Dynamic characterization of shock response in crystalline-metallic glass nanolaminates

Accepted Manuscript Dynamic Characterization of Shock Response in Crystalline-Metallic Glass Nanolaminates K. Vijay Reddy, Chuang Deng, Snehanshu Pal PII:

S1359-6454(18)30872-3

DOI:

https://doi.org/10.1016/j.actamat.2018.10.062

Reference:

AM 14940

To appear in:

Acta Materialia

Received Date: 13 August 2018 Revised Date:

5 October 2018

Accepted Date: 15 October 2018

Please cite this article as: K.V. Reddy, C. Deng, S. Pal, Dynamic Characterization of Shock Response in Crystalline-Metallic Glass Nanolaminates, Acta Materialia, https://doi.org/10.1016/ j.actamat.2018.10.062. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Dynamic Characterization of Shock Response in Crystalline-Metallic Glass Nanolaminates

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K. Vijay Reddya, Chuang Dengb, Snehanshu Pala* a

Department of Metallurgical and Materials Engineering, National Institute of Technology Rourkela, 769008, India. Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada. *Corresponding Author: Dr. Snehanshu Pal, email: [email protected], [email protected].

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Graphical Abstract

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Abstract

The dynamic response of crystalline Cu-amorphous Cu63Zr37 nanolaminates under shock loading has been investigated in the present study by atomistic simulations to provide an insight of their overall deformation behavior

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with respect to different grain structure in the crystalline region. The dynamic characterization of the structural evolution of the nanolaminates during shock loading has been carried out based on various techniques including common neighbor analysis, dislocation analysis, Voronoi cluster analysis, pressure profile, and kinetic energy maps. Pressure profiles of single crystalline Cu-Cu63Zr37 metallic glass (SC/MG) nanolaminate at relatively low shock

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velocity show the presence of an elastic precursor in the crystalline region owing to the plane-plane collision phenomenon. Increasing the shock velocities in the SC/MG specimen results in FCC to BCC phase transition in the

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crystalline region. In particular, the crystalline/amorphous interface causes the generation of reflected rarefaction wave back into the crystalline region which aids inthe evolution and stabilization of the BCC phase. In the NC/MG specimen, the misalignment of planes across different grains reduces the intensity of elastic precursor at low shock velocity due to disruption in the plane-plane collision, whereas the grain boundaries act as nucleating region for the BCC phase during the high-velocity shock propagation. The coordination number of the Cu63Zr37 glass region has

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been found to increase during high-velocity shock loading which can be accounted by the formation of <0 4 4 6> and <0 4 4 7> indexed Voronoi polyhedra.

Phase transition.

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1. Introduction

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Keywords: Molecular dynamics simulation; Shock compression; Nanolaminate; Crystalline-amorphous interface;

Shocks in condensed matter are a pervasive consequence of the swift movement of atoms at a rate faster than that of the adjacent atoms tending to move out of the way [1]. This causes deformation subjected to a high-pressure condition in the material which results into a wide range of responses such as phase transition [2, 3], elastic-plastic transformation [4, 5], amorphization [6, 7], and spallation [8,9]. These responses have thus attracted researchers to study the deformation mechanisms of materials under such extreme dynamic loading conditions and their effects on the material properties. For many decades the focus has been on the shock response of materials at micro- or mesoscale, for which numerous experimental and simulation studies have also been carried out [10-14]. Recently

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some attention has been directed towards the study of shock loading behavior of nanostructured/nanoscale materials [15, 16]. For instance, Skripnyak et al. have experimentally studied the mechanical behavior of nanostructured metal alloys under shock and consequently determined the spall and yield strength of those alloys [15]. In another study,

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Jian et al. analyzed the shock compression response of face-centered cubic (FCC) and body-centered cubic (BCC) structured high entropy alloys and determined their Hugoniot elastic limits and phase transitions [16]. While there are many more literature studies on the effect of shock on nanoscale materials and their consequent response, the experimental techniques have nevertheless lacked in presenting an elaborate atomic level dynamic characterization

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during the shock loading process of metallic systems. In this scenario, Molecular Dynamics (MD) simulation is a very resourceful tool for understanding and characterizing the underlying atomic level physics responsible for the

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deformation behaviorof nanoscale metallic systems [17-22]. Moreover, MD simulations also provide intricate information on atomistic mechanisms during the phase transition or amorphization process occurring due to the shock compression, which is difficult to obtain through post-mortem observations [23, 24]. However, most of the MD simulation studies related to shock loading of metallic systems have been inclined towards the investigation of only pure crystalline metallic systems [25,26], metallic glass (MG) systems [27-29] or crystalline-crystalline

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multilayers [30,31].

