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Flux-induced structural modification and phase transformations in a Pd40Ni40Si4P16 bulk-glassy alloy
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Acta Materialia 58 (2010) 5886–5897 www.elsevier.com/locate/actamat
Flux-induced structural modification and phase transformations in a Pd40Ni40Si4P16 bulk-glassy alloy N. Chen a,*, L. Gu a, G.Q. Xie b, D.V. Louzguine-Luzgin a,b, A.R. Yavari c, G. Vaughan d, S.D. Imhoff e, J.H. Perepezko e,**, T. Abe f, A. Inoue a,b a
WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan b Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan c SIMAP, Institut National Polytechnique de Grenoble, St-Martin-d’He`res Campus, BP 75, Grenoble 38402, France d European Synchrotron Radiation Facility, Grenoble 38042, France e Department of Materials Science and Engineering, University of Wisconsin-Madison, 1509 University Avenue, Madison, WI 53706, USA f Computational Materials Science Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Received 26 January 2010; received in revised form 3 June 2010; accepted 2 July 2010 Available online 30 July 2010
Abstract In order to uncover the mechanism of fluxing-enhanced undercooling, a study of the liquid structure in a Pd40Ni40Si4P16 bulk-glassy alloy was performed, which revealed that a flux-treated sample presents a shortened mean interatomic distance and an increased coordination number within the first shell, which results in a more densely packed local structure than in an unfluxed sample. In addition to the usual influence of fluxing to effect a deactivation of nucleation catalysts to yield enhanced undercooling, structural studies have discovered a new effect of fluxing. The local structural change induced by fluxing is associated with an increase in the delay time for the onset of nucleation. The prolonged transient period is also reflected by sluggish atomic transport in the fluxed sample, which promotes kinetic stability of the undercooled liquid. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Fluxing; Undercooling; Nucleation and growth; Phase transformation kinetics; Metallic glasses
1. Introduction Molten alloys often exhibit an undercooling below the equilibrium liquidus temperature before the onset of nucleation and growth of crystals during solidification. Impurities in contact with the liquid can trigger nucleation of crystalline phases, leading to a kinetics-controlled nucleation process. However, glassy phases rather than their crystalline counterparts are induced, provided that the supercooled liquid state is stabilized to a temperature below the glass transition temperature Tg [1–3]. In fact, fluxing techniques have been intro*
Corresponding author. Tel./fax: +81 22 217 5956. Corresponding author. E-mail addresses: [email protected] (N. Chen), perepezk @engr.wisc.edu (J.H. Perepezko). **
duced by Kui et al. to enhance undercooling sufficiently to promote bulk glass formation [4]. Bulk-glassy alloys are a modern research field in materials science and have been broadly explored since the identification of a variety of bulk-glassy alloy forming systems [5–7]. Based upon the stability of the oxide flux, which is often B2O3, with respect to the oxides of the target alloy constituent elements, this method is applied mostly to Pd- and Fe-based alloys [4,8–14]. Through trapping impurities inside and on the surface of molten alloys, the kinetics of the nucleation process is significantly retarded [15]; whereas the competing vitrification process becomes predominant. Exploiting this principle, the Pd40Ni20Cu20P20 glassy alloy can be prepared in a bulk form with diameters up to 72 mm [9]. The general idea is that fluxing inhibits the crystallization kinetics by suppressing heterogeneous nucleation,
1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.07.003
N. Chen et al. / Acta Materialia 58 (2010) 5886–5897
which can leave the crystalline products unchanged [9]. The prevailing mechanism for crystallization, however, remains to be kinetics controlled. It has been demonstrated that a cyclic heating–cooling–crystallization treatment with fluxing can significantly promote the purification effects, implying that impurities within the melting alloy can be driven to the surface by moving the solidification front and trapped subsequently by the fluxes during the thermal cycling treatment [13–16]. Consequently, the critical cooling rate (CCR) for glass formation can be reduced by one order of magnitude, indicating that the CCR is strongly dependent on the degree of heterogeneous nucleation [16]. However, a large portion of the devitrification driving force arises from thermodynamic contribution since the critical nucleus radius highly depends on undercooling. Therefore, the crystallization process and phase composition can be altered owing to the competition between kinetics and thermodynamics, provided that the molten alloy is clean enough and the thermodynamic driving force for nucleation becomes significant. However, very few reports are available so far to discuss the underlying mechanism as well as the influences of fluxing on glass formation, especially on the devitrification/crystallization of glassy phase [17]. This study reports the structural modification and devitrification behavior in a Pd40Ni40Si4P16 bulk metallic glasses (BMG) after thermal cycling flux treatment. In addition to the usual influence of fluxing to effect a deactivation of nucleation catalysts to yield an enhanced undercooling, structural studies have discovered a new effect of fluxing that acts to promote a more densely packed liquid arrangement which strongly inhibits crystallization. 2. Experimental procedure High purity raw materials Pd (99.9%), Ni (99.99%), Si (99.9%) and P (99.9999%) were used in preparation of the master ingots. Injection-cast specimens 2 mm in diameter were prepared by conventional copper mold casting. In addition, the as-cast Pd40Ni40Si4P16 ingots were further placed in fused silica with an inner diameter of 10 mm and purified in molten B2O3 at 1423 K for flux treatment. The structure of the alloys was investigated by X-ray diffractometry (XRD) with Cu Ka radiation and high-resolution transmission electron microscopy (HRTEM) performed using a JEOL 2010F transmission electron microscope. The liquidus temperature and the thermal stability of the differently processed samples were studied by differential thermal analysis (DTA). The thermal treatment procedure involved the following: in the first stage, the samples were heated to 1423 K at a heating rate of 0.083 K s1 and held isothermally for 3 min, followed by a cooling down process at a rate of 0.033 K s1. Differential isothermal calorimetry was applied to evaluate the devitrification behaviors of the unfluxed and fluxed specimens. The chemical composition of the samples was studied using energydispersive X-ray spectroscopy (EDX). The density measurements using the Archimedean principle were performed
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using a microbalance with sensitivity 0.01 lg. N-Tridecane was used as a liquid for measurements. The weight of every sample was measured three times in both liquid and air, and then the average values were applied to calculate the densities. Synchrotron radiation X-ray diffraction in transmission was carried out using a high-energy monochromatic beam at the ID11 Beam line of the European Synchrotron Radiation Facility (ESRF) equipped with a nitrogen-cooled double-silicon monochromator. The photon energy was 94 keV. After correction for air scattering, polarization, absorption [18] and Compton scattering [19], the measured intensity was converted to electron units per atom with the generalized Krogh–Moe–Norman method [20], using the X-ray atomic scattering factors and anomalous dispersion corrections [21]. The total structure factor S(Q) (Q = wave vector) and the interference function QI(Q) were obtained from the coherent scattering intensity using atomic scattering factors [22]. The values of QI(Q) < 18 nm1 were smoothly extrapolated to Q = 0. The radial distribution RDF(r) and pair distribution functions PDF(r) were obtained by the Fourier transformation of QI(Q) [23]. 3. Results 3.1. Structural characterization The XRD patterns of Pd40Ni40Si4P16 alloys prepared by water quenching combined with fluxing and conventional casting processes, respectively, are presented in Fig. 1a. All the alloys show typical broad diffraction peaks, indicating the formation of a glassy phase. The HRTEM images of the unfluxed and the fluxed Pd40Ni40Si4P16 alloys are shown in Fig. 1b, demonstrating that fine crystal precipitation is not present, which further confirms the glass formation in both samples. It is worthwhile pointing out that the flux-treated Pd40Ni40Si4P16 glassy alloys can be easily produced in bulk form with a diameter exceeding 10 mm, confirming that this alloy possesses good glass-forming ability (GFA). To probe the structural characteristics of the fluxed and unfluxed samples, synchrotron X-ray radiation measurements were carried out to determine the intensity I(Q) vs. wave-vector Q. After fluxing, the broad maximum of the first diffraction peak intensity I(Q) shifted to a larger Q, as shown in Fig. 2a, yielding a smaller mean atomic spacing, which is indicative of a denser atomic packing struc˚. ture. Note that the peak resolution is within ±.004 A The pair distribution functions g(r) of the unfluxed and the fluxed samples were then derived from QI(Q), revealing two important features. First, a visible peak shift is evident for the first three peaks: in particular, the first maximum, indicating that a local structural difference ˚ was induced. Second, there is a small shoulder at 2.35 A in both PDF curves, as shown in Fig. 2b, indicating certain atomic pairs formation with shorter bond distances. A similar shoulder can be found in the PDF curve of Pd82Si18
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Fig. 1. (a) XRD patterns and (b) HRTEM images of the unfluxed and fluxed Pd40Ni40Si4P16 alloys, respectively.
