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Structural behavior of amorphous and liquid metallic alloys at elevated temperatures
Journal of Non-Crystalline Solids 353 (2007) 3327–3331 www.elsevier.com/locate/jnoncrysol
Structural behavior of amorphous and liquid metallic alloys at elevated temperatures Norbert Mattern a
a,*
, Uta Ku¨hn a, Ju¨rgen Eckert
a,b
Leibniz-Institute for Solid State and Materials Research, IFW Dresden, P.O. Box 270116, D-01171 Dresden, Germany b Department for Material- and Geo-Sciences, Technical University Darmstadt, D-64287 Darmstadt, Germany Available online 23 July 2007
Abstract The thermal behavior of the short-range order of Pd40Cu30Ni10P20 bulk metallic glasses has been investigated in situ by means of hightemperature X-ray synchrotron diffraction. The dependence of the X-ray structure factor S(q) of the glassy state on temperature follows the Debye theory up to the glass transition. Above the glass transition temperature Tg, the temperature dependence of S(q) is altered toward a continuous development of structural changes in the liquid state with temperature. The behavior of the structure factor during heating and cooling through the glass transition gives experimental evidence for melting the glass, and for freezing the liquid, respectively at the caloric glass temperature. 2007 Elsevier B.V. All rights reserved. PACS: 61.43.Dq; 61.46.+w; 64.70.Nd Keywords: Amorphous metals; Metallic glasses; Liquid alloys and liquid metals; Diffraction and scattering measurements; Synchrotron radiation; X-ray diffraction; Glass formation; Glass transition; Structure; Thermal properties; X-rays
1. Introduction Bulk metallic glasses represent a new class of amorphous metallic alloys developed in recent years [1,2]. These multicomponent 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]. The aim of this work is to study the temperature dependence of the structure of Pd40Cu30Ni10P20 bulk metallic glass up to the liquid state by means of in situ by high-tem*
Corresponding author. Tel.: +49 351 4659 367; fax: +49 351 4659 452. E-mail address: [email protected] (N. Mattern).
0022-3093/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.05.079
perature synchrotron X-ray diffraction. Measurements of the temperature dependence of the structure factor were performed to get more insight into the structural behavior of the bulk metallic glass at the glass transition. 2. Experimental procedure Samples of Pd40Cu30Ni10P20 bulk glasses were prepared in form of rods with 5 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. To remove the influence of structural relaxation part of the samples were pre-annealed at 543 K for 7 days. The DSC experiments were performed employing a Netzsch DSC 404 calorimeter (heating rate 10 K/min). In situ XRD measurements were conducted at the high-energy beam-line BW5 at the storage ring DORIS at HASYLAB, Hamburg using a wavelength of k = 0.01067 nm. The experimental setup consisting of a high-temperature chamber and an
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image plate detector enables to record a diffraction pattern of 1 mm thick samples in transmission within 30 s and up to a scattering vector q = 4p sin h/k = 200 nm1 [5]. The sample was hold for 140 s at the corresponding temperature (30 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. The mass density was determined by the Archimedes principle by weighing samples in air and in dodecan (C12H26). 3. Results Fig. 1 shows some of the structure factors ST(q) of the Pd40Cu30Ni10P20 alloy measured at room temperature and at elevated temperatures. The structure factors were 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. The diffraction patterns indicate that the amorphous structure is retained up to 660 K, which is 90 K above the caloric glass transition temperature Tg (Table 1). The crystallization starts between 660 K and 673 K during our stepwise heating procedure. At T = 673 K several crystalline reflections become visible as the first step of crystallization in a qualitative agreement with the DSC data obtained during continuous heating (Table 1). It is well known that the crystallization temperature depends on
Fig. 1. Structure factor S(q) of Pd40Cu30Ni10P20 bulk metallic glass at elevated temperatures.
