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Microstructural evolution in amorphous-nanocrystalline ZrCu alloy under neutron irradiation
Acta Materialia 182 (2020) 18–28
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Microstructural evolution in amorphous-nanocrystalline ZrCu alloy under neutron irradiation Fan Xiong a, Ming-Fei Li a, Babafemi Malomo b, Liang Yang a,∗ a b
College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China Department of Mechanical Engineering, Obafemi Awolowo University, Ile-Ife, Nigeria
a r t i c l e
i n f o
Article history: Received 16 August 2019 Revised 8 October 2019 Accepted 11 October 2019 Available online 23 October 2019 Keywords: Irradiation effect Molecular dynamics Metallic glass Vacancies Self-healing
a b s t r a c t An extensive investigation on the microstructural evolution of an amorphous-nanocrystalline alloy (ANA) under neutron irradiation has been conducted by molecular dynamics simulation. The phenomenon of rapid and full annihilation of irradiation-induced vacancies was found in the nanocrystal zone and after structural relaxation, free volumes in the amorphous matrix were systematically self-recovered. An effective self-healing behavior of the nanocrystal zone subsequently sufficed, regardless of the thermal degradation effect caused by the intensity of collision cascades during quenching. As knocked-on atoms were arrested at the phase boundary, it is self-evident that, the mechanism of atomic diffusion was nonexistent at the interface between the nanocrystal grain and the neighboring amorphous zone. Consequently, from the foregoing, ANA materials have been found to demonstrate excellent resistance to neutron irradiation and prospectively, the results of this study will potentially facilitate the development of advanced materials with high irradiation resistance. © 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction The effect of particle irradiation changes in nuclear structural materials occurring at the micro-macroscopic transition scale is mostly responsible for their incipient failures in nuclear power applications [1]. The most commonly found nuclear structural materials are the Fe-, Zr-, and Ni-based crystalline alloys, possessing excellent mechanical and thermal properties [2,3]. In spite of this, the effect of structural damage and/or performance degradation is significant under particle irradiation and specifically, neutron irradiation over an extended period in service, leading to swelling, hardening, amorphization, embrittlement, etc [4,5]. The cumulative effect of these defects poses a serious threat to the safety, efficiency and longevity of operation of nuclear plants. Hence, it is highly imperative to design novel nuclear structural materials with high resistance to neutron irradiation damage. In the last decade and up until now, nanomaterials have been experiencing a rapid and burgeoning development which have drawn extensive scientific research attention from where it had been revealed that such advanced materials may possess excellent resistance to neutron irradiation. Bai et al. [6] recently carried out
∗
Corresponding author. E-mail address: [email protected] (L. Yang).
https://doi.org/10.1016/j.actamat.2019.10.026 1359-6454/© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
a theoretical study on the essential mechanisms of the self-healing behavior in nanocrystal metals, where it was discovered that, the grain boundaries (GBs) in a nano-scale copper model, contrary to traditional crystal materials do possess an unusual “loading and unloading” capacity to heal the irradiation-induced point defects, resulting in an enhanced irradiation resistance [7]. As the quest, for exceptional material performance in the nuclear industry continues to gain traction, a new class of alloy materials, known as the metallic glass (MG) is now the subject of an expanding and intense research interest, because of its unique properties such as, the high fracture strength, high hardness, high elastic limit, high fracture toughness, as well as amorphous features [8–10]. Recently, it has been reported that in comparison with crystalline alloys, MGs demonstrate a higher or complete self-healing efficiency in their microstructures [11], which is probably so, because they are not subject to the structural conditions (e.g. unit cells, GBs, dislocations, etc.) required to sink or arrest irradiation-induced interstitials or vacancies [9,12,13]. This implies that MGs may likely possess a high resistance against neutron irradiation. However, in spite of their attractive aforementioned attribute, MGs exhibit poor plasticity and as an implication are not the candidate structural materials in nuclear applications [14,15]. From a thermodynamic standpoint, MGs are classified as nonequilibrium materials, which implies that they can be transformed
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Fig. 1. Configurations of (a) the Zr2 Cu ANA model and (b) the four inserted nanocrystal grains. The grey and the red spheres denote the Zr and the Cu atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
into crystalline alloys. Therefore, based on MG materials, nanocrystalline alloys or amorphous-nanocrystalline composite alloys with excellent physical, chemical, and mechanical properties can be developed [16,17]. Moreover, now that it has been revealed that the precipitation of nanocrystal grains in the amorphous matrix could greatly enhance the strength and toughness of MGs [18,19]. It is an arguable assumption that the amorphous-nanocrystalline alloys (ANAs) probably would possess an excellent resistance to neutron irradiation since they are mixtures of MGs and nanocrystals grains, both of which have been confirmed to possess high irradiation resistance [6,11]. At any rate, the foregoing innuendos show that MGs are indeed a class of promising advanced materials justifying the need for a robust research interest on their applications. Recent research investigations have shown that nanocrystal grains have been employed in the study of the mechanical and magnetic properties of MGs, where the effects of neutron irradiation on ANAs remain largely unknown and unresolved [20,21]. This current work draws motivation from the preceding argument, and it seeks to investigate the microstructural evolution in ANAs under neutron irradiation through a series of molecular dynamics (MD) simulations and calculations with a view to determining the resistance to neutron irradiation in ANA materials.
2. Simulation methods 2.1. System selection It is known that Zr-based crystalline alloys (such as Zr-2 and Zr4) have been widely applied as nuclear structural materials [22], and many Zr-based ANAs (e.g. Zr–Cu, Zr–Cu–Ni, Zr–Cu–Ti, Zr–Cu– Ni–Al, Zr–Cu–Ni–Ti–Be–C etc.) can be fabricated, by isothermal annealing [23,24], ion irradiation [25,26], and by other techniques [27]. Specifically, Zr–Cu is a typical binary alloy system available for studying the microstructure [28], because it has a broad composition region (30–80 at% for Zr) forming MGs [29]. In this work, a Zr-rich composition alloy, Zr2 Cu, was selected as the research prototype, because it has been revealed that Zr2 Cu nanocrystal grains with the perfect C11b configuration (one of body-centered cubic structures) can be precipitated in the Zr2 Cu amorphous matrix, forming the ANA material [30].
2.2. Construction of an ANA model An MD simulation was performed to build the Zr2 Cu ANA model using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package [31]. The interatomic interactions were described by the embedded atom method (EAM) potential developed by Mendelev et al. [32], which is suitable for studying both amorphous and crystalline materials [33–35]. In addition, the short-range part of the potential employed was smoothly joined by the Ziegler–Biersack–Littmark (ZBL) function [36], so that the microstructural evolution of this model under irradiation could be simulated. First and foremost, a crystalline Zr2 Cu super cell containing more than 15,0 0 0 atoms was constructed, heated to molten state and equilibrated for 2 ns at 2500 K under zero applied pressure to obtain a liquid model. Subsequently, an MG model was fabricated by vitrifying the Zr2 Cu melt at a constant cooling rate of 1010 K/s in the NPT (constant number of particles, pressure, and temperature) ensemble [37], which performed time integration on Nose–Hoover style non-Hamiltonian equations. As a result, a relatively stable amorphous prototype was constructed. This MG model was replicated sixteen times to obtain a larger amorphous model, which was further relaxed for 2 ns at 300 K to avoid the boundary effect. Subsequently, four tetragonal holes with a size of 3.2 nm × 3.2 nm × 6.7 nm were created near the central region of the amorphous structure, by removing the atoms involved. Then, four Zr2 Cu nanocrystal grains with the same size of these holes were inserted into the MG model. The nanocrystalline-amorphous boundary is along the (100) crystal face, where there exists a correspondingly large interplanar spacing that would allow the spontaneous diffusion of atoms between the nanocrystalline and the amorphous regions. The problem of a potential overlap that may arise between various atoms and those at the boundary was addressed by merging an atomic pair into one atom provided their central distance is smaller than one-half the sum of their atomic radii. This model was further relaxed for another 2 ns to avoid an atomic mismatch at the boundaries between the amorphous matrix and the nanocrystal grains. Finally, a representative Zr2 Cu ANA model with a total size of 16.8 nm × 16.8 nm × 16.8 nm, was successfully constructed. The model contains more than 240,0 0 0 atoms, and it is as shown in Fig. 1.
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2.3. Collision cascades To simulate an irradiation event in MD, a primary knock-on atom (PKA) with a positive kinetic energy was required, which was determined by evaluating the projected range of Zr ion in the model of Zr2 Cu amorphous composition via the binary collision approximation code SRIM (The Stopping and Range of Ions in Matter) [38]. In addition, it was required that the PKA should not re-enter the simulation cell through the periodic boundaries. The longest distance of the Zr2 Cu ANA model is about 29.1 nm in the diagonal direction of this model. Therefore, a “hypothetical” Zr PKA with a suitable energy of 12.2 keV was adopted, because it has a maximal projected range of about 28 nm. This PKA was set at the corner of this model, and its direction of motion is along the diagonal. Three-dimensional periodic boundary conditions were applied, the atomic equations of motion were integrated in the NVE (constant number of particles, volume, and energy) ensemble [39], and a variable, dynamically adjusted integration time step was employed. Collision cascades were triggered by this PKA through which a number of atoms were collided, and moved in this model, lasting for not more than 15.0 ps. This was required to stimulate and cause structural instability the model. After the collision cascades period, the NVE was not required to simulate the cooling process of this MD model [40], but was further simulated in the NPT ensemble with a constant time step of 2 fs, lasting for 20 ns. Finally, a stable MD model was obtained after structural relaxation.
