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Structural modeling of liquid and amorphous Al91Tb9 by Monte Carlo simulations
Journal of Non-Crystalline Solids 405 (2014) 27–32
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
Structural modeling of liquid and amorphous Al91Tb9 by Monte Carlo simulations M. Ovun a, M.J. Kramer b, Y.E. Kalay a,⁎ a b
Department of Metallurgical and Materials Engineering, METU, Ankara 06800, Turkey Ames Laboratory US DOE, Ames, IA 50011, USA
a r t i c l e
i n f o
Article history: Received 27 June 2014 Received in revised form 13 August 2014 Available online xxxx Keywords: Monte-Carlo simulations; Medium-range ordering; Phase separation; Chemical and topological configuration; Al–RE metallic glass
a b s t r a c t Evolution of the chemical and topological inhomogeneities within the Al91Tb9 amorphous system from liquid to glass was investigated using Monte Carlo (MC) simulations. The interatomic potential for Al–Tb system was developed and three-dimensional atomic configurations of liquid and amorphous structures were modeled. The simulations coupled with Voronoi Tessellation and Warren–Cowley chemical short-range order analysis revealed a high degree of chemical inhomogeneity at nanoscale composed of pure Al clusters which were found to be increasing in number and size with decreasing temperature in the supercooled liquid region. These chemically isolated prenucleation clusters are thought to be the origin of extreme number. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Marginal glass forming alloys have been regarded as promising structural materials due to their continuous fine grain structure attributed primarily to their ability of forming very high number density of nuclei upon crystallization [1,2]. Marginal glass forming alloys, unlike bulk metallic glasses, require high cooling rates ~ 105 K/s to form a fully amorphous structure [3–5]. Lightweight high-strength Al–RE based alloys [1] and magnetically soft and hard Fe–RE (RE: Rare-earth element) based alloys [3] are two well-known examples for marginally glass forming alloys. The devitrification process of marginally amorphous metals quite often results in formation of very high number densities of primary crystals (1021–1024 m−3) with sizes of less than 50 nm. An extensive research in this area has still been in progress to give an exact explanation for the mechanism underlying the formation of such high density of nanocrystals. As the large percentage of bulk amorphous metals do not result in the formation of nanocrystals when subjected to similar heat-treatments; the answer for this enigmatic behavior may lay hidden within the structure of the as-quenched marginal glass forming alloys. The previous studies on Al–RE and Al–RE–TM amorphous alloys have resulted in two main speculations on the formation of highly populated nanocrystals after low-temperature annealing process. The first one relies on the fact that small fractions of crystallite nuclei already exist in the as-quenched solid [6]. The growth of these nuclei is suppressed by the rapid increasing viscosity near the glass transition ⁎ Corresponding author. Tel.: +90 312 210 2525; fax: +90 312 210 2518. E-mail address: [email protected] (Y.E. Kalay).
http://dx.doi.org/10.1016/j.jnoncrysol.2014.08.037 0022-3093/© 2014 Elsevier B.V. All rights reserved.
temperature (Tg) during quenching. Therefore some nuclei are trapped in the amorphous matrix and subsequent annealing below Tg results in the growth of these “quenched-in nuclei”. This hypothesis was tested by using melt-spun and cold-rolled Al–Sm amorphous specimens [6]. The existence of highly populated Al-nanocrystals, as observed for melt-spun specimens, was not detected in the cold-rolled specimens upon similar heat treatment processes. Moreover, fluctuation electron microscopy signals [7] indicating an fcc like medium-range order (MRO) for Al atoms in melt-spun alloy were absent for cold-rolled specimen. This agrees well with the hypothesis of having Al crystals being frozen during the quench of the as-spun ribbons. Cold-rolled specimens represent a different type of chemical and topological arrangement where fcc-like order is missing. The second approach is based on phase separation [5,8] effective in amorphous matrix by a mechanism similar to spinodal decomposition [8]. The origin of the phase-separation was explained through a time-independent homogeneous nucleation theory called coupled-flux nucleation [8,9]. According to this argument amorphous phase resulted by rapid-solidification phase separates into Al-rich and RE-rich regions prior to crystallization. Al-rich amorphous regions which extend to 74–126 nm [5] are held responsible for the nucleation of fcc-Al nanocrystals. Both approaches were questioned on different aspects [10–12]. For instance, a phase separation was reported for Al88Gd6La2Ni4 [8] alloy but not observed for Al88Gd6ErNi4 [13] where a two-stage fcc nanocrystallization was indicated for several Al–TM–RE amorphous which does not agree with “quenched-in” nuclei hyphothesis [14]. Recently, it has been stated that the phase separation in Al may actually be present at nanoscales in the as-quenched state [5,8–12,15] as well as in other systems such as Fe-based, Pd-based and Zr-based
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metallic glasses [16]. By using atom probe tomography (APT), Kalay et al. have demonstrated regions of 1 nm of pure Al in as quenched Al90Tb10 [11]. An approximate number density for these regions was calculated as 1025 m−3. APT results collected from the specimens annealed to temperatures just before the crystallization temperature point out coalescence of pure Al regions which reduce the population of pure Al clusters to 1021–22 m−3. According to small angle X-ray scattering studies, there occurs a phase separation in Al91Tb9 as well as in some other Al–rare-earth amorphous alloys prior to devitrification [17]. SAXS/WAXS measurements show that the further coarsening of these chemical fluctuations eventually triggers the nanocrystallization of primary fcc-Al phase [18,19]. Fluctuation electron microscopy (FEM) studies from both as-quenched and annealed specimens of Al– rare-earth alloys clearly reveal medium-range order up to some degree. Therefore, the phase-separated Al and RE rich regions may possess their own atomic structure at a first place in the as-quenched state. These structures do not have conventional crystal configurations, but still hold medium-range correlations. While above-mentioned experimental approaches are only able to probe the microstructural features resulting from the phase separation in nanoscale, the phase separation itself in Al–rare-earth system can only be investigated by using appropriate computational approaches at the present time. In this study, by investigating the short to medium range correlations, we demonstrate a possible kinetic pathway for the chemical and topological evolution of pure-Al regions during vitrification of Al91Tb9 alloy and their role as prenucleation clusters prior to primary crystallization of fcc-Al nanocrystals by using Monte Carlo (MC) simulations. 2. Experimental procedure The Al91Tb9 ingots were produced by electric arc melting under Ar atmosphere by using highly pure Al (99.99 wt.%) and Tb (99.9 wt.%) elements. The diffraction studies of liquid Al91Tb9 were previously performed by using the high-energy transmission synchrotron X-ray diffraction (HEXRD) at the Advanced Photon Source at Argonne National Laboratory. Specimens for liquid Al91Tb9 analysis were cast into 2 mm diameter rods, inserted into quartz capillaries and sealed under Ar atmosphere. Capillaries were lined with carbon to reduce the interaction between the quartz and the molten alloy at elevated temperatures. The sealed carbon-lined quartz capillaries were heated up to 1208 K and exposed to 100 keV of X-rays corresponding to a wavelength of 0.0124 nm. The diffraction data from molten alloy were collected in transmission (Debye–Scherrer) geometry by a MAR charge coupled device (CCD) with 60 s of exposure time. Similar diffraction patterns were collected from the blank holder and empty carbon-lined quartz capillary for background corrections. The raw HEXRD data collected from the liquid Al91Tb9 were corrected for polarization, absorption, multiple, Compton scattering and converted to the total structure factor function, S(Q) by a procedure described in [15]. The ab-initio molecular dynamics (AIMD) simulations were performed by using Vienna ab-initio Simulation Package (VASP). Periodic boundary conditions were applied with constant number of particles, volume and temperature (NVT) by using Nosé–Hoover thermostat to control the temperature [20–23]. Initial number densities for Al91Tb9 were estimated by using linear combination of pure Al and Tb elements. The exchange–correlation function has been described with generalized gradient approximation (GGA) of Perdew–Burke–Erhzernhof formulations. 200 atoms were distributed randomly in a periodic cell with correct stoichiometry of the produced alloys. Initially, the system was heated up to 2500 K to erase the memory effects for preparing the liquid Al–Tb alloy then subsequently cooled down to 1208 K and to room temperature (300 K). Reverse Monte Carlo (RMC) simulations of the experimental data were conducted by using RMC++ simulation package [24] in order to obtain partial pair correlation functions of liquid Al91Tb9. Lacking experimental data for the partial pairs, the RMC was constrained using the density and the partial pair-
