behavior of Pd40Cu30Ni10P20 and Zr60Ti2Cu20Ni8Al10 bulk metallic glasses has been investigated in situ through the glass transition by means of differential scanning calorimetry, high-temperature X-ray synchrotron diffraction, and electrical resistivity. The temperature dependence of the X-ray structure factor can be well described by the Debye theory within the glassy state with a Debye temperature of h = 296 K for Pd40Cu30Ni10P20, and h = 418 K for Zr60Ti2Cu20Ni8Al10, respectively. At the glass transition temperature the temperature dependence of the structure changes, pointing to a continuous development of structural changes in the liquid state with temperature. The electrical resistivity behaves similar to the structure factor in accordance with Ziman theory. Ó 2004 Elsevier B.V. All rights reserved. PACS: 61.43.Dq; 61.46.+w; 64.70.Nd
1. Introduction Bulk metallic glasses represent a new class of amorphous metallic alloys developed in recent years [1,2]. These multi-component metallic alloys can be obtained at low cooling rates, which allow the production of large-scale materials, by conventional casting processes [3]. Furthermore, bulk metallic glasses show a glass transition at the temperature Tg up to 120 K lower than the crystallization temperature Tx enabling hot deformation and shaping [3]. The transition of the glass into the supercooled liquid state upon constant rate heating is related to changes in thermodynamic properties e.g., the enthalpy, and in the thermal expansion coefficient [4]. A direct observation of the structural behavior at the calorimetric glass transition temperature is rather limited so far [5,6].
*
Corresponding author. Tel.:+49 351 4659 367; fax: +49 351 4659 452. E-mail address: [email protected] (N. Mattern). 0022-3093/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.08.197
The aim of this work is to study the reversible part of the temperature dependence of the structure of two different alloy types of bulk metallic glasses up to the supercooled liquid state by means of in situ by high-temperature synchrotron X-ray diffraction, and electrical resistivity measurements. To reduce the influence of relaxation the samples were preannealed at temperatures below the glass transition temperature Tg.
2. Experimental procedure Samples of Pd40Cu30Ni10P20 and Zr60Ti2Cu20Ni8Al10 bulk glasses were prepared in form of rods with 5 and 3 mm diameter and 50 mm length by copper mold casting of arc-melted prealloys. Discs of 1 mm height were cut from the rods for differential scanning calorimetry (DSC) and X-ray diffraction (XRD) experiments. Cylinders of 10 mm in length were used for the measurements of the electrical resistivity. To remove the influence of structural relaxation the samples were pre-annealed
N. Mattern et al. / Journal of Non-Crystalline Solids 345&346 (2004) 758–761
Tx
Heat flow endo up (a.u.)
Tg
Tx
Tg
Zr60Ti2Cu20Ni8Al10 Pd40Cu30Ni10P20
500
600
700
Temperature T ( K ) Fig. 1. DSC scans of Zr60Ti2Cu20Ni8Al10, and Pd40Cu30Ni10P10 bulk metallic glasses (heating rate 10 K/min).
(Pd40Cu30Ni10P20: 543 K for seven days; Zr60Ti2Cu20Ni8Al10: 653 K for 2 min). The DSC experiments were performed employing a Netzsch DSC 404 calorimeter (heating rate 10 K/min). In situ XRD measurements at elevated temperatures were conducted at the high-energy beam-line BW5 at the storage ring DORIS (HASYLAB, Hamburg) [7]. The sample was hold for 130 s at the corresponding temperature (20 s for exposure and additional 110 s for data read out time), and then heated up to the next temperature within 10 s. Immediately thereafter the measurement was started again. Standard four point geometry was applied to measure the electrical conductivity during continuous heating (heating rate 5 K/min). The mass density was determined by the Archimedes principle by weighing samples in air and in dodecan (C12H26).