Fig. 2. Variation of the simulation time step size with the simulation time.
3.2. Zones of collision cascades
3. Results and discussion
To specify the zone where the collision cascades took place in the ANA model, the spatial distribution of all the knocked-on Cu and Zr atoms whose kinetic energies were greater than 0.8 eV, is shown in Fig. 3. Because 0.8 eV is much larger than that caused by the thermal equilibrium, it would be considered as an excessive kinetic energy to set the atoms in motion [40]. In detail, except for the PKA, it is apparent that there is no atom with a kinetic energy larger than 0.8 eV in the model prior to the collision cascades. Therefore, with an increase in simulation time, the PKA will move in this model and collide with some atoms, in the process, forcing more chaotic collisions such that the initial kinetic energy of the PKA is readily transferred to various knocked-on atoms. In other words, all the atoms possessing higher kinetic energies than that indicated by thermal equilibrium, would be knocked-on atoms. In this way, the collision cascades zone is estimated. It was discovered that, as the total simulation time approached 0.3 ps, the range or area of collision cascades correspondingly attained a maximum value. Beyond the stated period of simulation, the number of the knocked-on Cu and Zr atoms decreased gradually and totally disappeared at the simulation time of 15.0 ps, indicating the end of the cascading process.
3.1. Collision cascades period
3.3. Detecting atomic-unfilled spaces
In this work, the total simulation time was 20 ns, which was divided into two parts, i.e., a collision cascades period lasting for 15.0 ps in the NVE ensemble and a cooling or structural relaxation process in the NPT ensemble. The variable time step as a function of the simulation time in the collision cascades period, was plotted in Fig. 2. It is found that the time step changes rapidly during the simulation time of zero to 0.4 ps, indicating the booming of collision cascades. After 0.4 ps, the time step increased much more slowly. This implies that high-energy collisions have been accomplished, while low-energy collisions still exist, in accordance with the suggestion that a chain reaction of atomic displacements (collision cascade) that generates multiple point defects should be a high-energy collision, if the knocked-on atoms must have a kinetic energy larger than 1 keV [48]. To track the structural evolution during the collision cascades period and the cooling or structural relaxation process, some typical snapshots of this model at 0.0 ps, 0.1 ps, 0.2 ps, 0.3 ps, 0.4 ps, 1.0 ps, 15.0 ps, 4.0 ns, and 20.0 ns, were selected for further study.
The as-constructed ANA model can be considered as a composite structure, which is made up of a homogenous amorphous matrix and four nanocrystal grains distributed separately in the amorphous matrix. It is known that the unfilled spaces in an MG are made up of both intrinsic atomic-unfilled spaces and the socalled free volumes [49], which could be detected by the method of a probe sphere [45,46]. In some previous works, it has been revealed that all of the intrinsic unfilled spaces and free volumes were smaller than the size of an atom in the as-prepared MGs [11,40]. However, with reference to the ANA structural model of this study, using the probe sphere method, all vacancies in the nanocrystal grains and vacancy-like defects in the amorphous matrix induced by collision cascades were detected with the exception of the intrinsic atomic-unfilled spaces and free volumes. This is because vacancies or vacancy-like defects are those whose radii ˚ are nearly similar to that of a Cu or Zr atom (1.28 A˚ and 1.58 A),
2.4. Analysis tools In principle, in any condensed matter, a number of atoms can be knocked-on to move and collide with one another, due to particle irradiation and the effect of collision cascades [41]. In this way, one PKA can transfer its kinetic energy to a number of atoms, and in the process, propel them away from their original sites. Eventually, these knocked-on atoms become the interstitial atoms, leaving corresponding vacancies and vacancy-like defects in crystalline alloys and MGs, respectively [6,42–44]. Therefore, it is essential to study the evolution of interstitial atoms, vacancies, or vacancy-like defects in this ANA model. To achieve this, a method for calculating all the unfilled spaces including vacancies, free volumes, or vacancy-like defects [11,40,45,46], and another program (Ovito) for detecting interstitial atoms [47], were employed.
but much larger than that of an intrinsic unfilled space or a free volume [50].
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Fig. 3. Distributions of knocked-on atoms with a kinetic energy larger than 0.8 eV. Representative snapshots of this model are shown, at the simulation time of (a) 0.0 ps, (b) 0.1 ps, (c) 0.2 ps, (d) 0.3 ps, (e) 0.4 ps, (f) 1.0 ps, (g) 15.0 ps, and (h) 20.0 ns. The grey and the red spheres denote the Zr and the Cu atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Relationship between the free volumes fraction and the simulation time in the ANA model, by simulating in the NVE ensemble (left panel) and the NPT ensemble (right panel).
3.4. Evolution of free volumes in the ANA model In this ANA model, the amorphous matrix has a large atomic fraction more than 95%, so that the zone of collision cascades is mainly involved in the amorphous zone. In our previous work, it was revealed that neutron irradiation-induced, vacancy-like defects were unstable and are easily transformed into free volumes. Subsequently, free volumes were found to rearrange themselves during the cooling or structural relaxation process, resulting into a selfhealing behavior in amorphous alloys [11]. Therefore, it may be assumed that free volumes could also be an indicator of irradiationinduced structural changes in the ANA model, and in particular, in the amorphous matrix. Fig. 4 shows the relationship between the fraction of free volumes in this model and the simulation time. It is found that the fraction of free volumes dramatically changes during the collision cascades period. In general, the fraction of free volumes increases rapidly at the early stage of the collision cascades, implying that, if many atoms are knocked-on by the PKA, a number of irradiation-induced defects would appear, accompa-
nied with more free volumes. However, the free volumes fraction drops down instantly as from the simulation time of 1.3 ps, indicating that a decrease of atomic-unfilled spaces has occurred, probably because many knocked-on atoms in the collision cascades had stopped moving. In addition, it is worth noting that the fraction of free volumes barely changes from the simulation time of 3.0 ps, until the end of the collision cascades period, probably because there were a few knocked-on atoms that could move during this process. It is interesting to note that, after the collision cascades period, the free volumes fraction continues to decrease. It has been proposed that a free volume is very likely to be annihilated when cooling a metallic melt or a high-temperature amorphous alloy [51]. In this work, the amorphous matrix possessed a high temperature during the collision cascades period, and was cooled by further MD simulation in the NPT ensemble. Therefore, it is reasonable to state that free volumes are reduced when the ANA model is quenched. In addition, as from the simulation time of 8.0 ns, the cooling stage was stopped and the fraction of free volumes no longer decreased. From then on, the model went into structural relaxation in order to achieve a new balance of structure and energy. In the structural relaxation process, free volumes cannot be annihilated anymore, giving rise to a saturation value of free volumes. Notably, the saturation value which is about 2% is quite similar to that of the as-constructed ANA model; and since a free volume is an indicator of a structural change in an amorphous model, specifically in the ANA model, it may be implied that this ANA model has an effective self-healing behavior against irradiation. 3.5. Evolution of atomic-unfilled spaces near the phase boundaries 3.5.1. Phase boundaries in an intercepted ANA model In principle, in a nanocrystal alloy, irradiation-induced vacancies inside the grains are not stable, hence they would migrate towards and sink at the GBs, unless they are healed by interstitial atoms [7,52]. However, since there are phase boundaries rather than GBs in this ANA composite structure, it would be interesting to discover the phenomena that governs the ability of the amorphous-nanocrystal phase boundaries in an ANA model to either absorb or capture vacancies, in similarity to the behavior of GBs in (nano)crystal alloys. This is crucial to determining whether the phase boundaries influence the irradiation-induced
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Fig. 5. The top and cross-sectional views of an as-constructed intercepted ANA model. The green lines denote the boundaries between the nanocrystal grain and its neighboring amorphous zone. The grey and the red spheres denote the Zr and the Cu atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
defects through a yet-to-be identified mechanism. Therefore, it is of utmost importance to study the evolution of atomic-unfilled spaces including vacancies, vacancy-like defects, and free volumes that are close to the phase boundaries. In this vein, an intercepted ANA model with a size of about 4.8 nm × 4.8 nm × 7.0 nm shown in Fig. 5 was selected. It is made up of a nanocrystal grain along with its neighboring amorphous zone and it is evident that phase boundaries exist between the two structures. In this work, each phase boundary was determined by finding the border between the periodic atomic packing in the nanocrystalline structure and the random atomic packing in the amorphous region. 3.5.2. 3D distribution of unfilled spaces in an intercepted ANA model Fig. 6 shows the distribution of atomic-unfilled spaces with a radius larger than 0.8 A˚ in the intercepted ANA model. It is highly pertinent to state that only the unfilled spaces whose radii are equal or close to 1.28 A˚ and 1.58 A˚ (radii of Cu and Zr atom, respectively) were considered as vacancies in the nanocrystal grain or vacancy-like defects in the amorphous matrix. Intrinsic atomicunfilled spaces are excluded here, because it was revealed that their size is smaller than 0.4 A˚ in the Zr2 Cu composition [11]. Only a few of the free volumes in the amorphous zone rather than in the nanocrystal grain, are shown in Fig. 6(a), implying the absence of vacancies in the as-constructed ANA model. However, from the simulation time of 0.1 ps, collision cascades appear, along with a zone that constitutes both the nanocrystal grain and its neighboring amorphous region. In addition, with the increase of simulation time, there are many vacancies or vacancy-like defects in the zone of collision cascades, accompanied by more and larger free volumes. It is interesting to observe that, after the simulation time of 0.4 ps when the high-energy collisions were almost accomplished, the vacancies or vacancy-like defects rapidly reduced. In a previous work, it was suggested that the irradiation-induced defects in an MG model are very unstable [53], and are readily trans-
formed into large free volumes in the neighborhood [40]. Therefore, this indicates with regard to the current ANA model, that vacancies or vacancy-like defects are also not stable, and the transformation from defect to free volumes also occurred. Vacancies or vacancy-like defects have been fully annihilated at the simulation time of 1.3 ps, leaving a lot of large free volumes in both the nanocrystal zone and the amorphous region. It is well-known that a free volume is a specific structural feature in amorphous materials and do not exist as crystals, hence, it follows from the foregoing that large free volumes in the nanocrystal zone are unstable and are likely to be annihilated or transformed into small ones [11]. As the structural model was cooled and relaxed at the simulation time of 20.0 ns, surprisingly, only a few of the large free volumes were found in the amorphous zone of the intercepted ANA model. At the very least, not even a small or negligible free volume can be found in the nanocrystal grain. This is similar in characteristics to that of the as-constructed model, implying a highly effective self-healing phenomenon in the intercepted ANA model. Therefore, since this intercepted ANA model is the region mostly affected by the collision cascades, it is suggested that other parts of the ANA model probably possess a higher self-healing efficiency.