metallic glass [24]. Compared with Pd and Ni, Si and P have smaller atomic radii and larger negative heats of mixing with Pd or Ni, which favors the formation of strong atomic bonds. In addition, the typical Ni–P and Ni–Si sin˚ and 2.36 A ˚ [25], comparable gle bond distances are 2.28 A ˚ obtained in this study. Therefore, it can be conwith 2.35 A cluded that the small shoulder appearing at short atomic distances should be attributed mainly to metal (Pd or Ni)–metalloid (Si or P) atomic pairs. Combining the pair distribution with the density measurements, the mean nearest atomic distances and the first nearest coordination numbers can be calculated as listed in Table 1. The fluxed sample displays a more densely packed structure with a smaller mean atomic distance and larger coordination number in the first shell. The densification of the flux-treated sample is 0.76%, which is greater than the typical density increase of
<0.5% during structural relaxation [26], and is indicative of the intrinsic difference in local atomic configurations such as short-range ordering (typically first- and secondnearest neighbors of atomic configurations). Such a difference in local atomic packing gives rise to an enhancement of the plasticity of the fluxed sample associated with a larger volume of shear transformation zones [27]. 3.2. Thermal analysis Fig. 3 shows the DTA traces of the unfluxed and fluxed Pd40Ni40Si4P16 BMG. The differently processed samples exhibit almost the same glass transition temperature Tg and liquidus temperature Tlh as determined by the heating curves. Both Tg and Tlh are important material characteristics which are sensitive to the alloy composition [28]. The similar behaviors in glass transition and melting (in addi-
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Fig. 2. (a) Intensity I(Q) vs. wave-vector Q at the first diffracted peak and (b) PDF derived from QI(Q) by the usual Fourier transformation.
Table 1 Density and structural parameters calculated based on the PDF and density. Density (±0.005 g cm3)
Fluxed Unfluxed
9.420 9.349
g(r) First peak ˚) r1 (A
Second peak ˚) r2 (A r2/r1
Subsidiary peak r3
r3/r1
2.72 2.74
4.48 4.51
5.17 5.16
1.90 1.88
tion to EDX compositional analysis) confirm the compositional identity of the fluxed and unfluxed Pd40Ni40Si4P16 alloys. A very small shoulder appears on the high-temperature side of melting peaks for both samples, indicating
1.65 1.65
1st nearest coordination number
12.1 11.7
that the alloy composition is slightly off the eutectic. The thermodynamic data derived from the DTA traces are shown in Table 2. The supercooled liquid regions for both the unfluxed and fluxed samples surpass 100 K, which can
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Fig. 3. DTA traces of (a) the fluxed and (b) the unfluxed Pd40Ni40Si4P16 BMG.
Table 2 Thermodynamic parameters derived from the DTA traces shown in Fig. 2. Alloys
Tg (±2 K)
Tx (±2 K)
Tlh (±2 K)
Tsc (±2 K)
DT (K)
Fluxed Unfluxed
579 579
688 683
971 971
769 872
202 99
provide a wide experimental temperature region and time window to measure the corresponding thermodynamic and kinetic properties in the supercooled state. It is obvious from Table 2 that crystallization of the fluxed Pd40Ni40Si4P16 alloy is much more sluggish than that of the unfluxed sample upon cooling; since the crystallization of the fluxed sample took place at 769 K, while the crystallization of the unfluxed sample started at 872 K. The crystallization temperature determined on cooling of the unfluxed and fluxed samples varies as much as 103 K. In addition, the undercooling DT (Tlh Tsc, where Tsc is the temperature at which solidification by cooling starts) of the fluxed sample reaches 202 K. Hence, it is evident that the flux treatment significantly improves the GFA of the Pd40Ni40Si4P16 alloy. 3.3. Crystallization behavior The devitrification kinetics behavior of the glassy structure was investigated by isothermal calorimetry measurements at given temperatures of 653 K, 663 K and 673 K, which are near the upper temperature range of the undercooled liquid interval. As shown in Fig. 4a and b, a longer incubation time for the onset of crystallization is required for the flux-treated sample than for the unfluxed sample. Furthermore, the width of the exothermic peaks in the flux-treated sample is much broader than that in the unfluxed specimen, indicating a slower transformation reac-
tion. The isothermal transformation kinetics for the nucleation and growth process can usually be described using the Johnson–Mehl–Avrami (JMA) equation: f ¼ 1 expðKðt t0 Þn Þ
ð1Þ
where K is a constant, and n is characteristic of specific nucleation and growth mechanisms. The volume fraction f transformed as a function of time (t t0) (t is the incubation time) in differential scanning calorimetry (DSC) is assumed to scale with the fraction of total heat release, which can be then derived from the isothermal calorimetry data shown in Fig. 4c. The results are plotted in terms of the logarithmic form of Eq. (1) in Fig. 4d. The Avrami exponents n which were determined from the slopes of the plot in Fig. 4d are 2.8 for the non-fluxed sample and 2.6 for the fluxed samples. Note that these values are <3 in both cases. It is noteworthy that the XRD patterns of the two fully crystallized samples are to a certain extent different, as shown in Fig. 5a and b. Combining the TEM investigation and compositional analysis, a ternary eutectic mixture obtained in the fluxed and unfluxed samples was identified to be a metallic face-centered cubic (fcc) Ni–Pd solid solution, a Pd-rich phosphide (orthorhombic, a = 0.598 nm, b = 0.715 nm, c = 0.517 nm) with a structure similar to that of Pd3P, and a Ni-rich orthorhombic phase (orthorhombic, a = 0.639 nm, b = 0.463 nm, c = 0.735 nm), which agrees with the crystalline products reported for Pd40Ni40P20 BMG [29,30]. These three phases coexist in the ternary eutectic mixture, so that it is difficult to distinguish them, since the composition analyses provide averaged compositional information for the phases. In addition, the perforations in the foils (Fig. 6a and b) indicate that some phases are preferentially thinned during sample preparation, further increasing the uncertainty in
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Fig. 4. Isothermal calorimetry data of (a) the unfluxed and (b) the fluxed Pd40Ni40Si4P16 BMG, and (c) the derived transformation curves from (a) and (b) and thus (d) the calculated Avrami exponents.
