Due to their nanoscale features, nanometric multilayers can have a large variation in properties for varying bilayer heights. While the hardening at small feature sizes and the consequent softening at even smaller feature sizes have been observed for decades, the underlying mechanisms are still under debate. In this study, molecular dynamics uniaxial compression simulations are employed to study the mechanical properties of Al/Ni multilayers for bilayer heights h from 100 nm down to 5 nm. The effect of the microstructure on Young’s modulus and the yield strength was investigated. Furthermore, the mechanical properties of equiatomic and equivolumetric multilayers were compared. A comparison with experimental results from the literature showed good agreement. Both the hardening at intermediate bilayer heights as well as the softening at very small bilayer heights were observed. The results are discussed in the context of possible hardening and softening mechanisms. While the Hall–Petch effect with a h 1 / 2 scaling is not contradicted, it is shown that, although the underlying mechanisms are different, both the hardening as well as the softening are based on a general size effect with a scaling of ln ( h ) / h.

Nanometric metallic multilayers are composed of two or more components, of which at least one contains a metallic element. Binary multilayers are made up of two elements and are characterized by their bilayer height h, which is the sum of the heights of one layer of each element. These bilayer heights usually range from a few nanometers to a few hundred nanometers. Varying the bilayer height allows tuning the properties of the multilayers with the potential of achieving properties that are superior than those that can be achieved by conventional single-element films. This results in, among others, materials with enhanced shock-resistance,1 radiation-resistance,2 as well as optical3 or mechanical properties.4,5 This allows the production of materials with exceptional strength and ductility.6 

The strength of metallic multilayers can be characterized by their yield strength σ y. The change in strength with the bilayer height is related to the change in the height of the individual layers, as well as the change in grain size, which is limited by the layer height. Historically, it was divided into three regimes: the Hall–Petch regime7,8 at layer heights of a few hundred nanometers down to below 100 nm, the confined layer slip (CLS) regime at layer heights down to 10s of nanometers, and the inverse Hall–Petch regime at very small layer heights.9 In the Hall–Petch regime, the dislocation pileup at grain boundaries and interfaces leads to an increase in strength with decreasing bilayer height10 and the strength is observed to scale with the grain size (and consequently in multilayers with the layer height) as h 1 / 2. In the CLS regime, the strength is further increased with decreasing layer height, which is explained by the confinement of the dislocation glide to single layers,11 leading to a ln ( h ) / h scaling of the strength. As the Hall–Petch regime has been developed based on experimental observations (and not underlying mechanisms), its existence has been questioned in more recent literature studies.12 Instead, it is argued that there is only one hardening regime (CLS regime), which is based on a size effect on the dislocation curvature, leading to a general ln ( h ) / h scaling of the strength,13 which is supported by experimental data.12 In the inverse Hall–Petch regime, the strength starts to decrease with decreasing layer height. The three main explanations for the softening are, on the one hand, that the mechanical properties are dominated by the interfaces,10 which make up a significant part of the full system. On the other hand, sharp interfaces can allow for dislocations crossing the interfaces, which also leads to softening.11 Finally, it is argued that the stability of dislocations decreases with decreasing layer height.9 

While the experiment allows the observation of the different regimes, molecular dynamics (MD) simulations are a great tool that allows to link the mechanical properties to the underlying mechanisms on the atomic scale (such as dislocations or the nature of the interface). Compression MD simulations have been carried out in copper,14 where the tension–compression asymmetry was investigated, while another work studied NiTi,15 where pseudoelasticity was investigated. In the context of multilayers, MD simulations of the compression of Cu/graphene multilayers have been carried out to investigate the strengthening mechanism as well as its dependence on the bilayer height.16 Instead of looking at compression, a large number of papers investigate tension via MD simulations. This way, interface fracture and phase transformations in Cu/Ta multilayers have been investigated.17 Furthermore, the mechanical properties of nanocrystalline aluminum have been investigated.18 Finally, in the AlNi system, the size effect in the deformation of a void at the Ni/Ni 3Al interface has been studied via uniaxial tension MD simulations.19 