correlation functions from the AIMD simulation [24,25]. The resulting fit of the experimental data is shown in Fig. 1a. The combination of the RMC and AIMD provides a robust determination of the longer range partial pair correlations that cannot be obtained by AIMD alone due to the limited size of the system [26]. Inverse Monte Carlo (IMC) algorithm [27] was utilized with a reliable atomic model, to develop an interatomic potential for the Al–Tb system. Partial pair distribution functions obtained from RMC were used as input in the algorithm. Using the interatomic potentials, sequential Monte Carlo simulations were conducted using NVT ensemble from 1200 K to 300 K with temperature decrements of 100 K. For each temperature, the volume of the simulation cell is determined by the number densities that are obtained from AIMD simulation. In order to reach to a relatively stable state, the Al91Tb9 system of 32,000 atoms was initialized in fcc configuration and equilibrated for 100,000 steps at 1200 K. At subsequent temperatures, the initial atomic configuration for the next simulation is taken from final atomic configuration of the previous one, and equilibrated 50,000 steps sufficient for the system to reach a relatively stable state. After the energy minimization is complete, the structural data was collected for 5 sets between intervals of 1000 steps. 3. Results and discussion The interatomic pair potentials obtained from IMC algorithm are shown in Fig. 1b. The relatively limited representation of Tb–Tb interactions resulted in a wavy E(r)-r behavior. On the other hand, the resulting partial g(r) functions obtained from MC simulation at 1200 K governed by the developed interatomic pair potentials almost perfectly fit with partial g(r) functions obtained from RMC (red-dotted line) as shown in Fig. 2a–c. Therefore, we believe that the interatomic pair potentials developed using IMC are successfully represent the paired Al– Tb interactions. Evolution of the partial g(r) functions obtained from subsequent isothermal MC simulations 1200 K to 300 K is shown in Fig. 2a–c. The trend of the change in average atomic volume with respect to temperature in AIMD simulation and that of corresponding MC simulations is given in Fig. 3a. It can be deduced that the system undergoes a glass transition near 600 K due to the rapid decrease in the rate of volume change. The evolution of the local atomic configuration of Al-centered clusters was initially investigated using Voronoi Tessellation [15]. In Voronoi Tessellation analysis of topologically disordered systems, each atom in the space can be represented by a Voronoi polyhedron while the number of faces forming a polyhedron corresponds to the coordination number of the given atom. Every single face of the polyhedron determines the border between the central atom and one of its neighboring atoms, and the number of edges forming the face gives the number of common neighbors of the corresponding atom pair. All polyhedrons were defined by 5-digit Voronoi indices in the form of bN3 N4 N5 N6 N7N where each digit represents Ni number of i-edged faces. The Voronoi polyhedra can be roughly separated into three categories: icosahedral-like, crystal-like and mixed [30]. Within these categories b0 0 12 0 0N, having 12 neighbors, each represented by N5 faces, represents the nearly perfect icosahedral structure, b0 1 10 2 0N is a commonly observed icosahedral derivative, and b0 2 8 4 0N can be interpreted as either a highly distorted icosahedral-like or a mixedtype cluster. The b0 3 6 × 0N represents a common mixed-type cluster family, and clusters relatively dominated by N4 and N6 faces such as b0 4 4 6 0N are considered as crystal-like. As shown in Fig. 3b, the population of certain Al-centered clusters considerably increases during vitrification which is the first sign of particular ordering. Icosahedaral-like clusters such as b0 1 10 2 0N and b0 0 12 0 0N steeply dominated the topology near glass transition, and b0 3 6 4 0N clusters among the other mixed-type clusters become more preferred with a steady increase in number with decreasing temperature, while b0 2 8 4 0N exhibits a behavior in between. The amount of crystal-like b0 4 4 6 0N slightly increases in the amorphous state, whereas some other populous clusters
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Fig. 1. (a) Structure factor, S(Q), data obtained from HEXRD experiment (black line), and RMC simulation (red dotted line), (b) the interatomic pair potentials developed using IMC. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of the liquid phase such as b1 3 4 5 1N, b1 2 6 3 1N, and b0 3 6 3 0N do not exhibit a remarkable change in number during within glass. It is worth to note that the populous Al-centered clusters are mainly located in Alrich regions. Tb-rich regions mostly consist of irregularly shaped Alcentered clusters and there is no predominance of any Voronoi indices. In Tb-centered clusters, there is no specific type of clustering observed in liquid. However, as the temperature decreases, b0 1 10 × 0N and b0 2 8 × 0N cluster families stand out, as seen in Fig. 3c. While the former type is readily attributed to icosahedral-like symmetry commonly observed in glass structure, the latter one may also be related to a further ordering of Tb-rich regions precedent for metastable intermetallic compounds. Since aluminum and rare-earth atoms are highly correlated as shown in the current and previous studies [15], Tb-rich regions have a structure such that Tb atoms are mostly surrounded by Al atoms and preferentially located with a certain distance with respect to each
other forming a network. This structural feature also highly resembles the related intermetallics of this system such as trigonal Al3Tb (SG:R3m) and metastable hexagonal Al17Tb2 (SG:P63/mmc). Moreover the peak appeared at 0.42 nm in PDF of Tb–Tb pair (Fig. 2c) due to branching of the first shell also coincides with the closest Tb–Tb distance of trigonal Al3Tb intermetallic crystal. This type of quasi-periodic medium range ordering may also be the structural origin of the prepeak observed on amorphous diffraction patterns, also called as first sharp diffraction peak [31]. The so-called “superatoms” [11], RE centered clusters between the highly pure Al regions, are seen responsible to generate a strong pre-peak commonly observed in Al–RE marginal glass forming alloys [10–12,15]. In similar systems, our previous studies with Al90Sm10 marginal glass forming alloys, some MRO structure corresponding to a high-temperature metastable tetragonal Al11Sm3 (SG: I4/mmm) were detected by HEXRD and RMC studies [15]. Similarly,
Fig. 2. Evolution of partial pair distribution functions, g(r), of (a) Al–Al, (b) Al–Tb, and (c) Tb–Tb atomic pairs from Monte Carlo simulations and partial pair distribution functions at 1208 K from RMC (dotted line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 3. (a) Average atomic volume in AIMD simulation and corresponding MC simulations at different temperatures and changes in the population of selected Voronoi clusters in (b) Al-centered and (c) Tb-centered atoms.