Fig. 5. XRD patterns of the fully crystallized (a) fluxed and (b) unfluxed samples.
compositional analysis. However, EDX analysis indicated that the Pd-rich orthorhombic crystalline phases exhibited
an average composition of about Pd59.1Ni12.6Si13.8P14.5 in the fluxed sample; whereas an average composition of
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Fig. 6. BF-TEM images of a eutectic colony in (a) the unfluxed and (b) the fluxed samples. HRTEM images: (cI) fcc metallic solid solution, (dI) Pd-rich orthorhombic phase and (eI) Ni-rich orthorhombic phase; and their corresponding diffraction spots (cII), (dII) and (eII) obtained by FFT.
about Ni42.3Pd32.1Si4.1P21.5 was obtained for the Ni-rich orthorhombic phase in the unfluxed sample. Interlamellar spacing between crystalline phases in eutectic is around several tens of nanometers, as seen in Fig. 6a and b. Fig. 6c–e shows the HRTEM images and the corresponding diffractogram obtained by fast Fourier transformation (FFT) of the typical crystalline phases in the two samples. Fig. 6c shows the crystalline structure of a fcc phase acquired along the [1 1 0] orientation, which can be observed in both samples. Fig. 6d represents the atomic arrangement of the Pd3P-type orthorhombic phase with the crystal normal to [1 1 2] in the fluxed sample, while Fig. 6e shows the crystalline structure of the Ni-rich orthorhombic phase in the orientation of [2 1 0] for the unfluxed sample. 4. Discussion The DTA curves of Pd40Ni40Si4P16 alloys showed only one exothermic reaction on heating, implying that the composition of Pd40Ni40Si4P16 is close to the eutectic. In addition, the compositional analysis using EDX shows that the
crystallized region and the residual matrix have similar compositions within the error range. Thus, one can expect that the crystallization should proceed by nucleation and interface-controlled growth due to the similar composition between the glassy matrix and the transformed crystalline phases, which would yield a value of Avrami exponent n larger than 3. A theoretical Avrami exponent n of 3 corresponds to the eutectic reaction with zero nucleation rate and three-dimensional interface-controlled growth of preexisting nuclei [31]. In the present study, however, the Avrami exponent n for the unfluxed and fluxed sample is 2.7, and the plots are reasonably linear, which may indicate steady-state crystallization. Thus, the low values obtained of n below 3 are puzzling to understand for eutectic reactions. Similar kinetic results were reported in Fe–B metallic glasses, with some doubt about the accuracy of the associated volume fraction f determinations [32,33]. In order to solve this problem, further analysis of the crystallization process was carried out. Fig. 7 shows crystallization in the unfluxed and fluxed samples annealed at 673 K. According to the microstructure of the unfluxed and fluxed samples annealed for
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Fig. 7. (a and b) Microstructure and (c and d) the corresponding histograms for the eutectic colony diameter distribution of the partially crystallized unfluxed and fluxed samples annealed for 9 min at 673 K; (e and f) the variation of the largest crystal diameter with annealing time in the unfluxed and fluxed samples annealed at 673 K. The fitting lines of both samples give constant growth rate.
9 min at 673 K shown in Fig. 7a and b, the histograms for the eutectic colony diameter distribution can be plotted (see Fig. 7c and d), indicating that crystallization of both samples proceeded by heterogeneous transient nucleation [34,35]. Furthermore, even though the annealing time is prolonged, homogeneous nucleation for both samples does not occur. The crystals grow in terms of linear growth, as shown in Fig. 7e and f. A growth rate of 8.4 ± 0.3 108 m s1 and 11.3 ± 0.6 108 m s1 can be obtained
for the unfluxed and fluxed samples, respectively. This demonstrates that the growth of crystals is indeed eutectic, without involving any compositional change, as the EDX analysis shows. The fitted lines extended to the time axis in Fig. 7e and f give different intersected time values of 120 s and 160 s for the unfluxed and fluxed samples, respectively, which exactly coincide with the experimental delay time for isothermal crystallization at 673 K. Meanwhile, the nucleation product density of both samples
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shows early saturation (see Appendix). The number density of the unfluxed sample is on the order of 1012m3, about one order of magnitude higher than that of the fluxed sample, which supports a cleaning action by fluxing on removing heterogeneous nucleation sites. Combining the number density and growth rate, the steady-state nucleation rate can be estimated to be 4.7 109 m3 s1 and 2.6 108 m3 s1 for the unfluxed and fluxed samples. Thus the nucleation analysis and growth rate demonstrate that crystallization of both samples proceeds by heterogeneous nucleation and eutectic growth, obviously deviating from the predictions by the Avrami exponents derived on the basis the JMA equation. One should also consider possible phase separation before crystallization. The calculated results concerning the possibility of phase separation are presented in Fig. 8 for the quaternary Pd40Ni40Si4P16 alloy system, using PANDAT [36]. The composition of Pd40Ni40Si4P16 lies out of the spinodal line, indicating an absence of spinodal decomposition in this case (Fig. 8a). In contrast, phase separation preceded by a nucleation and growth mechanism may occur <500 K, as shown in Fig. 7b–d. Note that 500 K is below the glass transition temperature (579 K), while isothermal calorimetry measurements were performed at given temperatures >Tg, implying that Pd40Ni40Si4P16 alloy would crystallize without any phase separation, owing to the single liquid phase region above Tg. However, compositional fluctuations may be induced as “quenched-in’’ nuclei during the solidification of the liquid melt at a cooling rate of 40 K min1 with water quenching [37]. Actually, some evidence for similar quenched-in arrangements has been reported by Hirotsu et al. [38] for a Pd40Ni40P20 BMG. Growth of these “quenched-in” nuclei is thermodynamically unfavorable when they are subjected to isothermal calorimetry measurements at temperatures higher than that of the phase separation boundary [39]. In this case, there is competition between the dissolution of these “quenched-in” compositional fluctuations and the formation of new nuclei. So it can be concluded that this is a complicated kinetics process for nucleation, which is beyond the conditions that apply for the JMA equation. Looking closely into the above results, it is obvious that fluxing strongly influences crystallization of the Pd40Ni40Si4P16 glassy alloys, owing to the variations in devitrification both thermodynamically and kinetically in terms of a significant reduction in the melt crystallization temperature (at 103 K). According to the classic nucleation theory, the homogeneous nucleation rate of a liquid melt usually yields a rapid increase at a critical undercooling of 0.2Tl [40]. The fluxed sample showed an undercooling of 202 K, close to 0.2Tl (200 K for the Pd40Ni40Si4P16 alloy). Conventional solidification, however, occurs at a relatively low undercooling for heterogeneous nuclei, due to the presence of impurities that catalyze the nucleation by reducing the volume of the critical-sized nucleus, as the unfluxed Pd40Ni40Si4P16 alloy exhibited an undercooling of 99 K, much less than that
Fig. 8. (a) Two phase regions calculated at various temperatures and the corresponding compositional variation of Pd, Ni, Si and P elements with temperature in (b) liquid 1 and (c) liquid 2; (d) the calculated phase diagram of the quaternary Pd–Ni–Si–P alloy.