More recently, uniaxial compression MD simulations were compared to nanoindentation MD simulations for bilayer heights h 25 nm.20 At this bilayer height, the inverse Hall–Petch regime was observed and it was shown that the presence of a premixed interlayer only influences the mechanical properties when it makes up significantly more than 50 percent of the whole system. Shock compression MD simulations showed comparable trends for the effective modulus.21 There have been additional investigations of Al/Ni multilayers via MD nanoindentation simulations for systems consisting of single crystal layers22 as well as systems consisting of layers with columnar and nanocrystalline grains.23 So far, MD simulations have not been directly compared to experimental results, even if such results exist for Al/Ni multilayers. A first study on roll-bonded Al/Ni multilayers observed an increase in strength with decreasing bilayer height.24 A more recent study investigated the mechanical properties and the wear behavior of Al/Ni multilayers with bilayer heights of h = 20 nm and h = 100 nm.25 The multilayer with a lower bilayer height showed at the same time a higher strength and a lower wear rate. The mechanical properties of Al/Ni multilayers for both varying bilayer heights26,27 along with varying stoichiometry28 were investigated more extensively using micropillar compression as well as nanoindentation. For varying bilayer height, the observed strengthening was observed to follow the Hall–Petch strengthening down to bilayer heights of h = 40 nm, while it followed CLS strengthening down to bilayer heights of h = 20 nm.26,27 When varying the stoichiometry, both strength and stiffness increased with increasing Ni content.28 

The aim of this work is to directly compare the results from MD simulations with experimental results. Uniaxial compression MD simulations are conducted for a large range of bilayer heights 5, 7.25, 10, 15, 25, 50, 75, and 100 nm. Furthermore, the influence of the microstructure on the mechanical properties is discussed and both equiatomic plus equivolumetric systems are investigated. It is shown that both Young’s modulus E and yield strength σ y obtained via MD simulations are very comparable to the values obtained in the experiment. Furthermore, the underlying mechanisms are investigated and discussed.

The molecular dynamics (MD) simulations were conducted using the large-scale atomic/molecular massively parallel simulator (LAMMPS) package.29 The embedded-atom-method (EAM) force field by Pun et al.30 was employed to calculate the interatomic forces between Al and Ni. This is the most widely used force field for the AlNi system. Even if the interfacial forces are not calculated explicitly, they are calculated implicitly via the pair forces of the atoms at the interface. While the elastic constants are not reproduced exactly, the difference in Young’s modulus compared to the experiment is up to 10%31 and it is well suited for qualitative investigations.

Multilayers with bilayer heights h in the range of 5, 7.25, 10, 15, 25, 50, 75, and 100 nm are studied. The dimensions of the systems are L x × L y × L z, where L x 30 nm, L y 30 nm and L z 40 nm. This means, when h 40 nm, L z = h and when h < 40 nm, L z = i × h where the smallest i is chosen that fulfills L z 40 nm. Periodic boundary conditions were applied in all dimensions.

Two different kinds of systems were studied. The first kind is the equiatomic systems, where the individual layer heights h A l + h N i = h are chosen such that there is an equal amount of Al and Ni atoms N A l N N i. This means h A l 0.6 × h. Al/Ni multilayers are mainly studied as reactive multilayers,32 where the equiatomic system is the standard system, as it releases the largest amount of energy. Experimental studies of the mechanical properties of Al/Ni multilayers on the other hand focus on equivolumetric systems.26,27 For direct comparison with the experiment, the second kind of system studied is the equivolumetric system, where h A l = h N i. The Ni layers are of a nanocrystalline nature with grain sizes d N i = min(10 nm, h N i). The microstructure of the Al layers depends on the bilayer height. For h 50 nm, the Al layer consists of columnar grains with grain size d A l = h A l. As there need to be at least two grains in x- and y-directions, for larger bilayer heights, the systems would contain such a large amount of atoms, that it becomes computationally very expensive. Thus, for h 50 nm, the Al layer was of a single crystal nature. The overlap was chosen to evaluate the validity of the single crystal assumption for larger bilayer heights. The grain orientation was chosen randomly and was different from grain to grain. Such a kind of microstructure has also been observed in the experiment.33 It has to be mentioned that the microstructure has a strong dependence on the deposition conditions, leading to a large variance in the microstructures that are observed for nominally the same systems. To evaluate the influence of the microstructure, the results from this study are compared to results from a previous MD study,20 where the grains in both the Al and the Ni layers were columnar.