Crystalline-amorphous nanolaminate structures possess simultaneous high strength and ductility [32-34], a combination of properties that are otherwise not easy to obtain for the individual constituent bulk materials [35, 36]. In particular, studies on Cu/CuZr nanolaminates have gained considerable attention due to their superior mechanical

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properties [37-41] mainly owing to the high density of crystalline-amorphous interfaces. Apart from high strength and ductility, studies have also shown that the high density of crystalline-amorphous interfaces also significantly

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improve the fracture toughness of the Cu-CuZr nanolaminates [41]. Also during extreme loading conditions such as shock propagation, the difference in atomic packing in the crystalline and amorphous region causes periodic heterogeneity in the nanolaminate which may leads to scattering of the shock wave and change the wave structure. This ability of crystalline-amorphous nanolaminates can aid in attenuation of the shock wave which makes it a potential structural material in armors, aircraft and satellite sectors. However, although Cu-CuZr nanolaminates have shown superior properties under regular mechanical testing, a detailed deformation study of those structures under extreme pressure conditions (such as shock loading) is still lacking till date. In the present paper, we have carried out systematic MD simulations to dynamically characterize the shock response and the corresponding deformation

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behavior of Cu-CuZr nanolaminates. In particular, the effect of shock velocity on both crystalline and amorphous region has been explored. From the specimen perspective, we have considered three different types of nanolaminates, i.e. CuZr MG layered with single crystalline (SC), columnar grained (CG), and nanocrystalline (NC)

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Cu. The phase transitions and topological changes occurring in the specimens have also been analyzed and reported in this paper.

2. Simulation details

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Bilayer specimens of Cu (crystalline phase) and Cu63Zr37 MG (amorphous phase) were created with a cross-section of 12 × 12 nm and a total length of 55 nm (crystalline phase ~23 nm and amorphous phase ~32 nm). Three different

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types of Cu crystals were considered for the bilayer specimen i.e. SC Cu, CG Cu, and NC Cu with a grain size of ~6 nm as shown in Fig. 1. For preparing the MG layer, 37 at.% Cu atoms were randomly replaced by Zr atoms and subsequently heated to 2000 K which was followed by a rapid cooling to 1000 K at a cooling rate of 4 K/ps. After that, the specimen was cooled at a slower cooling rate of 0.1 K/ps up to 700 K during which the glass transition occurred (i.e. approximately at 750 K [42]). The specimen was then cooled to 100 K at a rate of 1 K/ps to obtain the final amorphous layer. It has to be noted that during the heating and rapid cooling process, the specimen was relaxed

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in the length direction (X-direction) such that change in length was possible to avoid the generation of internal stresses in the crystalline region and crystalline-amorphous interface. Before applying the shock loading, the bilayer specimens were relaxed by energy minimization using the conjugate gradient method [43]. Then the specimens were

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equilibrated at 100 K and zero pressure under NPT (N is the number of particles, P is the pressure, and T is the temperature) ensemble. After the sample preparation, shock loading was carried out along the X-direction which

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was induced by driving a rigid piston at the crystalline end (~ 6 Å thickness) with a constant inward velocity (Up). The shock loading was performed at 100 K under NVE (N is the number of particles, V is the volume, and E is the total energy) ensemble. The simulation time step was 1 fs. The shock propagation has been investigated for different piston velocities such as 0.5 km/s, 0.8 km/s, 1.1 km/s and 1.4 km/s to analyze the effect of piston velocity on the deformation behavior. Free boundary conditions were applied along the shock loading direction (i.e. X-direction) whereas periodic boundary conditions were applied along the other two transverse directions. All simulations were carried out using large-scale atomic/molecular massively parallel simulator (LAMMPS) [43]. The interatomic interactions of Cu-Cu, Cu-Zr, and Zr-Zr were described by an Embedded Atom method (EAM) potential developed

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by Mendelev et al. [42]. The post visualization and analysis of the atomic configuration during the shock propagation was realized by OVITO [44]. Common Neighbor Analysis (CNA) [45], Dislocation Analysis (DXA) [46] and Voronoi polyhedral analysis [47,48] have been performed during the shock deformation process in the

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bilayer specimen.

NC/MG specimen.

3. Results and Discussion

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3.1. Pressure profiles during the shock

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Fig. 1: Centro-symmetry parameter (CSP) snapshots of the (a) SC/MG specimen, (b) CG/MG specimen, and (c)

In order to investigate the pressure distribution dependency on shock velocities at different time steps, the pressure profiles of the specimens with respect to distance have been plotted during the shock propagation for different piston velocities. Fig. 2(a), (b), (c) and (d) illustrate the variation in the compressive pressure in SC/MG specimen for

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piston velocities of 0.5 km/s, 0.8 km/s, 1.1 km/s and 1.4 km/s respectively during the shock loading from crystalline region. It is found that at slower piston velocity (i.e. 0.5 km/s), elastic precursors were formed in the crystalline