3.5.3. Size distributions of unfilled spaces in an intercepted ANA model Fig. 7 shows the size distributions of atomic-unfilled spaces in the intercepted ANA model. It is worth noting that, during the early stage of the collision cascades, the number of small atomic˚ decreased with the simula˚ < r < 0.6 A) unfilled spaces (0 A ˚ marginally intion time, while that of larger ones (r > 0.6 A) creased, indicating that large free volumes are induced by the collision cascades. However, when more and more knocked-on atoms have stopped moving, large free volumes are decreased with the
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Fig. 6. 3D distributions of the atomic-unfilled spaces with a radius larger than 0.8 A˚ from the snapshots of the intercepted ANA model, at the simulation time of (a) 0.0 ps, (b) 0.1 ps, (c) 0.2 ps, (d) 0.3 ps, (e) 0.4 ps, (f) 1.0 ps, (g) 1.3 ps, (h) 15.0 ps, and (I) 20.0 ns. The red spheres denote the vacancies or vacancy-like defects, and the green spheres stand for the large free volumes. The blue dashed frame represents the initial region of the nanocrystal grain. (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. 7. Distributions of atomic-unfilled spaces with different size ranges, from the snapshots of the intercepted ANA model, at the simulation time of 0.0 ps, 0.1 ps, 0.2 ps, 0.3 ps, 0.4 ps, 1.0 ps, 1.3 ps, 15.0 ps, and 20.0 ns.
smaller ones increasing instead, because large free volumes are readily transformed into small ones. In addition, the evolutions ˚ and vacancies or ˚ < r < 1.28 A) of the large free volumes (0.8 A vacancy-like defects are shown in Fig. 7(b). It is found that both of them increased at the early stage of collision cascades, but subsequently were decreased after the booming of collision cascades. Most importantly, vacancies or vacancy-like defects were annihilated, due to their transformation to free volumes. Large free volumes continued to decrease till the end of structural relaxation of this model which also indicates that the structural selfhealing behavior in the ANA model, is consistent with that shown in Fig. 6. 3.6. The role of phase boundaries in defects annihilation It has been reported that, in order to achieve a new structural and energetic balance in (nano)crystalline materials subjected to irradiation effects, some residual vacancies would have to migrate towards and sink at the GBs [54,55]. Conversely, for amorphous alloys, it was revealed that the irradiation-induced defects are rapidly and fully annihilated by a concurrent compression of neighboring atoms, leading to the rearrangement of free volumes [11,40]. In similarity to the aforementioned, it was found for the ANA model that, the irradiation-induced defects are not stable, but were rapidly and fully annihilated, like those in MG materials. However, unlike in the MG models, phase boundaries were found between the nanocrystal grain and the amorphous matrix. This raises a serious question as to whether a new mechanism is responsible for the annihilation of defects in ANA materials and if so, does the phase boundary in any way play a role in the healing of defects? To address these issues, the evolutions of irradiationinduced defects as well as amorphous-crystal boundaries in the intercepted ANA model, are shown in Fig. 8. It is found that, at the early stage of collision cascades, there were some irradiationinduced vacancies in the nanocrystal grain and vacancy-like defects in the neighboring amorphous zone and it is interesting to note that most of them disappeared instantaneously. In particular, vacancies in the nanocrystal grain are fully annihilated at a very short time of about 0.8 ps, which is much smaller than the time that interstitials are emitted from GBs to heal the vacancies or vacancies themselves migrant to the GBs [6]. In other words, vacancies hardly change their positions at a short time less than 1.0 ps [6]. Therefore, it is thought-provoking how these vacancies
were annihilated. However, it could be readily observed that the amorphous-crystal boundary dramatically changes with the simulation time. Hence, there is a tendency that this boundary will advance towards the crystal zone. Interestingly, it seemed that vacancies create points of arrests to capture the phase boundary in motion. Therefore, once a vacancy makes contact with the phase boundary, it is instantaneously and totally annihilated. This indicates a new mechanism for the healing of defects in the ANA model, which is a different phenomenon from what is known to govern in (nano)crystals or amorphous alloys. At the simulation time of 0.8 ps, the last vacancy is annihilated by the phase boundary. From this point and onwards the phase boundary no longer advances towards the crystal zone, but surprisingly changes its direction towards the amorphous region. This novel characteristic feature indicates an effective self-healing of the nanocrystal grain. In a previous work, it was suggested that irradiation would induce some melted local regions in an MG model, which, subsequently are easily transformed into amorphous solid by quenching at an ultra-high cooling rate, leading to the well-known superquenched effect [56]. Therefore, because the atomic kinetic energy could be calculated in the ANA model, some melted local regions were estimated accordingly, by applying a method developed in a previous work [41], which indicates a relationship between the temperature and the kinetic energy,
E=
3 kT 2
(1)
Where, E, k, and T are the kinetic energy, the Boltzmann constant (1.380649 × 10−23 J/K), and the temperature, respectively. According to the heating process of the MD simulation, the melting temperature of this Zr2 Cu model was estimated to be about 1800 K, corresponding to an average kinetic energy of 0.234 eV for each atom. Therefore, all the atoms with a kinetic energy larger than 0.234 eV were selected, and the temperature of the zone filled with these atoms was calculated. In this way, a liquid region was estimated. The estimated liquid region in some typical snapshots of the intercepted ANA model, as well as its average temperature are shown in Fig. 9. It is found that the nanocrystalline-liquid border is roughly consistent with the nanocrystalline-amorphous boundary, suggesting that the nanocrystalline-amorphous boundary is determined by the liquid phase at high temperatures. When the liquid region disappeared during the quenching, the nanocrystalline-amorphous boundary
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Fig. 8. Evolutions of the amorphous-crystal phase boundaries and the irradiation-induced vacancies (blue spheres) in nanocrystal grain and vacancy-like defects (brown spheres) in amorphous matrix, of the intercepted ANA model. Various snapshots of this model are shown, at the simulation time of (a) 0.0 ps, (b) 0.2 ps, (c) 0.4 ps, (d) 0.6 ps, (e) 0.8 ps, (f) 1.3 ps, (g) 4.0 ns, and (h) 20.0 ns. The black, the red, and the blue lines, denote the phase boundaries at the simulation time of 0.0 ps, 0.8 ps, and 20.0 ns, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
still advanced towards the amorphous region, suggesting a transformation between the nanocrystalline and amorphous phases, occurring probably due to the relaxation of the ANA model. In addition, it could be inferred that the motion of the amorphous-crystal boundary at high temperatures is due to the expansion of melted regions in the intercepted ANA model. At the tail end of the collision cascades period, the melted regions began
to quench automatically. Based on this scenario, it may be readily deduced that the cooling rate of melted local regions in the intercepted ANA model is much lower than those of an amorphous zone located far away from the nanocrystal region. In other words, there is no super-quenched effect in the intercepted ANA model. It is known that an intrinsic competition exists between the crystal and the amorphous solid phases during the quenching of a metallic
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Fig. 9. The estimated liquid region in the intercepted ANA model, as well as its average temperature calculated in the snapshots at the simulation time of (a) 0.2 ps, (b) 0.4 ps, (c) 0.6 ps, and (d) 0.8 ps. The green dashed line and the red solid line denote the nano-crystalline boundary and the border of the liquid region, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 10. Evolution of two interstitial atoms (purple spheres) that originated from the nanocrystal grain. Representative snapshots are shown, at the simulation time of (a) 0.0 ps, (b) 0.2 ps, (c) 0.4 ps, (d) 0.6 ps, (e) 0.8 ps, (f) 1.3 ps, (g) 4.0 ns, and (h) 20.0 ns. The green line is the nanocrystal-amorphous boundary in each model snapshot. Note that only the atoms in the initial nanocrystal grain are shown here. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
melt [57,58], and that, which is significantly affected by the cooling rate; hence, the nanocrystal phase is competitive during the quenching of the melted local regions at a relatively low cooling rate. As a result, some parts of the melted local regions in the intercepted ANA model transform into the nanocrystal phase, leading to the self-healing of the nanocrystal grain.