The systems were created utilizing a Voronoi tesselation in the Open Source command line program Atomsk.34 The microstructure of one system is illustrated in Fig. 1. A premixed interlayer of height w = 2 nm was added by removing atoms at the interface and replacing them with an amorphous AlNi phase, such that the ratio between Al and Ni atoms stays approximately constant. The choice and nature of such an interlayer was extensively discussed in Ref. 35. Illustrations, coloring the atoms by type or by crystal structure, were created using the open-source scientific visualization and analysis software OVITO.36 

After the systems were created, they were equilibrated in an NPT (constant number of particles, constant pressure, constant temperature) ensemble for 0.4 ns at a temperature of 300 K and zero pressure. To extract the mechanical properties, the systems were compressed with a strain rate of ϵ r a t e = 10 8 s 1 up to a maximum strain of 0.1, recording the stress in x-, y-, and z-directions every 100 time steps. Young’s modulus E is then extracted from the slope of the elastic region, while the yield strength σ y , i is extracted from the stress at the yield point. The yield point ϵ y , i is determined by the lowest strain for which ϵ × E σ > 0.05 (see Fig. 2). These quantities were shown to be strain-rate independent and can be compared to experimental results of equivolumetric Al/Ni multilayers from Refs. 26 and 27. Young’s modulus is compared to experimental results obtained via nanoindentation.26 In our previous work, we have shown that Young’s modulus obtained via nanoindentation MD simulations is comparable to Young’s modulus obtained via uniform uniaxial compression MD simulations.20 The yield strength is compared to experimental results obtained via micropillar compression.27 While the influence of the pillar geometry on the deformation should be negligible, the surface of the micropillar might provide additional nucleation sites for dislocations. Just as in the MD simulation, the orientation of the multilayer is perpendicular to the direction of compression, resulting in the shear planes having an orientation of 45 ° with respect to the Al–Ni interfaces. In the experiment, the yield strength is defined as the 0.2% yield strength, which is also illustrated in Fig. 2. For the MD simulations, the 0.2% yield strength is also calculated, but it is almost 1 GPa larger than the immediate yield strength. This is likely due to the fact that, statistically, at smaller volumes, which are studied in MD simulations, the plastic events are less likely at smaller strains.37 Furthermore, a higher strain rate increases the critical stress for dislocation formation.38 This leads to the high slope of the stress–strain curve just after the first plastic event observed in MD simulations, as well as the high ultimate strength. Assuming, σ y , 0.2 % σ y , i for a large volume and at small strain rates, the experimental yield strengths are compared with the immediate yield strength from MD simulations. The MD compression was implemented by rescaling the z-coordinate at every time step. The compression simulations were also conducted in an NPT ensemble at a temperature of 300 K and zero pressure in x- and y-directions. This allows for an expansion in x- and y-directions during compression, following the system’s natural Poisson ratio. The time step was always chosen as 2 fs. The temperature was controlled using a Nosé–Hoover thermostat with a damping parameter of 0.2 ps, the pressure was controlled using a Nosé–Hoover barostat with a damping parameter of 2 ps.

FIG. 1.

Equivolumetric system with bilayer height h = 25 nm. (a) Front view with atom types, Al atoms are in yellow, Ni atoms in blue. (b) Front view colored by grains. (c) Top view Al layer colored by grains. (d) Top view Ni layer colored by grains.

FIG. 1.

Equivolumetric system with bilayer height h = 25 nm. (a) Front view with atom types, Al atoms are in yellow, Ni atoms in blue. (b) Front view colored by grains. (c) Top view Al layer colored by grains. (d) Top view Ni layer colored by grains.