for the fluxed sample. The degree of the undercooling of a given system is governed by the difficulty in nucleation, which initiates the solidification of a melt. The microscopic
N. Chen et al. / Acta Materialia 58 (2010) 5886–5897
Fig. 8 (continued)
process of nucleation is therefore of great importance for understanding undercooling. Applying the classical nucleation treatment [41], the steady-state of homogeneous nucleation rate Iss can be described as follows: DG I ss ¼ N L bZ exp kBT DGa DG ¼ 4pr2 C s a2 vN L Z exp exp ð2Þ kBT kBT For spherical nuclei: 16pr3 3DGV b ¼ 4pr2 DC s a4
DG ¼
Z¼
DG2V V a
pffiffiffiffiffiffiffiffiffiffiffiffiffi 8p k B T r3
ð3Þ ð4Þ ð5Þ
where NL is the total number of atoms in the undercooled melt and is on the order of 1028 m3, v is the vibration frequency of the atoms in the liquid state, DG is the activation energy for the formation of critical nuclei, r is the interface energy, DGV is the Gibbs free-energy difference, kB is Boltzmann’s constant, D is the diffusivity in the glass, which can be approximated as a2t exp[DGa/kBT], with a interatomic spacing, and DGa denoting the kinetic barrier corresponding to the activation energy for atomic diffusion in the glass, Cs is the solute concentration, r is the critical radius, and Va is the volume per atom. In order to take account of impurity catalysts, Eq. (2) is modified by replacing DG by DGf(h), where f(h) is a contact angle, h is a function that varies between 0 and 1, NL now represents the density of catalytic sites, and 4pr2/a2 is replaced by 2pr2(1 cos h)/a2. According to Eq. (2), the nucleation rate Iss of the liquid is governed by two exponential terms, demonstrating that the activation energy for the formation of critical nuclei dominates at high temperatures, while the activation
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energy for atomic diffusion becomes overriding at low temperatures. At high temperatures with small undercooling, atoms have high mobility, so that the barrier DGa associated with the activation energy for atomic diffusion can easily be surmounted. In this case, the activation energy for the formation of critical nuclei dominates the nucleation process. Inclusions that develop from impurities in contact with the liquid can serve to trigger nucleation for crystalline phases, leading to a reduction in the activation energy for the formation of critical nuclei and thus accelerate nucleation. Note that both the fluxed and unfluxed samples contacted with the container walls during the above DTA measurements, which could provide nucleation sites for the liquid and induce surface crystallization. If the heterogeneous surface nucleation is the main factor terminating the undercooling of the melts, as mentioned in Ref. [42], the undercooling of the fluxed and unfluxed samples should be similar. Obviously, this is not the case. It can therefore be deduced that, apart from the crucial influence of container walls on surface nucleation, the intrinsic difference in their liquid melts, including impurities, particularly impurity size and local structure, should be taken into account for the huge difference in their undercooling. First, it is apparent that impurities acting as nucleation sites within the liquid melt have been passivated to a large degree, owing to pre-fluxing treatment. A pronounced effect of overheating is observed on the undercooling behavior for the Zr-based BMG, which suggests that heterogeneities are dissolved by heating above a threshold overheating temperature and reform during cooling [43–45]. Furthermore, the effect of impurities on undercooling depends on the size of the catalyst particle relative to the critical nucleus [46], whereby those that are much smaller than the critical nucleus are inactive catalyst particles. During the whole fluxing treatment, the alloy melt is encased by the flux at 1323 K with an overheat of 352 K. Simultaneously, the sample in the flux experienced a number of cyclic heating–cooling–crystallization treatments during fluxing, which promotes “nucleant refining” due to cyclic precipitation and dissolution of oxide nucleants corresponding to cooling–heating cycles [47]. It is evident that the reduction in active nucleation sites is irreversible, which is responsible for the increased undercooling of the prefluxed liquid melt. When the liquid is undercooled until the second stage, the activation energy for atomic diffusion becomes predominant, where the local structural units limiting atomic diffusion should play an important role in inhibiting crystallization. The Pd–Ni–Si–P alloy studied can be regarded as a pseudo-binary alloy (Pd, Ni)–(Si, P), in which the atomic units with a trigonal prism-type structure dominate the short-range order in a transition metal–metalloid alloy [48,49]. Furthermore, with increasing undercooling, the degree of short-range order increases [50]. Then, the chemical bonding between the constituents must be broken, and the atoms involved in the trigonal prisms must rearrange prior to crystallization, owing to
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its incompatibility with the translational long-range order of crystalline phases [50]. Therefore, the local structures of the supercooled liquids influence the kinetic barrier for atomic diffusion. A direct consequence of the local structural changes induced by fluxing will be manifested in the diffusion process, leading to the evolution of the nucleation cluster distribution. The kinetics of this process is reflected by the delay (or incubation) time for the onset of crystallization. The incorporation of the transient nucleation factor for the time dependent nucleation rate I(t) is expressed by s IðtÞ ¼ I ss exp ð6Þ t where the delay time s is given by s¼
1 8k B T ra4 ¼ 2 bZ DDG2V C s m2a
ð7Þ
The delay time s can provide an estimate of the controlling diffusivity. To evaluate the delay time, one can approximate DGV by DHf(Tl Tx)/Tl, where DHf is the latent heat. Collecting the main temperature terms, one has 2 DGa Tl Tx C ð8Þ ¼ exp s kBT Tl where C i is a constant. In this case, a plot of h ðT l Þ2 ln sðT T Þ2 vs: ð T1 Þ should yield a straight line with slope l
x
on the experimental delay time s, plots via DGha/kB. Based i ðT l Þ2 ln sðT T Þ2 vs: ð T1 Þ were obtained as presented in l
x
Fig. 9. Then the activation energies DGa for atomic diffusion can be derived to be 250 ± 12 and 340 ± 16 kJ mol1 for the unfluxed and fluxed samples, respectively. The DGa value for the unfluxed sample is in agreement with the value of 236 kJ mol1 for crystallization of a Pd40Cu30Ni10P20 BMG reported by Nishiyama and Inoue [51], where a long delay time for crystallization was also observed. The high activation energy is consistent with the sluggish diffusion kinetics, which is probably ascribed to the more closely packed atomic structure in the fluxed
sample, which inhibits nucleation and thus facilitates further undercooling. 5. Conclusion The structure and devitrification behavior of Pd40Ni40Si4P16 BMG in the fluxed and unfluxed states were studied using XRD, including synchrotron radiation XRD, DSC and TEM. It was demonstrated that fluxing leads to a local structural difference and influences the devitrification behavior of Pd40Ni40Si4P16 BMG. Upon cooling, the difference in the crystallization temperature between the unfluxed and fluxed samples is as large as 103 K, and the fluxed sample achieved an undercooling of 202 K. Fluxing can act in two ways to enhance undercooling: passivation of active heterogeneous nucleation sites and increased difficulty in surpassing the kinetic barrier to nucleation; and substantial growth that is reflected in modified values of the diffusion barrier. Acknowledgements The authors appreciate the technical support from Dr. H. Kato, and valuable comments from Dr. A. Takeuchi. This work was partially supported by the Research and Development Project on Advanced Metallic Glasses, Inorganic Materials and Joining Technology and Grant-in-Aid “Priority Area on Science and Technology of MicrowaveInduced, Thermally Non-Equilibrium Reaction Field” No. 18070001, from the Ministry of Education, Culture, Sports, Science and Technology, Japan. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.actamat.2010. 07.003. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
Fig. 9. Plots of ln
h
ðT l Þ2 sðT l T x Þ2
i
vs: T1 for the unfluxed and fluxed samples.
[15] [16] [17] [18]
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N. Chen et al. / Acta Materialia 58 (2010) 5886–5897 [19] Cromer DT. J Chem Phys 1969;47:4857. [20] Wagner CNJ, Ocken H, Joshi ML. Naturforschung 1965;20a:325. [21] Ibers JA, Hamilton WC, editors. International tables for X-ray crystallography, vol. 4. Birmingem: Kynoch; 1974. p. 1. [22] Waseda T, editor. The structure of non-crystalline materials. New York: McGraw-Hill; 1980. p. 26. [23] Louzguine-Luzgine DV, Georgarakis K, Yavari AR, Vaughan G, Xie G, Inoue A. J Mater Res 2009;24:274. [24] Ohkubo T, Kai H, Hirotsu Y. Mater Sci Eng A 2001;304–306:300. [25] Miracle DB, Louzguine-Luzgin DV, Louzguine-Luzgina L, Inoue A. Int. Mater. Rev. 2010 in press. [26] Chen HS. J Appl Phys 1978;49:3289. [27] Chen N, Pan D, Louzguine-Luzgin DV, Xie GQ, Chen MW, Inoue A. Scr Mater 2009;57:631. [28] Chen N, Louzguine-Luzgin DV, Xie GQ, Wada T, Inoue A. Acta Mater 2009;57:2775. [29] Donovan PE, Evans PV, Greer AL. J Mater Sci 1986;5:951. [30] Escorial AG, Greer AL. J Mater Sci 1987;22:4388. [31] Christian JW, editor. The theory of transformations in metals and alloys. Oxford: Pergamon Press; 1965. p. 489. [32] Schaafsma AS, Woude SF, Drijver JW, Raderlaar S. Phys Rev B 1979;20:4423. [33] Greer AL. Acta Metall 1982;30:171. [34] Ko¨ster U, Schu¨nemann U. In: Liebermann HH, editor. Rapidly solidified alloys: processes, structure, properties, applications. New York: Marcel Dekker; 1993. p. 303.
