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Length scale-dependent structural relaxation in Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 metallic glass
Journal of Alloys and Compounds 639 (2015) 465–469
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Length scale-dependent structural relaxation in Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 metallic glass S. Scudino a,⇑, M. Stoica a, I. Kaban a,b, K.G. Prashanth a, G.B.M. Vaughan c, J. Eckert a,b a
IFW Dresden, Institut für Komplexe Materialien, Helmholtzstraße 20, D-01069 Dresden, Germany TU Dresden, Institut für Werkstoffwissenschaft, D-01062 Dresden, Germany c European Synchrotron Radiation Facilities ESRF, BP 220, 38043 Grenoble, France b
a r t i c l e
i n f o
Article history: Received 28 January 2015 Received in revised form 4 March 2015 Accepted 23 March 2015 Available online 28 March 2015 Keywords: Metallic glasses Mechanical alloying Free volume Structural relaxation X-ray diffraction
a b s t r a c t Structural relaxation in ball-milled Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 glassy powders has been investigated by in-situ high-energy X-ray diffraction. The studies in reciprocal and real space reveal a contrasting behavior between medium- (MRO) and short-range order (SRO). The free volume is not uniformly distributed across the atoms: annihilation of free volume (i.e. shrinking) during heating is observed in the MRO, whereas an increase of free volume (i.e. expansion) occurs in the SRO, implying a denser SRO in the as-milled powder compared to the structurally relaxed material. This behavior is in agreement with the concepts of free volume and anti-free volume and can be attributed to the change of the coordination number in the first nearest-neighbor shell. Finally, the results demonstrate that the first diffuse diffraction maximum in reciprocal space is a reliable indicator to evaluate the structural changes occurring in the MRO. Ó 2015 Published by Elsevier B.V.
1. Introduction As-quenched metallic glasses are not in a state of internal equilibrium and, on annealing below the glass transition temperature, their structure evolves toward an ideal glassy state through a smooth variation of structural configurations with higher density [1]. This behavior, the structural relaxation, has significant impact on several properties of metallic glasses, including density and volume changes, and modifications of elastic modulus, mechanical properties, viscosity, diffusivity and Curie temperature [2]. Therefore, structure and property variations induced by structural relaxation have been the focus of several investigations since the early days of metallic glasses. The concept of free volume, originally proposed by Cohen and Turnbull [3] to explain diffusion in liquids and glasses, and its annihilation during annealing, has been extensively used to rationalize the structural relaxation in metallic glasses [4–7]. The free volume of an atom has been defined as that part of its nearest neighbor cage in which the atom can move without an energy change [2]. If the free volume exceeds a critical value, the atom may jump to a neighboring cage, giving rise to material transport [8]. Structural relaxation reduces the free volume of the glass, causing
⇑ Corresponding author. Tel.: +49 351 4659 838; fax: +49 351 4659 452. E-mail address: [email protected] (S. Scudino). http://dx.doi.org/10.1016/j.jallcom.2015.03.179 0925-8388/Ó 2015 Published by Elsevier B.V.
densification and the related variation of the physical and mechanical properties. The annealing-induced annihilation of the free volume in metallic glasses can be estimated directly by experimental methods, such as dilatometry and density measurements [1,9,10], and indirectly through the evaluation of the heat release by differential scanning calorimetry (DSC) [4–6,11]. Alternatively, the free volume change has been determined using in-situ X-ray diffraction (XRD) by measuring the variation of the position of the first diffuse diffraction maximum during heating cycles [12–14]. Although the results from XRD experiments are in excellent agreement with the data obtained from dilatometry [12], recent studies pose doubts about the validity of this approach for the evaluation of the free volume in metallic glasses on the basis of the different behavior characterizing the change of position of the first and second amorphous diffraction maxima during heating [15]. To clarify this question, in this work the free volume content in ball-milled Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 glassy powders was quantified by high-energy XRD in reciprocal space using the position of both the first and the second scattering maxima and in real space using the position of the peaks in the pair correlation functions. The Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 alloy was selected for this investigation because it displays a distinct structural relaxation (shadowed area in Fig. 1(a)) and, therefore, it offers the possibility to analyze any structural variation occurring during heating in detail.
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Fig. 1. (a) DSC scan of the as-milled Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 powder displaying a strong structural relaxation (shadowed area). (b) Typical structure factor for the ball-milled powder showing the position of the Q1 and Q2 peaks.