Close modal
FIG. 2.

Stress–strain plot of the equivolumetric system with bilayer height h = 25 nm. The red circle marks the immediate yield strength σ y , i, while the magenta circle shows the 0.2% yield strength σ y , 0.2 %.

FIG. 2.

Stress–strain plot of the equivolumetric system with bilayer height h = 25 nm. The red circle marks the immediate yield strength σ y , i, while the magenta circle shows the 0.2% yield strength σ y , 0.2 %.

Close modal

Figure 3 shows Young’s modulus and yield strength as a function of the bilayer height. Comparing MD results for systems with different microstructures shows that for small bilayer heights, columnar grains and nanocrystalline grains in the Ni layer result in the same mechanical properties. While for h > 15 nm, Young’s modulus for the two systems is still comparable, the yield strength differs significantly. At h = 50 nm, the yield strength of the multilayer with columnar Ni grains is almost twice as large as the one of the multilayer with nanocrystalline grains. The two data points for nanocrystalline systems at h = 50 nm show the multilayer with a columnar Al layer and a single crystal Al layer, respectively. It verifies that the microstructure of the Al layer can be approximated as single crystalline for large bilayer heights. Generally, experimental results and MD results for the systems with nanocrystalline Ni layers agree very well. For bilayer heights below 50 nm, there is an offset between the experimental results and the MD results of Young’s modulus, while the yield strength agrees well across the whole range. The difference between the equivolumetric and the equiatomic systems is very small in both Young’s modulus and yield strength. Furthermore, Fig. 3(c) shows that there is an offset of around 1 GPa between the immediate yield strength and the 0.2% yield strength from MD simulations, while the qualitative change with bilayer height is highly comparable.

FIG. 3.

Plot of the mechanical properties as a function of the bilayer height. The results for the equiatomic systems with columnar grains in the Ni layer are taken from Ref. 20 (a) Plot of Young’s modulus as a function of bilayer height, experimental results obtained via nanoindentation.26 (b) Plot of yield strength vs bilayer height for different microstructures and stoichiometric. (c) Plot of yield strength vs bilayer height for equivolumetric systems showing both the immediate yield strength σ y , i as well as the 0.2% yield strength σ y , 0.2 %, experimental results obtained via micropillar compression.27 

FIG. 3.

Plot of the mechanical properties as a function of the bilayer height. The results for the equiatomic systems with columnar grains in the Ni layer are taken from Ref. 20 (a) Plot of Young’s modulus as a function of bilayer height, experimental results obtained via nanoindentation.26 (b) Plot of yield strength vs bilayer height for different microstructures and stoichiometric. (c) Plot of yield strength vs bilayer height for equivolumetric systems showing both the immediate yield strength σ y , i as well as the 0.2% yield strength σ y , 0.2 %, experimental results obtained via micropillar compression.27 

Close modal

The yield strength from Fig. 3(c) is replotted vs h in Fig. 4(a). At large bilayer heights of h  50 nm, the strength of the MD systems is changing linearly with ln ( h ) / h, just as in the experiment by Nasim et al.27 While in the experiment, the strength is leveling off for small bilayer heights, it is decreasing linearly with increasing h (decreasing h) in MD simulations. All three datasets are also fitted to the function σ y = A × l n ( B × h ) / h, for h  15 nm. Smaller bilayer heights are not considered, as the high fraction of interfaces leads to a decrease in the rate of softening. The results of the fitting are summarized in Table I. Figure 4(b) is a log–log plot of the strength vs the bilayer height. For large bilayer heights, the strength decreases with a h 1 / 2 dependency on the bilayer height. The limit of the Hall–Petch h 1 / 2 scaling can be observed at around h = 40 nm, while the strength follows ln ( h ) / h scaling down to bilayer heights of h = 15 nm.

FIG. 4.

Analysis of yield strength from Figs. 3(b) and 3(c) (experimental results from27) (a) Plot of yield strength as a function of h. The dashed lines underline the linear behavior of the strength with l n ( h ) / h for both strengthening and softening. They represent a fit to the respective data to the function σ y = A × l n ( B × h ) / h. (b) Log-log plot of yield strength as a function of the bilayer height. The dashed line corresponds to a h 1 / 2 scaling.

