Introduction

Reactive multilayer foils (RMF) of nickel and aluminum (Ref 1) are used for joining applications as an alternative method to standard processes. The reactive metals are either deposited by magnetron sputtering directly onto the materials to be joined or commercially available as free-standing foils (Nanofoils®). Ni-Al nanofoils are widely used for bonding metals and alloys, at room temperature and in air (Ref 2, 3). Recently, bonding ceramic devices either to ceramics or to thermally mismatched metallic devices was realized using Ni-Al multilayers (Ref 4). The foils are used for their capabilities of undergoing a self-sustaining exothermic reaction (SHS) and thus act as a controllable heat source to melt braze. The use of Ni-Al multilayer nanofilms for joining purposes should be improved if the process properties are well controlled. Other interesting studies demonstrate that different types of nanolayers are promising for low-temperature brazing applications such as copper-based nanostructured coatings (Ref 5). The SHS-based joining technique opens new application fields such as joining of thermal and mechanical sensitive materials (i.e., ceramic-metal joints) and precision joining of microscale components (i.e., MEMS packaging and/or optical components) (Ref 6).

SHS process in RMF is represented in Fig. 1. After ignition, a reaction front propagates throughout the system without any further supply of heat. The self-sustained character of the front is due to the strong exothermicity of the reactive process. The heat released locally induces the reaction in contiguous regions and so forth. The exothermicity may be associated with either dissolution or phase formation, or both. The dissolution and the resulting mixing are estimated to be responsible for about 60% of heat release in SHS processes (Ref 7, 8). The reactive wave structure exhibits a “large” region corresponding to the partial dissolution of Ni atoms into Al liquid layers, as a function of the local temperature along the front. The rectangle, depicted in Fig. 1, indicates a zigzagged reaction zone that starts at the melting temperature of aluminum and ends at the combustion temperature of burned material.

Fig. 1
figure 1

Self-sustaining reactive wave in an Ni-Al multilayer nanofilm. Blue and yellow layers correspond to Al and Ni, respectively. The preheating zone is made of alternated reactants, while the afterburning zone is filled with products (in red). The box corresponds to the reactive dissolution zone

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In this study, we have focused on the dissolution processes in Ni-Al RMF using molecular dynamics (MD) simulations. Our purpose was to determine the elemental mechanisms occurring at the microscopic level.

Simulation Details

LAMMPS software package (Ref 9) was used to perform MD simulations of reactive nanofoils. The simulated metallic multilayer was composed of one inner layer of liquid Al in between two outer layers made of solid fcc Ni with a (100) orientation of the interface. Despite the fact that the NiAl nanofoils used in the experiments were deposited with a (111) texture, the (001) orientation was chosen in the MD simulations to simplify the analysis of the MD results. Nevertheless, we have shown that both the nature and the sequence of elemental mechanisms were not modified by the choice of the interface orientation ((001) or (111)). Only the epitaxy between NiAl grains and Ni substrate may be affected by the specific interface orientation [to be published].

A many-body potential (EAM) developed by Purja and Mishin was used to describe the Ni and Al atomic interactions (Ref 10). The fitting of the Ni-Al cross-interactions requires an extensive database including experimental cohesive energy, lattice parameter, elastic constants, and ab initio formation energies of several intermetallic compounds. The resulting potential is very well suited to study the reactive behavior of Ni-Al nano-systems as it describes precisely the pure elements and two intermetallic phases NiAl and Ni3Al. Furthermore, the melting temperature of the elements and intermetallic compounds agrees well with the experimental data (see Table 1).

Table 1 Melting temperatures (in K) computed with the EAM potential described in (Ref 10) and comparison with experimental data (Ref 11, 12)
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We performed MD runs in the isothermal/isobaric ensemble (NPT) by maintaining constant the number of atoms (N), the total pressure (P), and the temperature (T). To do so, the equations of motions were integrated with a time-step of 2 fs and the Parrinello-Rahman barostat (anisotropic)/Nose-Hoover thermostat was implemented in LAMMPS. Typical simulation duration is 4 ns and thermostatting and barostatting time scales are 0.2 and 2.0 ps, respectively.

The Nisol-Alliq-Nisol layered system was produced with a specific procedure presented in (Ref 13). The reference system was made up of 100,000 Ni atoms and 73,960 Al atoms. After relaxation, the thickness of the Al liquid layer was 4.4 nm high for a bilayer thickness of 7.98 nm. Lengths of the simulation box in x and y directions are similar and equal to 17.8 nm. To distinguish liquid from solid parts of the samples, we adapted the well-known method of Ackland and Jones (Ref 14), which is based on the angle distribution of the nearest neighbors to identify the local environment of atoms. In our approach, we performed first an Ackland and Jones analysis to determine the type of each atom (fcc, bcc, or others). Then, if a specific fcc (bcc) atom has more than 8 neighbors in a shell of 0.3 nm of the same type, it is labeled with this fcc (bcc) type. Otherwise, it is considered as a liquid atom. This modification of the standard Ackland and Jones analysis is very powerful to study systems with liquid and solid phase coexistence [for more details, see the Appendix in (Ref 13)].