using fluctuation electron microscopy (FEM), MRO of pseudo-trigonal Al3Tb was highlighted for as-quenched Al90Tb10 alloy [11]. The overall topological evolution is consistent with Frank's hypothesis [32] suggesting that the dominance of energetically favorable local icosahedral-like configurations with restricted translational symmetry inhibits the development of long-range crystalline ordering. Warren–Cowley chemical short range order analysis was used in order to detect the chemical inhomogeneities [28,29]. Fig. 4a reveals the fraction of aluminum atoms belonging to pure aluminum clusters and the corresponding average number of atoms per cluster calculated using Warren–Cowley's approach [28,29]. According to this analysis, the degree of Al–Al clustering propagated progressively at lower temperatures. Furthermore, considerable amount of Al-centered clusters having Warren–Cowley parameters equal to the unity was found for
the center atom as well as all of the neighboring atoms. This clearly indicates the isolation of highly pure Al regions beyond the first-shell neighborhood and supports the hypothesis that pure aluminum clusters developed in the medium-range order scale. Therefore, pure Al clusters are identified as regions of Al atoms having only Al neighbors in first two coordination shells. These regions having number densities in the order of 1025 m−3 and an average size of 100–200 aluminum atoms confirm the results of the previous studies using APT [5,11] which were indicated that there is a network of interconnected rare-earth centered clusters separating pure aluminum regions with an average size of 1 nm in Al90Tb10 glass and sub-nanometer sized pure Al zones and coarser scale Al-rich regions in Al88Y7Fe5 glass. According to previous APT and the current MC results, it is hypothesized that the interconnected network of terbium centered clusters and pure aluminum atoms that exist in the amorphous state may possess medium-range order (MRO) structure having some pseudo-crystal periodicity which gives rise of the pre-peak at low scattering angles. It should be noted that the same pre-peak also present for the liquid state has lower intensity [15]. This offers an experimental evidence for the same clustering effect at a lower degree in the molten metal at elevated temperatures. Therefore, in terms of the atomic distribution, the molten liquid is not as homogeneous as it is expected. In the current Monte Carlo study, the presence of pure aluminum clusters in liquid and their development from liquid to glass through supercooled liquid region support the experimental observation [11,15]. As shown in Fig. 4a, the fraction of Al-atoms belonging to the pure Al clusters as well as the average size of individual clusters increases with decreasing temperature. Furthermore, the continuous growth and spatial domination of the clusters accelerate near the glass transition and then cease below the glass transition temperature. In previous studies on similar Al-based marginal metallic glass systems, the critical nucleus size for fcc-Al is reported as approximately 90–120 atoms [5,33]. In Fig. 4b–e, we present the spatial evolution of pure Al clusters with decreasing temperature. The clusters are color coded according to their size emphasizing the population of clusters exceeding the critical size for nucleation of fcc-Al nanocrystals. These clusters above the critical size having number densities on the order of 1025 m− 3 are entrapped in the glass state and isolated from each other by the rare-earth rich network. Therefore, during the first stage of devitrification the intermittent growth of these nanocrystals due to retarded long-range diffusion among the solute-rich network [34] results in fcc-Al nanocrystals with number densities of 1021–1024 m−3. This picture exhibits a very special case of nanoscale chemical heterogeneity excluded by the theory of classical nucleation. Recently, Wallace et al. [35] showed that similar type of inhomogeneities in liquid and development of prenucleation clusters resulting in non-classical nucleation pathways are also present in other systems. Therefore, although it may sound speculative, according to the previous APT and HEXRD [11, 15] and the current simulation results we believe that the origin of the solid state chemical separation can be attributed to parental liquid state. During structural relaxation at low-temperature annealing, the resulting nanoscale chemical heterogeneity is responsible of (i) pureAl prenucleation clusters acting as potential nucleation sites for fcc-Al nanocrystals, (ii) rare-earth concentrated network enveloping these clusters, acting as a diffusion barrier due to its low atomic mobility and resulting the suspended growth of nanocrystals [36], and (iii) extremely high density of nanocrystal nucleation which cannot be predicted by classical nucleation theory. 4. Conclusion In summary, the enigmatic fcc-Al nanocrystallization during the first stages of devitrification of Al–RE marginal glass forming alloys with an extreme nucleation density underlines the limitations of the classical nucleation theory. Rapid build-up of Al-centered icosahedral-like configurations near glass transition is believed to inhibit crystallization of
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Fig. 4. (a) Fraction of aluminum atoms belonging to pure aluminum clusters (black), and average number of atoms per cluster (red) determined by Monte Carlo simulations. Glass transition temperature (Tg) is shown by vertical line. Size and spatial distribution of pure aluminum clusters at (b) 300 K, (c) 600 K, (d) 900 K, and (e) 1200 K. The cluster size is shown as number of atoms with scaled colors. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
fcc-Al during vitrification. According to previous APT and current MC results, it is hypothesized that the special correlation of Tb atoms (which can be also attributed to other RE) with Al atoms within the liquid structures results in nanoscale chemical separation as Tb and Al-rich regions. Terbium-rich network divides the matrix into nanoscopic regions forming isolated clusters of pure aluminum in which the initiation of crystallization is unable upon rapid solidification. The as-solidified glass structure has similar chemical separation with larger correlation lengths. Our findings on pure aluminum clusters obtained from structural and chemical analysis on MC simulations based on X-ray scattering
experiments are consistent with the recent similar experimental results in the Al–Tb system with similar composition in glassy state by atom probe tomography and reveal the structural origins of the chemically separated domains in liquid at temperatures higher than the melting temperature. Acknowledgement This work was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under grant no. 113M346. Work
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at Ames Laboratory was supported by the US Department of Energy, Basic Energy Sciences, Division of Materials Science and Engineering, under contract no. DE-AC02-07CH11358. The high-energy X-ray experiments were performed at the XOR beamline (sector 6) of the Advanced Photon Source, Argonne National Laboratory, under grant no. DE-AC0206CH11357.