3.7. Arrest of interstitial atoms It is known that a point defect is made up of a pair of a vacancy and an interstitial atom. During the collision cascades period, numerous atoms were knocked-on to become the interstitials, leaving in their wake, a myriad of vacancies at their initial positions, to es-
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tablish that some point defects were induced by irradiation. Previously, it has been reported that both the vacancies and interstitials are unstable, such that most of the point defects are rapidly annihilated, leading to the self-healing effect [59]. In crystalline materials, some residual vacancies and interstitials are very likely to be arrested at the GBs, in order to achieve a new balance of structure and energy. To a large extent, it is germane to remark that it is a profound discovery to observe that vacancies or vacancy-like defects were fully and rapidly annihilated during the collision cascades period. Regardless, it remains a further challenge to determine the implications of this phenomenon on knocked-on atoms, and in particular, on the interstitial atoms in the nano-grain. To resolve this complexity, the program of Ovito was implemented to capture the position and kinetic energy of each atom in the ANA model in order to track the motions of the knocked-on atoms. Concerning the intercepted ANA model which was significantly affected by the collision cascades, it was revealed that the amorphous-nanocrystal boundary changes with the simulation time. Therefore, the knocked-on atoms in the collision cascades were separated by this phase boundary. It could be stated that only those knocked-on atoms located in the nanocrystal grain may be strictly considered as interstitials, because a crystal lattice that exists in the nanocrystal grain, is absent in the amorphous matrix. Furthermore, it was observed that no knocked-on atom could penetrate the phase boundary during the entire simulation. However, in general, a number of knocked-on atoms that possess some positive velocity and could move in the model, were either arrested in some short-range local regions or absorbed at the phase boundaries. As a result, there is no knocked-on atom originating from the amorphous region that could penetrate the boundaries. Thus, it may be stated unequivocally, that the phase boundaries in the ANA model play the role of an absorber of knocked-on atoms, like those of the GBs in crystalline materials. Nonetheless, it was astounding to note that several interstitial atoms that originated from the nanocrystal grain successfully passed through the phase boundaries. To analyze this scenario, the evolutions of the positions and kinetic energies of interstitial atoms were studied and are as shown in Fig. 10. From thence, it could be inferred that two Zr interstitial atoms penetrated the boundaries rapidly at the onset of the collision cascades. These are the Zr1 and Zr2 atoms. Interestingly, it was observed that the Zr1 atom was quickly arrested in the local region of the amorphous matrix and its kinetic energy transferred to the neighboring atoms in the process. At the end of collision cascades period, the energy of this atom is negligible (less than 0.1 eV) retarding its motion and preventing it from escaping from the local region. On the other hand, it is significant to note that the kinetic energy of the Zr2 atom increased rapidly to 1.1 eV, due to the collisions with other atoms in the amorphous zone. Hence, the Zr2 atom was not arrested in any local region, but rather, it advanced to the phase boundaries. Previously, it had been stated that the diffusion energy for an interstitial to move and sink at the GB is about 0.1 eV [6]. Therefore, it follows that the Zr2 atom could only reach the phase boundary because its kinetic energy is greater than its diffusion energy. Fig. 10 showed a depiction of this scenario, indicating how the energy of the Zr2 atom was decreasing rapidly during its motion, causing it to be spontaneously arrested at the boundary. In general, during the collision cascades period, the process of atomic diffusion was not established between the nanocrystal grain and the neighboring amorphous zone, because at the phase boundaries, most of the knocked-on atoms were easily absorbed. 4. Conclusions The atomic-scale structural evolution of a nanocrystalamorphous alloy model has been investigated using an MD
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simulation coupled with a series of calculations. The following inferences can be drawn from the study: (1) The evolution of free volume indicates that, free volumes can spontaneously and fully recover after the cooling and structural relaxation processes, regardless of the complex behavior exhibited under the collision cascades phenomenon. This suggests that ANA materials possess a high resistance to neutron irradiation. (2) Unlike what is generally observed in (nano)crystalline materials or amorphous alloys, a novel and unique mechanism is found regarding ANA materials, which suggests that irradiation-induced vacancies are rapidly and fully annihilated at the boundary existing between the nanocrystal grain and its neighboring amorphous zone. (3) The nanocrystal-amorphous boundary is driven by the expansion of melted local regions towards the nanocrystal region. Some of these melted local regions are then transformed into the nanocrystal phase during the cooling process, indicating an effective self-healing behavior of the nanocrystal grain. (4) There is virtually no atomic diffusion effect between the nanocrystal grain and the neighboring amorphous zone, because most of the knocked-on atoms were spontaneously and readily absorbed by the phase boundary. Declaration of Competing Interest There are no conflicts to declare. Acknowledgements Financial supports from the National Natural Science Foundation of China (Grant No. 51471088) and the Fundamental Research Funds for the Central Universities (Grant No. NE2015004), are gratefully acknowledged. References [1] C.C. Fu, J.D. Torre, F. Willaime, J.L. Bocquet, A. Barbu, Multiscale modelling of defect kinetics in irradiated iron, Nat. Mater. 4 (2004) 68–74. [2] P. Yvon, F. Carre, Structural materials challenges for advanced reactor systems, J. Nucl. Mater. 385 (2009) 217–222. [3] S.J. Zinkle, G.S. Was, Materials challenges in nuclear energy, Acta Mater. 61 (2013) 735–758. [4] T.D.D.L. Rubia, H.M. Zbib, T.A. Khraishi, B.D. Wirth, M. Victoria, M.J. Caturla, Multiscale modelling of plastic flow localization in irradiated materials, Nature 406 (20 0 0) 871–874. [5] K.E. Sickafus, R.W. Grimes, J.A. Valdez, C. Antony, M. Tang, I. Manabu, S.M. Corish, C.R. Stanek, B.P. Uberuaga, Radiation-induced amorphization resistance and radiation tolerance in structurally related oxides, Nat. Mater. 6 (2007) 217–223. [6] X.M. Bai, A.F. Voter, R.G. Hoagland, N. Michael, B.P. Uberuaga, Efficient annealing of radiation damage near grain boundaries via interstitial emission, Science 327 (2010) 1631–1634. [7] Y. Chimi, A. Iwase, N. Ishikawa, A. Kobiyama, T. Inami, S. Okuda, Accumulation and recovery of defects in ion-irradiated nanocrystalline gold, J. Nucl. Mater. 297 (2001) 355–357. [8] A.L. Greer, Confusion by design, Nature 366 (1993) 303–304. [9] W.L. Johnson, Bulk glass-forming metallic alloys: science and technology, MRS Bull. 24 (1999) 42–56. [10] Q.S. Zeng, et al., General 2.5 power law of metallic glasses, Proc. Natl. Acad. Sci. 113 (2016) 1714–1718. [11] L. Yang, et al., Structural responses of metallic glasses under neutron irradiation, Sci. Rep. 7 (2017) 16739. [12] X.N. Zhang, X.X. Mei, Q. Zhang, X.N. Li, Y.M. Wang, Y.N. Wang, Study of irradiation damage induced by He2+ ion irradiation in Ni62 Ta38 metallic glass and W metal, Nucl. Instrum. Methods Phys. Res. Sect. B 406 (2017) 548–554. [13] J.A. Shi, C.R. Cao, Q.H. Zhang, Y.T. Sun, C. Wang, W.H. Wang, H.Y. Bai, L. Gu, In situ atomic level observations of Al2 O3 forming on surface of metallic glasses, Scr. Mater. 136 (2017) 68–73. [14] Z. Fan, Q. Li, J. Li, S.C. Xue, H.Y. Wang, X.H. Zhang, Tailoring plasticity of metallic glasses via interfaces in Cu/amorphous CuNb laminates, J. Mater. Res. 32 (2017) 2680–2689.