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[35] Ko¨ster U, Janlewing R. In: Busch R, Hufnagel T, Eckert J, Inoue A, Johnson WL, Yavari AR, editors. Mater Res Soc Symp Proc, vol. 806. Materials Research Society; 2004. p. 3. [36] Chen S-L, Daniel S, Zhang F, Chang YA, Yan X-Y, Xie F-Y, et al. CALPHAD 2002;26:175. [37] Cahn JW, Charles RJ. Phys Chem Glasses 1965;6:181. [38] Hirotsu Y, Nieh TG, Hirata A, Ohkubo T, Tanaka N. Phys Rev B 2006;73:012205. [39] James RF. J Mater Sci 1975;10:1802. [40] Cahn RW, Hassen P, editors. Physical metallurgy. Amsterdam: North-Holland; 1983. p. 486. [41] Russell KC. Adv Colloid Interface Sci 1980;13:205. [42] Schroers J, Wu Y, Johnson WL. Philos Mag A 2002;82:1207. [43] Mukherjee S, Zhou Z, Schroers J, Johnson WL, Rhim WK. Appl Phys Lett 2004;84:5010. [44] Hays CC, Johnson WL. J Non-cryst Solids 1999;250–252:596. [45] Lin XH, Johnson WL, Rhim WK. Mater Trans JIM 1997;38:473. [46] Rulison AJ, Rhim W-K, Bayuzick R, Hofmeister W, Morton C. Acta Mater 1997;45:1237. [47] Wilde G, Sebright JL, Perepezko JH. Acta Mater 2006;54:4759. [48] Gaskell PH. J Non-cryst Solids 1979;32:207. [49] Gaskell PH. Nature 1981;289:474. [50] Tanaka H. Phys Rev Lett 2003;90:055701. [51] Nishiyama N, Inoue A. Acta Mater. 1999;47:1487.
Acta Materialia 58 (2010) 5886–5897 www.elsevier.com/locate/actamat
Flux-induced structural modification and phase transformations in a Pd40Ni40Si4P16 bulk-glassy alloy N. Chen a,*, L. Gu a, G.Q. Xie b, D.V. Louzguine-Luzgin a,b, A.R. Yavari c, G. Vaughan d, S.D. Imhoff e, J.H. Perepezko e,**, T. Abe f, A. Inoue a,b a
WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan b Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan c SIMAP, Institut National Polytechnique de Grenoble, St-Martin-d’He`res Campus, BP 75, Grenoble 38402, France d European Synchrotron Radiation Facility, Grenoble 38042, France e Department of Materials Science and Engineering, University of Wisconsin-Madison, 1509 University Avenue, Madison, WI 53706, USA f Computational Materials Science Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Received 26 January 2010; received in revised form 3 June 2010; accepted 2 July 2010 Available online 30 July 2010
Abstract In order to uncover the mechanism of fluxing-enhanced undercooling, a study of the liquid structure in a Pd40Ni40Si4P16 bulk-glassy alloy was performed, which revealed that a flux-treated sample presents a shortened mean interatomic distance and an increased coordination number within the first shell, which results in a more densely packed local structure than in an unfluxed sample. In addition to the usual influence of fluxing to effect a deactivation of nucleation catalysts to yield enhanced undercooling, structural studies have discovered a new effect of fluxing. The local structural change induced by fluxing is associated with an increase in the delay time for the onset of nucleation. The prolonged transient period is also reflected by sluggish atomic transport in the fluxed sample, which promotes kinetic stability of the undercooled liquid. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Fluxing; Undercooling; Nucleation and growth; Phase transformation kinetics; Metallic glasses
1. Introduction Molten alloys often exhibit an undercooling below the equilibrium liquidus temperature before the onset of nucleation and growth of crystals during solidification. Impurities in contact with the liquid can trigger nucleation of crystalline phases, leading to a kinetics-controlled nucleation process. However, glassy phases rather than their crystalline counterparts are induced, provided that the supercooled liquid state is stabilized to a temperature below the glass transition temperature Tg [1–3]. In fact, fluxing techniques have been intro*
Corresponding author. Tel./fax: +81 22 217 5956. Corresponding author. E-mail addresses: [email protected] (N. Chen), perepezk @engr.wisc.edu (J.H. Perepezko). **
duced by Kui et al. to enhance undercooling sufficiently to promote bulk glass formation [4]. Bulk-glassy alloys are a modern research field in materials science and have been broadly explored since the identification of a variety of bulk-glassy alloy forming systems [5–7]. Based upon the stability of the oxide flux, which is often B2O3, with respect to the oxides of the target alloy constituent elements, this method is applied mostly to Pd- and Fe-based alloys [4,8–14]. Through trapping impurities inside and on the surface of molten alloys, the kinetics of the nucleation process is significantly retarded [15]; whereas the competing vitrification process becomes predominant. Exploiting this principle, the Pd40Ni20Cu20P20 glassy alloy can be prepared in a bulk form with diameters up to 72 mm [9]. The general idea is that fluxing inhibits the crystallization kinetics by suppressing heterogeneous nucleation,
1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.07.003
N. Chen et al. / Acta Materialia 58 (2010) 5886–5897
which can leave the crystalline products unchanged [9]. The prevailing mechanism for crystallization, however, remains to be kinetics controlled. It has been demonstrated that a cyclic heating–cooling–crystallization treatment with fluxing can significantly promote the purification effects, implying that impurities within the melting alloy can be driven to the surface by moving the solidification front and trapped subsequently by the fluxes during the thermal cycling treatment [13–16]. Consequently, the critical cooling rate (CCR) for glass formation can be reduced by one order of magnitude, indicating that the CCR is strongly dependent on the degree of heterogeneous nucleation [16]. However, a large portion of the devitrification driving force arises from thermodynamic contribution since the critical nucleus radius highly depends on undercooling. Therefore, the crystallization process and phase composition can be altered owing to the competition between kinetics and thermodynamics, provided that the molten alloy is clean enough and the thermodynamic driving force for nucleation becomes significant. However, very few reports are available so far to discuss the underlying mechanism as well as the influences of fluxing on glass formation, especially on the devitrification/crystallization of glassy phase [17]. This study reports the structural modification and devitrification behavior in a Pd40Ni40Si4P16 bulk metallic glasses (BMG) after thermal cycling flux treatment. In addition to the usual influence of fluxing to effect a deactivation of nucleation catalysts to yield an enhanced undercooling, structural studies have discovered a new effect of fluxing that acts to promote a more densely packed liquid arrangement which strongly inhibits crystallization. 2. Experimental procedure High purity raw materials Pd (99.9%), Ni (99.99%), Si (99.9%) and P (99.9999%) were used in preparation of the master ingots. Injection-cast specimens 2 mm in diameter were prepared by conventional copper mold casting. In addition, the as-cast Pd40Ni40Si4P16 ingots were further placed in fused silica with an inner diameter of 10 mm and purified in molten B2O3 at 1423 K for flux treatment. The structure of the alloys was investigated by X-ray diffractometry (XRD) with Cu Ka radiation and high-resolution transmission electron microscopy (HRTEM) performed using a JEOL 2010F transmission electron microscope. The liquidus temperature and the thermal stability of the differently processed samples were studied by differential thermal analysis (DTA). The thermal treatment procedure involved the following: in the first stage, the samples were heated to 1423 K at a heating rate of 0.083 K s1 and held isothermally for 3 min, followed by a cooling down process at a rate of 0.033 K s1. Differential isothermal calorimetry was applied to evaluate the devitrification behaviors of the unfluxed and fluxed specimens. The chemical composition of the samples was studied using energydispersive X-ray spectroscopy (EDX). The density measurements using the Archimedean principle were performed