2. Experimental Pre-alloyed ingots with composition Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 were prepared from pure elements (purity > 99.9 wt.%) by arc melting in a titanium-gettered argon atmosphere. The ingots were remelted several times in order to increase homogeneity in composition. The glassy powders were prepared by mechanical alloying of the pre-alloyed ingots with structure consisting of a mixture of intermetallic compounds. Ball milling experiments were carried out using a Retsch PM400 planetary ball mill operating at a milling intensity of 150 rpm (for additional details on sample preparation see [16]). In order to minimize atmospheric contamination during milling, all sample handling was carried out in a glove box under purified argon atmosphere (less than 1 ppm O2 and H2O). The thermal stability was investigated in constant-rate heating mode (10 K/min) by DSC with a PerkinElmer DSC7 calorimeter under a continuous flow of purified argon. The DSC curve of the as-milled powder (Fig. 1(a)) displays a broad exothermic event due to structural relaxation starting at about 420 K followed by the crystallization of the glass, which occurs at about Tx = 710 K. The structure evolution of the powders during heating was studied by XRD in transmission using a high-intensity high-energy monochromatic synchrotron beam (k = 0.13 Å) at the ID11 beamline of the European Synchrotron Radiation Facilities (ESRF). The powders were sealed in capillary tubes under argon atmosphere and placed in a computer-controlled Linkam hot stage. Heating was carried out at a constant heating rate of 10 K/min in order to compare the structural evolution with the thermal stability data obtained by DSC. The powders were first heated to 673 K to induce structural relaxation, then cooled down to room temperature at 10 K/min, and finally heated to 700 K to analyze the relaxed structure. The XRD patterns were collected using a two-dimensional charge coupled device (CCD) Frelon camera [17]. The resulting two-dimensional patterns were then azimuthally integrated between 0 and 2p using the Fit2D program [18] to give onedimensional intensity distributions as a function of the wave vector Q = 4p sin h/k. From this, the Faber–Ziman [19] structure factors S(Q), the pair correlation functions g(r) and the radial distribution functions RDF(r) were obtained as described in [20]. The position of the first (Q1) and second (Q2) diffuse diffraction maxima of the structure factors S(Q) (Fig. 1(b)) were evaluated by fitting using a pseudoVoigt function. The variation of free volume during heating was estimated according to Yavari et al. [12] from the positions of Q1 through the equation
n o3 n o Q 1 ðT 0 Þ=Q 1 ðTÞ ¼ VðTÞ=VðT 0 Þ ;
ð1Þ
where V(T)/V(T0) is the reduced mean atomic volume at the temperature T, and T0 is a reference temperature (corresponding here to the starting temperature of the second heating) [12]. The same approach was used to evaluate the free volume from the variation of Q2.
3. Results and discussion 3.1. Structural relaxation in reciprocal space The variation of the reduced mean atomic volume with temperature is shown in Fig. 2(a). During the first heating, the reduced volume evaluated from Q1 (hereafter named V 1 ðQ 1 Þ; black squares in Fig. 2(a)) increases linearly with increasing temperature up to
Fig. 2. (a) Variation of the reduced mean atomic volume with temperature during the first and second heating steps evaluated from Q1 and Q2. (b) Reduced volume as a function of temperature for the peaks at r2 and r6 of the pair correlation functions.
about 500 K as a consequence of thermal expansion and the resulting increase of the mean atomic spacing (i.e. dilatation) [12]. With further heating, annihilation of free volume (i.e. densification) overcomes the dilatational effect of thermal expansion and V 1 ðQ 1 Þ decreases with temperature. The corresponding variation of the atomic volume from Q2 during the first heating (hereafter named V 1 ðQ 2 Þ; green stars in Fig. 2(a)) is characterized at low temperatures by the same linear increase observed for V 1 ðQ 1 Þ. However, in contrast to the behavior of V 1 ðQ 1 Þ, V 1 ðQ 2 Þ does not decrease but rather continues to increase with a steeper slope for T > 450 K with respect to the previous temperature regime and only finally, at T > 630 K, V 1 ðQ 2 Þ displays free volume annihilation. The behavior observed during the first heating is irreversible. During the second heating, both V 2 ðQ 1 Þ and V 2 ðQ 2 Þ (red1 triangles and blue circles in Fig. 2(a)) increase linearly with the same slope throughout the entire heating process as a result of the thermal expansion and no sign of structural relaxation is visible at this stage. The change of free volume due to heating (DVðQ i Þ ¼ V 1 ðQ i Þ V 2 ðQ i Þ) can be estimated from the volume difference between the initial relaxed state (i.e. the starting point of the second heating) and the initial as-milled condition (i.e. the starting point of the first heating). Annihilation of free volume and 1 For interpretation of color in Fig. 2, the reader is referred to the web version of this article.