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Full length article
Microstructural evolution in amorphous-nanocrystalline ZrCu alloy under neutron irradiation Fan Xiong a, Ming-Fei Li a, Babafemi Malomo b, Liang Yang a,∗ a b
College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China Department of Mechanical Engineering, Obafemi Awolowo University, Ile-Ife, Nigeria
a r t i c l e
i n f o
Article history: Received 16 August 2019 Revised 8 October 2019 Accepted 11 October 2019 Available online 23 October 2019 Keywords: Irradiation effect Molecular dynamics Metallic glass Vacancies Self-healing
a b s t r a c t An extensive investigation on the microstructural evolution of an amorphous-nanocrystalline alloy (ANA) under neutron irradiation has been conducted by molecular dynamics simulation. The phenomenon of rapid and full annihilation of irradiation-induced vacancies was found in the nanocrystal zone and after structural relaxation, free volumes in the amorphous matrix were systematically self-recovered. An effective self-healing behavior of the nanocrystal zone subsequently sufficed, regardless of the thermal degradation effect caused by the intensity of collision cascades during quenching. As knocked-on atoms were arrested at the phase boundary, it is self-evident that, the mechanism of atomic diffusion was nonexistent at the interface between the nanocrystal grain and the neighboring amorphous zone. Consequently, from the foregoing, ANA materials have been found to demonstrate excellent resistance to neutron irradiation and prospectively, the results of this study will potentially facilitate the development of advanced materials with high irradiation resistance. © 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction The effect of particle irradiation changes in nuclear structural materials occurring at the micro-macroscopic transition scale is mostly responsible for their incipient failures in nuclear power applications [1]. The most commonly found nuclear structural materials are the Fe-, Zr-, and Ni-based crystalline alloys, possessing excellent mechanical and thermal properties [2,3]. In spite of this, the effect of structural damage and/or performance degradation is significant under particle irradiation and specifically, neutron irradiation over an extended period in service, leading to swelling, hardening, amorphization, embrittlement, etc [4,5]. The cumulative effect of these defects poses a serious threat to the safety, efficiency and longevity of operation of nuclear plants. Hence, it is highly imperative to design novel nuclear structural materials with high resistance to neutron irradiation damage. In the last decade and up until now, nanomaterials have been experiencing a rapid and burgeoning development which have drawn extensive scientific research attention from where it had been revealed that such advanced materials may possess excellent resistance to neutron irradiation. Bai et al. [6] recently carried out
∗
Corresponding author. E-mail address: [email protected] (L. Yang).
https://doi.org/10.1016/j.actamat.2019.10.026 1359-6454/© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
a theoretical study on the essential mechanisms of the self-healing behavior in nanocrystal metals, where it was discovered that, the grain boundaries (GBs) in a nano-scale copper model, contrary to traditional crystal materials do possess an unusual “loading and unloading” capacity to heal the irradiation-induced point defects, resulting in an enhanced irradiation resistance [7]. As the quest, for exceptional material performance in the nuclear industry continues to gain traction, a new class of alloy materials, known as the metallic glass (MG) is now the subject of an expanding and intense research interest, because of its unique properties such as, the high fracture strength, high hardness, high elastic limit, high fracture toughness, as well as amorphous features [8–10]. Recently, it has been reported that in comparison with crystalline alloys, MGs demonstrate a higher or complete self-healing efficiency in their microstructures [11], which is probably so, because they are not subject to the structural conditions (e.g. unit cells, GBs, dislocations, etc.) required to sink or arrest irradiation-induced interstitials or vacancies [9,12,13]. This implies that MGs may likely possess a high resistance against neutron irradiation. However, in spite of their attractive aforementioned attribute, MGs exhibit poor plasticity and as an implication are not the candidate structural materials in nuclear applications [14,15]. From a thermodynamic standpoint, MGs are classified as nonequilibrium materials, which implies that they can be transformed
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Fig. 1. Configurations of (a) the Zr2 Cu ANA model and (b) the four inserted nanocrystal grains. The grey and the red spheres denote the Zr and the Cu atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
into crystalline alloys. Therefore, based on MG materials, nanocrystalline alloys or amorphous-nanocrystalline composite alloys with excellent physical, chemical, and mechanical properties can be developed [16,17]. Moreover, now that it has been revealed that the precipitation of nanocrystal grains in the amorphous matrix could greatly enhance the strength and toughness of MGs [18,19]. It is an arguable assumption that the amorphous-nanocrystalline alloys (ANAs) probably would possess an excellent resistance to neutron irradiation since they are mixtures of MGs and nanocrystals grains, both of which have been confirmed to possess high irradiation resistance [6,11]. At any rate, the foregoing innuendos show that MGs are indeed a class of promising advanced materials justifying the need for a robust research interest on their applications. Recent research investigations have shown that nanocrystal grains have been employed in the study of the mechanical and magnetic properties of MGs, where the effects of neutron irradiation on ANAs remain largely unknown and unresolved [20,21]. This current work draws motivation from the preceding argument, and it seeks to investigate the microstructural evolution in ANAs under neutron irradiation through a series of molecular dynamics (MD) simulations and calculations with a view to determining the resistance to neutron irradiation in ANA materials.
2. Simulation methods 2.1. System selection It is known that Zr-based crystalline alloys (such as Zr-2 and Zr4) have been widely applied as nuclear structural materials [22], and many Zr-based ANAs (e.g. Zr–Cu, Zr–Cu–Ni, Zr–Cu–Ti, Zr–Cu– Ni–Al, Zr–Cu–Ni–Ti–Be–C etc.) can be fabricated, by isothermal annealing [23,24], ion irradiation [25,26], and by other techniques [27]. Specifically, Zr–Cu is a typical binary alloy system available for studying the microstructure [28], because it has a broad composition region (30–80 at% for Zr) forming MGs [29]. In this work, a Zr-rich composition alloy, Zr2 Cu, was selected as the research prototype, because it has been revealed that Zr2 Cu nanocrystal grains with the perfect C11b configuration (one of body-centered cubic structures) can be precipitated in the Zr2 Cu amorphous matrix, forming the ANA material [30].
2.2. Construction of an ANA model An MD simulation was performed to build the Zr2 Cu ANA model using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package [31]. The interatomic interactions were described by the embedded atom method (EAM) potential developed by Mendelev et al. [32], which is suitable for studying both amorphous and crystalline materials [33–35]. In addition, the short-range part of the potential employed was smoothly joined by the Ziegler–Biersack–Littmark (ZBL) function [36], so that the microstructural evolution of this model under irradiation could be simulated. First and foremost, a crystalline Zr2 Cu super cell containing more than 15,0 0 0 atoms was constructed, heated to molten state and equilibrated for 2 ns at 2500 K under zero applied pressure to obtain a liquid model. Subsequently, an MG model was fabricated by vitrifying the Zr2 Cu melt at a constant cooling rate of 1010 K/s in the NPT (constant number of particles, pressure, and temperature) ensemble [37], which performed time integration on Nose–Hoover style non-Hamiltonian equations. As a result, a relatively stable amorphous prototype was constructed. This MG model was replicated sixteen times to obtain a larger amorphous model, which was further relaxed for 2 ns at 300 K to avoid the boundary effect. Subsequently, four tetragonal holes with a size of 3.2 nm × 3.2 nm × 6.7 nm were created near the central region of the amorphous structure, by removing the atoms involved. Then, four Zr2 Cu nanocrystal grains with the same size of these holes were inserted into the MG model. The nanocrystalline-amorphous boundary is along the (100) crystal face, where there exists a correspondingly large interplanar spacing that would allow the spontaneous diffusion of atoms between the nanocrystalline and the amorphous regions. The problem of a potential overlap that may arise between various atoms and those at the boundary was addressed by merging an atomic pair into one atom provided their central distance is smaller than one-half the sum of their atomic radii. This model was further relaxed for another 2 ns to avoid an atomic mismatch at the boundaries between the amorphous matrix and the nanocrystal grains. Finally, a representative Zr2 Cu ANA model with a total size of 16.8 nm × 16.8 nm × 16.8 nm, was successfully constructed. The model contains more than 240,0 0 0 atoms, and it is as shown in Fig. 1.
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2.3. Collision cascades To simulate an irradiation event in MD, a primary knock-on atom (PKA) with a positive kinetic energy was required, which was determined by evaluating the projected range of Zr ion in the model of Zr2 Cu amorphous composition via the binary collision approximation code SRIM (The Stopping and Range of Ions in Matter) [38]. In addition, it was required that the PKA should not re-enter the simulation cell through the periodic boundaries. The longest distance of the Zr2 Cu ANA model is about 29.1 nm in the diagonal direction of this model. Therefore, a “hypothetical” Zr PKA with a suitable energy of 12.2 keV was adopted, because it has a maximal projected range of about 28 nm. This PKA was set at the corner of this model, and its direction of motion is along the diagonal. Three-dimensional periodic boundary conditions were applied, the atomic equations of motion were integrated in the NVE (constant number of particles, volume, and energy) ensemble [39], and a variable, dynamically adjusted integration time step was employed. Collision cascades were triggered by this PKA through which a number of atoms were collided, and moved in this model, lasting for not more than 15.0 ps. This was required to stimulate and cause structural instability the model. After the collision cascades period, the NVE was not required to simulate the cooling process of this MD model [40], but was further simulated in the NPT ensemble with a constant time step of 2 fs, lasting for 20 ns. Finally, a stable MD model was obtained after structural relaxation.