3. Results The thermal behavior of Zr60Ti2Cu20Ni8Al10, Pd40Cu30Ni10P10 bulk metallic glasses is shown in Fig. 1 by the DSC measurement. The glass transition is indicated by to the endothermal event, which corresponds to
759
the increase Dcp of the specific heat of the supercooled liquid. The crystallization at the exothermal peak starts from the supercooled liquid region spreading over 70 K for both alloys. The calorimetric glass transition temperatures Tg and the crystallization temperatures Tx for the two investigated alloys are given in Table 1 (both characteristic temperatures are here defined as the onset temperatures of the respective endothermic and exothermic DSC heat flow events). The mass density of the bulk metallic glass is only 0.5% smaller than that of the corresponding crystallized material (Table 1), which indicates a high degree of dense packed atomic configuration in these materials. The structure factor S(q) was calculated from the measured intensities after radial integration of the image plate data and applying the usual corrections and normalization procedure to determine the coherent scattered intensity in absolute electron units. Fig. 2 shows some of the structure factors ST(q) of the Zr60Ti2Cu20Ni8Al10 alloy measured at room temperature and at elevated temperatures. The amorphous structure is preserved up to 733 K, which is 77 K above Tg. We find no indication of a general structural change between the glassy and the supercooled liquid state. The crystallization starts between 733 K and 753 K during our stepwise heating procedure. At T = 753 K several crystalline reflections become visible as the first step of crystallization starts. Cubic NiZr2 and tetragonal CuZr2 are formed by eutectic-type crystallization from the supercooled liquid. The diffraction curves of the amorphous state of the sample within the temperature range 293 K 6 T 6 733 K exhibit only small changes with increasing temperature. The same is observed for Pd40Cu30Ni10P20 bulk glass 293 K 6 T 6 670 K. Fig. 3 exhibits the normalized temperature dependence of the height of the structure factor S(q) at the positions of the first, second, third maximum S(qi) for Pd40Cu30Ni10P20 bulk glass, and of the first maximum for Zr60Ti2Cu20Ni8Al10. A linear decrease of S(q1) with increasing temperature is observed for the glass up to the corresponding glass transition temperature Tg. The temperature behavior of the structure factor is altered at the glass transition temperature and the slope of dS(q)/dT changes (Fig. 3). As long as no crystallization sets in,
Table 1 Glass transition temperature Tg, crystallization temperature Tx1 mass density r, position of the first maximum q1, electrical resistivity qel at 300 K, thermal coefficient of electrical resistivity aq, a: amorphous, l: supercooled liquid, and c: crystallized state Alloy composition
Tg (K)
Tx1 (K)
r (g cm3)
q1 (nm1)
q (300 K) (lX cm)
aq-measured (10–5/K)
aq-calculated (10–5/K)
Zr60Ti2Cu20Ni8Al10
656 ± 5
733 ± 5
a: 6.64 ± 0.01
25.9 ± 0.1
a: 140 ± 5
a: 7 ± 1 l: 13 ± 2 c: +85 ± 2
a: 6 l: 39
a: 11 ± 1 l: 33 ± 2 c: +69 ± 2
a: 13 l: 55
c: 6.66 ± 0.01 Pd40Cu30Ni10P20
569 ± 5
663 ± 5
a: 9.27 ± 0.01 c: 9.31 ± 0.01
c: 73 ± 5 29.0 ± 0.1
a: 150 ± 5 c: 80 ± 5
N. Mattern et al. / Journal of Non-Crystalline Solids 345&346 (2004) 758–761
Structure factor S(q)
T = 753 K T =733 K
10
T = 713 K T = 693 K T = 673 K T =653 K T = 633 K T = 613 K
5
T = 593 K T = 573 K T = 300 K
Electrical resistivity ρ / ρ300K
760
1.00 0.98 0.96 0.94 Zr60Ti2Cu20Al10Ni8 Pd40Cu30Ni10P20
0.92 0.90
300
400
500
600
700
800
Temperature ( K )
0 20
40
60
80
100 120 140
Scattering vector q ( nm-1 )
Fig. 4. Temperature dependence of the electrical resisitivity of Zr60Ti2Cu20Ni8Al10, and Pd40Cu30Ni10P10 bulk metallic glasses.
Fig. 2. Structure factor S(q) of Zr60Ti2Cu20Ni8Al10 bulk metallic glass at elevated temperatures.
Height of structure factor ST / ST=290K
300 K to 773 K, and the room-temperature resistivity is about 50% of the value of the glassy phase (Table 1). 1.0
4. Discussion The temperature dependence of the X-ray intensities can be described within the framework of the Debye theory [8]. The structure factor at a temperature T2 can be calculated from any temperature T1 by the relation
0.9
0.8
S T 2 ðqÞ 1 ¼ expf2½W T 2 ðqÞ W T 1 ðqÞg; S T 1 ðqÞ 1 2 Z H=T 3h2 q2 T 1 1 þ z WT ¼ z dz; 2 e 1 2ma k B H H 0
Zr-based S(q ) 1 Pd-based S(q ) 1
Pd-based S(q ) 2 Pd-based S(q )
0.7
3
300
400
500
600
700
Temperature T ( K ) Fig. 3. Temperature dependence of the normalized heights of maxima of the structure factor S(q) of Zr60Ti2Cu20Ni8Al10, and Pd40Cu30Ni10P10 bulk metallic glasses.