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region at an initial time period (i.e. 2.5 ps) as evident from the trend of pressure change in Fig. 2(a). The alternate increase and decrease in the pressure profile, which is similar to the harmonic oscillator, represents the compression and release process respectively. The oscillating profile indicates that once the piston driven shock propagates, the front region of the wavefront compresses the atomic planes resulting in a decrease of the inter-planar spacing which creates a high pressure zone (formation of a crest). Consequently, increase in the inter-planar spacing at the rear end of the piston driven shock wave results in a low pressure zone (formation of a trough). Inset in Fig. 2(a) illustrates that the distance between a crest and trough is 6 Å which is also the approximate thickness of the piston. This mechanism indicates that the initial oscillating behaviour (at ~2.5 ps time period) of the pressure profile is due to the

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plane-plane collision that has occurred during the shock propagation. A similar phenomenon of occurrence of elastic precursors has also been reported for single crystals under shock in the literature [49]. However, with the increase in piston velocity (Fig. 2(b), (c), and (d)), the alternate increase and decrease nature in the pressure profile vanished

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which indicates that plastic deformation has dominated over elastic deformation resulting into amorphization and phase transition which will be discussed in more details in a later section. With the propagation of shock towards the crystalline-amorphous interface (i.e. at 5 ps and a distance of ~25 nm in Fig. 2(a)), it is found that the pressure profile shows a dip near the crystalline region and a peak near the amorphous region. The dip in pressure profile

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characterizes the transition from elastically compressed region to plastically compressed region. It can be seen that at a relatively lower piston velocity, the dip was extended to a larger crystalline region as lower velocities aid the

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elastic compression; as the piston velocity increased the extended dip in the crystalline region decreased (Fig. 2(d)).

Fig. 2: Pressure profiles of SC/MG specimen for a shock velocity of: (a) 0.5 km/s, (b) 0.8 km/s, (c) 1.1 km/s, (d) 1.4 km/s. Shock wave propagates from left (crystalline region) to right (amorphous region).

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Fig. 3: Pressure profiles of SC/MG specimen for a shock velocity of: (a) 0.5 km/s, (b) 0.8 km/s, (c) 1.1 km/s, (d) 1.4

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km/s. Shock wave propagates from right (amorphous region) to left (crystalline region).

The shock loading has also been carried out from the reverse direction i.e. initiated from the MG region and the pressure distribution dependency has been investigated on shock velocities at different time steps. Fig. 3(a)-(d)

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illustrate the variation in the compressive pressure in SC/MG specimen for piston velocities of 0.5 km/s, 0.8 km/s, 1.1 km/s and 1.4 km/s respectively during the shock loading from MG region. It is observed that as the shock

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wavefront propagates towards the interface, the pressure in the amorphous region continuously increases. A maximum pressure of approximately 12 GPa, 22 GPa, 31 GPa, and 40 GPa is observed for piston velocities of 0.5 km/s, 0.8 km/s, 1.1 km/s and 1.4 km/s respectively. Also, it can be observed that the shock wavefront reaches the interface after a time period of 6 ps for all the shock velocities and reaches the end of the specimen at approximately 12 ps time period. This is because the amorphous region has no long range ordering through which plane-plane collision might occur and hence the movement of shock wavefront is slower. Literature studies have also shown that the shock moves faster in the crystal lattice (having long range ordering) and slows down near grain boundary or amorphous region [50]. Another important observation is the occurrence of elastic precursor in the crystalline region

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even at high shock velocities (up to 1.1 km/s velocity). On comparison to the previous pressure profiles, elastic precursors in the crystalline region are only observed during the low velocity shock wave propagation. This indicates that as the shock wave has propagated from the amorphous region, the intensity of the shock has

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continuously decreased and the shock wavefront has started to attenuate. The attenuation of the shock wave is also evident from the pressure curves at 9 ps and 12 ps time period (Fig. 3(c) and (d)) which shows a gradual decrease of the pressure in the crystalline region.

In the case of the shock wave propagation from the crystalline region in CG/MG specimen, nominal elastic

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precursors are observed in the crystalline region at an initial time period (i.e. 2.5 ps) as shown in Fig. 4(a). In addition, it is noticed that the amplitude of the wave in the pressure profile has decreased as compared to that for the

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specimen with SC Cu (Fig. 2(a)), which can be attributed to the misalignment of planes in different grains in the crystalline part in this specimen. The CG region of the specimen consists of 7 grains with different plane orientations along the X-, Y- and Z- direction. The presence of these grains with different plane orientation disrupts the plane-plane collision during the shock propagation thus inhibiting the elastic compression. Similar to the interfacial behavior of SC/MG specimen, a dip and peak in the pressure profile are also observed near the crystalline

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and amorphous region respectively in the CG/MG specimen. However, the extended dip (which represents elastic compression) in the present case (Fig. 4(b)-(d)) is narrower when compared with the previous case (Fig. 2(b)-(d)). It suggests that during higher velocity shock compression process, partial amorphization has occurred in the crystal lattice which has led to the mitigation of elastic precursors. With the increase in the number of grains (and