the heating rate, which is not well defined in the applied stepwise measuring regime with an average of about 20 K/min in the temperature range between room temperature and 523 K, and 5 K/min between 523 K and 673 K, respectively. Between 673 K 6 T 6 823 K, we observe increase of crystalline reflections (not shown here). The weak and broad reflections at the beginning of the crystallization at T = 673 K (Fig. 1) are due to low volume fraction of crystalline phase and small size of the crystals as well as instrumental broadening (instrumental width is 1 nm1). At T = 873 K, the alloy is melted. The diffuse character of the structure factor for T P 873 K indicates the liquid state of the alloy in agreement with the liquidus temperature (Table 1). The diffraction curves of the amorphous state of the sample exhibit only small changes with increasing temperature. Fig. 2 shows the temperature dependence of the position q1 of the first maximum of the structure factor for the as-cast and the annealed sample. A continuous shift of q1 with temperature to lower q-values is observed. No change is observed in the slope of q1(T) at the glass transition temperature and the extrapolation to temperatures above the liquidus temperature is in agreement with the experimental data for the melt. There is no difference in q1 detectable between the as-cast and the annealed material. The behavior of the height of the first maximum of the structure factor S q1 ðT Þ is shown in Fig. 3. The height decreases with increasing temperature. At the caloric glass transition temperature Tg the slope of dS q1 ðT Þ=dT is altered. Extrapolating the temperature dependence of S q1 ðT Þ from the supercooled liquid state to higher temperatures one obtains approximately the experimental values for the molten Pd40Cu30Ni10P20 alloy (not shown here). As long as no crystallization sets in, the change of the temperature dependence of the structure factor at Tg is reversible upon heating as well as upon cooling. The data shown in Fig. 3 were obtained for thermal cycling by heating up to 648 K, cooling down to 373 K and subsequent reheating from 373 K to 648 K. The values of S q1 ðT Þ for the cooling route become smaller below 625 K compared to those of the first heating, and they are identical with the data of the second reheating. The behavior of S q1 ðT Þ of the as-cast material is also shown in Fig. 3. The height is lower compared to that of the annealed state, and decreases with temperature with the same slope as for the annealed sample. Near the glass transition S q1 ðT Þ increases, and decreases above Tg again. For T > 650 K identical values are observed (Fig. 3). To analyze the structural behavior in real space the atomic pair correlation functions g(r) = q(r)/q0 were calcu-
Table 1 Glass transition temperature Tg, crystallization temperature Tx1, liquidus temperature Tliquidus, mass density r, position of the first maximum q1, and linear thermal expansion coefficient a of Pd40Cu30Ni10P20 (a: glass, l: liquid, and c: crystallized state) Tg (K)
Tx1 (K)
Tliquidus (K)
r (gcm3)
q1 (nm1)
a(105/K)
569 ± 5
663 ± 5
864 ± 10
a: 9.27 ± 0.01 c: 9.31 ± 0.01
28.98 ± 0.007
a: 1.2 ± 0.1 l: 3.1 ± 0.1
N. Mattern et al. / Journal of Non-Crystalline Solids 353 (2007) 3327–3331
Fig. 2. Temperature dependence of q1 of three different samples of Pd40Cu30Ni10P10 bulk metallic glass (1:-, 2:X, 3:K, line as guide to the eyes).
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Fig. 4. Atomic pair correlation function g(r) of Pd40Cu30Ni10P20 at different temperatures (maximum positions ri for T = 296 K : r1 = 0.277 nm, r2 = 0.455 nm, r3 = 0.520 nm, r4 = 0.692 nm, r5 = 0.921 nm, r6 = 1.136 nm).