References [1] A. Inoue, Amorphous, nanoquasicrystalline and nanocrystalline alloys in Al-based systems, Prog. Mater. Sci. 43 (1998) 365–520. [2] J.H. Perepezko, R.J. Hebert, R.I.Wu. Wilde, Primary crystallization in amorphous Al-based alloys, J. Non-Cryst. Solids 317 (2003) 52–61. [3] T. Kulik, Nanocrystallization of metallic glasses, J. Non-Cryst. Solids 287 (2001) 145–161. [4] L. Battezzati, S. Pozzovivo, P. Rizzi, Nanocrystalline aluminum alloys, ENN 6 (2004) 341–364. [5] K.F. Kelton, M.K. Miller, K.K. Sahu, N.A. Mauro, L. Longsreth-Spoor, D. Saha, Z. Nussinov, Phase separation mediated devitrification of Al88Y7Fe5 glasses, Acta Mater. 58 (2010) 4199–4206. [6] G. Wilde, H. Sieber, JH. Perepezko, Glass formation versus nanocrystallization in an Al92Sm8 alloy, Scripta Mater. 40 (1999) 779–783. [7] W.G. Stratton, J. Hamann, J.H. Perepezko, P.M. Voyles, Aluminum nanoscale order in amorphous Al92Sm8 measured by fluctuation electron microcopy, Appl. Phys. Lett. 86 (2005) 141910–1–3. [8] A.K. Gangopadhyay, T.K. Croat, K.F. Kelton, The effect of phase separation on subsequent crystallization in Al88Gd6La2Ni4, Acta Mater. 48 (2000) 4035–4043. [9] K.F. Kelton, Time-dependent nucleation in partitioning transformations, Acta Mater. 48 (2000) 1967–1980. [10] Y.E. Kalay, C. Yeager, L.S. Chumbley, M.J. Kramer, I.E. Anderson, Initial crystallization in a nanostructured Al–Sm rare earth alloy, J. Non-Cryst. Solids 356 (2010) 1416–1424. [11] Y.E. Kalay, I. Kalay, J. Hwang, P.M. Voyles, M.J. Kramer, Local chemical and topological order in Al–Tb and its role in controlling nanocrystal formation, Acta Mater. 60 (2012) 994–1003. [12] Y.E. Kalay, L.S. Chumbley, I.E. Anderson, Characterization of a marginal glass former alloy solidified in gas atomized powders, Mater. Sci. Eng. A 490 (2008) 72–80. [13] N. Tian, M. Ohnuma, T. Ohkubo, K. Hono, Primary crystallization of an Al88Gd6Er2Ni4 metallic glass, Mater. Trans. JIM 46 (2005) 2880–2885. [14] Q. Li, E. Johnson, A. Johansen, L. Sharlot-Kristensen, On glass formation in rapidly solidified aluminum-based alloys, J. Mater. Res. 7 (1992) 2756–2764. [15] Y.E. Kalay, L.S. Chumbley, M.J. Kramer, I.E. Anderson, Local structure in marginal glass forming Al–Sm alloy, Intermetallics 18 (2010) 1676–1682. [16] D.H. Kim, W.T. Kim, E.S. Park, N. Mattern, J. Eckert, Phase separation in metallic glasses, Prog. Mater. Sci. 58 (2013) 1103–1172.
[17] J. Antonowicz, Atomic packing and phase separation in Al–rare earth metallic glasses, J. Mater. Sci. 45 (2010) 5040–5044. [18] J. Antonowicz, Phase separation and nanocrystal formation in Al-based metallic glasses, J. Alloys Compd. 434–435 (2007) 126–130. [19] J. Antonowicz, E. Jezierska, M. Kedzierski, A.R. Yavari, L. Greer, P. Panine P, M. Sztucki, Early stages of phase separation and nanocrystallization in Al–rare earth metallic glasses studied using SAXS/WAXS and HRTEM methods, Rev. Adv. Mater. Sci. 18 (2008) 454–458. [20] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmentedwave method, Phys. Rev. B 59 (1999) 1758–1775. [21] G. Kresse, J. Hafner, Abinitio molecular-dynamics for liquid-metals, Phys. Rev. B 47 (1993) 558–561. [22] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169–11186. [23] G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6 (1996) 15–50. [24] R.L. McGreevy, Reverse Monte Carlo modelling, J. Phys. Condens. Matter 13 (2001) 877–913. [25] Y.Q. Cheng, E. Ma, Atomic-level structure and structure–property relationship in metallic glasses, Prog. Mater. Sci. 56 (2011) 379–473. [26] M.I. Mendelev, M.J. Kramer, S.G. Hao, K.M. Ho, C.Z. Wang, Development of interatomic potentials appropriate for simulation of liquid and glass properties of NiZr2 alloy, Philos. Mag. 92 (35) (2012) 4454–4469. [27] N.G. Almarza, E. Lomba, Determination of the interaction potential from the pair distribution function: an inverse Monte Carlo technique, Phys. Rev. E. 68 (2003) 011202. [28] B.E. Warren, X-ray Diffraction, Dover Publications Inc., New York, 1990. [29] J.M. Cowley, X‐ray measurement of order in single crystals of Cu3Au, J. Appl. Phys. 21 (1950) 24–29. [30] J. Hwang, Z.H. Malgarejo, Y.E. Kalay, I. Kalay, M.J. Kramer, D.S. Stone, P.M. Voyles, Nanoscale structure and structural relaxation in Zr50Cu45Al5 bulk metallic glass, Phys. Rev. Lett. 108 (195505) (2012) 1–5. [31] Q. Jingyu, B. Xiufang, S.I. Sliusarenko, W. Weimin, Pre-peak in the structure factor of liquid Al–Fe alloy, J. Phys. Condens. Matter 10 (1998) 1211. [32] F.C. Frank, Supercooling of liquids, Proc. Roy. Soc. London. A Mat. 215 (1952) 43–46. [33] D.R. Allen, J.C. Foley, J.H. Perepezko, Nanocrystal development during primary crystallization of amorphous alloys, Acta Mater. 46 (1998) 431–440. [34] Y.Q. Cheng, H.W. Sheng, E. Ma, Relationship between structure, dynamics and mechanical properties in metallic glass-forming alloys, Phys. Rev. B 78 (014207) (2008) 1–7. [35] A.F. Wallace, L.O. Hedges, A. Fernandez-Martinez, P. Raiteri, J.D. Gale, G.A. Waychunas, S. Whitelam, J.F. Banfield, J.J. De Yoreo, Microscopic evidence for liquid–liquid separation in supersaturated CaCO3 solutions, Science 341 (2013) 885–889. [36] T. Demirtas, Y.E. Kalay, Kinetics of fcc-Al nanocrystallization in Al90Tb10 metallic glass, J. Non-Cryst. Solids 378 (2013) 71–78.