the temperature dependence of the structure factor is reversible within an error limit of about 0.1% (relative changes) for the determination of S(q1). The beginning crystallization is detected sensitively by an increase of S(q1) (not shown here). The measured dependence of the electrical resistivity is shown in Fig. 4. The resistivity of both glassy alloys decreases with temperature. At Tg, the slope of the curves changes. The experimental curves are qualitatively in accordance with the behavior of the structure factor. The values specific electrical resistiviy and the temperature coefficients are given in Table 1. The onset of crystallization is followed by a rapid decrease of the resistivity (not shown here). The crystallized alloy has a positive temperature coefficient in the range from
ð1Þ
where exp(2WT) denotes the Debye–Waller factor, ⁄ is the PlanckÕs constant, kB is the BoltzmannÕs constant, ma is the atomic mass, and h is the Debye temperature. The latter one can be calculated by a least squares fit of Eq. (1) to the data for the temperature dependence of the height of the first maximum of I(q). One obtains h = (296 ± 12) K for the Pd40Cu30Ni10P20 bulk glass, and h = (418 ± 10) K for the Zr60Ti2Cu20Ni8Al10 bulk glass, respectively. Using Eq. (1) choosing T1 = 293 K, the theoretical structure factor of any high temperature T2 can be calculated from the experimental curve measured at room temperature T1. Within the temperature range of the glassy state the calculated interference functions and the experimental curves agree well for both alloys. This confirms the conclusion that only effects of atomic thermal vibrations but no structural changes appear within the temperature range from room temperature up to the glass transition temperature. The temperature dependence of S(q1) in the supercooled liquid state gives a fictive lower Debye temperature. The calculations of S(q) in the supercooled liquid state differ from the measured S(q) curves clearly. This behavior is also expressed by the different slopes of dS(qi)/dT
N. Mattern et al. / Journal of Non-Crystalline Solids 345&346 (2004) 758–761
(i = 1, 2, 3) for the Pd40Cu30Ni10P20 bulk glass as shown in Fig. 3. The differences of the slopes of in the glassy state is due to the q-dependence of the structure factor. In the supercooled liquid state the slope dS(qi)/dT is rather similar for the different maxima. This means that the temperature dependence of the structure of the liquid state cannot be described by a temperature factor only. From this follows, starting at Tg a continuous development of structural changes appears with temperature. The electrical conductivity of liquid and amorphous metals is semi-quantitatively described within the framework of the extended Ziman theory [9–11]. For temperatures T P h the temperature coefficient of the electrical resistivity aq is related to the value of the structure factor ST(q) at q = 2kFwhere kF is the Fermi wave vector [10]: aq ¼
1 oq 1 S T ð2k F Þ oW ðT Þ 2 q oT S T ð2k F Þ oT 2
k F ¼ ð3p q0 ZÞ
quantitative numbers differ for the liquid state probably to the structural changes with temperature. 5. Conclusions The temperature dependence of the structure of the glassy state and the structural behavior at the glass transition of two different bulk metallic alloys could be studied by means of in situ by high-temperature synchrotron XRD, and by electrical resistivity measurements. Up to the glass transition temperature Tg, the changes of the structure factor are determined by the Debye-Waller temperature factor. Above Tg structural changes develop continuously in the supercooled liquid state with temperature. The temperature dependence of the electrical resistivity corresponds to the behavior of the structure factor.
ð2Þ
2
oW ðT Þ 3 h2 ð2k F Þ ¼ ; oT 2M k B h2
761
1=3
:
Here, q0 is the average number density of atoms (Pd40Cu30Ni10P20: q0 = 76 nm3; Zr60Ti2Cu20Ni8Al10: q0 = 52 nm3 – from mass density in Table 1) and Z is the mean number of valence electrons per atom. Assuming Z = 1.5, 2kF = 30.0 nm1 is estimated for Pd40Cu30Ni10P20, and 2kF = 26.4 nm1 for Zr60Ti2Cu20Ni8Al10. The values of the Fermi wave vector corresponds to the position of the first maximum of the structure factor giving a negative sign for the temperature coefficient of the electrical resistivity aq. Taking into account the data from the temperature dependence of the structure factor one obtains the calculated values of aq given in Table 1. The experimental values for aq (Table 1) agree well with the calculated values for the glassy state. The decrease of aq at temperatures above Tg is reproduced, but the
References [1] T. Zang, A. Inoue, T. Masumoto, Mater. Trans. JIM 32 (1991) 1005. [2] A. Peker, W.L. Johnson, Appl. Phys. Lett. 63 (1993) 2342. [3] A. Inoue, A. Takeuchi, Mater. Trans. JIM 43 (2002) 1892. [4] I.-R. Lu, G.P. Go¨rler, H.-J. Fecht, R. Willnecker, J. Non-Cryst. Solids 274 (2000) 294. [5] H. Schumacher, U. Herr, D. Oelschlaeger, A. Traverse, K. Samwer, J. Appl. Phys. 82 (1997) 155. [6] N. Mattern, J. Eckert, U. Kuehn, H. Hermann, J. Sakowski, G. Herms, J. Neuefeind, Appl. Phys. Lett. 80 (2002) 4525. [7] J. Sakowski, G. Herms, Hasylab Annual Report, Part 1, 985, 2000. [8] S. Sinha, P.L. Srivastava, R.N. Singh, J. Phys.: Condens. Matter 1 (1989) 1695. [9] J.M. Ziman, Philos. Mag. 6 (1961) 1013. [10] S.R. Nagel, Phys. Rev. B 16 (1977) 1694. [11] O. Dreirach, R. Evans, H.-J. Gu¨nthherrodt, A.-U. Ku¨nzi, J. Phys. F: Met. Phys. 2 (1972) 709.