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using a microbalance with sensitivity 0.01 lg. N-Tridecane was used as a liquid for measurements. The weight of every sample was measured three times in both liquid and air, and then the average values were applied to calculate the densities. Synchrotron radiation X-ray diffraction in transmission was carried out using a high-energy monochromatic beam at the ID11 Beam line of the European Synchrotron Radiation Facility (ESRF) equipped with a nitrogen-cooled double-silicon monochromator. The photon energy was 94 keV. After correction for air scattering, polarization, absorption [18] and Compton scattering [19], the measured intensity was converted to electron units per atom with the generalized Krogh–Moe–Norman method [20], using the X-ray atomic scattering factors and anomalous dispersion corrections [21]. The total structure factor S(Q) (Q = wave vector) and the interference function QI(Q) were obtained from the coherent scattering intensity using atomic scattering factors [22]. The values of QI(Q) < 18 nm1 were smoothly extrapolated to Q = 0. The radial distribution RDF(r) and pair distribution functions PDF(r) were obtained by the Fourier transformation of QI(Q) [23]. 3. Results 3.1. Structural characterization The XRD patterns of Pd40Ni40Si4P16 alloys prepared by water quenching combined with fluxing and conventional casting processes, respectively, are presented in Fig. 1a. All the alloys show typical broad diffraction peaks, indicating the formation of a glassy phase. The HRTEM images of the unfluxed and the fluxed Pd40Ni40Si4P16 alloys are shown in Fig. 1b, demonstrating that fine crystal precipitation is not present, which further confirms the glass formation in both samples. It is worthwhile pointing out that the flux-treated Pd40Ni40Si4P16 glassy alloys can be easily produced in bulk form with a diameter exceeding 10 mm, confirming that this alloy possesses good glass-forming ability (GFA). To probe the structural characteristics of the fluxed and unfluxed samples, synchrotron X-ray radiation measurements were carried out to determine the intensity I(Q) vs. wave-vector Q. After fluxing, the broad maximum of the first diffraction peak intensity I(Q) shifted to a larger Q, as shown in Fig. 2a, yielding a smaller mean atomic spacing, which is indicative of a denser atomic packing struc˚. ture. Note that the peak resolution is within ±.004 A The pair distribution functions g(r) of the unfluxed and the fluxed samples were then derived from QI(Q), revealing two important features. First, a visible peak shift is evident for the first three peaks: in particular, the first maximum, indicating that a local structural difference ˚ was induced. Second, there is a small shoulder at 2.35 A in both PDF curves, as shown in Fig. 2b, indicating certain atomic pairs formation with shorter bond distances. A similar shoulder can be found in the PDF curve of Pd82Si18
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Fig. 1. (a) XRD patterns and (b) HRTEM images of the unfluxed and fluxed Pd40Ni40Si4P16 alloys, respectively.
metallic glass [24]. Compared with Pd and Ni, Si and P have smaller atomic radii and larger negative heats of mixing with Pd or Ni, which favors the formation of strong atomic bonds. In addition, the typical Ni–P and Ni–Si sin˚ and 2.36 A ˚ [25], comparable gle bond distances are 2.28 A ˚ obtained in this study. Therefore, it can be conwith 2.35 A cluded that the small shoulder appearing at short atomic distances should be attributed mainly to metal (Pd or Ni)–metalloid (Si or P) atomic pairs. Combining the pair distribution with the density measurements, the mean nearest atomic distances and the first nearest coordination numbers can be calculated as listed in Table 1. The fluxed sample displays a more densely packed structure with a smaller mean atomic distance and larger coordination number in the first shell. The densification of the flux-treated sample is 0.76%, which is greater than the typical density increase of
<0.5% during structural relaxation [26], and is indicative of the intrinsic difference in local atomic configurations such as short-range ordering (typically first- and secondnearest neighbors of atomic configurations). Such a difference in local atomic packing gives rise to an enhancement of the plasticity of the fluxed sample associated with a larger volume of shear transformation zones [27]. 3.2. Thermal analysis Fig. 3 shows the DTA traces of the unfluxed and fluxed Pd40Ni40Si4P16 BMG. The differently processed samples exhibit almost the same glass transition temperature Tg and liquidus temperature Tlh as determined by the heating curves. Both Tg and Tlh are important material characteristics which are sensitive to the alloy composition [28]. The similar behaviors in glass transition and melting (in addi-
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Fig. 2. (a) Intensity I(Q) vs. wave-vector Q at the first diffracted peak and (b) PDF derived from QI(Q) by the usual Fourier transformation.
Table 1 Density and structural parameters calculated based on the PDF and density. Density (±0.005 g cm3)
Fluxed Unfluxed
9.420 9.349
g(r) First peak ˚) r1 (A
Second peak ˚) r2 (A r2/r1
Subsidiary peak r3
r3/r1
2.72 2.74
4.48 4.51
5.17 5.16
1.90 1.88
tion to EDX compositional analysis) confirm the compositional identity of the fluxed and unfluxed Pd40Ni40Si4P16 alloys. A very small shoulder appears on the high-temperature side of melting peaks for both samples, indicating
1.65 1.65
1st nearest coordination number
12.1 11.7
that the alloy composition is slightly off the eutectic. The thermodynamic data derived from the DTA traces are shown in Table 2. The supercooled liquid regions for both the unfluxed and fluxed samples surpass 100 K, which can
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Fig. 3. DTA traces of (a) the fluxed and (b) the unfluxed Pd40Ni40Si4P16 BMG.
Table 2 Thermodynamic parameters derived from the DTA traces shown in Fig. 2. Alloys
Tg (±2 K)
Tx (±2 K)
Tlh (±2 K)
Tsc (±2 K)
DT (K)
Fluxed Unfluxed
579 579
688 683
971 971
769 872
202 99
provide a wide experimental temperature region and time window to measure the corresponding thermodynamic and kinetic properties in the supercooled state. It is obvious from Table 2 that crystallization of the fluxed Pd40Ni40Si4P16 alloy is much more sluggish than that of the unfluxed sample upon cooling; since the crystallization of the fluxed sample took place at 769 K, while the crystallization of the unfluxed sample started at 872 K. The crystallization temperature determined on cooling of the unfluxed and fluxed samples varies as much as 103 K. In addition, the undercooling DT (Tlh Tsc, where Tsc is the temperature at which solidification by cooling starts) of the fluxed sample reaches 202 K. Hence, it is evident that the flux treatment significantly improves the GFA of the Pd40Ni40Si4P16 alloy. 3.3. Crystallization behavior The devitrification kinetics behavior of the glassy structure was investigated by isothermal calorimetry measurements at given temperatures of 653 K, 663 K and 673 K, which are near the upper temperature range of the undercooled liquid interval. As shown in Fig. 4a and b, a longer incubation time for the onset of crystallization is required for the flux-treated sample than for the unfluxed sample. Furthermore, the width of the exothermic peaks in the flux-treated sample is much broader than that in the unfluxed specimen, indicating a slower transformation reac-
tion. The isothermal transformation kinetics for the nucleation and growth process can usually be described using the Johnson–Mehl–Avrami (JMA) equation: f ¼ 1 expðKðt t0 Þn Þ
ð1Þ
where K is a constant, and n is characteristic of specific nucleation and growth mechanisms. The volume fraction f transformed as a function of time (t t0) (t is the incubation time) in differential scanning calorimetry (DSC) is assumed to scale with the fraction of total heat release, which can be then derived from the isothermal calorimetry data shown in Fig. 4c. The results are plotted in terms of the logarithmic form of Eq. (1) in Fig. 4d. The Avrami exponents n which were determined from the slopes of the plot in Fig. 4d are 2.8 for the non-fluxed sample and 2.6 for the fluxed samples. Note that these values are <3 in both cases. It is noteworthy that the XRD patterns of the two fully crystallized samples are to a certain extent different, as shown in Fig. 5a and b. Combining the TEM investigation and compositional analysis, a ternary eutectic mixture obtained in the fluxed and unfluxed samples was identified to be a metallic face-centered cubic (fcc) Ni–Pd solid solution, a Pd-rich phosphide (orthorhombic, a = 0.598 nm, b = 0.715 nm, c = 0.517 nm) with a structure similar to that of Pd3P, and a Ni-rich orthorhombic phase (orthorhombic, a = 0.639 nm, b = 0.463 nm, c = 0.735 nm), which agrees with the crystalline products reported for Pd40Ni40P20 BMG [29,30]. These three phases coexist in the ternary eutectic mixture, so that it is difficult to distinguish them, since the composition analyses provide averaged compositional information for the phases. In addition, the perforations in the foils (Fig. 6a and b) indicate that some phases are preferentially thinned during sample preparation, further increasing the uncertainty in
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Fig. 4. Isothermal calorimetry data of (a) the unfluxed and (b) the fluxed Pd40Ni40Si4P16 BMG, and (c) the derived transformation curves from (a) and (b) and thus (d) the calculated Avrami exponents.