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
Structural modeling of liquid and amorphous Al91Tb9 by Monte Carlo simulations M. Ovun a, M.J. Kramer b, Y.E. Kalay a,⁎ a b
Department of Metallurgical and Materials Engineering, METU, Ankara 06800, Turkey Ames Laboratory US DOE, Ames, IA 50011, USA
a r t i c l e
i n f o
Article history: Received 27 June 2014 Received in revised form 13 August 2014 Available online xxxx Keywords: Monte-Carlo simulations; Medium-range ordering; Phase separation; Chemical and topological configuration; Al–RE metallic glass
a b s t r a c t Evolution of the chemical and topological inhomogeneities within the Al91Tb9 amorphous system from liquid to glass was investigated using Monte Carlo (MC) simulations. The interatomic potential for Al–Tb system was developed and three-dimensional atomic configurations of liquid and amorphous structures were modeled. The simulations coupled with Voronoi Tessellation and Warren–Cowley chemical short-range order analysis revealed a high degree of chemical inhomogeneity at nanoscale composed of pure Al clusters which were found to be increasing in number and size with decreasing temperature in the supercooled liquid region. These chemically isolated prenucleation clusters are thought to be the origin of extreme number. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Marginal glass forming alloys have been regarded as promising structural materials due to their continuous fine grain structure attributed primarily to their ability of forming very high number density of nuclei upon crystallization [1,2]. Marginal glass forming alloys, unlike bulk metallic glasses, require high cooling rates ~ 105 K/s to form a fully amorphous structure [3–5]. Lightweight high-strength Al–RE based alloys [1] and magnetically soft and hard Fe–RE (RE: Rare-earth element) based alloys [3] are two well-known examples for marginally glass forming alloys. The devitrification process of marginally amorphous metals quite often results in formation of very high number densities of primary crystals (1021–1024 m−3) with sizes of less than 50 nm. An extensive research in this area has still been in progress to give an exact explanation for the mechanism underlying the formation of such high density of nanocrystals. As the large percentage of bulk amorphous metals do not result in the formation of nanocrystals when subjected to similar heat-treatments; the answer for this enigmatic behavior may lay hidden within the structure of the as-quenched marginal glass forming alloys. The previous studies on Al–RE and Al–RE–TM amorphous alloys have resulted in two main speculations on the formation of highly populated nanocrystals after low-temperature annealing process. The first one relies on the fact that small fractions of crystallite nuclei already exist in the as-quenched solid [6]. The growth of these nuclei is suppressed by the rapid increasing viscosity near the glass transition ⁎ Corresponding author. Tel.: +90 312 210 2525; fax: +90 312 210 2518. E-mail address: [email protected] (Y.E. Kalay).
http://dx.doi.org/10.1016/j.jnoncrysol.2014.08.037 0022-3093/© 2014 Elsevier B.V. All rights reserved.
temperature (Tg) during quenching. Therefore some nuclei are trapped in the amorphous matrix and subsequent annealing below Tg results in the growth of these “quenched-in nuclei”. This hypothesis was tested by using melt-spun and cold-rolled Al–Sm amorphous specimens [6]. The existence of highly populated Al-nanocrystals, as observed for melt-spun specimens, was not detected in the cold-rolled specimens upon similar heat treatment processes. Moreover, fluctuation electron microscopy signals [7] indicating an fcc like medium-range order (MRO) for Al atoms in melt-spun alloy were absent for cold-rolled specimen. This agrees well with the hypothesis of having Al crystals being frozen during the quench of the as-spun ribbons. Cold-rolled specimens represent a different type of chemical and topological arrangement where fcc-like order is missing. The second approach is based on phase separation [5,8] effective in amorphous matrix by a mechanism similar to spinodal decomposition [8]. The origin of the phase-separation was explained through a time-independent homogeneous nucleation theory called coupled-flux nucleation [8,9]. According to this argument amorphous phase resulted by rapid-solidification phase separates into Al-rich and RE-rich regions prior to crystallization. Al-rich amorphous regions which extend to 74–126 nm [5] are held responsible for the nucleation of fcc-Al nanocrystals. Both approaches were questioned on different aspects [10–12]. For instance, a phase separation was reported for Al88Gd6La2Ni4 [8] alloy but not observed for Al88Gd6ErNi4 [13] where a two-stage fcc nanocrystallization was indicated for several Al–TM–RE amorphous which does not agree with “quenched-in” nuclei hyphothesis [14]. Recently, it has been stated that the phase separation in Al may actually be present at nanoscales in the as-quenched state [5,8–12,15] as well as in other systems such as Fe-based, Pd-based and Zr-based
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metallic glasses [16]. By using atom probe tomography (APT), Kalay et al. have demonstrated regions of 1 nm of pure Al in as quenched Al90Tb10 [11]. An approximate number density for these regions was calculated as 1025 m−3. APT results collected from the specimens annealed to temperatures just before the crystallization temperature point out coalescence of pure Al regions which reduce the population of pure Al clusters to 1021–22 m−3. According to small angle X-ray scattering studies, there occurs a phase separation in Al91Tb9 as well as in some other Al–rare-earth amorphous alloys prior to devitrification [17]. SAXS/WAXS measurements show that the further coarsening of these chemical fluctuations eventually triggers the nanocrystallization of primary fcc-Al phase [18,19]. Fluctuation electron microscopy (FEM) studies from both as-quenched and annealed specimens of Al– rare-earth alloys clearly reveal medium-range order up to some degree. Therefore, the phase-separated Al and RE rich regions may possess their own atomic structure at a first place in the as-quenched state. These structures do not have conventional crystal configurations, but still hold medium-range correlations. While above-mentioned experimental approaches are only able to probe the microstructural features resulting from the phase separation in nanoscale, the phase separation itself in Al–rare-earth system can only be investigated by using appropriate computational approaches at the present time. In this study, by investigating the short to medium range correlations, we demonstrate a possible kinetic pathway for the chemical and topological evolution of pure-Al regions during vitrification of Al91Tb9 alloy and their role as prenucleation clusters prior to primary crystallization of fcc-Al nanocrystals by using Monte Carlo (MC) simulations. 2. Experimental procedure The Al91Tb9 ingots were produced by electric arc melting under Ar atmosphere by using highly pure Al (99.99 wt.%) and Tb (99.9 wt.%) elements. The diffraction studies of liquid Al91Tb9 were previously performed by using the high-energy transmission synchrotron X-ray diffraction (HEXRD) at the Advanced Photon Source at Argonne National Laboratory. Specimens for liquid Al91Tb9 analysis were cast into 2 mm diameter rods, inserted into quartz capillaries and sealed under Ar atmosphere. Capillaries were lined with carbon to reduce the interaction between the quartz and the molten alloy at elevated temperatures. The sealed carbon-lined quartz capillaries were heated up to 1208 K and exposed to 100 keV of X-rays corresponding to a wavelength of 0.0124 nm. The diffraction data from molten alloy were collected in transmission (Debye–Scherrer) geometry by a MAR charge coupled device (CCD) with 60 s of exposure time. Similar diffraction patterns were collected from the blank holder and empty carbon-lined quartz capillary for background corrections. The raw HEXRD data collected from the liquid Al91Tb9 were corrected for polarization, absorption, multiple, Compton scattering and converted to the total structure factor function, S(Q) by a procedure described in [15]. The ab-initio molecular dynamics (AIMD) simulations were performed by using Vienna ab-initio Simulation Package (VASP). Periodic boundary conditions were applied with constant number of particles, volume and temperature (NVT) by using Nosé–Hoover thermostat to control the temperature [20–23]. Initial number densities for Al91Tb9 were estimated by using linear combination of pure Al and Tb elements. The exchange–correlation function has been described with generalized gradient approximation (GGA) of Perdew–Burke–Erhzernhof formulations. 200 atoms were distributed randomly in a periodic cell with correct stoichiometry of the produced alloys. Initially, the system was heated up to 2500 K to erase the memory effects for preparing the liquid Al–Tb alloy then subsequently cooled down to 1208 K and to room temperature (300 K). Reverse Monte Carlo (RMC) simulations of the experimental data were conducted by using RMC++ simulation package [24] in order to obtain partial pair correlation functions of liquid Al91Tb9. Lacking experimental data for the partial pairs, the RMC was constrained using the density and the partial pair-