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subsequent increase in the grain boundary area) in case of NC/MG specimen, the elastic precursor became nonexistent and the extended dip further narrowed down (Supplementary Fig. S1, which show the pressure profiles of

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NC/MG specimen). Another important observation during the shock wave propagation is that given the same time, at each initial velocity the wave would propagate less distance in CG/MG specimen than in SC/MG specimen. Moreover, the velocity of the wave propagation further decreases in NC/MG specimen (refer Supplementary Fig. S1) as compared with the other two specimens. This is due to the plane misalignment in different grains of the CG/MG specimen. The misalignment has restricted the plane-plane collision and hence disrupted the free propagation of shock wave. As the number of grains increases, in addition to the plane misalignment, grain boundary area also plays an important role in slowing down the shock wave [50]. Furthermore, it is found in all specimens that after the shock wave has propagated into the MG region, there is a slight pressure release in the

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crystalline region which is absent in the amorphous region. This effect is due to the presence of rarefaction wave that trails the shock wavefront (after the shock wave has reached the interface) which in turn led to the release of

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pressure and strain in the crystalline region of the specimen [51].

Fig. 4: Pressure profiles of CG/MG specimen for a shock velocity of: (a) 0.5 km/s, (b) 0.8 km/s, (c) 1.1 km/s, (d) 1.4

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km/s. Shock wave propagates from left (crystalline region) to right (amorphous region). For comparative study, the shock loading has also been initiated from the MG side and the pressure distribution

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dependency has been investigated on shock velocities at different time steps. Fig. 5(a)-(d) illustrate the variation in the compressive pressure in CG/MG specimen for piston velocities of 0.5 km/s, 0.8 km/s, 1.1 km/s and 1.4 km/s respectively during the shock loading from MG region (Supplementary Fig. S2 show the pressure profiles of NC/MG specimens). Similar to the previous case where the shock wave has been initiated from the amorphous region (Fig. 3), elastic precursors are also observed in the crystalline region at higher shock velocities. However, the intensity of the oscillation has decreased due to the presence of columnar grains. In addition, the pressure profiles (Fig. 5(c) and (d)) show a gradual decrease of the pressure indicating the attenuation of the shock wave as it traverses through the crystalline region.

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Fig. 5: Pressure profiles of CG/MG specimen for a shock velocity of: (a) 0.5 km/s, (b) 0.8 km/s, (c) 1.1 km/s, (d) 1.4

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km/s. Shock wave propagates from right (amorphous region) to left (crystalline region).

3.2. Stress profile and kinetic energy map during the shock

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The atomistic response of each nanolaminate Cu-CuZr specimen under shock compression can also be illustrated through the spatial and time-based evolution of quantities such as stress and energy (kinetic energy in specific). Fig.

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6 shows the stress profiles along with the kinetic energy map during the shock compression process of the SC/MG specimen at a piston velocity of 0.5 km/s. The oscillating wave, which is an exemplification of elastic wave, is observed in the stress profile during the shock propagation as shown in Fig. 6(a) and (b). The average compressive stress detected in the crystalline part started with approximately 5 GPa and increased up to approximately 6 GPa. The kinetic energy map also illustrates an alternating region of higher and lower kinetic energy which is in turn complementary to the stress profiles. Once the wavefront reached the crystalline-amorphous interface, the elastic wave in the stress profile gradually diminished (Fig. 6(c)). However, Fig. 6(c) shows the presence of oscillating stress curve in the amorphous region of the nanolaminate specimen at approximately 4 ps. At this time period, the

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elastic wave propagates very close to the interface; it indicates that the compressive shock wave causes a medium range ordering in the amorphous region near the interface (refer supplementary Fig. S3). Hence, the elastic wave continues to propagate even after it crosses the interface (though the amplitude drastically decreases because of

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absence of long range ordering as present in the crystalline region). But, this medium range ordering is observed only close to the interface and hence the elastic wave attenuates rapidly as it further traverses into the amorphous region as observed in Fig. 6(d). With the shock wavefront reaching and traveling in the amorphous region, the compressive stress was also released in the crystalline region to below 5 GPa stress as found in Fig. 6(d) and (e).

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The stress distribution in Fig. 6(f) shows that the release of stress in the amorphous region of the specimen has impeded. This can be inferred to the absence of periodicity in the amorphous region and the structural

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transformation occurring at the atomic scale.

A similar effect of shock propagation in the NC/MG specimen at a piston velocity of 0.5 km/s is observed and illustrated in Fig. 7. The main difference between the two processes is in the intensity of the elastic wave and its subsequent effect on the stress profiles. As discussed earlier, the weakening of the elastic wave is due to the misalignment of planes in different grain in the crystalline region. It can be observed that, in contrast to the previous

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stress profile of SC/MG specimen, there is no stress release in the crystalline region of the specimen with NC Cu even after the shock wave has traversed to the amorphous region. Moreover, the atoms in the amorphous region

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have displayed a marginally higher kinetic energy when compared with the atoms in the crystalline region.