0.115), and Pd–P (2wPd–P = 0.102) atomic pairs. The maximum position corresponds to the atomic diameter of palladium. The peaks of the pair correlation functions of Pd40Cu30Ni10P20 at elevated temperature become broader with increasing temperature. coordination number N1, which is obtained by integration from 0.20 nm to 0.35 nm over the first maximum in g(r) is constant within the error limits. The value of N1 = 14.2 ± 1 is calculated for the glass at room temperature, and 13.8 ± 1 for the liquid at T = 973 K, respectively. The split second maximum in g(r) is also present in the melt with a reduced height of the first component. Fig. 5 shows the change in g(r) with temperature by the corresponding difference quotient (dg(r,T)/dT)T. Within the glassy state from room temperature up to 560 K the curves represent mainly the broadening of the Fig. 3. Height of the first maximum S(q1) versus temperature (lines as guide to the eyes).
lated by the Fourier transformation of S(q) between 0 6 q 6 140 nm1 according to [6]: Z 2 4p r q0 ðgðrÞ 1Þ ¼ ðSðqÞ 1Þ q sinðq rÞ dq p ð1Þ where q(r) is the radial atomic pair density distribution function and q0 is the mean atomic density (q0 = 76 nm3 follows from the measured mass density r = (9.27 ± 0.01) g cm3). Fig. 4 shows some of the calculated g(r) curves. S(q) and g(r) look very similar to those of many metallic glasses. The first maximum in g(r) at r1 = 0.277 nm has a shoulder on the low r-side and contains contributions of the different partial pair correlations pairs, which cannot be individually resolved. The main contributions come from the Pd–Pd (weighting factor wPd–Pd = 0.313), Pd–Cu (2wPd–Cu = 0.296), Pd–Ni (2wPd–Ni =
Fig. 5. Difference quotient (dg(r,T)/dT)T of glassy and liquid Pd40Cu30Ni10P20 for different temperature regions.
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Fig. 6. Normalized 1st and 2nd peak heights, g(r1) and g(r2), of the atomic pair correlation function versus temperature (lines as guide to the eyes).
peaks due to the thermal oscillations. The broadening of the first maximum is asymmetric with increasing atomic pair fractions at the larger distance site. In the supercooled liquid state additional changes occur in g(r) with temperature. The asymmetry becomes much more extended and the height of first component of the second maximum at r2 decreases more distinctive. Fig. 6 shows the relative heights of the first and the second maxima in g(r). The heights decrease with temperature. The glass transition is clearly indicated by a change in the temperature dependence. 4. Discussion The temperature dependence of the structure factor can be described in the harmonic approximation by the Debye– Waller factor [7,8], which corresponds to a thermal mean square displacement hu2i i of the atoms i. The structure factor at a temperature T2 is related to that at any temperature T1 by the relation S T 2 ðqÞ ¼ 1 þ ðS T 1 ðqÞ 1Þ expð2ðW T 2 ðqÞ W T 1 ðqÞÞÞ ð2Þ where exp(2WT) is the Debye-Waller factor and 2 Z H=T 3 h2 q2 T 1 1 þ z WT ¼ zdz 2 e 1 2 ma k B H H 0 with h Planck’s constant, kB Boltzmann’s constant, ma the atomic weight, and H the Debye temperature (for T H is WT T and ST S0(1 a Æ T) is approximately linear with temperature). Expression (2) was used to determine the Debye temperature being the only free parameter. From the temperature dependence of the height of the first maximum of I(q) one obtains h = (296 ± 12) K for the Pd40Cu30Ni10P20 bulk glass. Applying Eq. (2) and choosing T1 = 293 K, the structure factor of any temperature T2 can be calculated from the experimental curve measured at