correlation functions from the AIMD simulation [24,25]. The resulting fit of the experimental data is shown in Fig. 1a. The combination of the RMC and AIMD provides a robust determination of the longer range partial pair correlations that cannot be obtained by AIMD alone due to the limited size of the system [26]. Inverse Monte Carlo (IMC) algorithm [27] was utilized with a reliable atomic model, to develop an interatomic potential for the Al–Tb system. Partial pair distribution functions obtained from RMC were used as input in the algorithm. Using the interatomic potentials, sequential Monte Carlo simulations were conducted using NVT ensemble from 1200 K to 300 K with temperature decrements of 100 K. For each temperature, the volume of the simulation cell is determined by the number densities that are obtained from AIMD simulation. In order to reach to a relatively stable state, the Al91Tb9 system of 32,000 atoms was initialized in fcc configuration and equilibrated for 100,000 steps at 1200 K. At subsequent temperatures, the initial atomic configuration for the next simulation is taken from final atomic configuration of the previous one, and equilibrated 50,000 steps sufficient for the system to reach a relatively stable state. After the energy minimization is complete, the structural data was collected for 5 sets between intervals of 1000 steps. 3. Results and discussion The interatomic pair potentials obtained from IMC algorithm are shown in Fig. 1b. The relatively limited representation of Tb–Tb interactions resulted in a wavy E(r)-r behavior. On the other hand, the resulting partial g(r) functions obtained from MC simulation at 1200 K governed by the developed interatomic pair potentials almost perfectly fit with partial g(r) functions obtained from RMC (red-dotted line) as shown in Fig. 2a–c. Therefore, we believe that the interatomic pair potentials developed using IMC are successfully represent the paired Al– Tb interactions. Evolution of the partial g(r) functions obtained from subsequent isothermal MC simulations 1200 K to 300 K is shown in Fig. 2a–c. The trend of the change in average atomic volume with respect to temperature in AIMD simulation and that of corresponding MC simulations is given in Fig. 3a. It can be deduced that the system undergoes a glass transition near 600 K due to the rapid decrease in the rate of volume change. The evolution of the local atomic configuration of Al-centered clusters was initially investigated using Voronoi Tessellation [15]. In Voronoi Tessellation analysis of topologically disordered systems, each atom in the space can be represented by a Voronoi polyhedron while the number of faces forming a polyhedron corresponds to the coordination number of the given atom. Every single face of the polyhedron determines the border between the central atom and one of its neighboring atoms, and the number of edges forming the face gives the number of common neighbors of the corresponding atom pair. All polyhedrons were defined by 5-digit Voronoi indices in the form of bN3 N4 N5 N6 N7N where each digit represents Ni number of i-edged faces. The Voronoi polyhedra can be roughly separated into three categories: icosahedral-like, crystal-like and mixed [30]. Within these categories b0 0 12 0 0N, having 12 neighbors, each represented by N5 faces, represents the nearly perfect icosahedral structure, b0 1 10 2 0N is a commonly observed icosahedral derivative, and b0 2 8 4 0N can be interpreted as either a highly distorted icosahedral-like or a mixedtype cluster. The b0 3 6 × 0N represents a common mixed-type cluster family, and clusters relatively dominated by N4 and N6 faces such as b0 4 4 6 0N are considered as crystal-like. As shown in Fig. 3b, the population of certain Al-centered clusters considerably increases during vitrification which is the first sign of particular ordering. Icosahedaral-like clusters such as b0 1 10 2 0N and b0 0 12 0 0N steeply dominated the topology near glass transition, and b0 3 6 4 0N clusters among the other mixed-type clusters become more preferred with a steady increase in number with decreasing temperature, while b0 2 8 4 0N exhibits a behavior in between. The amount of crystal-like b0 4 4 6 0N slightly increases in the amorphous state, whereas some other populous clusters
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Fig. 1. (a) Structure factor, S(Q), data obtained from HEXRD experiment (black line), and RMC simulation (red dotted line), (b) the interatomic pair potentials developed using IMC. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of the liquid phase such as b1 3 4 5 1N, b1 2 6 3 1N, and b0 3 6 3 0N do not exhibit a remarkable change in number during within glass. It is worth to note that the populous Al-centered clusters are mainly located in Alrich regions. Tb-rich regions mostly consist of irregularly shaped Alcentered clusters and there is no predominance of any Voronoi indices. In Tb-centered clusters, there is no specific type of clustering observed in liquid. However, as the temperature decreases, b0 1 10 × 0N and b0 2 8 × 0N cluster families stand out, as seen in Fig. 3c. While the former type is readily attributed to icosahedral-like symmetry commonly observed in glass structure, the latter one may also be related to a further ordering of Tb-rich regions precedent for metastable intermetallic compounds. Since aluminum and rare-earth atoms are highly correlated as shown in the current and previous studies [15], Tb-rich regions have a structure such that Tb atoms are mostly surrounded by Al atoms and preferentially located with a certain distance with respect to each
other forming a network. This structural feature also highly resembles the related intermetallics of this system such as trigonal Al3Tb (SG:R3m) and metastable hexagonal Al17Tb2 (SG:P63/mmc). Moreover the peak appeared at 0.42 nm in PDF of Tb–Tb pair (Fig. 2c) due to branching of the first shell also coincides with the closest Tb–Tb distance of trigonal Al3Tb intermetallic crystal. This type of quasi-periodic medium range ordering may also be the structural origin of the prepeak observed on amorphous diffraction patterns, also called as first sharp diffraction peak [31]. The so-called “superatoms” [11], RE centered clusters between the highly pure Al regions, are seen responsible to generate a strong pre-peak commonly observed in Al–RE marginal glass forming alloys [10–12,15]. In similar systems, our previous studies with Al90Sm10 marginal glass forming alloys, some MRO structure corresponding to a high-temperature metastable tetragonal Al11Sm3 (SG: I4/mmm) were detected by HEXRD and RMC studies [15]. Similarly,
Fig. 2. Evolution of partial pair distribution functions, g(r), of (a) Al–Al, (b) Al–Tb, and (c) Tb–Tb atomic pairs from Monte Carlo simulations and partial pair distribution functions at 1208 K from RMC (dotted line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 3. (a) Average atomic volume in AIMD simulation and corresponding MC simulations at different temperatures and changes in the population of selected Voronoi clusters in (b) Al-centered and (c) Tb-centered atoms.