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Fig. 6: Atomic snapshots and stress profiles of SC/MG specimen for a shock velocity of 0.5 km/s at: (a) 2 ps, (b) 3

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ps, (c) 4 ps (d) 5 ps, (e) 6 ps, and (f) 8 ps.

Fig. 7: Atomic snapshots and stress profiles of NC/MG specimen for a shock velocity of 0.5 km/s at: (a) 2 ps, (b) 3 ps, (c) 4 ps (d) 5 ps, (e) 6 ps, and (f) 8 ps.

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Fig. 8 shows the stress distribution profiles along with kinetic energy map during the shock compression process of SC/MG nanolaminate specimen at a higher piston velocity of 1.4 km/s. It is observed that the two component of shock wave i.e. the elastic wave and the plastic wave move at different velocities; the plastic wave trailing the elastic

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wavefront. The stress profiles in Fig. 8(a) and (b) show a gradual drop in the compressive stress at approximately 10 nm and 15 nm respectively. Literature studies have correlated such drop in the stress/pressure profiles with the

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transformation from elastic to plastic wave [52]. In the present study, the decrease in the compressive stress marks the initiation of the elastic wave in the specimen which indeed signifies that the elastic wave precedes the plastic wave. In correspondence to the stress profiles, the kinetic energy map also clearly indicates that the elastic wave moves at a faster rate than that of the plastic wavefor a higher piston velocity. However, it is observed from the kinetic energy map that the relative velocity between the elastic and the plastic wave reduces as the distance between both the fronts narrow down during shock wave propagation in the amorphous region of the specimen (Fig. 8(c)- (e)). Furthermore, the stress profiles in Fig. 8(f) shows a sudden drop in the compressive stress which can be attributed to the coalescence of the elastic and plastic wave in the amorphous region.

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ps, (c) 4 ps (d) 5 ps, (e) 6 ps, and (f) 8 ps.

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Fig. 8: Atomic snapshots and stress profiles of SC/MG specimen for a shock velocity of 1.4 km/s at: (a) 2 ps, (b) 3

Fig. 9: Atomic snapshots and stress profiles of NC/MG specimen for a shock velocity of 1.4 km/s at: (a) 2 ps, (b) 3 ps, (c) 4 ps (d) 5 ps, (e) 6 ps, and (f) 8 ps

Similarly, Fig. 9 illustrates the stress distribution profiles and the kinetic energy map during the shock compression process of NC/MG specimen at a piston velocity of 1.4 km/s. At the initial period (Fig. 9(a)-(c)), the shock wave consisted of an elastic wave and a plastic wave as evident from the gradual decrease in the compressive stress in the stress profiles. However, the difference in the velocity of the elastic and plastic wave is not as large as in the SC/MG

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specimen. This is also evident from the kinetic energy map which shows that the elastic front and plastic front are closer to each other than in the specimen with SC Cu. Kinetic energy map in Fig. 9(c) displays a sudden elasticplastic collapse in the crystalline region as the shock wave approaches the crystalline-amorphous interface. In

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correspondence, the stress profile also shows a small peak near the interface of the specimen which led to the elastic-plastic collapse. Once the shock wave has traversed beyond the interface and into the amorphous region, the difference in the velocity between elastic wave and plastic wave became zero as they both coalesced and traversed as a single wave which is also evident from the sudden rise in the compressive stress (Fig. 9(d)-(f)). For reference,

presented in the supplementary figures Fig. S4 and S5 respectively.

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the stress profile and kinetic energy map for the CG/MG specimen for piston velocity of 0.5 km/s and 1.4 km/s are

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3.3. Structural transformation in the crystalline region during the shock

Fig. 10 and Fig. 11 are representative illustration of CNA snapshots of NC/MG specimen before and after the shock propagation for different piston velocities i.e. 0.5 km/s, 0.8 km/s, 1.1 km/s and 1.4 km/s during the shock propagation from the crystalline region and amorphous region respectively. The CNA snapshots of the other specimens are provided in the supplementary figures Fig. S6 - S9. The main objective of analyzing the structural

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transformation during the shock propagation is to study the coupling mode between the phase transition (or atomic level structural evolution) and plasticity in each specimen. Although both crystalline and amorphous regions have undergone plastic co-deformation during the shock compression process, this section only concentrates on the phase

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later.

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transition in the crystalline region during the process whereas the structural evolution in the MG region is discussed

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Fig. 10: Common-neighbor analysis (CNA) snapshot during structural transformation of NC/MG specimen for shock velocity of (a) 0.5 km/s, (b) 0.8 km/s, (c) 1.1 km/s and (d) 1.4 km/s. Red arrows show the direction of shock

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propagation. Black arrows in (b) and (c) show the presence and absence of grain boundaries in the specimen at the

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initial and final time period respectively.