room temperature T1. Such calculated structure factors agree well with the experimental curves within the glassy state. The reversible behavior of S(q) and g(r) confirms that the effects of atomic thermal vibrations are the dominant within the temperature range from room temperature up to the glass transition temperature. The analysis of temperature dependence of S(q) and g(r) above Tg clearly indicates deviation from the Debye-Waller behavior. In the supercooled liquid state additional changes occur in g(r) with temperature. The asymmetry becomes much more extended and especially the height of the second maximum decreases more distinctively. At Tg structural changes start to develop continuously with temperature from the supercooled liquid state up to the equilibrium melt. The height of the first maximum of S(q) is related to structural disorder and quenched defects. The as-cast state has usually frozen defects. Annealing lead to an annihilation of defects which results in small sharpening of peaks in S(q) and g(r) [9–11]. The increase of the first maximum in Fig. 3 indicates relaxation of the as-cast material at T > 550 K. The observable changes are also influenced by the dynamics of the system. With increasing temperature there is a cross over between relaxation and glass transition. For T > 620 K the ergodic region is reached and the curves coincide. The cooling curve in Fig. 3 shows that a structural state above Tg is frozen in. The time during reheating in our diffraction experiment is not sufficient to relax the material. The behavior of the peak positions q1 of the first maximum of the structure factor is shown in Fig. 3. The change in q1 is approximately linear with temperature up to the liquid state with linear temperature coefficient of (1/q1)* (dq1/dT) = 1.1 · 105 K1 (error limit in 2h with Dh = ±0.005 at 2h = 2.5 gives Dq1 ± 0.05 nm1). The shift in position is related to thermal expansion (Table 1) if there is no structural change with temperature. This is true for the glassy state of Pd40Cu30Ni10P20. At the glass transition temperature the linear expansion coefficient changes by factor of about 2.5 for the liquid state. This transition is obviously not reflected by the temperature dependence of q1. A similar linear dependence of q1 versus temperature was measured recently for Zr60Ti2Al10Cu20Ni8 bulk metallic glass from room temperature up to the melt [12]. The position q1 of rapidly quenched ribbons and bulk glass of Pd40Cu30Ni10P20 at room temperature were compared using XRD measurement with Cu Ka radiation. Special care was done for the adjustment of the sample height using total reflection. By this procedure the error of 2h can be minimized to Dh = ±0.01 at 2h = 41.67, which gives q1 = 28.98 nm1 and Dq1 ± 0.007 nm1. The obtained value of q1=28.93 nm1 at room temperature for the synchrotron measurements (Fig. 2) is within the larger error limit of the image plate detection due to possible errors in position of the sample. Within this error limit there is no difference between rapidly quenched ribbon, cast and annealed bulk samples.
N. Mattern et al. / Journal of Non-Crystalline Solids 353 (2007) 3327–3331
5. Conclusions The temperature dependence of the structure of the glassy state and the structural behavior at the glass transition of Pd40Cu30Ni10P20 bulk metallic alloys could be studied by means of in situ by high-temperature synchrotron XRD. 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 behavior of the structure factor and corresponding atomic pair correlation functions during heating and cooling through the glass transition gives experimental evidence for melting the glass, and for freezing the liquid, respectively at Tg. Acknowledgements We thank HASYLAB in Hamburg for use of the synchrotron radiation facilities. The experimental support by
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J. Sakowski, B. Opitz, G. Herms and U. Precht is gratefully acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
T. Zang, A. Inoue, T. Masumoto, Mater. Trans. JIM 32 (1991) 1005. A. Peker, W.L. Johnson, Appl. Phys. Lett. 63 (1993) 2342. A. Inoue, A. Takeuchi, Mater. Trans. JIM 43 (2002) 1892. I.-R. Lu, G.P. Go¨rler, H.-J. Fecht, R. Willnecker, J. Non-Cryst. Solids 274 (2000) 294. J. Sakowski and G. Herms, in: Hasylab Annual Report, Part 1, (2000) 985. C.N.J. Wagner, Liquid Metals, Chemistry and Physics, in: S.Z. Beer (Ed.), Marcel Dekker Inc., New York, 1972, p. 257. S.R. Nagel, Phys. Rev. B 16 (1977) 1694. S. Sinha, P.L. Srivastava, R.N. Singh, J. Phys.: Condens. Matter 1 (1989) 1695. T. Egami, Mater. Res. Bull. 13 (1977) 557. D. Srolovitz, T. Egami, V. Vitek, Phys. Rev. B 24 (1981) 6936. R. Bru¨ning, J.O. Stro¨m-Olsen, Phys. Rev. B 41 (1990) 2678. N. Mattern, U. Kuehn, J. Eckert, J. Metastable Nanocryst. Mater. 20–21 (2004) 59.