using fluctuation electron microscopy (FEM), MRO of pseudo-trigonal Al3Tb was highlighted for as-quenched Al90Tb10 alloy [11]. The overall topological evolution is consistent with Frank's hypothesis [32] suggesting that the dominance of energetically favorable local icosahedral-like configurations with restricted translational symmetry inhibits the development of long-range crystalline ordering. Warren–Cowley chemical short range order analysis was used in order to detect the chemical inhomogeneities [28,29]. Fig. 4a reveals the fraction of aluminum atoms belonging to pure aluminum clusters and the corresponding average number of atoms per cluster calculated using Warren–Cowley's approach [28,29]. According to this analysis, the degree of Al–Al clustering propagated progressively at lower temperatures. Furthermore, considerable amount of Al-centered clusters having Warren–Cowley parameters equal to the unity was found for
the center atom as well as all of the neighboring atoms. This clearly indicates the isolation of highly pure Al regions beyond the first-shell neighborhood and supports the hypothesis that pure aluminum clusters developed in the medium-range order scale. Therefore, pure Al clusters are identified as regions of Al atoms having only Al neighbors in first two coordination shells. These regions having number densities in the order of 1025 m−3 and an average size of 100–200 aluminum atoms confirm the results of the previous studies using APT [5,11] which were indicated that there is a network of interconnected rare-earth centered clusters separating pure aluminum regions with an average size of 1 nm in Al90Tb10 glass and sub-nanometer sized pure Al zones and coarser scale Al-rich regions in Al88Y7Fe5 glass. According to previous APT and the current MC results, it is hypothesized that the interconnected network of terbium centered clusters and pure aluminum atoms that exist in the amorphous state may possess medium-range order (MRO) structure having some pseudo-crystal periodicity which gives rise of the pre-peak at low scattering angles. It should be noted that the same pre-peak also present for the liquid state has lower intensity [15]. This offers an experimental evidence for the same clustering effect at a lower degree in the molten metal at elevated temperatures. Therefore, in terms of the atomic distribution, the molten liquid is not as homogeneous as it is expected. In the current Monte Carlo study, the presence of pure aluminum clusters in liquid and their development from liquid to glass through supercooled liquid region support the experimental observation [11,15]. As shown in Fig. 4a, the fraction of Al-atoms belonging to the pure Al clusters as well as the average size of individual clusters increases with decreasing temperature. Furthermore, the continuous growth and spatial domination of the clusters accelerate near the glass transition and then cease below the glass transition temperature. In previous studies on similar Al-based marginal metallic glass systems, the critical nucleus size for fcc-Al is reported as approximately 90–120 atoms [5,33]. In Fig. 4b–e, we present the spatial evolution of pure Al clusters with decreasing temperature. The clusters are color coded according to their size emphasizing the population of clusters exceeding the critical size for nucleation of fcc-Al nanocrystals. These clusters above the critical size having number densities on the order of 1025 m− 3 are entrapped in the glass state and isolated from each other by the rare-earth rich network. Therefore, during the first stage of devitrification the intermittent growth of these nanocrystals due to retarded long-range diffusion among the solute-rich network [34] results in fcc-Al nanocrystals with number densities of 1021–1024 m−3. This picture exhibits a very special case of nanoscale chemical heterogeneity excluded by the theory of classical nucleation. Recently, Wallace et al. [35] showed that similar type of inhomogeneities in liquid and development of prenucleation clusters resulting in non-classical nucleation pathways are also present in other systems. Therefore, although it may sound speculative, according to the previous APT and HEXRD [11, 15] and the current simulation results we believe that the origin of the solid state chemical separation can be attributed to parental liquid state. During structural relaxation at low-temperature annealing, the resulting nanoscale chemical heterogeneity is responsible of (i) pureAl prenucleation clusters acting as potential nucleation sites for fcc-Al nanocrystals, (ii) rare-earth concentrated network enveloping these clusters, acting as a diffusion barrier due to its low atomic mobility and resulting the suspended growth of nanocrystals [36], and (iii) extremely high density of nanocrystal nucleation which cannot be predicted by classical nucleation theory. 4. Conclusion In summary, the enigmatic fcc-Al nanocrystallization during the first stages of devitrification of Al–RE marginal glass forming alloys with an extreme nucleation density underlines the limitations of the classical nucleation theory. Rapid build-up of Al-centered icosahedral-like configurations near glass transition is believed to inhibit crystallization of
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Fig. 4. (a) Fraction of aluminum atoms belonging to pure aluminum clusters (black), and average number of atoms per cluster (red) determined by Monte Carlo simulations. Glass transition temperature (Tg) is shown by vertical line. Size and spatial distribution of pure aluminum clusters at (b) 300 K, (c) 600 K, (d) 900 K, and (e) 1200 K. The cluster size is shown as number of atoms with scaled colors. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
fcc-Al during vitrification. According to previous APT and current MC results, it is hypothesized that the special correlation of Tb atoms (which can be also attributed to other RE) with Al atoms within the liquid structures results in nanoscale chemical separation as Tb and Al-rich regions. Terbium-rich network divides the matrix into nanoscopic regions forming isolated clusters of pure aluminum in which the initiation of crystallization is unable upon rapid solidification. The as-solidified glass structure has similar chemical separation with larger correlation lengths. Our findings on pure aluminum clusters obtained from structural and chemical analysis on MC simulations based on X-ray scattering
experiments are consistent with the recent similar experimental results in the Al–Tb system with similar composition in glassy state by atom probe tomography and reveal the structural origins of the chemically separated domains in liquid at temperatures higher than the melting temperature. Acknowledgement This work was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under grant no. 113M346. Work
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at Ames Laboratory was supported by the US Department of Energy, Basic Energy Sciences, Division of Materials Science and Engineering, under contract no. DE-AC02-07CH11358. The high-energy X-ray experiments were performed at the XOR beamline (sector 6) of the Advanced Photon Source, Argonne National Laboratory, under grant no. DE-AC0206CH11357.