Fig. 5. XRD patterns of the fully crystallized (a) fluxed and (b) unfluxed samples.
compositional analysis. However, EDX analysis indicated that the Pd-rich orthorhombic crystalline phases exhibited
an average composition of about Pd59.1Ni12.6Si13.8P14.5 in the fluxed sample; whereas an average composition of
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Fig. 6. BF-TEM images of a eutectic colony in (a) the unfluxed and (b) the fluxed samples. HRTEM images: (cI) fcc metallic solid solution, (dI) Pd-rich orthorhombic phase and (eI) Ni-rich orthorhombic phase; and their corresponding diffraction spots (cII), (dII) and (eII) obtained by FFT.
about Ni42.3Pd32.1Si4.1P21.5 was obtained for the Ni-rich orthorhombic phase in the unfluxed sample. Interlamellar spacing between crystalline phases in eutectic is around several tens of nanometers, as seen in Fig. 6a and b. Fig. 6c–e shows the HRTEM images and the corresponding diffractogram obtained by fast Fourier transformation (FFT) of the typical crystalline phases in the two samples. Fig. 6c shows the crystalline structure of a fcc phase acquired along the [1 1 0] orientation, which can be observed in both samples. Fig. 6d represents the atomic arrangement of the Pd3P-type orthorhombic phase with the crystal normal to [1 1 2] in the fluxed sample, while Fig. 6e shows the crystalline structure of the Ni-rich orthorhombic phase in the orientation of [2 1 0] for the unfluxed sample. 4. Discussion The DTA curves of Pd40Ni40Si4P16 alloys showed only one exothermic reaction on heating, implying that the composition of Pd40Ni40Si4P16 is close to the eutectic. In addition, the compositional analysis using EDX shows that the
crystallized region and the residual matrix have similar compositions within the error range. Thus, one can expect that the crystallization should proceed by nucleation and interface-controlled growth due to the similar composition between the glassy matrix and the transformed crystalline phases, which would yield a value of Avrami exponent n larger than 3. A theoretical Avrami exponent n of 3 corresponds to the eutectic reaction with zero nucleation rate and three-dimensional interface-controlled growth of preexisting nuclei [31]. In the present study, however, the Avrami exponent n for the unfluxed and fluxed sample is 2.7, and the plots are reasonably linear, which may indicate steady-state crystallization. Thus, the low values obtained of n below 3 are puzzling to understand for eutectic reactions. Similar kinetic results were reported in Fe–B metallic glasses, with some doubt about the accuracy of the associated volume fraction f determinations [32,33]. In order to solve this problem, further analysis of the crystallization process was carried out. Fig. 7 shows crystallization in the unfluxed and fluxed samples annealed at 673 K. According to the microstructure of the unfluxed and fluxed samples annealed for
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Fig. 7. (a and b) Microstructure and (c and d) the corresponding histograms for the eutectic colony diameter distribution of the partially crystallized unfluxed and fluxed samples annealed for 9 min at 673 K; (e and f) the variation of the largest crystal diameter with annealing time in the unfluxed and fluxed samples annealed at 673 K. The fitting lines of both samples give constant growth rate.
9 min at 673 K shown in Fig. 7a and b, the histograms for the eutectic colony diameter distribution can be plotted (see Fig. 7c and d), indicating that crystallization of both samples proceeded by heterogeneous transient nucleation [34,35]. Furthermore, even though the annealing time is prolonged, homogeneous nucleation for both samples does not occur. The crystals grow in terms of linear growth, as shown in Fig. 7e and f. A growth rate of 8.4 ± 0.3 108 m s1 and 11.3 ± 0.6 108 m s1 can be obtained
for the unfluxed and fluxed samples, respectively. This demonstrates that the growth of crystals is indeed eutectic, without involving any compositional change, as the EDX analysis shows. The fitted lines extended to the time axis in Fig. 7e and f give different intersected time values of 120 s and 160 s for the unfluxed and fluxed samples, respectively, which exactly coincide with the experimental delay time for isothermal crystallization at 673 K. Meanwhile, the nucleation product density of both samples
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shows early saturation (see Appendix). The number density of the unfluxed sample is on the order of 1012m3, about one order of magnitude higher than that of the fluxed sample, which supports a cleaning action by fluxing on removing heterogeneous nucleation sites. Combining the number density and growth rate, the steady-state nucleation rate can be estimated to be 4.7 109 m3 s1 and 2.6 108 m3 s1 for the unfluxed and fluxed samples. Thus the nucleation analysis and growth rate demonstrate that crystallization of both samples proceeds by heterogeneous nucleation and eutectic growth, obviously deviating from the predictions by the Avrami exponents derived on the basis the JMA equation. One should also consider possible phase separation before crystallization. The calculated results concerning the possibility of phase separation are presented in Fig. 8 for the quaternary Pd40Ni40Si4P16 alloy system, using PANDAT [36]. The composition of Pd40Ni40Si4P16 lies out of the spinodal line, indicating an absence of spinodal decomposition in this case (Fig. 8a). In contrast, phase separation preceded by a nucleation and growth mechanism may occur <500 K, as shown in Fig. 7b–d. Note that 500 K is below the glass transition temperature (579 K), while isothermal calorimetry measurements were performed at given temperatures >Tg, implying that Pd40Ni40Si4P16 alloy would crystallize without any phase separation, owing to the single liquid phase region above Tg. However, compositional fluctuations may be induced as “quenched-in’’ nuclei during the solidification of the liquid melt at a cooling rate of 40 K min1 with water quenching [37]. Actually, some evidence for similar quenched-in arrangements has been reported by Hirotsu et al. [38] for a Pd40Ni40P20 BMG. Growth of these “quenched-in” nuclei is thermodynamically unfavorable when they are subjected to isothermal calorimetry measurements at temperatures higher than that of the phase separation boundary [39]. In this case, there is competition between the dissolution of these “quenched-in” compositional fluctuations and the formation of new nuclei. So it can be concluded that this is a complicated kinetics process for nucleation, which is beyond the conditions that apply for the JMA equation. Looking closely into the above results, it is obvious that fluxing strongly influences crystallization of the Pd40Ni40Si4P16 glassy alloys, owing to the variations in devitrification both thermodynamically and kinetically in terms of a significant reduction in the melt crystallization temperature (at 103 K). According to the classic nucleation theory, the homogeneous nucleation rate of a liquid melt usually yields a rapid increase at a critical undercooling of 0.2Tl [40]. The fluxed sample showed an undercooling of 202 K, close to 0.2Tl (200 K for the Pd40Ni40Si4P16 alloy). Conventional solidification, however, occurs at a relatively low undercooling for heterogeneous nuclei, due to the presence of impurities that catalyze the nucleation by reducing the volume of the critical-sized nucleus, as the unfluxed Pd40Ni40Si4P16 alloy exhibited an undercooling of 99 K, much less than that
Fig. 8. (a) Two phase regions calculated at various temperatures and the corresponding compositional variation of Pd, Ni, Si and P elements with temperature in (b) liquid 1 and (c) liquid 2; (d) the calculated phase diagram of the quaternary Pd–Ni–Si–P alloy.