Structural behavior of amorphous and liquid metallic alloys at elevated temperatures Norbert Mattern a
a,*
, Uta Ku¨hn a, Ju¨rgen Eckert
a,b
Leibniz-Institute for Solid State and Materials Research, IFW Dresden, P.O. Box 270116, D-01171 Dresden, Germany b Department for Material- and Geo-Sciences, Technical University Darmstadt, D-64287 Darmstadt, Germany Available online 23 July 2007
Abstract The thermal behavior of the short-range order of Pd40Cu30Ni10P20 bulk metallic glasses has been investigated in situ by means of hightemperature X-ray synchrotron diffraction. The dependence of the X-ray structure factor S(q) of the glassy state on temperature follows the Debye theory up to the glass transition. Above the glass transition temperature Tg, the temperature dependence of S(q) is altered toward a continuous development of structural changes in the liquid state with temperature. The behavior of the structure factor during heating and cooling through the glass transition gives experimental evidence for melting the glass, and for freezing the liquid, respectively at the caloric glass temperature. 2007 Elsevier B.V. All rights reserved. PACS: 61.43.Dq; 61.46.+w; 64.70.Nd Keywords: Amorphous metals; Metallic glasses; Liquid alloys and liquid metals; Diffraction and scattering measurements; Synchrotron radiation; X-ray diffraction; Glass formation; Glass transition; Structure; Thermal properties; X-rays
1. Introduction Bulk metallic glasses represent a new class of amorphous metallic alloys developed in recent years [1,2]. These multicomponent 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]. The aim of this work is to study the temperature dependence of the structure of Pd40Cu30Ni10P20 bulk metallic glass up to the liquid state by means of in situ by high-tem*
Corresponding author. Tel.: +49 351 4659 367; fax: +49 351 4659 452. E-mail address: [email protected] (N. Mattern).
0022-3093/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.05.079
perature synchrotron X-ray diffraction. Measurements of the temperature dependence of the structure factor were performed to get more insight into the structural behavior of the bulk metallic glass at the glass transition. 2. Experimental procedure Samples of Pd40Cu30Ni10P20 bulk glasses were prepared in form of rods with 5 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. To remove the influence of structural relaxation part of the samples were pre-annealed at 543 K for 7 days. The DSC experiments were performed employing a Netzsch DSC 404 calorimeter (heating rate 10 K/min). In situ XRD measurements were conducted at the high-energy beam-line BW5 at the storage ring DORIS at HASYLAB, Hamburg using a wavelength of k = 0.01067 nm. The experimental setup consisting of a high-temperature chamber and an
3328
N. Mattern et al. / Journal of Non-Crystalline Solids 353 (2007) 3327–3331
image plate detector enables to record a diffraction pattern of 1 mm thick samples in transmission within 30 s and up to a scattering vector q = 4p sin h/k = 200 nm1 [5]. The sample was hold for 140 s at the corresponding temperature (30 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. The mass density was determined by the Archimedes principle by weighing samples in air and in dodecan (C12H26). 3. Results Fig. 1 shows some of the structure factors ST(q) of the Pd40Cu30Ni10P20 alloy measured at room temperature and at elevated temperatures. The structure factors were 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. The diffraction patterns indicate that the amorphous structure is retained up to 660 K, which is 90 K above the caloric glass transition temperature Tg (Table 1). The crystallization starts between 660 K and 673 K during our stepwise heating procedure. At T = 673 K several crystalline reflections become visible as the first step of crystallization in a qualitative agreement with the DSC data obtained during continuous heating (Table 1). It is well known that the crystallization temperature depends on
Fig. 1. Structure factor S(q) of Pd40Cu30Ni10P20 bulk metallic glass at elevated temperatures.