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Fig. 11: Common-neighbor analysis (CNA) snapshot during structural transformation of NC/MG specimen for shock velocity of (a) 0.5 km/s, (b) 0.8 km/s, (c) 1.1 km/s and (d) 1.4 km/s. Red arrows show the direction of shock propagation. Black arrows in (b) and (d) show the presence and absence of grain boundaries in the specimen at the

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initial and final time period respectively.

It is shown in Fig. 10 and Fig. 11 that with the increase in the piston velocity, the length of the final specimen have been correspondingly reduced to a greater magnitude respectively. In addition, shock compression from the

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crystalline region and with a lower piston velocity results in the generation of stacking faults and twin boundaries (Fig. 10(a)). In comparison, the stacking faults and twin boundaries are minimal in volume when the shock wave

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traverses from the amorphous region (Fig. 11(a)). With the increase in the piston velocity, the martensitic transformation has been observed in the specimen; with higher piston velocity, the higher volume fraction of BCC phase was formed (Fig. 10 and 11(b)-(d)). The martensitic transformation during the shock wave propagation was driven by the nucleation of the BCC phase which may be through the epitaxial Bain path [53]. On comparing both cases (Fig. 10 and Fig. 11), it is observed that the volume of BCC phase during the shock propagation from the crystalline phase is greater than that of BCC phase during the shock propagation from the amorphous phase. This is due to the generation of rarefaction waves in the previous case which aided in the stabilization of the BCC phase. A detailed discussion is presented on the importance of interface on the stabilization of BCC phase in later section.

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Meanwhile, it is worth mentioning that although overall the plastic deformation during the shock propagation at a lower piston velocity (i.e. 0.5 km/s) was controlled through the formation of stacking faults and twin boundaries as shown in Fig. 10 and 11(a), the martensitic transformation has been involved. Specifically, during the propagation

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of the shock wave from the crystalline region, the martensitic transformation was initially triggered near the grain boundaries which also correspondingly resulted in the decrease in the Shockley partial dislocation density (having burger vector 1/6 <1 1 2>) of the FCC Cu (Supplementary video V1). Once the shock wave has crossed the interface (after a distance of ~25 nm and at ~5 ps) and the rarefaction wave has released some amount of strain in the

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crystalline region, the martensitic transformation was reversed and the mechanism to accommodate the plastic strain shifted back towards the formation of twins and stacking faults. After a similar period of time, the Shockley partial

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dislocation density also shows a gradual increase as observed from Fig. 12(a).

With the increase in the piston velocity to 0.8 km/s, it is observed that along with the formation of a few stacking faults to accommodate the plastic deformation, a small volume fraction of BCC phase is also present close to the grain boundaries, the crystalline-amorphous interface, and the surface of the specimen. Fig. 10(b) shows accommodation of the plastic strain in the crystalline region and such kind of plastic strain accommodation can

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occur through FCC to BCC transition, grain boundary compression, grain rotation and consequently its coupled motion in the crystalline region. The occurrence of grain boundary rotation, in this case, can be inferred from the elimination of grain boundary between two adjacent grain marked in Fig. 10(b) and (c). Correspondingly, Fig. 12(b) shows a decrease in the Shockley partial dislocation density (having burger vector 1/6 <1 1 2>) till ~5 ps after which

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a steady curve is observed. Simultaneously, the partial dislocation density due to the BCC phase (having burger vector 1/2 <1 1 1>) shows a gradual increase. With increase in the piston velocity to 1.1 km/s and 1.4 km/s (Fig.

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12(c) and (d) respectively), it can be seen that the partial dislocation density due to the BCC phase increased to a higher extent than that of the Shockley partial dislocation density due to the FCC phase indicating that complete FCC to BCC phase transformation has occurred in the crystalline region of the specimen. However, the dislocation density curves show a zig-zag trend after the shock has propagated through the crystalline region. This is caused by the re-adjustment of the microstructure (to release the strain) through grain rotation and grain boundary sliding during the propagation of the rarefaction wave due to which generation and annihilation of partial dislocations occurred.

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Fig. 12: Dislocation density vs. time plots ofNC/MG specimen during shock at a velocity of: (a) 0.5 km/s, (b) 0.8

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km/s, (c) 1.1 km/s, and (d) 1.4 km/s.

Figs. 13(a) and (b) show the RDF plots at different time period for the SC/MG specimen during the shock propagation at the piston velocities of 0.5 km/s and 1.4 km/s respectively. In both RDF plots, the first peak splitting was observed only at t = 4 ps. In addition, the splitting was more prominent at higher piston velocity. The peak splitting at high-pressure conditions is a characteristic feature in some inorganic amorphous compounds (such as Germania and Silica) due to the increase in the edge-bond sharing [54]. In the present study, the first peak splitting at 4 ps time period signifies that the BCC phase has been formed from the amorphous phase in the crystalline region of the specimen. An intermediate amorphous phase was formed for a brief period of time before transforming into