References [1] A. Inoue, Amorphous, nanoquasicrystalline and nanocrystalline alloys in Al-based systems, Prog. Mater. Sci. 43 (1998) 365–520. [2] J.H. Perepezko, R.J. Hebert, R.I.Wu. Wilde, Primary crystallization in amorphous Al-based alloys, J. Non-Cryst. Solids 317 (2003) 52–61. [3] T. Kulik, Nanocrystallization of metallic glasses, J. Non-Cryst. Solids 287 (2001) 145–161. [4] L. Battezzati, S. Pozzovivo, P. Rizzi, Nanocrystalline aluminum alloys, ENN 6 (2004) 341–364. [5] K.F. Kelton, M.K. Miller, K.K. Sahu, N.A. Mauro, L. Longsreth-Spoor, D. Saha, Z. Nussinov, Phase separation mediated devitrification of Al88Y7Fe5 glasses, Acta Mater. 58 (2010) 4199–4206. [6] G. Wilde, H. Sieber, JH. Perepezko, Glass formation versus nanocrystallization in an Al92Sm8 alloy, Scripta Mater. 40 (1999) 779–783. [7] W.G. Stratton, J. Hamann, J.H. Perepezko, P.M. Voyles, Aluminum nanoscale order in amorphous Al92Sm8 measured by fluctuation electron microcopy, Appl. Phys. Lett. 86 (2005) 141910–1–3. [8] A.K. Gangopadhyay, T.K. Croat, K.F. Kelton, The effect of phase separation on subsequent crystallization in Al88Gd6La2Ni4, Acta Mater. 48 (2000) 4035–4043. [9] K.F. Kelton, Time-dependent nucleation in partitioning transformations, Acta Mater. 48 (2000) 1967–1980. [10] Y.E. Kalay, C. Yeager, L.S. Chumbley, M.J. Kramer, I.E. Anderson, Initial crystallization in a nanostructured Al–Sm rare earth alloy, J. Non-Cryst. Solids 356 (2010) 1416–1424. [11] Y.E. Kalay, I. Kalay, J. Hwang, P.M. Voyles, M.J. Kramer, Local chemical and topological order in Al–Tb and its role in controlling nanocrystal formation, Acta Mater. 60 (2012) 994–1003. [12] Y.E. Kalay, L.S. Chumbley, I.E. Anderson, Characterization of a marginal glass former alloy solidified in gas atomized powders, Mater. Sci. Eng. A 490 (2008) 72–80. [13] N. Tian, M. Ohnuma, T. Ohkubo, K. Hono, Primary crystallization of an Al88Gd6Er2Ni4 metallic glass, Mater. Trans. JIM 46 (2005) 2880–2885. [14] Q. Li, E. Johnson, A. Johansen, L. Sharlot-Kristensen, On glass formation in rapidly solidified aluminum-based alloys, J. Mater. Res. 7 (1992) 2756–2764. [15] Y.E. Kalay, L.S. Chumbley, M.J. Kramer, I.E. Anderson, Local structure in marginal glass forming Al–Sm alloy, Intermetallics 18 (2010) 1676–1682. [16] D.H. Kim, W.T. Kim, E.S. Park, N. Mattern, J. Eckert, Phase separation in metallic glasses, Prog. Mater. Sci. 58 (2013) 1103–1172.
[17] J. Antonowicz, Atomic packing and phase separation in Al–rare earth metallic glasses, J. Mater. Sci. 45 (2010) 5040–5044. [18] J. Antonowicz, Phase separation and nanocrystal formation in Al-based metallic glasses, J. Alloys Compd. 434–435 (2007) 126–130. [19] J. Antonowicz, E. Jezierska, M. Kedzierski, A.R. Yavari, L. Greer, P. Panine P, M. Sztucki, Early stages of phase separation and nanocrystallization in Al–rare earth metallic glasses studied using SAXS/WAXS and HRTEM methods, Rev. Adv. Mater. Sci. 18 (2008) 454–458. [20] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmentedwave method, Phys. Rev. B 59 (1999) 1758–1775. [21] G. Kresse, J. Hafner, Abinitio molecular-dynamics for liquid-metals, Phys. Rev. B 47 (1993) 558–561. [22] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169–11186. [23] G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6 (1996) 15–50. [24] R.L. McGreevy, Reverse Monte Carlo modelling, J. Phys. Condens. Matter 13 (2001) 877–913. [25] Y.Q. Cheng, E. Ma, Atomic-level structure and structure–property relationship in metallic glasses, Prog. Mater. Sci. 56 (2011) 379–473. [26] M.I. Mendelev, M.J. Kramer, S.G. Hao, K.M. Ho, C.Z. Wang, Development of interatomic potentials appropriate for simulation of liquid and glass properties of NiZr2 alloy, Philos. Mag. 92 (35) (2012) 4454–4469. [27] N.G. Almarza, E. Lomba, Determination of the interaction potential from the pair distribution function: an inverse Monte Carlo technique, Phys. Rev. E. 68 (2003) 011202. [28] B.E. Warren, X-ray Diffraction, Dover Publications Inc., New York, 1990. [29] J.M. Cowley, X‐ray measurement of order in single crystals of Cu3Au, J. Appl. Phys. 21 (1950) 24–29. [30] J. Hwang, Z.H. Malgarejo, Y.E. Kalay, I. Kalay, M.J. Kramer, D.S. Stone, P.M. Voyles, Nanoscale structure and structural relaxation in Zr50Cu45Al5 bulk metallic glass, Phys. Rev. Lett. 108 (195505) (2012) 1–5. [31] Q. Jingyu, B. Xiufang, S.I. Sliusarenko, W. Weimin, Pre-peak in the structure factor of liquid Al–Fe alloy, J. Phys. Condens. Matter 10 (1998) 1211. [32] F.C. Frank, Supercooling of liquids, Proc. Roy. Soc. London. A Mat. 215 (1952) 43–46. [33] D.R. Allen, J.C. Foley, J.H. Perepezko, Nanocrystal development during primary crystallization of amorphous alloys, Acta Mater. 46 (1998) 431–440. [34] Y.Q. Cheng, H.W. Sheng, E. Ma, Relationship between structure, dynamics and mechanical properties in metallic glass-forming alloys, Phys. Rev. B 78 (014207) (2008) 1–7. [35] A.F. Wallace, L.O. Hedges, A. Fernandez-Martinez, P. Raiteri, J.D. Gale, G.A. Waychunas, S. Whitelam, J.F. Banfield, J.J. De Yoreo, Microscopic evidence for liquid–liquid separation in supersaturated CaCO3 solutions, Science 341 (2013) 885–889. [36] T. Demirtas, Y.E. Kalay, Kinetics of fcc-Al nanocrystallization in Al90Tb10 metallic glass, J. Non-Cryst. Solids 378 (2013) 71–78.