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densification occur for the data evaluated from Q1 (DV(Q1) = 1.6%), as reported by Yavari et al. [12] for a Pd-based metallic glass. In contrast, no significant free volume change between the initial states is observed when the second diffraction maximum Q2 is considered; yet, an apparent free volume increase (DV(Q2) = 0.6%) occurs in the temperature range between 450 and 630 K. The different effect of structural relaxation on Q1 and Q2 is particularly evident in Fig. 3, where the ratio Q2/Q1 is shown as a function of temperature. During the first heating, Q2/Q1 is constant at about 1.691 up to 450 K. This implies a similar variation of Q1 and Q2 in this temperature range, as already observed in Fig. 2(a). Q2/Q1 then decreases with increasing temperature to about 1.684, indicative of a different effect of free volume annihilation on Q1 and Q2. This is corroborated by the variation of Q2/Q1 for the structurally-relaxed glass (i.e. during the second heating). Here, Q2/Q1 is again constant at 1.683, which indicates that thermal expansion has the same effect on Q1 and Q2. In the view of a free volume uniformly distributed across the amorphous structure, these findings might suggest that the method based on the variation of the position of the diffuse diffraction maxima in reciprocal space cannot be used to determine the free volume change, as concluded by Mattern et al. [15]. It is therefore worth investigating the free volume-related structural changes in real space. A possible explanation for the contrasting behavior between DV(Q1) and DV(Q2) may be related to the different types of structural information that can be gained by considering the shift of different diffraction maxima. In order to clarify this question, the Fourier transform (FT) of the normalized structure factor S(Q) (i.e. the pair correlation functions g(r)) has been calculated for the ranges 2–3.5 Å1 and 3.5–5.65 Å1 (where the diffraction maxima Q1 and Q2 occur; indicated by dotted lines in Fig. 1(b)); the results are shown in Fig. 4 along with the g(r) of the entire range 0–15 Å1. Information on the structure beyond the first nearestneighbors (i.e. the MRO) is largely contained in the range of the first diffraction maximum Q1, as originally observed by Cargill [21] and later by other authors [22,23]. However, Q1 is also influenced by the SRO, as demonstrated by the occurrence of the peak corresponding to the first nearest-neighbors at about r = 3 Å. On the other hand, the FT of the range 3.5–5.65 Å1 reveals that the second maximum Q2 is more sensitive to structural changes involving the first nearest-neighbors. These findings indicate that Q1 describes structural changes spanning over the entire range from SRO to MRO, which explains the fact that the relaxation results obtained from XRD experiments of metallic glasses are in good agreement with those achieved by dilatometry [12]. In contrast, the structural variations evaluated from Q2 cannot be used to describe the average relaxation behavior of the material as they are mostly sensitive to a local portion of the structure (i.e. the SRO). 3.2. Structural relaxation in real space Structural relaxation was further analyzed in real space by estimating the reduced volume during the first (V 1 ðr i Þ) and second (V 2 ðr i Þ) heating steps through the shift of the peaks of the pair correlation functions at ri (i = 1, . . ., 6; see arrows in Fig. 4) as
n o3 V j ðri Þ ¼ r i ðTÞ=ri ðT 0 Þ ;
ð2Þ
where j = 1, 2 refer to the first and second heating, respectively. Selected results are shown in Fig. 5(a) as a function of r. Structural relaxation during the first heating is strongly length scale-dependent: the reduced volume varies significantly within the first atomic shell and then it remains approximately constant for r P 5 Å. Reduced, yet evident, length-scale dependence is also visible during the second heating, where the material is
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Fig. 3. Temperature dependence of the ratio Q2/Q1, revealing the different effect of structural relaxation on Q1 and Q2.
Fig. 4. Pair correlation functions g(r) calculated through the Fourier transform (FT) of the structure factor (300 K) for the ranges 2–3.5 and 3.5–5.65 Å1, where the Q1 and Q2 peaks are located, and for the entire range 0–15 Å1.
structurally relaxed. Similar length-scale dependence has been observed during in-situ XRD strain measurements under mechanical loading in the elastic regime [24–26] and ex-situ investigations of plastically deformed BMGs [27]: the strain is smallest in the first-nearest shell (i.e. the SRO) and it increases with increasing distances of the outer shells. Strain anisotropy has been ascribed to the higher stiffness of the SRO (described as being formed of dense and stiff solute-centered clusters with strong solute–solvent bonds) with respect to the MRO (represented as less dense and more compliant solvent–solvent bonds connecting the SRO clusters) [28]. Analogously, thermal oscillations during heating would increase from SRO to MRO as a result of the different packing density and bond strength, explaining the length scale-dependent thermal behavior observed in Fig. 5(a). It is significant that Vðri Þ < 1 for the first nearest-neighbors, whereas the mean volume is constantly larger than one for the peaks at r > r2 (Fig. 5(a)), which implies a denser atomic arrangement of the SRO in the as-milled powder with respect to the structurally relaxed metallic glass. This is in apparent contrast to the concept of free volume, which instead would require a less compact structure, as observed for r > r2 (i.e. the MRO). The apparent creation of free volume during heating evaluated from the shift of Q2 is also observed in real space (compare V(Q2) and V(r2) in Fig. 2(a) and (b)). During the first heating, V 1 ðr2 Þ displays inverse thermal expansion up to about 450 K and then the volume
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Fig. 5. (a) Reduced volume as a function of r for the sample heated to 400 K during the first and second heating steps evaluated through the shift of the peaks of the pair correlation functions. (b) Effect of the structural relaxation on the coordination number and peak positions of the pair correlation functions.