Fig. 2. Variation of the simulation time step size with the simulation time.
3.2. Zones of collision cascades
3. Results and discussion
To specify the zone where the collision cascades took place in the ANA model, the spatial distribution of all the knocked-on Cu and Zr atoms whose kinetic energies were greater than 0.8 eV, is shown in Fig. 3. Because 0.8 eV is much larger than that caused by the thermal equilibrium, it would be considered as an excessive kinetic energy to set the atoms in motion [40]. In detail, except for the PKA, it is apparent that there is no atom with a kinetic energy larger than 0.8 eV in the model prior to the collision cascades. Therefore, with an increase in simulation time, the PKA will move in this model and collide with some atoms, in the process, forcing more chaotic collisions such that the initial kinetic energy of the PKA is readily transferred to various knocked-on atoms. In other words, all the atoms possessing higher kinetic energies than that indicated by thermal equilibrium, would be knocked-on atoms. In this way, the collision cascades zone is estimated. It was discovered that, as the total simulation time approached 0.3 ps, the range or area of collision cascades correspondingly attained a maximum value. Beyond the stated period of simulation, the number of the knocked-on Cu and Zr atoms decreased gradually and totally disappeared at the simulation time of 15.0 ps, indicating the end of the cascading process.
3.1. Collision cascades period
3.3. Detecting atomic-unfilled spaces
In this work, the total simulation time was 20 ns, which was divided into two parts, i.e., a collision cascades period lasting for 15.0 ps in the NVE ensemble and a cooling or structural relaxation process in the NPT ensemble. The variable time step as a function of the simulation time in the collision cascades period, was plotted in Fig. 2. It is found that the time step changes rapidly during the simulation time of zero to 0.4 ps, indicating the booming of collision cascades. After 0.4 ps, the time step increased much more slowly. This implies that high-energy collisions have been accomplished, while low-energy collisions still exist, in accordance with the suggestion that a chain reaction of atomic displacements (collision cascade) that generates multiple point defects should be a high-energy collision, if the knocked-on atoms must have a kinetic energy larger than 1 keV [48]. To track the structural evolution during the collision cascades period and the cooling or structural relaxation process, some typical snapshots of this model at 0.0 ps, 0.1 ps, 0.2 ps, 0.3 ps, 0.4 ps, 1.0 ps, 15.0 ps, 4.0 ns, and 20.0 ns, were selected for further study.
The as-constructed ANA model can be considered as a composite structure, which is made up of a homogenous amorphous matrix and four nanocrystal grains distributed separately in the amorphous matrix. It is known that the unfilled spaces in an MG are made up of both intrinsic atomic-unfilled spaces and the socalled free volumes [49], which could be detected by the method of a probe sphere [45,46]. In some previous works, it has been revealed that all of the intrinsic unfilled spaces and free volumes were smaller than the size of an atom in the as-prepared MGs [11,40]. However, with reference to the ANA structural model of this study, using the probe sphere method, all vacancies in the nanocrystal grains and vacancy-like defects in the amorphous matrix induced by collision cascades were detected with the exception of the intrinsic atomic-unfilled spaces and free volumes. This is because vacancies or vacancy-like defects are those whose radii ˚ are nearly similar to that of a Cu or Zr atom (1.28 A˚ and 1.58 A),
2.4. Analysis tools In principle, in any condensed matter, a number of atoms can be knocked-on to move and collide with one another, due to particle irradiation and the effect of collision cascades [41]. In this way, one PKA can transfer its kinetic energy to a number of atoms, and in the process, propel them away from their original sites. Eventually, these knocked-on atoms become the interstitial atoms, leaving corresponding vacancies and vacancy-like defects in crystalline alloys and MGs, respectively [6,42–44]. Therefore, it is essential to study the evolution of interstitial atoms, vacancies, or vacancy-like defects in this ANA model. To achieve this, a method for calculating all the unfilled spaces including vacancies, free volumes, or vacancy-like defects [11,40,45,46], and another program (Ovito) for detecting interstitial atoms [47], were employed.
but much larger than that of an intrinsic unfilled space or a free volume [50].
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Fig. 3. Distributions of knocked-on atoms with a kinetic energy larger than 0.8 eV. Representative snapshots of this model are shown, at the simulation time of (a) 0.0 ps, (b) 0.1 ps, (c) 0.2 ps, (d) 0.3 ps, (e) 0.4 ps, (f) 1.0 ps, (g) 15.0 ps, and (h) 20.0 ns. The grey and the red spheres denote the Zr and the Cu atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Relationship between the free volumes fraction and the simulation time in the ANA model, by simulating in the NVE ensemble (left panel) and the NPT ensemble (right panel).
3.4. Evolution of free volumes in the ANA model In this ANA model, the amorphous matrix has a large atomic fraction more than 95%, so that the zone of collision cascades is mainly involved in the amorphous zone. In our previous work, it was revealed that neutron irradiation-induced, vacancy-like defects were unstable and are easily transformed into free volumes. Subsequently, free volumes were found to rearrange themselves during the cooling or structural relaxation process, resulting into a selfhealing behavior in amorphous alloys [11]. Therefore, it may be assumed that free volumes could also be an indicator of irradiationinduced structural changes in the ANA model, and in particular, in the amorphous matrix. Fig. 4 shows the relationship between the fraction of free volumes in this model and the simulation time. It is found that the fraction of free volumes dramatically changes during the collision cascades period. In general, the fraction of free volumes increases rapidly at the early stage of the collision cascades, implying that, if many atoms are knocked-on by the PKA, a number of irradiation-induced defects would appear, accompa-
nied with more free volumes. However, the free volumes fraction drops down instantly as from the simulation time of 1.3 ps, indicating that a decrease of atomic-unfilled spaces has occurred, probably because many knocked-on atoms in the collision cascades had stopped moving. In addition, it is worth noting that the fraction of free volumes barely changes from the simulation time of 3.0 ps, until the end of the collision cascades period, probably because there were a few knocked-on atoms that could move during this process. It is interesting to note that, after the collision cascades period, the free volumes fraction continues to decrease. It has been proposed that a free volume is very likely to be annihilated when cooling a metallic melt or a high-temperature amorphous alloy [51]. In this work, the amorphous matrix possessed a high temperature during the collision cascades period, and was cooled by further MD simulation in the NPT ensemble. Therefore, it is reasonable to state that free volumes are reduced when the ANA model is quenched. In addition, as from the simulation time of 8.0 ns, the cooling stage was stopped and the fraction of free volumes no longer decreased. From then on, the model went into structural relaxation in order to achieve a new balance of structure and energy. In the structural relaxation process, free volumes cannot be annihilated anymore, giving rise to a saturation value of free volumes. Notably, the saturation value which is about 2% is quite similar to that of the as-constructed ANA model; and since a free volume is an indicator of a structural change in an amorphous model, specifically in the ANA model, it may be implied that this ANA model has an effective self-healing behavior against irradiation. 3.5. Evolution of atomic-unfilled spaces near the phase boundaries 3.5.1. Phase boundaries in an intercepted ANA model In principle, in a nanocrystal alloy, irradiation-induced vacancies inside the grains are not stable, hence they would migrate towards and sink at the GBs, unless they are healed by interstitial atoms [7,52]. However, since there are phase boundaries rather than GBs in this ANA composite structure, it would be interesting to discover the phenomena that governs the ability of the amorphous-nanocrystal phase boundaries in an ANA model to either absorb or capture vacancies, in similarity to the behavior of GBs in (nano)crystal alloys. This is crucial to determining whether the phase boundaries influence the irradiation-induced
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Fig. 5. The top and cross-sectional views of an as-constructed intercepted ANA model. The green lines denote the boundaries between the nanocrystal grain and its neighboring amorphous zone. The grey and the red spheres denote the Zr and the Cu atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
defects through a yet-to-be identified mechanism. Therefore, it is of utmost importance to study the evolution of atomic-unfilled spaces including vacancies, vacancy-like defects, and free volumes that are close to the phase boundaries. In this vein, an intercepted ANA model with a size of about 4.8 nm × 4.8 nm × 7.0 nm shown in Fig. 5 was selected. It is made up of a nanocrystal grain along with its neighboring amorphous zone and it is evident that phase boundaries exist between the two structures. In this work, each phase boundary was determined by finding the border between the periodic atomic packing in the nanocrystalline structure and the random atomic packing in the amorphous region. 3.5.2. 3D distribution of unfilled spaces in an intercepted ANA model Fig. 6 shows the distribution of atomic-unfilled spaces with a radius larger than 0.8 A˚ in the intercepted ANA model. It is highly pertinent to state that only the unfilled spaces whose radii are equal or close to 1.28 A˚ and 1.58 A˚ (radii of Cu and Zr atom, respectively) were considered as vacancies in the nanocrystal grain or vacancy-like defects in the amorphous matrix. Intrinsic atomicunfilled spaces are excluded here, because it was revealed that their size is smaller than 0.4 A˚ in the Zr2 Cu composition [11]. Only a few of the free volumes in the amorphous zone rather than in the nanocrystal grain, are shown in Fig. 6(a), implying the absence of vacancies in the as-constructed ANA model. However, from the simulation time of 0.1 ps, collision cascades appear, along with a zone that constitutes both the nanocrystal grain and its neighboring amorphous region. In addition, with the increase of simulation time, there are many vacancies or vacancy-like defects in the zone of collision cascades, accompanied by more and larger free volumes. It is interesting to observe that, after the simulation time of 0.4 ps when the high-energy collisions were almost accomplished, the vacancies or vacancy-like defects rapidly reduced. In a previous work, it was suggested that the irradiation-induced defects in an MG model are very unstable [53], and are readily trans-
formed into large free volumes in the neighborhood [40]. Therefore, this indicates with regard to the current ANA model, that vacancies or vacancy-like defects are also not stable, and the transformation from defect to free volumes also occurred. Vacancies or vacancy-like defects have been fully annihilated at the simulation time of 1.3 ps, leaving a lot of large free volumes in both the nanocrystal zone and the amorphous region. It is well-known that a free volume is a specific structural feature in amorphous materials and do not exist as crystals, hence, it follows from the foregoing that large free volumes in the nanocrystal zone are unstable and are likely to be annihilated or transformed into small ones [11]. As the structural model was cooled and relaxed at the simulation time of 20.0 ns, surprisingly, only a few of the large free volumes were found in the amorphous zone of the intercepted ANA model. At the very least, not even a small or negligible free volume can be found in the nanocrystal grain. This is similar in characteristics to that of the as-constructed model, implying a highly effective self-healing phenomenon in the intercepted ANA model. Therefore, since this intercepted ANA model is the region mostly affected by the collision cascades, it is suggested that other parts of the ANA model probably possess a higher self-healing efficiency.