Results and Discussion

The system was followed at constant temperature, above the melting point of Al, with several indicators. The number density for thin slices (0.1 nm) along the direction perpendicular to the interface with well-defined peaks shows whether the system is structured in (001) atomic planes. The same quantity evaluated on a coarse grid (0.25 nm) gives the local composition expressed in atomic percentage. Each atom was labeled by several indexes: type (Ni or Al), state (liquid or solid), and local crystallographic configuration if solid (fcc or bcc) according to original and modified Ackland and Jones analysis (Ref 13, 14). Figure 2 shows the number density of the reference system at different times and the corresponding snapshots. The very initial state corresponds to an unstable configuration (Ni)sol-(Al)liq-(Ni)sol. As soon as the liquid layer (Al)liq was put in contact with the solid substrate (Ni)sol (t = 0.1 ns—Fig. 2a), some individual Ni atoms crossed the solid-liquid interface barrier. Once in the inner layer, these atoms moved as liquid atoms exhibiting a diffusive motion. On the other side, Al liquid atoms felt the effect of the solid Ni substrate and self-organized in (001) pseudo-solid planes near the interface. A few hundreds of picoseconds later (t = 0.4 ns—Fig. 2b), a significant number of Ni atoms were found in the inner layer. Most of them remained stacked close to the interface. At 2 ns (Fig. 2c), Ni atoms were distributed overall in the inner layer and Ni at.% was flat. As shown in Fig. 2(a) to (c), the sharp concentration gradient of Ni in the liquid was smoothed in about 2 ns. After this transient of a few nanoseconds, the profile of Ni attained the shape that it will keep for the subsequent evolution. After the first Ni atoms were gone easily into the liquid, they stayed confined near interfaces for a while before they succeeded to mix with Al atoms (Fig. 2d-f). The dissolution process is thus directly related to the mixing between Ni and Al atoms. As the mixing is the exothermic process that self-sustains the propagation, it is interesting to determine the mechanisms that control dissolution. Let us carefully analyze the MD simulations results. The Ni atoms close to the interfaces went away more easily than atoms located deeper in the substrate. Al atoms occupied the vacancies created by outgoing Ni atoms. The snapshots 2d-f show that Al atoms remained in layers close to interfaces. Some of these atoms (dark blue) adopted a local fcc arrangement. However, the flux of incoming Al atoms (104 atoms in 3.5 ns) in the substrate was not compensated by the flux of outgoing Ni atoms (3.5 × 104 atoms in 3.5 ns). These observations prove that the initial configuration is unstable. Figure 3 shows the evolution of a (001) plane just below the solid-liquid interface. At 0.1 ns, the plane was mostly covered by fcc Ni atoms (Fig. 3a, d). At 0.4 ns, Al atoms had occupied the numerous free sites liberated by outgoing Ni atoms (Fig. 3b). A large part of Al atoms was in fcc local configuration (Fig. 3e). Later, atoms lost their local organization and became liquid (Fig. 3c, f). The formation of a transient solid solution (Ni + Al)ss has occurred plane by plane before melting. After the disappearance of 3 atomic planes at each interface, the system reaches a configuration (Ni)sol-(Ni + Al)ss-(Ni + Al)liq-(Ni + Al)ss-(Ni)sol in which the inner layer is saturated by nickel. Over time, the number of liquid (Ni and Al) atoms increased due to dissolution before a slowdown, as shown in Fig. 4 (lines af, ac, ab). This proves that mixing in the liquid state is favorable for a layered system of miscible metals.

Fig. 2
figure 2

(a-c) Number density profiles at t = 0.1, 0.4, and 2 ns in direction z, perpendicular to the interfaces. For visualization purposes, the scale of the number of atoms is normalized to 100. Local atomic percentages for Ni and liquid atoms within slices of thickness 0.25 nm are also shown. The black dashed lines indicate the limits of the inner liquid layer. Temperature is 1200 K. (d-f) Snapshots of the system: Ni atoms are shown as yellow spheres, liquid Al atoms as light blue spheres, and solid fcc Al atoms as dark blue ones

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Fig. 3
figure 3

Snapshots of a (001) representative plane in the solid substrate undergoing melting. Al and Ni are shown as blue and yellow spheres, respectively. Fcc solid atoms and liquid atoms, whatever their type (Al or Ni), are shown as green and red spheres, respectively

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Fig. 4
figure 4

Evolution of the fraction of liquid atoms at 1200, 1400, and 1500 K. The marks a-b, a-c, and a-f indicate the time range of the dissolution process at these temperatures. The dotted line f-g corresponds to the sudden and complete melting. The marks c-d-e figure the arrest of the dissolution process because of the nucleation and growth of the new B2-NiAl phase