increases during heating to higher temperatures. Conversely, the peak at r6, as well as all of the peaks at r2 < r < r6 (not shown here), display the conventional structural relaxation behavior already observed for the peak at Q1: thermal expansion followed by volume shrinking due to relaxation. This further corroborates the earlier assumption that Q2 bears information primarily about the SRO, whereas Q1 mainly describes the MRO. The use of Q1 as a reliable indicator for the structural changes occurring in the MRO is confirmed by the data presented in Fig. 6, where the values of V(Q1) and V(r6) are in excellent agreement. Inverse thermal expansion (i.e. shrinkage) of the first nearestneighbors during heating has been reported for metallic glasses as well as for metallic melts [29–32]. This behavior has been ascribed to the change of the coordination number (CN) in the first-nearest shell resulting from the reduction of the fraction of high-coordination polyhedra with increasing temperature, as shown by Lou et al. [32] using molecular dynamics simulations. The variation of the coordination numbers due to structural relaxation for the present glassy powder is shown in Fig. 5(b) along with the change of the peak position (ri) of the pair correlation functions. The coordination numbers were evaluated by integrating the area under the peaks of the radial distribution functions (Fig. 7) and the variations of CN and r were calculated as
ðCN1k CN2k Þ=CN2k and ðr1i r2i Þ=r 2i ;
Fig. 6. Comparison between the values of reduced volume evaluated from Q1 and r6, corroborating the use of Q1 as a reliable indicator for the structural changes occurring in the medium-range order.
ð3Þ
where CN1k and r 1i represent the coordination number and the peak position evaluated at 300 K during the first heating, CN2k and r 2i are the values calculated at 300 K during the second heating step and the subscripts k = 1, . . ., 5 represents the atomic shells and i = 1, . . ., 6 the peak positions of the pair correlation functions. Both CNk and ri display a similar trend (Fig. 5(b)): the average atomic distance and the coordination number of the first nearestneighbors are reduced in the as-milled powder with respect to the relaxed material. This indicates that the free volume is not uniformly distributed across the atoms and, in analogy with the results of Lou et al. [32], suggests that the denser atomic configuration of the unrelaxed SRO is due to a high density of low-coordination polyhedra within the first nearest-neighbors. This also agrees with the concept of anti-free volume introduced by Egami [33]. According to this view, the total volume change due to structural relaxation is the sum of two opposite contributions: (1) the free volume-like part (n-type defects), related to regions of low density, and (2) the anti-free volume part (p-type defects), related to regions of high density. During structural relaxation, the n-type and p-type defects recombine [33]: annihilation of the n-type
Fig. 7. Characteristic radial distribution function for the ball-milled Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 powder showing the atomic shell considered for the evaluation of the coordination numbers (CNk).
defects decreases the overall volume of the material, whereas annihilation of the p-type increases it. The present results confirm these assumptions. The high-density SRO can be considered as a
S. Scudino et al. / Journal of Alloys and Compounds 639 (2015) 465–469
preferential location for p-type defects, whereas the low-density MRO is most likely characterized by n-type defects. During relaxation, such positive and negative density fluctuations evolve toward a more homogeneous and stable state corresponding to the equilibrium structural configuration characteristic of the relaxation temperature: the SRO expands and the MRO shrinks, explaining the results shown in Fig. 2(a) and (b). 4. Conclusions Structural relaxation in Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 glassy powders has been studied in both reciprocal and real space by in-situ high-energy X-ray diffraction. The analysis of the data indicates that the shift of the first scattering maximum Q1 in the reciprocal space corresponds to the annihilation of the free volume. In contrast, the shift of the second scattering peak Q2 reflects an apparent increase of free volume. The Fourier transform of the structure factor for the ranges covering the first and second maxima indicates that Q1 describes the structural changes occurring in both the SRO and MRO, whereas Q2 bears information predominantly about the first nearest-neighbors, thus validating the use of Q1 as an indicator of free volume. The relaxation behavior was further analyzed in real space. Structural relaxation is inhomogeneous: the mean atomic volume varies significantly within the first atomic shell but remains constant for the outer shells. This can be ascribed to the different packing density and bond strength of SRO and MRO. The apparent creation of free volume during heating evaluated from the shift of Q2 is also observed in real space for the SRO, implying a denser SRO packing in the as-milled powder compared to the structurally relaxed metallic glass. This behavior is in agreement with the positive and negative density fluctuations related to the concepts of free volume and anti-free volume and can be attributed to the change of the coordination number in the first-nearest shell resulting from the reduction of the fraction of high-coordination polyhedral, supporting the model proposed by Lou et al. [32] and Egami [33]. Acknowledgments The authors thank J. Wright for technical assistance. The support from ESRF through the experiment HC-1178 and from the German Science Foundation under the Leibniz Program (Grant EC 111/26-1) is gratefully acknowledged. References [1] A.L. Greer, Structural relaxation and atomic transport in amorphous alloys, in: H.H. Liebermann (Ed.), Rapidly Solidified Alloys, Marcel Dekker, New York, 1993. [2] R.W. Cahn, A.L. Greer, Metastable states of alloys, in: R.W. Cahn, P. Haasen (Eds.), Physical Metallurgy, Elsevier Science BV, Amsterdam, 1996. [3] M.H. Cohen, D. Turnbull, Molecular transport in liquids and glasses, J. Chem. Phys. 31 (1959) 1164. [4] A. van den Beukel, J. Sietsma, The glass transition as a free volume related kinetic phenomenon, Acta Metall. Mater. 38 (1990) 383. [5] A. Slipenyuk, J. Eckert, Correlation between enthalpy change and free volume reduction during structural relaxation of Zr55Cu30Al10Ni5 metallic glass, Scr. Mater. 50 (2004) 39.