3.5.3. Size distributions of unfilled spaces in an intercepted ANA model Fig. 7 shows the size distributions of atomic-unfilled spaces in the intercepted ANA model. It is worth noting that, during the early stage of the collision cascades, the number of small atomic˚ decreased with the simula˚ < r < 0.6 A) unfilled spaces (0 A ˚ marginally intion time, while that of larger ones (r > 0.6 A) creased, indicating that large free volumes are induced by the collision cascades. However, when more and more knocked-on atoms have stopped moving, large free volumes are decreased with the
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Fig. 6. 3D distributions of the atomic-unfilled spaces with a radius larger than 0.8 A˚ from the snapshots of the intercepted ANA model, at the simulation time of (a) 0.0 ps, (b) 0.1 ps, (c) 0.2 ps, (d) 0.3 ps, (e) 0.4 ps, (f) 1.0 ps, (g) 1.3 ps, (h) 15.0 ps, and (I) 20.0 ns. The red spheres denote the vacancies or vacancy-like defects, and the green spheres stand for the large free volumes. The blue dashed frame represents the initial region of the nanocrystal grain. (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. 7. Distributions of atomic-unfilled spaces with different size ranges, from the snapshots of the intercepted ANA model, at the simulation time of 0.0 ps, 0.1 ps, 0.2 ps, 0.3 ps, 0.4 ps, 1.0 ps, 1.3 ps, 15.0 ps, and 20.0 ns.
smaller ones increasing instead, because large free volumes are readily transformed into small ones. In addition, the evolutions ˚ and vacancies or ˚ < r < 1.28 A) of the large free volumes (0.8 A vacancy-like defects are shown in Fig. 7(b). It is found that both of them increased at the early stage of collision cascades, but subsequently were decreased after the booming of collision cascades. Most importantly, vacancies or vacancy-like defects were annihilated, due to their transformation to free volumes. Large free volumes continued to decrease till the end of structural relaxation of this model which also indicates that the structural selfhealing behavior in the ANA model, is consistent with that shown in Fig. 6. 3.6. The role of phase boundaries in defects annihilation It has been reported that, in order to achieve a new structural and energetic balance in (nano)crystalline materials subjected to irradiation effects, some residual vacancies would have to migrate towards and sink at the GBs [54,55]. Conversely, for amorphous alloys, it was revealed that the irradiation-induced defects are rapidly and fully annihilated by a concurrent compression of neighboring atoms, leading to the rearrangement of free volumes [11,40]. In similarity to the aforementioned, it was found for the ANA model that, the irradiation-induced defects are not stable, but were rapidly and fully annihilated, like those in MG materials. However, unlike in the MG models, phase boundaries were found between the nanocrystal grain and the amorphous matrix. This raises a serious question as to whether a new mechanism is responsible for the annihilation of defects in ANA materials and if so, does the phase boundary in any way play a role in the healing of defects? To address these issues, the evolutions of irradiationinduced defects as well as amorphous-crystal boundaries in the intercepted ANA model, are shown in Fig. 8. It is found that, at the early stage of collision cascades, there were some irradiationinduced vacancies in the nanocrystal grain and vacancy-like defects in the neighboring amorphous zone and it is interesting to note that most of them disappeared instantaneously. In particular, vacancies in the nanocrystal grain are fully annihilated at a very short time of about 0.8 ps, which is much smaller than the time that interstitials are emitted from GBs to heal the vacancies or vacancies themselves migrant to the GBs [6]. In other words, vacancies hardly change their positions at a short time less than 1.0 ps [6]. Therefore, it is thought-provoking how these vacancies
were annihilated. However, it could be readily observed that the amorphous-crystal boundary dramatically changes with the simulation time. Hence, there is a tendency that this boundary will advance towards the crystal zone. Interestingly, it seemed that vacancies create points of arrests to capture the phase boundary in motion. Therefore, once a vacancy makes contact with the phase boundary, it is instantaneously and totally annihilated. This indicates a new mechanism for the healing of defects in the ANA model, which is a different phenomenon from what is known to govern in (nano)crystals or amorphous alloys. At the simulation time of 0.8 ps, the last vacancy is annihilated by the phase boundary. From this point and onwards the phase boundary no longer advances towards the crystal zone, but surprisingly changes its direction towards the amorphous region. This novel characteristic feature indicates an effective self-healing of the nanocrystal grain. In a previous work, it was suggested that irradiation would induce some melted local regions in an MG model, which, subsequently are easily transformed into amorphous solid by quenching at an ultra-high cooling rate, leading to the well-known superquenched effect [56]. Therefore, because the atomic kinetic energy could be calculated in the ANA model, some melted local regions were estimated accordingly, by applying a method developed in a previous work [41], which indicates a relationship between the temperature and the kinetic energy,
E=
3 kT 2
(1)
Where, E, k, and T are the kinetic energy, the Boltzmann constant (1.380649 × 10−23 J/K), and the temperature, respectively. According to the heating process of the MD simulation, the melting temperature of this Zr2 Cu model was estimated to be about 1800 K, corresponding to an average kinetic energy of 0.234 eV for each atom. Therefore, all the atoms with a kinetic energy larger than 0.234 eV were selected, and the temperature of the zone filled with these atoms was calculated. In this way, a liquid region was estimated. The estimated liquid region in some typical snapshots of the intercepted ANA model, as well as its average temperature are shown in Fig. 9. It is found that the nanocrystalline-liquid border is roughly consistent with the nanocrystalline-amorphous boundary, suggesting that the nanocrystalline-amorphous boundary is determined by the liquid phase at high temperatures. When the liquid region disappeared during the quenching, the nanocrystalline-amorphous boundary
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Fig. 8. Evolutions of the amorphous-crystal phase boundaries and the irradiation-induced vacancies (blue spheres) in nanocrystal grain and vacancy-like defects (brown spheres) in amorphous matrix, of the intercepted ANA model. Various snapshots of this model are shown, at the simulation time of (a) 0.0 ps, (b) 0.2 ps, (c) 0.4 ps, (d) 0.6 ps, (e) 0.8 ps, (f) 1.3 ps, (g) 4.0 ns, and (h) 20.0 ns. The black, the red, and the blue lines, denote the phase boundaries at the simulation time of 0.0 ps, 0.8 ps, and 20.0 ns, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
still advanced towards the amorphous region, suggesting a transformation between the nanocrystalline and amorphous phases, occurring probably due to the relaxation of the ANA model. In addition, it could be inferred that the motion of the amorphous-crystal boundary at high temperatures is due to the expansion of melted regions in the intercepted ANA model. At the tail end of the collision cascades period, the melted regions began
to quench automatically. Based on this scenario, it may be readily deduced that the cooling rate of melted local regions in the intercepted ANA model is much lower than those of an amorphous zone located far away from the nanocrystal region. In other words, there is no super-quenched effect in the intercepted ANA model. It is known that an intrinsic competition exists between the crystal and the amorphous solid phases during the quenching of a metallic
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Fig. 9. The estimated liquid region in the intercepted ANA model, as well as its average temperature calculated in the snapshots at the simulation time of (a) 0.2 ps, (b) 0.4 ps, (c) 0.6 ps, and (d) 0.8 ps. The green dashed line and the red solid line denote the nano-crystalline boundary and the border of the liquid region, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 10. Evolution of two interstitial atoms (purple spheres) that originated from the nanocrystal grain. Representative snapshots are shown, at the simulation time of (a) 0.0 ps, (b) 0.2 ps, (c) 0.4 ps, (d) 0.6 ps, (e) 0.8 ps, (f) 1.3 ps, (g) 4.0 ns, and (h) 20.0 ns. The green line is the nanocrystal-amorphous boundary in each model snapshot. Note that only the atoms in the initial nanocrystal grain are shown here. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
melt [57,58], and that, which is significantly affected by the cooling rate; hence, the nanocrystal phase is competitive during the quenching of the melted local regions at a relatively low cooling rate. As a result, some parts of the melted local regions in the intercepted ANA model transform into the nanocrystal phase, leading to the self-healing of the nanocrystal grain.