the heating rate, which is not well defined in the applied stepwise measuring regime with an average of about 20 K/min in the temperature range between room temperature and 523 K, and 5 K/min between 523 K and 673 K, respectively. Between 673 K 6 T 6 823 K, we observe increase of crystalline reflections (not shown here). The weak and broad reflections at the beginning of the crystallization at T = 673 K (Fig. 1) are due to low volume fraction of crystalline phase and small size of the crystals as well as instrumental broadening (instrumental width is 1 nm1). At T = 873 K, the alloy is melted. The diffuse character of the structure factor for T P 873 K indicates the liquid state of the alloy in agreement with the liquidus temperature (Table 1). The diffraction curves of the amorphous state of the sample exhibit only small changes with increasing temperature. Fig. 2 shows the temperature dependence of the position q1 of the first maximum of the structure factor for the as-cast and the annealed sample. A continuous shift of q1 with temperature to lower q-values is observed. No change is observed in the slope of q1(T) at the glass transition temperature and the extrapolation to temperatures above the liquidus temperature is in agreement with the experimental data for the melt. There is no difference in q1 detectable between the as-cast and the annealed material. The behavior of the height of the first maximum of the structure factor S q1 ðT Þ is shown in Fig. 3. The height decreases with increasing temperature. At the caloric glass transition temperature Tg the slope of dS q1 ðT Þ=dT is altered. Extrapolating the temperature dependence of S q1 ðT Þ from the supercooled liquid state to higher temperatures one obtains approximately the experimental values for the molten Pd40Cu30Ni10P20 alloy (not shown here). As long as no crystallization sets in, the change of the temperature dependence of the structure factor at Tg is reversible upon heating as well as upon cooling. The data shown in Fig. 3 were obtained for thermal cycling by heating up to 648 K, cooling down to 373 K and subsequent reheating from 373 K to 648 K. The values of S q1 ðT Þ for the cooling route become smaller below 625 K compared to those of the first heating, and they are identical with the data of the second reheating. The behavior of S q1 ðT Þ of the as-cast material is also shown in Fig. 3. The height is lower compared to that of the annealed state, and decreases with temperature with the same slope as for the annealed sample. Near the glass transition S q1 ðT Þ increases, and decreases above Tg again. For T > 650 K identical values are observed (Fig. 3). To analyze the structural behavior in real space the atomic pair correlation functions g(r) = q(r)/q0 were calcu-
Table 1 Glass transition temperature Tg, crystallization temperature Tx1, liquidus temperature Tliquidus, mass density r, position of the first maximum q1, and linear thermal expansion coefficient a of Pd40Cu30Ni10P20 (a: glass, l: liquid, and c: crystallized state) Tg (K)
Tx1 (K)
Tliquidus (K)
r (gcm3)
q1 (nm1)
a(105/K)
569 ± 5
663 ± 5
864 ± 10
a: 9.27 ± 0.01 c: 9.31 ± 0.01
28.98 ± 0.007
a: 1.2 ± 0.1 l: 3.1 ± 0.1
N. Mattern et al. / Journal of Non-Crystalline Solids 353 (2007) 3327–3331
Fig. 2. Temperature dependence of q1 of three different samples of Pd40Cu30Ni10P10 bulk metallic glass (1:-, 2:X, 3:K, line as guide to the eyes).
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Fig. 4. Atomic pair correlation function g(r) of Pd40Cu30Ni10P20 at different temperatures (maximum positions ri for T = 296 K : r1 = 0.277 nm, r2 = 0.455 nm, r3 = 0.520 nm, r4 = 0.692 nm, r5 = 0.921 nm, r6 = 1.136 nm).