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Length scale-dependent structural relaxation in Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 metallic glass S. Scudino a,⇑, M. Stoica a, I. Kaban a,b, K.G. Prashanth a, G.B.M. Vaughan c, J. Eckert a,b a
IFW Dresden, Institut für Komplexe Materialien, Helmholtzstraße 20, D-01069 Dresden, Germany TU Dresden, Institut für Werkstoffwissenschaft, D-01062 Dresden, Germany c European Synchrotron Radiation Facilities ESRF, BP 220, 38043 Grenoble, France b
a r t i c l e
i n f o
Article history: Received 28 January 2015 Received in revised form 4 March 2015 Accepted 23 March 2015 Available online 28 March 2015 Keywords: Metallic glasses Mechanical alloying Free volume Structural relaxation X-ray diffraction
a b s t r a c t Structural relaxation in ball-milled Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 glassy powders has been investigated by in-situ high-energy X-ray diffraction. The studies in reciprocal and real space reveal a contrasting behavior between medium- (MRO) and short-range order (SRO). The free volume is not uniformly distributed across the atoms: annihilation of free volume (i.e. shrinking) during heating is observed in the MRO, whereas an increase of free volume (i.e. expansion) occurs in the SRO, implying a denser SRO in the as-milled powder compared to the structurally relaxed material. This behavior is in agreement with the concepts of free volume and anti-free volume and can be attributed to the change of the coordination number in the first nearest-neighbor shell. Finally, the results demonstrate that the first diffuse diffraction maximum in reciprocal space is a reliable indicator to evaluate the structural changes occurring in the MRO. Ó 2015 Published by Elsevier B.V.
1. Introduction As-quenched metallic glasses are not in a state of internal equilibrium and, on annealing below the glass transition temperature, their structure evolves toward an ideal glassy state through a smooth variation of structural configurations with higher density [1]. This behavior, the structural relaxation, has significant impact on several properties of metallic glasses, including density and volume changes, and modifications of elastic modulus, mechanical properties, viscosity, diffusivity and Curie temperature [2]. Therefore, structure and property variations induced by structural relaxation have been the focus of several investigations since the early days of metallic glasses. The concept of free volume, originally proposed by Cohen and Turnbull [3] to explain diffusion in liquids and glasses, and its annihilation during annealing, has been extensively used to rationalize the structural relaxation in metallic glasses [4–7]. The free volume of an atom has been defined as that part of its nearest neighbor cage in which the atom can move without an energy change [2]. If the free volume exceeds a critical value, the atom may jump to a neighboring cage, giving rise to material transport [8]. Structural relaxation reduces the free volume of the glass, causing
⇑ Corresponding author. Tel.: +49 351 4659 838; fax: +49 351 4659 452. E-mail address: [email protected] (S. Scudino). http://dx.doi.org/10.1016/j.jallcom.2015.03.179 0925-8388/Ó 2015 Published by Elsevier B.V.
densification and the related variation of the physical and mechanical properties. The annealing-induced annihilation of the free volume in metallic glasses can be estimated directly by experimental methods, such as dilatometry and density measurements [1,9,10], and indirectly through the evaluation of the heat release by differential scanning calorimetry (DSC) [4–6,11]. Alternatively, the free volume change has been determined using in-situ X-ray diffraction (XRD) by measuring the variation of the position of the first diffuse diffraction maximum during heating cycles [12–14]. Although the results from XRD experiments are in excellent agreement with the data obtained from dilatometry [12], recent studies pose doubts about the validity of this approach for the evaluation of the free volume in metallic glasses on the basis of the different behavior characterizing the change of position of the first and second amorphous diffraction maxima during heating [15]. To clarify this question, in this work the free volume content in ball-milled Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 glassy powders was quantified by high-energy XRD in reciprocal space using the position of both the first and the second scattering maxima and in real space using the position of the peaks in the pair correlation functions. The Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 alloy was selected for this investigation because it displays a distinct structural relaxation (shadowed area in Fig. 1(a)) and, therefore, it offers the possibility to analyze any structural variation occurring during heating in detail.
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Fig. 1. (a) DSC scan of the as-milled Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 powder displaying a strong structural relaxation (shadowed area). (b) Typical structure factor for the ball-milled powder showing the position of the Q1 and Q2 peaks.