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The temperature plays an important role in the dissolution. Figure 4 reveals three typical behaviors. The case corresponding to T = 1200 K was already discussed in detail. For an isothermal system at T = 1400 K, the fraction of liquid increased until a plateau was reached (c, Fig. 4) before decreasing abruptly. The sudden breaking is due to the formation of a new solid phase: the B2-NiAl intermetallic compound. The fraction of liquid atoms continued to decrease in favor of the growth of the grain (d, Fig. 4). After 2 ns, the majority of the inner region was transformed into B2-NiAl phase. The situation is drastically different at T = 1500 K. The dissolution process was amplified until it reached the saturation of Al liquid by Ni atoms (f, Fig. 4). The fast dissolution is associated with a reduction in the thickness of the Ni solid substrate. The solid Ni layer became very thin and the solid solution (Ni + Al)ss was unstable. Below a thickness of a few nanometers (1 to 2 nm), the remaining solid solution melted at once. This observation may explain the melting point depression observed experimentally (Ref 15). Figure 4 shows that the plateau value observed in the fraction of liquid atoms depends on the temperature. A higher temperature makes it possible to dissolve more nickel into the molten aluminum. Let us note that the characteristic time of the dissolution process was found to depend both on diffusion coefficient and thickness of the inner Al layer.

The inner liquid layer is a liquid solution (Al + Ni)liq with a fraction of Ni that depends on the temperature. Above 1500 K, the system was completely melted. In the temperature range from 1100 to 1400 K, nucleation of B2-NiAl was observed. The phase transformation was possible because of solid phase stability of NiAl, in this temperature range (T < T melt(NiAl)). Furthermore, the liquid composition was compatible with the formation of B2-NiAl, at least locally. For instance, for the system at T = 1400 K, the fraction of Ni in the liquid was reaching asymptotically 0.5 while nucleation started. The seeds appeared at the liquid-solid interface and grew to form round-shaped grains. The grains are depicted in Fig. 5. The local atomic arrangement of atoms in the solid solution (Ni + Al)ss was changed, from fcc to bcc, when these atoms adhered to the lower surface of the NiAl grains (for the lower interface) or, from liquid to bcc, when the nucleation and growth started in the liquid phase. Grain formation slowed down the dissolution process: NiAl grains at the interface acted as a diffusion barrier for further displacement of atoms from solid to liquid and vice versa. As shown in Fig. 5, the nucleation process occurs in a different way, as a function of temperature. At T = 1100 K, many grains of small size appeared randomly at the interface (Fig. 5a, b). At T = 1400 K, only one big grain was observed (Fig. 5e, f); smaller grains did not survive. This behavior can be related to a well-known result of classical nucleation theory that tells that the critical nucleus size is inversely proportional to undercooling degree ∆T. Moreover, the number of critical seeds, n *, depends on the undercooling n * ≈ n 0 exp(−K/∆T 2), where n 0 is the number of sites on which the nucleation is possible and K is a thermodynamic factor (Ref 16). The presence of many grains at the initial stage has a direct consequence on the microstructure. In view of the fact that small grains presented different orientations (four have been observed in this case), no coherent intermetallic layer was formed at the end of the growth process. Contrariwise, at higher temperature (T = 1400 K), the majority of the inner region was transformed into a B2-NiAl layer (Fig. 5g, h). In this case, the formation of B2-NiAl was stopped by the lack of Al. The system was staying in this configuration because the off-stoichiometry did not allow the complete conversion of the system. The persistence of solid Ni layers at some stage of the evolution is very important, due to the fact that it allows the heterogeneous nucleation of a new phase.

Fig. 5
figure 5

Snapshots (perspective view) of the system at T = 1100 K (a-d) and T = 1400 K (e-h) during the nucleation and growth of the B2-NiAl intermetallic compound. Solid fcc atoms are shown as light blue spheres, and solid bcc atoms are shown as green spheres, whatever their type (Al or Ni). Atoms in grain boundaries (liquid or surface atoms) are represented in red in (d) and (h) snapshots

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Conclusions

We have studied solid-liquid reactive Ni-Al nanolayers at temperatures ranging from 1100 to 1500 K. In this range, Al is liquid while the bulk of Ni remains solid. MD analysis at a given temperature reveals the mechanisms occurring at nanoscale. The process proceeds through a sequence of transformations: diffusion-controlled dissolution of Ni into the liquid layer; creation of vacancies in the solid substrate and subsequent substitution by the Al atoms; and melting of the crystallographic plane if the coverage by Al exceeds a threshold. Depending on the temperature, the system evolves toward a complete mixing associated with the melting of the substrate or toward the formation of a new phase. Our analysis proves to be useful in elucidating elemental mechanisms governing dissolution, melting, reactive diffusion, and phase formation at nanoscale.