0.115), and Pd–P (2wPd–P = 0.102) atomic pairs. The maximum position corresponds to the atomic diameter of palladium. The peaks of the pair correlation functions of Pd40Cu30Ni10P20 at elevated temperature become broader with increasing temperature. coordination number N1, which is obtained by integration from 0.20 nm to 0.35 nm over the first maximum in g(r) is constant within the error limits. The value of N1 = 14.2 ± 1 is calculated for the glass at room temperature, and 13.8 ± 1 for the liquid at T = 973 K, respectively. The split second maximum in g(r) is also present in the melt with a reduced height of the first component. Fig. 5 shows the change in g(r) with temperature by the corresponding difference quotient (dg(r,T)/dT)T. Within the glassy state from room temperature up to 560 K the curves represent mainly the broadening of the Fig. 3. Height of the first maximum S(q1) versus temperature (lines as guide to the eyes).
lated by the Fourier transformation of S(q) between 0 6 q 6 140 nm1 according to [6]: Z 2 4p r q0 ðgðrÞ 1Þ ¼ ðSðqÞ 1Þ q sinðq rÞ dq p ð1Þ where q(r) is the radial atomic pair density distribution function and q0 is the mean atomic density (q0 = 76 nm3 follows from the measured mass density r = (9.27 ± 0.01) g cm3). Fig. 4 shows some of the calculated g(r) curves. S(q) and g(r) look very similar to those of many metallic glasses. The first maximum in g(r) at r1 = 0.277 nm has a shoulder on the low r-side and contains contributions of the different partial pair correlations pairs, which cannot be individually resolved. The main contributions come from the Pd–Pd (weighting factor wPd–Pd = 0.313), Pd–Cu (2wPd–Cu = 0.296), Pd–Ni (2wPd–Ni =
Fig. 5. Difference quotient (dg(r,T)/dT)T of glassy and liquid Pd40Cu30Ni10P20 for different temperature regions.
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Fig. 6. Normalized 1st and 2nd peak heights, g(r1) and g(r2), of the atomic pair correlation function versus temperature (lines as guide to the eyes).
peaks due to the thermal oscillations. The broadening of the first maximum is asymmetric with increasing atomic pair fractions at the larger distance site. In the supercooled liquid state additional changes occur in g(r) with temperature. The asymmetry becomes much more extended and the height of first component of the second maximum at r2 decreases more distinctive. Fig. 6 shows the relative heights of the first and the second maxima in g(r). The heights decrease with temperature. The glass transition is clearly indicated by a change in the temperature dependence. 4. Discussion The temperature dependence of the structure factor can be described in the harmonic approximation by the Debye– Waller factor [7,8], which corresponds to a thermal mean square displacement hu2i i of the atoms i. The structure factor at a temperature T2 is related to that at any temperature T1 by the relation S T 2 ðqÞ ¼ 1 þ ðS T 1 ðqÞ 1Þ expð2ðW T 2 ðqÞ W T 1 ðqÞÞÞ ð2Þ where exp(2WT) is the Debye-Waller factor and 2 Z H=T 3 h2 q2 T 1 1 þ z WT ¼ zdz 2 e 1 2 ma k B H H 0 with h Planck’s constant, kB Boltzmann’s constant, ma the atomic weight, and H the Debye temperature (for T H is WT T and ST S0(1 a Æ T) is approximately linear with temperature). Expression (2) was used to determine the Debye temperature being the only free parameter. From the temperature dependence of the height of the first maximum of I(q) one obtains h = (296 ± 12) K for the Pd40Cu30Ni10P20 bulk glass. Applying Eq. (2) and choosing T1 = 293 K, the structure factor of any temperature T2 can be calculated from the experimental curve measured at