2. Experimental Pre-alloyed ingots with composition Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 were prepared from pure elements (purity > 99.9 wt.%) by arc melting in a titanium-gettered argon atmosphere. The ingots were remelted several times in order to increase homogeneity in composition. The glassy powders were prepared by mechanical alloying of the pre-alloyed ingots with structure consisting of a mixture of intermetallic compounds. Ball milling experiments were carried out using a Retsch PM400 planetary ball mill operating at a milling intensity of 150 rpm (for additional details on sample preparation see [16]). In order to minimize atmospheric contamination during milling, all sample handling was carried out in a glove box under purified argon atmosphere (less than 1 ppm O2 and H2O). The thermal stability was investigated in constant-rate heating mode (10 K/min) by DSC with a PerkinElmer DSC7 calorimeter under a continuous flow of purified argon. The DSC curve of the as-milled powder (Fig. 1(a)) displays a broad exothermic event due to structural relaxation starting at about 420 K followed by the crystallization of the glass, which occurs at about Tx = 710 K. The structure evolution of the powders during heating was studied by XRD in transmission using a high-intensity high-energy monochromatic synchrotron beam (k = 0.13 Å) at the ID11 beamline of the European Synchrotron Radiation Facilities (ESRF). The powders were sealed in capillary tubes under argon atmosphere and placed in a computer-controlled Linkam hot stage. Heating was carried out at a constant heating rate of 10 K/min in order to compare the structural evolution with the thermal stability data obtained by DSC. The powders were first heated to 673 K to induce structural relaxation, then cooled down to room temperature at 10 K/min, and finally heated to 700 K to analyze the relaxed structure. The XRD patterns were collected using a two-dimensional charge coupled device (CCD) Frelon camera [17]. The resulting two-dimensional patterns were then azimuthally integrated between 0 and 2p using the Fit2D program [18] to give onedimensional intensity distributions as a function of the wave vector Q = 4p sin h/k. From this, the Faber–Ziman [19] structure factors S(Q), the pair correlation functions g(r) and the radial distribution functions RDF(r) were obtained as described in [20]. The position of the first (Q1) and second (Q2) diffuse diffraction maxima of the structure factors S(Q) (Fig. 1(b)) were evaluated by fitting using a pseudoVoigt function. The variation of free volume during heating was estimated according to Yavari et al. [12] from the positions of Q1 through the equation
n o3 n o Q 1 ðT 0 Þ=Q 1 ðTÞ ¼ VðTÞ=VðT 0 Þ ;
ð1Þ
where V(T)/V(T0) is the reduced mean atomic volume at the temperature T, and T0 is a reference temperature (corresponding here to the starting temperature of the second heating) [12]. The same approach was used to evaluate the free volume from the variation of Q2.
3. Results and discussion 3.1. Structural relaxation in reciprocal space The variation of the reduced mean atomic volume with temperature is shown in Fig. 2(a). During the first heating, the reduced volume evaluated from Q1 (hereafter named V 1 ðQ 1 Þ; black squares in Fig. 2(a)) increases linearly with increasing temperature up to
Fig. 2. (a) Variation of the reduced mean atomic volume with temperature during the first and second heating steps evaluated from Q1 and Q2. (b) Reduced volume as a function of temperature for the peaks at r2 and r6 of the pair correlation functions.
about 500 K as a consequence of thermal expansion and the resulting increase of the mean atomic spacing (i.e. dilatation) [12]. With further heating, annihilation of free volume (i.e. densification) overcomes the dilatational effect of thermal expansion and V 1 ðQ 1 Þ decreases with temperature. The corresponding variation of the atomic volume from Q2 during the first heating (hereafter named V 1 ðQ 2 Þ; green stars in Fig. 2(a)) is characterized at low temperatures by the same linear increase observed for V 1 ðQ 1 Þ. However, in contrast to the behavior of V 1 ðQ 1 Þ, V 1 ðQ 2 Þ does not decrease but rather continues to increase with a steeper slope for T > 450 K with respect to the previous temperature regime and only finally, at T > 630 K, V 1 ðQ 2 Þ displays free volume annihilation. The behavior observed during the first heating is irreversible. During the second heating, both V 2 ðQ 1 Þ and V 2 ðQ 2 Þ (red1 triangles and blue circles in Fig. 2(a)) increase linearly with the same slope throughout the entire heating process as a result of the thermal expansion and no sign of structural relaxation is visible at this stage. The change of free volume due to heating (DVðQ i Þ ¼ V 1 ðQ i Þ V 2 ðQ i Þ) can be estimated from the volume difference between the initial relaxed state (i.e. the starting point of the second heating) and the initial as-milled condition (i.e. the starting point of the first heating). Annihilation of free volume and 1 For interpretation of color in Fig. 2, the reader is referred to the web version of this article.