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BCC phase (Supplementary video V2). Correlating the phase transition with RDF plots, it can be said that the shock compression disturbs the FCC crystal structure by bringing the atoms closer and thus enhancing the bond sharing which results into an intermediate amorphous structure and finally forms the BCC phase. It can be seen that after 4

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ps, the split peak disappeared and a smoother first peak in the RDF plot was observed. Similarly, Fig. 14 shows the RDF plots at the different time period and shock velocities for the NC/MG specimen during the shock propagation. It is found that the intensity of peaks in the initial RDF plot (at t = 0 ps) is lower than that of the previous case. This is due to the presence of grain boundaries in the crystalline region of the specimen. Fig. 14 (a) shows that with the

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increase in time, there is not much variation in the RDF plots indicating that amorphization and phase transition is not very prominent during the shock compression process. However, at a higher piston velocity (Fig. 14(b)), a very

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indistinct splitting of the first peak is observed and a broadened peak is found with decreased peak intensity. This indicates that a diminutive amount of amorphous phase has been formed in the crystalline region of the specimen though substantial phase transition has nucleated from the grain boundary region. From the RDF plots (Fig. 13 and Fig. 14) it can be concluded that the FCC to BCC transition during the shock compression process occurred through the formation of an intermediate amorphous phase. Additionally, the presence of pre-existing grain boundaries has assisted in the phase transitions process in the NC/MG specimen. For reference, the RDF plots for CG/MG

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specimens during the shock propagation at the piston velocities of 0.5 km/s and 1.4 km/s are presented in Fig. S10.

Fig. 13: Radial Distribution Function (RDF) plots during the shock propagation in SC/MG specimen.

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Fig. 14: Radial Distribution Function (RDF) plots during the shock propagation in NC/MG specimen

3.5. Structural changes in the amorphous region during the shock

Once the shock wave propagates through the crystalline region and the interface, it transverses into the amorphous region of the specimen. Unlike the wave propagation in crystalline region, the wave front in the amorphous region

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propagates through formation of localized high strain regions (i.e. shear transformation zone (STZ)). Literature studies have shown that the STZs carry the shock wave front in the forward direction and causes plastic deformation in the metallic glasses [27]. Fig. 15(a) and (b) illustrates the atomic strain snapshot of the amorphous region in SC/MG specimen for 0.5 km/s and 1.4 km/s respectively after a time period of 9 ps. It is observed that at lower

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shock velocity (Fig. 15(a)), the STZs are scarcely dispersed behind the shock front after it has traversed along the amorphous region of the specimen. However, as the shock velocity is increased (Fig. 15(b)); the intensity of the

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formation of STZs also increased and the distribution became more homogenous. Though the formation of STZs aid in propagation of the shock front, these regions of high strain cause structural instability in the metallic glass region and consequently leads to the disordering of full icosahedral clusters. Literature studies have shown that the disintegration of full icosahedral cluster is a structural signature of shear localization process in metallic glasses [55, 56]. In the present case, as the intensity of STZs increases (at higher shock velocities), the localized high strain

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regions also increases which in turn tends to disintegrate the full icosahedral clusters in the specimen.

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indicate the shock direction and the dotted line indicates the interface.

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Fig. 15: Atomic strain snapshot of the amorphous phase in SG/MG specimen at a time period of 9 ps. Red arrows

In order to characterize the topological changes in the MG region of each specimen, Voronoi polyhedral analysis has been implemented [46, 47]. It is well accepted that icosahedral clusters and networks are the key building blocks in Cu-based MGs [57, 58] and hence their population fraction is important to be analyzed during the deformation processes. Fig. 16 show the comparative plots of the variation in the population of icosahedral clusters during the shock compression process of the SC/MG and NC/MG specimens at different piston velocities. It is found that at a

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lower piston velocity (Fig. 16(a)), the number of icosahedral clusters started to decrease for both the specimens after ~4 ps. However, the decrease of icosahedral clusters in the SC/MG specimen is marginally steeper than that of the NC/MG specimen. With the increase in the piston velocity, the rate of decrease in the population of icosahedral

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clusters for both specimens also increased as shown in Fig. 16(b)-(d). Meanwhile, the difference in the population of icosahedral clusters (at t = 10 ps) also persistently decreased for both specimens with increasing piston velocities;

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the population of icosahedral clusters in NC/MG specimen became less than that of the SC/MG specimen at 1.4 km/s piston velocity as shown in Fig. 16(d). These plots indicate that due to the high-pressure compression process, the icosahedral clusters (having a coordination number (CN) equals to 12) have collapsed under the shock loading. However, it is observed that due to the amorphization process and presence of grain boundaries in the crystalline region of the specimen, the impact of the shock in the metallic glass region was negated at lower piston velocities. A comparatively higher population of icosahedral clusters in the SC/MG specimen at 1.4 km/s piston velocity can be attributed to the extensive amorphization that has occurred in the crystalline region of the specimen before the shock

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front reached the interface, which was not observed during the shock compression of the NC/MG specimen under

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the same shock velocity.