for the fluxed sample. The degree of the undercooling of a given system is governed by the difficulty in nucleation, which initiates the solidification of a melt. The microscopic
N. Chen et al. / Acta Materialia 58 (2010) 5886–5897
Fig. 8 (continued)
process of nucleation is therefore of great importance for understanding undercooling. Applying the classical nucleation treatment [41], the steady-state of homogeneous nucleation rate Iss can be described as follows: DG I ss ¼ N L bZ exp kBT DGa DG ¼ 4pr2 C s a2 vN L Z exp exp ð2Þ kBT kBT For spherical nuclei: 16pr3 3DGV b ¼ 4pr2 DC s a4
DG ¼
Z¼
DG2V V a
pffiffiffiffiffiffiffiffiffiffiffiffiffi 8p k B T r3
ð3Þ ð4Þ ð5Þ
where NL is the total number of atoms in the undercooled melt and is on the order of 1028 m3, v is the vibration frequency of the atoms in the liquid state, DG is the activation energy for the formation of critical nuclei, r is the interface energy, DGV is the Gibbs free-energy difference, kB is Boltzmann’s constant, D is the diffusivity in the glass, which can be approximated as a2t exp[DGa/kBT], with a interatomic spacing, and DGa denoting the kinetic barrier corresponding to the activation energy for atomic diffusion in the glass, Cs is the solute concentration, r is the critical radius, and Va is the volume per atom. In order to take account of impurity catalysts, Eq. (2) is modified by replacing DG by DGf(h), where f(h) is a contact angle, h is a function that varies between 0 and 1, NL now represents the density of catalytic sites, and 4pr2/a2 is replaced by 2pr2(1 cos h)/a2. According to Eq. (2), the nucleation rate Iss of the liquid is governed by two exponential terms, demonstrating that the activation energy for the formation of critical nuclei dominates at high temperatures, while the activation
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energy for atomic diffusion becomes overriding at low temperatures. At high temperatures with small undercooling, atoms have high mobility, so that the barrier DGa associated with the activation energy for atomic diffusion can easily be surmounted. In this case, the activation energy for the formation of critical nuclei dominates the nucleation process. Inclusions that develop from impurities in contact with the liquid can serve to trigger nucleation for crystalline phases, leading to a reduction in the activation energy for the formation of critical nuclei and thus accelerate nucleation. Note that both the fluxed and unfluxed samples contacted with the container walls during the above DTA measurements, which could provide nucleation sites for the liquid and induce surface crystallization. If the heterogeneous surface nucleation is the main factor terminating the undercooling of the melts, as mentioned in Ref. [42], the undercooling of the fluxed and unfluxed samples should be similar. Obviously, this is not the case. It can therefore be deduced that, apart from the crucial influence of container walls on surface nucleation, the intrinsic difference in their liquid melts, including impurities, particularly impurity size and local structure, should be taken into account for the huge difference in their undercooling. First, it is apparent that impurities acting as nucleation sites within the liquid melt have been passivated to a large degree, owing to pre-fluxing treatment. A pronounced effect of overheating is observed on the undercooling behavior for the Zr-based BMG, which suggests that heterogeneities are dissolved by heating above a threshold overheating temperature and reform during cooling [43–45]. Furthermore, the effect of impurities on undercooling depends on the size of the catalyst particle relative to the critical nucleus [46], whereby those that are much smaller than the critical nucleus are inactive catalyst particles. During the whole fluxing treatment, the alloy melt is encased by the flux at 1323 K with an overheat of 352 K. Simultaneously, the sample in the flux experienced a number of cyclic heating–cooling–crystallization treatments during fluxing, which promotes “nucleant refining” due to cyclic precipitation and dissolution of oxide nucleants corresponding to cooling–heating cycles [47]. It is evident that the reduction in active nucleation sites is irreversible, which is responsible for the increased undercooling of the prefluxed liquid melt. When the liquid is undercooled until the second stage, the activation energy for atomic diffusion becomes predominant, where the local structural units limiting atomic diffusion should play an important role in inhibiting crystallization. The Pd–Ni–Si–P alloy studied can be regarded as a pseudo-binary alloy (Pd, Ni)–(Si, P), in which the atomic units with a trigonal prism-type structure dominate the short-range order in a transition metal–metalloid alloy [48,49]. Furthermore, with increasing undercooling, the degree of short-range order increases [50]. Then, the chemical bonding between the constituents must be broken, and the atoms involved in the trigonal prisms must rearrange prior to crystallization, owing to
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its incompatibility with the translational long-range order of crystalline phases [50]. Therefore, the local structures of the supercooled liquids influence the kinetic barrier for atomic diffusion. A direct consequence of the local structural changes induced by fluxing will be manifested in the diffusion process, leading to the evolution of the nucleation cluster distribution. The kinetics of this process is reflected by the delay (or incubation) time for the onset of crystallization. The incorporation of the transient nucleation factor for the time dependent nucleation rate I(t) is expressed by s IðtÞ ¼ I ss exp ð6Þ t where the delay time s is given by s¼
1 8k B T ra4 ¼ 2 bZ DDG2V C s m2a
ð7Þ
The delay time s can provide an estimate of the controlling diffusivity. To evaluate the delay time, one can approximate DGV by DHf(Tl Tx)/Tl, where DHf is the latent heat. Collecting the main temperature terms, one has 2 DGa Tl Tx C ð8Þ ¼ exp s kBT Tl where C i is a constant. In this case, a plot of h ðT l Þ2 ln sðT T Þ2 vs: ð T1 Þ should yield a straight line with slope l
x
on the experimental delay time s, plots via DGha/kB. Based i ðT l Þ2 ln sðT T Þ2 vs: ð T1 Þ were obtained as presented in l
x
Fig. 9. Then the activation energies DGa for atomic diffusion can be derived to be 250 ± 12 and 340 ± 16 kJ mol1 for the unfluxed and fluxed samples, respectively. The DGa value for the unfluxed sample is in agreement with the value of 236 kJ mol1 for crystallization of a Pd40Cu30Ni10P20 BMG reported by Nishiyama and Inoue [51], where a long delay time for crystallization was also observed. The high activation energy is consistent with the sluggish diffusion kinetics, which is probably ascribed to the more closely packed atomic structure in the fluxed
sample, which inhibits nucleation and thus facilitates further undercooling. 5. Conclusion The structure and devitrification behavior of Pd40Ni40Si4P16 BMG in the fluxed and unfluxed states were studied using XRD, including synchrotron radiation XRD, DSC and TEM. It was demonstrated that fluxing leads to a local structural difference and influences the devitrification behavior of Pd40Ni40Si4P16 BMG. Upon cooling, the difference in the crystallization temperature between the unfluxed and fluxed samples is as large as 103 K, and the fluxed sample achieved an undercooling of 202 K. Fluxing can act in two ways to enhance undercooling: passivation of active heterogeneous nucleation sites and increased difficulty in surpassing the kinetic barrier to nucleation; and substantial growth that is reflected in modified values of the diffusion barrier. Acknowledgements The authors appreciate the technical support from Dr. H. Kato, and valuable comments from Dr. A. Takeuchi. This work was partially supported by the Research and Development Project on Advanced Metallic Glasses, Inorganic Materials and Joining Technology and Grant-in-Aid “Priority Area on Science and Technology of MicrowaveInduced, Thermally Non-Equilibrium Reaction Field” No. 18070001, from the Ministry of Education, Culture, Sports, Science and Technology, Japan. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.actamat.2010. 07.003. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
Fig. 9. Plots of ln
h
ðT l Þ2 sðT l T x Þ2
i
vs: T1 for the unfluxed and fluxed samples.
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