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densification occur for the data evaluated from Q1 (DV(Q1) = 1.6%), as reported by Yavari et al. [12] for a Pd-based metallic glass. In contrast, no significant free volume change between the initial states is observed when the second diffraction maximum Q2 is considered; yet, an apparent free volume increase (DV(Q2) = 0.6%) occurs in the temperature range between 450 and 630 K. The different effect of structural relaxation on Q1 and Q2 is particularly evident in Fig. 3, where the ratio Q2/Q1 is shown as a function of temperature. During the first heating, Q2/Q1 is constant at about 1.691 up to 450 K. This implies a similar variation of Q1 and Q2 in this temperature range, as already observed in Fig. 2(a). Q2/Q1 then decreases with increasing temperature to about 1.684, indicative of a different effect of free volume annihilation on Q1 and Q2. This is corroborated by the variation of Q2/Q1 for the structurally-relaxed glass (i.e. during the second heating). Here, Q2/Q1 is again constant at 1.683, which indicates that thermal expansion has the same effect on Q1 and Q2. In the view of a free volume uniformly distributed across the amorphous structure, these findings might suggest that the method based on the variation of the position of the diffuse diffraction maxima in reciprocal space cannot be used to determine the free volume change, as concluded by Mattern et al. [15]. It is therefore worth investigating the free volume-related structural changes in real space. A possible explanation for the contrasting behavior between DV(Q1) and DV(Q2) may be related to the different types of structural information that can be gained by considering the shift of different diffraction maxima. In order to clarify this question, the Fourier transform (FT) of the normalized structure factor S(Q) (i.e. the pair correlation functions g(r)) has been calculated for the ranges 2–3.5 Å1 and 3.5–5.65 Å1 (where the diffraction maxima Q1 and Q2 occur; indicated by dotted lines in Fig. 1(b)); the results are shown in Fig. 4 along with the g(r) of the entire range 0–15 Å1. Information on the structure beyond the first nearestneighbors (i.e. the MRO) is largely contained in the range of the first diffraction maximum Q1, as originally observed by Cargill [21] and later by other authors [22,23]. However, Q1 is also influenced by the SRO, as demonstrated by the occurrence of the peak corresponding to the first nearest-neighbors at about r = 3 Å. On the other hand, the FT of the range 3.5–5.65 Å1 reveals that the second maximum Q2 is more sensitive to structural changes involving the first nearest-neighbors. These findings indicate that Q1 describes structural changes spanning over the entire range from SRO to MRO, which explains the fact that the relaxation results obtained from XRD experiments of metallic glasses are in good agreement with those achieved by dilatometry [12]. In contrast, the structural variations evaluated from Q2 cannot be used to describe the average relaxation behavior of the material as they are mostly sensitive to a local portion of the structure (i.e. the SRO). 3.2. Structural relaxation in real space Structural relaxation was further analyzed in real space by estimating the reduced volume during the first (V 1 ðr i Þ) and second (V 2 ðr i Þ) heating steps through the shift of the peaks of the pair correlation functions at ri (i = 1, . . ., 6; see arrows in Fig. 4) as
n o3 V j ðri Þ ¼ r i ðTÞ=ri ðT 0 Þ ;
ð2Þ
where j = 1, 2 refer to the first and second heating, respectively. Selected results are shown in Fig. 5(a) as a function of r. Structural relaxation during the first heating is strongly length scale-dependent: the reduced volume varies significantly within the first atomic shell and then it remains approximately constant for r P 5 Å. Reduced, yet evident, length-scale dependence is also visible during the second heating, where the material is
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Fig. 3. Temperature dependence of the ratio Q2/Q1, revealing the different effect of structural relaxation on Q1 and Q2.
Fig. 4. Pair correlation functions g(r) calculated through the Fourier transform (FT) of the structure factor (300 K) for the ranges 2–3.5 and 3.5–5.65 Å1, where the Q1 and Q2 peaks are located, and for the entire range 0–15 Å1.
structurally relaxed. Similar length-scale dependence has been observed during in-situ XRD strain measurements under mechanical loading in the elastic regime [24–26] and ex-situ investigations of plastically deformed BMGs [27]: the strain is smallest in the first-nearest shell (i.e. the SRO) and it increases with increasing distances of the outer shells. Strain anisotropy has been ascribed to the higher stiffness of the SRO (described as being formed of dense and stiff solute-centered clusters with strong solute–solvent bonds) with respect to the MRO (represented as less dense and more compliant solvent–solvent bonds connecting the SRO clusters) [28]. Analogously, thermal oscillations during heating would increase from SRO to MRO as a result of the different packing density and bond strength, explaining the length scale-dependent thermal behavior observed in Fig. 5(a). It is significant that Vðri Þ < 1 for the first nearest-neighbors, whereas the mean volume is constantly larger than one for the peaks at r > r2 (Fig. 5(a)), which implies a denser atomic arrangement of the SRO in the as-milled powder with respect to the structurally relaxed metallic glass. This is in apparent contrast to the concept of free volume, which instead would require a less compact structure, as observed for r > r2 (i.e. the MRO). The apparent creation of free volume during heating evaluated from the shift of Q2 is also observed in real space (compare V(Q2) and V(r2) in Fig. 2(a) and (b)). During the first heating, V 1 ðr2 Þ displays inverse thermal expansion up to about 450 K and then the volume
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Fig. 5. (a) Reduced volume as a function of r for the sample heated to 400 K during the first and second heating steps evaluated through the shift of the peaks of the pair correlation functions. (b) Effect of the structural relaxation on the coordination number and peak positions of the pair correlation functions.