Fig. 16: Plots of variation in the number of icosahedral clusters with respect to time for SC/MG specimen and

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NC/MG specimen for shock velocity of (a) 0.5 km/s, (b) 0.8 km/s, (c) 1.1 km/s, and (d) 1.4 km/s.

Fig. 17(a) and (b) shows the variation in the population of various Voronoi clusters for the SC/MG specimen at 0.5 km/s and 1.4 km/s piston velocities respectively whereas Fig. 17(c) and (d) shows the same for the NC/MG specimen. It shows that in all cases, the population of clusters with indices <0 4 4 6> and <0 4 4 7> increased with time whereas the population of clusters with index <0 2 8 1> decreased with time. In contrast,the <0 4 4 4> indexed clusters showed very minor change with respect to time. This indicates that the shock compression process, due to high-pressure, induces an increase in the coordination of the atoms and consequently increases the coordination number. This is evident from the present study as the clusters with indices <0 4 4 6> and <0 4 4 7> have a CN of 14

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and 15 respectively whereas clusters with index <0 2 8 1> have a CN of 11. Similar findings have also been reported in the literature studies [59]. Moreover, the clusters with indices <0 4 4 6> and <0 4 4 7> faintly represent distortedFCC like cluster [60], indicating that the glassy nature of the Cu-Zr MG was reduced with the shock compression

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process.

Fig. 17: Plots of variation in the population of different Voronoi cluster with respect to time for SC/MG specimen at piston velocity: (a) 0.5 km/s, and (b) 1.4 km/s and for NC/MG specimen at piston velocity: (c) 0.5 km/s, and (d) 1.4 km/s.

3.6. The influence of crystalline-amorphous interface

For the nanolaminate structures, the crystalline-amorphous interface has a vital contribution towards the phase transition mechanism during high-velocity shock loading. It is observed that when the high-velocity shock front

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reached and passed through the interface into the amorphous region, a rarefaction wave was generated into the crystalline region. The rarefaction wave was then reflected by the compressive shock wave due to the presence of interface which acted as a disruption to the periodicity of the crystalline phase similar to the effect of a surface. Due

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to the propagation of rarefaction wave into the crystalline region, the stresses were slightly released which in turn helped in the evolution and stabilization of the BCC phase from the intermediate amorphous phase. This phenomenon, which is prominently seen in SC/MG specimens, can be validated through kinetic energy map in Fig. 8(d)-(f) which shows that after the shock wave has travelled towards the amorphous region, the kinetic energy of the

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atoms in the crystalline region has slightly increased indicating the restructuring of atoms into BCC phase. On the other hand, the phase transition results (Fig. 10 and Fig. 11) show that the volume of BCC phase during the shock

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propagation from the amorphous region is lesser than the volume of BCC phase during the shock propagation from the crystalline region. This is because of the absence of reflected rarefaction wave during the shock propagation from the amorphous region. It is also observed that during high-velocity shock loading in SC/MG specimen (Supplementary video V2), the BCC phase has started to form from the surface of the crystalline region; it is after the rarefaction wave propagation (reflected by the crystalline-amorphous interface).

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4. Conclusions

In the present study, MD simulations have been used to investigate the shock response of crystalline-amorphous nanolaminate specimens and evaluate the underlying deformation mechanisms. Based on the simulation results and

•

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various analyses that have been performed, the following conclusions can be made:

The pressure profiles of the SC/MG specimen show that the occurrence of elastic precursors in the

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crystalline region is attributed to the plane-plane collision. Increase in the number of grains cause misalignment of planes which results in decrease in the intensity of the elastic precursor due to disruption

in the plane-plane collision.

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According to the pressure profile near the crystalline-amorphous interface, all the specimens show dip near the crystalline region and a peak near the amorphous region and such dip in pressure profile during shock loading process indicates the transition from elastically compressed region to plastically compressed region.

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•

RDF plots of SC/MG specimen show a characteristic first peak splitting which signifies that a BCC phase has been formed from the intermediate amorphous phase in the crystalline region.

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Voronoi analysishas shown that the shock loading has increased the coordination number (CN) which is

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attributed to the formation of high CN clusters such as <0 4 4 6> and <0 4 4 7>. On the other hand, the population of icosahedral clusters decreases due to the shock loading process and the rate of decrease is directly relative to the increase in the piston velocity. •

During the shock propagation from the crystalline to amorphous region, the presence of crystalline-

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amorphous interface has caused the generation of reflected rarefaction wave in the crystalline region which aids in the evolution and stabilization of the BCC phase from the intermediate amorphous phase thus

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increasing the martensite volume fraction.

It is hoped that this work can give insights into the atomistic mechanisms during the shock loading process of crystalline-amorphous nanolaminates which can contribute towards designing nanolaminates to withstand high impact and shock loads.

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Acknowledgments

We acknowledge the support from NSERC Discovery Grant under RGPIN 430800-2013, Canada. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET:

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References

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