3.7. Arrest of interstitial atoms It is known that a point defect is made up of a pair of a vacancy and an interstitial atom. During the collision cascades period, numerous atoms were knocked-on to become the interstitials, leaving in their wake, a myriad of vacancies at their initial positions, to es-
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tablish that some point defects were induced by irradiation. Previously, it has been reported that both the vacancies and interstitials are unstable, such that most of the point defects are rapidly annihilated, leading to the self-healing effect [59]. In crystalline materials, some residual vacancies and interstitials are very likely to be arrested at the GBs, in order to achieve a new balance of structure and energy. To a large extent, it is germane to remark that it is a profound discovery to observe that vacancies or vacancy-like defects were fully and rapidly annihilated during the collision cascades period. Regardless, it remains a further challenge to determine the implications of this phenomenon on knocked-on atoms, and in particular, on the interstitial atoms in the nano-grain. To resolve this complexity, the program of Ovito was implemented to capture the position and kinetic energy of each atom in the ANA model in order to track the motions of the knocked-on atoms. Concerning the intercepted ANA model which was significantly affected by the collision cascades, it was revealed that the amorphous-nanocrystal boundary changes with the simulation time. Therefore, the knocked-on atoms in the collision cascades were separated by this phase boundary. It could be stated that only those knocked-on atoms located in the nanocrystal grain may be strictly considered as interstitials, because a crystal lattice that exists in the nanocrystal grain, is absent in the amorphous matrix. Furthermore, it was observed that no knocked-on atom could penetrate the phase boundary during the entire simulation. However, in general, a number of knocked-on atoms that possess some positive velocity and could move in the model, were either arrested in some short-range local regions or absorbed at the phase boundaries. As a result, there is no knocked-on atom originating from the amorphous region that could penetrate the boundaries. Thus, it may be stated unequivocally, that the phase boundaries in the ANA model play the role of an absorber of knocked-on atoms, like those of the GBs in crystalline materials. Nonetheless, it was astounding to note that several interstitial atoms that originated from the nanocrystal grain successfully passed through the phase boundaries. To analyze this scenario, the evolutions of the positions and kinetic energies of interstitial atoms were studied and are as shown in Fig. 10. From thence, it could be inferred that two Zr interstitial atoms penetrated the boundaries rapidly at the onset of the collision cascades. These are the Zr1 and Zr2 atoms. Interestingly, it was observed that the Zr1 atom was quickly arrested in the local region of the amorphous matrix and its kinetic energy transferred to the neighboring atoms in the process. At the end of collision cascades period, the energy of this atom is negligible (less than 0.1 eV) retarding its motion and preventing it from escaping from the local region. On the other hand, it is significant to note that the kinetic energy of the Zr2 atom increased rapidly to 1.1 eV, due to the collisions with other atoms in the amorphous zone. Hence, the Zr2 atom was not arrested in any local region, but rather, it advanced to the phase boundaries. Previously, it had been stated that the diffusion energy for an interstitial to move and sink at the GB is about 0.1 eV [6]. Therefore, it follows that the Zr2 atom could only reach the phase boundary because its kinetic energy is greater than its diffusion energy. Fig. 10 showed a depiction of this scenario, indicating how the energy of the Zr2 atom was decreasing rapidly during its motion, causing it to be spontaneously arrested at the boundary. In general, during the collision cascades period, the process of atomic diffusion was not established between the nanocrystal grain and the neighboring amorphous zone, because at the phase boundaries, most of the knocked-on atoms were easily absorbed. 4. Conclusions The atomic-scale structural evolution of a nanocrystalamorphous alloy model has been investigated using an MD
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simulation coupled with a series of calculations. The following inferences can be drawn from the study: (1) The evolution of free volume indicates that, free volumes can spontaneously and fully recover after the cooling and structural relaxation processes, regardless of the complex behavior exhibited under the collision cascades phenomenon. This suggests that ANA materials possess a high resistance to neutron irradiation. (2) Unlike what is generally observed in (nano)crystalline materials or amorphous alloys, a novel and unique mechanism is found regarding ANA materials, which suggests that irradiation-induced vacancies are rapidly and fully annihilated at the boundary existing between the nanocrystal grain and its neighboring amorphous zone. (3) The nanocrystal-amorphous boundary is driven by the expansion of melted local regions towards the nanocrystal region. Some of these melted local regions are then transformed into the nanocrystal phase during the cooling process, indicating an effective self-healing behavior of the nanocrystal grain. (4) There is virtually no atomic diffusion effect between the nanocrystal grain and the neighboring amorphous zone, because most of the knocked-on atoms were spontaneously and readily absorbed by the phase boundary. Declaration of Competing Interest There are no conflicts to declare. Acknowledgements Financial supports from the National Natural Science Foundation of China (Grant No. 51471088) and the Fundamental Research Funds for the Central Universities (Grant No. NE2015004), are gratefully acknowledged. References [1] C.C. Fu, J.D. Torre, F. Willaime, J.L. Bocquet, A. Barbu, Multiscale modelling of defect kinetics in irradiated iron, Nat. Mater. 4 (2004) 68–74. [2] P. Yvon, F. Carre, Structural materials challenges for advanced reactor systems, J. Nucl. Mater. 385 (2009) 217–222. [3] S.J. Zinkle, G.S. Was, Materials challenges in nuclear energy, Acta Mater. 61 (2013) 735–758. [4] T.D.D.L. Rubia, H.M. Zbib, T.A. Khraishi, B.D. Wirth, M. Victoria, M.J. Caturla, Multiscale modelling of plastic flow localization in irradiated materials, Nature 406 (20 0 0) 871–874. [5] K.E. Sickafus, R.W. Grimes, J.A. Valdez, C. Antony, M. Tang, I. Manabu, S.M. Corish, C.R. Stanek, B.P. Uberuaga, Radiation-induced amorphization resistance and radiation tolerance in structurally related oxides, Nat. Mater. 6 (2007) 217–223. [6] X.M. Bai, A.F. Voter, R.G. Hoagland, N. Michael, B.P. Uberuaga, Efficient annealing of radiation damage near grain boundaries via interstitial emission, Science 327 (2010) 1631–1634. [7] Y. Chimi, A. Iwase, N. Ishikawa, A. Kobiyama, T. Inami, S. Okuda, Accumulation and recovery of defects in ion-irradiated nanocrystalline gold, J. Nucl. Mater. 297 (2001) 355–357. [8] A.L. Greer, Confusion by design, Nature 366 (1993) 303–304. [9] W.L. Johnson, Bulk glass-forming metallic alloys: science and technology, MRS Bull. 24 (1999) 42–56. [10] Q.S. Zeng, et al., General 2.5 power law of metallic glasses, Proc. Natl. Acad. Sci. 113 (2016) 1714–1718. [11] L. Yang, et al., Structural responses of metallic glasses under neutron irradiation, Sci. Rep. 7 (2017) 16739. [12] X.N. Zhang, X.X. Mei, Q. Zhang, X.N. Li, Y.M. Wang, Y.N. Wang, Study of irradiation damage induced by He2+ ion irradiation in Ni62 Ta38 metallic glass and W metal, Nucl. Instrum. Methods Phys. Res. Sect. B 406 (2017) 548–554. [13] J.A. Shi, C.R. Cao, Q.H. Zhang, Y.T. Sun, C. Wang, W.H. Wang, H.Y. Bai, L. Gu, In situ atomic level observations of Al2 O3 forming on surface of metallic glasses, Scr. Mater. 136 (2017) 68–73. [14] Z. Fan, Q. Li, J. Li, S.C. Xue, H.Y. Wang, X.H. Zhang, Tailoring plasticity of metallic glasses via interfaces in Cu/amorphous CuNb laminates, J. Mater. Res. 32 (2017) 2680–2689.
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