increases during heating to higher temperatures. Conversely, the peak at r6, as well as all of the peaks at r2 < r < r6 (not shown here), display the conventional structural relaxation behavior already observed for the peak at Q1: thermal expansion followed by volume shrinking due to relaxation. This further corroborates the earlier assumption that Q2 bears information primarily about the SRO, whereas Q1 mainly describes the MRO. The use of Q1 as a reliable indicator for the structural changes occurring in the MRO is confirmed by the data presented in Fig. 6, where the values of V(Q1) and V(r6) are in excellent agreement. Inverse thermal expansion (i.e. shrinkage) of the first nearestneighbors during heating has been reported for metallic glasses as well as for metallic melts [29–32]. This behavior has been ascribed to the change of the coordination number (CN) in the first-nearest shell resulting from the reduction of the fraction of high-coordination polyhedra with increasing temperature, as shown by Lou et al. [32] using molecular dynamics simulations. The variation of the coordination numbers due to structural relaxation for the present glassy powder is shown in Fig. 5(b) along with the change of the peak position (ri) of the pair correlation functions. The coordination numbers were evaluated by integrating the area under the peaks of the radial distribution functions (Fig. 7) and the variations of CN and r were calculated as
ðCN1k CN2k Þ=CN2k and ðr1i r2i Þ=r 2i ;
Fig. 6. Comparison between the values of reduced volume evaluated from Q1 and r6, corroborating the use of Q1 as a reliable indicator for the structural changes occurring in the medium-range order.
ð3Þ
where CN1k and r 1i represent the coordination number and the peak position evaluated at 300 K during the first heating, CN2k and r 2i are the values calculated at 300 K during the second heating step and the subscripts k = 1, . . ., 5 represents the atomic shells and i = 1, . . ., 6 the peak positions of the pair correlation functions. Both CNk and ri display a similar trend (Fig. 5(b)): the average atomic distance and the coordination number of the first nearestneighbors are reduced in the as-milled powder with respect to the relaxed material. This indicates that the free volume is not uniformly distributed across the atoms and, in analogy with the results of Lou et al. [32], suggests that the denser atomic configuration of the unrelaxed SRO is due to a high density of low-coordination polyhedra within the first nearest-neighbors. This also agrees with the concept of anti-free volume introduced by Egami [33]. According to this view, the total volume change due to structural relaxation is the sum of two opposite contributions: (1) the free volume-like part (n-type defects), related to regions of low density, and (2) the anti-free volume part (p-type defects), related to regions of high density. During structural relaxation, the n-type and p-type defects recombine [33]: annihilation of the n-type
Fig. 7. Characteristic radial distribution function for the ball-milled Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 powder showing the atomic shell considered for the evaluation of the coordination numbers (CNk).
defects decreases the overall volume of the material, whereas annihilation of the p-type increases it. The present results confirm these assumptions. The high-density SRO can be considered as a
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preferential location for p-type defects, whereas the low-density MRO is most likely characterized by n-type defects. During relaxation, such positive and negative density fluctuations evolve toward a more homogeneous and stable state corresponding to the equilibrium structural configuration characteristic of the relaxation temperature: the SRO expands and the MRO shrinks, explaining the results shown in Fig. 2(a) and (b). 4. Conclusions Structural relaxation in Zr57.5Ti7.5Nb5Cu12.5Ni10Al7.5 glassy powders has been studied in both reciprocal and real space by in-situ high-energy X-ray diffraction. The analysis of the data indicates that the shift of the first scattering maximum Q1 in the reciprocal space corresponds to the annihilation of the free volume. In contrast, the shift of the second scattering peak Q2 reflects an apparent increase of free volume. The Fourier transform of the structure factor for the ranges covering the first and second maxima indicates that Q1 describes the structural changes occurring in both the SRO and MRO, whereas Q2 bears information predominantly about the first nearest-neighbors, thus validating the use of Q1 as an indicator of free volume. The relaxation behavior was further analyzed in real space. Structural relaxation is inhomogeneous: the mean atomic volume varies significantly within the first atomic shell but remains constant for the outer shells. This can be ascribed to the different packing density and bond strength of SRO and MRO. The apparent creation of free volume during heating evaluated from the shift of Q2 is also observed in real space for the SRO, implying a denser SRO packing in the as-milled powder compared to the structurally relaxed metallic glass. This behavior is in agreement with the positive and negative density fluctuations related to the concepts of free volume and anti-free volume and can be attributed to the change of the coordination number in the first-nearest shell resulting from the reduction of the fraction of high-coordination polyhedral, supporting the model proposed by Lou et al. [32] and Egami [33]. Acknowledgments The authors thank J. Wright for technical assistance. The support from ESRF through the experiment HC-1178 and from the German Science Foundation under the Leibniz Program (Grant EC 111/26-1) is gratefully acknowledged. References [1] A.L. Greer, Structural relaxation and atomic transport in amorphous alloys, in: H.H. Liebermann (Ed.), Rapidly Solidified Alloys, Marcel Dekker, New York, 1993. [2] R.W. Cahn, A.L. Greer, Metastable states of alloys, in: R.W. Cahn, P. Haasen (Eds.), Physical Metallurgy, Elsevier Science BV, Amsterdam, 1996. [3] M.H. Cohen, D. Turnbull, Molecular transport in liquids and glasses, J. Chem. Phys. 31 (1959) 1164. [4] A. van den Beukel, J. Sietsma, The glass transition as a free volume related kinetic phenomenon, Acta Metall. Mater. 38 (1990) 383. [5] A. Slipenyuk, J. Eckert, Correlation between enthalpy change and free volume reduction during structural relaxation of Zr55Cu30Al10Ni5 metallic glass, Scr. Mater. 50 (2004) 39.
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