room temperature T1. Such calculated structure factors agree well with the experimental curves within the glassy state. The reversible behavior of S(q) and g(r) confirms that the effects of atomic thermal vibrations are the dominant within the temperature range from room temperature up to the glass transition temperature. The analysis of temperature dependence of S(q) and g(r) above Tg clearly indicates deviation from the Debye-Waller behavior. In the supercooled liquid state additional changes occur in g(r) with temperature. The asymmetry becomes much more extended and especially the height of the second maximum decreases more distinctively. At Tg structural changes start to develop continuously with temperature from the supercooled liquid state up to the equilibrium melt. The height of the first maximum of S(q) is related to structural disorder and quenched defects. The as-cast state has usually frozen defects. Annealing lead to an annihilation of defects which results in small sharpening of peaks in S(q) and g(r) [9–11]. The increase of the first maximum in Fig. 3 indicates relaxation of the as-cast material at T > 550 K. The observable changes are also influenced by the dynamics of the system. With increasing temperature there is a cross over between relaxation and glass transition. For T > 620 K the ergodic region is reached and the curves coincide. The cooling curve in Fig. 3 shows that a structural state above Tg is frozen in. The time during reheating in our diffraction experiment is not sufficient to relax the material. The behavior of the peak positions q1 of the first maximum of the structure factor is shown in Fig. 3. The change in q1 is approximately linear with temperature up to the liquid state with linear temperature coefficient of (1/q1)* (dq1/dT) = 1.1 · 105 K1 (error limit in 2h with Dh = ±0.005 at 2h = 2.5 gives Dq1 ± 0.05 nm1). The shift in position is related to thermal expansion (Table 1) if there is no structural change with temperature. This is true for the glassy state of Pd40Cu30Ni10P20. At the glass transition temperature the linear expansion coefficient changes by factor of about 2.5 for the liquid state. This transition is obviously not reflected by the temperature dependence of q1. A similar linear dependence of q1 versus temperature was measured recently for Zr60Ti2Al10Cu20Ni8 bulk metallic glass from room temperature up to the melt [12]. The position q1 of rapidly quenched ribbons and bulk glass of Pd40Cu30Ni10P20 at room temperature were compared using XRD measurement with Cu Ka radiation. Special care was done for the adjustment of the sample height using total reflection. By this procedure the error of 2h can be minimized to Dh = ±0.01 at 2h = 41.67, which gives q1 = 28.98 nm1 and Dq1 ± 0.007 nm1. The obtained value of q1=28.93 nm1 at room temperature for the synchrotron measurements (Fig. 2) is within the larger error limit of the image plate detection due to possible errors in position of the sample. Within this error limit there is no difference between rapidly quenched ribbon, cast and annealed bulk samples.
N. Mattern et al. / Journal of Non-Crystalline Solids 353 (2007) 3327–3331
5. Conclusions The temperature dependence of the structure of the glassy state and the structural behavior at the glass transition of Pd40Cu30Ni10P20 bulk metallic alloys could be studied by means of in situ by high-temperature synchrotron XRD. 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 behavior of the structure factor and corresponding atomic pair correlation functions during heating and cooling through the glass transition gives experimental evidence for melting the glass, and for freezing the liquid, respectively at Tg. Acknowledgements We thank HASYLAB in Hamburg for use of the synchrotron radiation facilities. The experimental support by
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J. Sakowski, B. Opitz, G. Herms and U. Precht is gratefully acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
T. Zang, A. Inoue, T. Masumoto, Mater. Trans. JIM 32 (1991) 1005. A. Peker, W.L. Johnson, Appl. Phys. Lett. 63 (1993) 2342. A. Inoue, A. Takeuchi, Mater. Trans. JIM 43 (2002) 1892. I.-R. Lu, G.P. Go¨rler, H.-J. Fecht, R. Willnecker, J. Non-Cryst. Solids 274 (2000) 294. J. Sakowski and G. Herms, in: Hasylab Annual Report, Part 1, (2000) 985. C.N.J. Wagner, Liquid Metals, Chemistry and Physics, in: S.Z. Beer (Ed.), Marcel Dekker Inc., New York, 1972, p. 257. S.R. Nagel, Phys. Rev. B 16 (1977) 1694. S. Sinha, P.L. Srivastava, R.N. Singh, J. Phys.: Condens. Matter 1 (1989) 1695. T. Egami, Mater. Res. Bull. 13 (1977) 557. D. Srolovitz, T. Egami, V. Vitek, Phys. Rev. B 24 (1981) 6936. R. Bru¨ning, J.O. Stro¨m-Olsen, Phys. Rev. B 41 (1990) 2678. N. Mattern, U. Kuehn, J. Eckert, J. Metastable Nanocryst. Mater. 20–21 (2004) 59.