FIG. 4.

Analysis of yield strength from Figs. 3(b) and 3(c) (experimental results from27) (a) Plot of yield strength as a function of h. The dashed lines underline the linear behavior of the strength with l n ( h ) / h for both strengthening and softening. They represent a fit to the respective data to the function σ y = A × l n ( B × h ) / h. (b) Log-log plot of yield strength as a function of the bilayer height. The dashed line corresponds to a h 1 / 2 scaling.

Close modal
TABLE I.

Results of fitting the strength to the function σy = A × ln(B × h)/h.

DatasetA (GPa × nm)B (nm−1)
σy,i MD 56.26 0.099 
σ y , 0.2 % MD 85.96 0.096 
σ y , 0.2 % exp 51.70 0.103 
DatasetA (GPa × nm)B (nm−1)
σy,i MD 56.26 0.099 
σ y , 0.2 % MD 85.96 0.096 
σ y , 0.2 % exp 51.70 0.103 

The yield point across all systems is at a strain of ϵ y = 0.02 or below. To have representative systems for each region, the analysis of dislocations, grain boundaries, and crystal structure is focused on the four equivolume systems with h = 7.25 , 10 , 50 , 100 nm (see Figs. 5 and 6). The most notable observation that can be made across all systems is that the vast majority of dislocations are formed in the Ni layer. This is also true for very small bilayer heights, where the grain sizes in the Al and Ni layers are comparable ( h 25 nm). At this bilayer height, the grains in the Ni layer are quasi-columnar. For h < 50 nm, there is neither a notable difference in dislocation density nor in dislocation movement when varying the bilayer height. On the other hand, the fraction of interface and grain boundary atoms increases with h 1, which has already been observed and discussed in our previous work.20 Furthermore, already at ϵ = 0.03, steps can be observed in the grain boundaries, and the higher fraction of grain boundary atoms transforming from amorphous to hcp hints at a higher degree of order in the grain boundary. One final observation is that for h 7.25 nm, the Al layer is already very unstable after equilibration and amorphizes completely under compression, as illustrated in Fig. 5.

FIG. 5.

Crystal structure of equivolume systems at ϵ = 0.0 [(a) and (d)] and ϵ = 0.03 [(b) and (e)], ϵ = 0.1 [(c) and (f)]. The bilayer heights are h = 7.25 nm [(a)–(c)] and h = 10 nm [(d)–(f)]. Atoms are colored according to the crystal structure: fcc (green), hcp (red), and amorphous (gray).

FIG. 5.

Crystal structure of equivolume systems at ϵ = 0.0 [(a) and (d)] and ϵ = 0.03 [(b) and (e)], ϵ = 0.1 [(c) and (f)]. The bilayer heights are h = 7.25 nm [(a)–(c)] and h = 10 nm [(d)–(f)]. Atoms are colored according to the crystal structure: fcc (green), hcp (red), and amorphous (gray).

Close modal
FIG. 6.

Crystal structure of equivolume systems at ϵ = 0.03 [(a) and (c)] and ϵ = 0.1 [(b) and (d)]. The bilayer heights are h = 50 nm [(a) and (b)] and h = 100 nm [(c) and (d)]. Atoms are colored according to the crystal structure: fcc (green), hcp (red), and amorphous (gray).

FIG. 6.

Crystal structure of equivolume systems at ϵ = 0.03 [(a) and (c)] and ϵ = 0.1 [(b) and (d)]. The bilayer heights are h = 50 nm [(a) and (b)] and h = 100 nm [(c) and (d)]. Atoms are colored according to the crystal structure: fcc (green), hcp (red), and amorphous (gray).

Close modal

Comparing the systems with h = 50 nm and h = 100 nm at a strain of ϵ = 0.03 (just above the yield point), it can be observed that while there are already some dislocations in the Al layer in the h = 100 nm system, while there are none in the h = 50 nm system (see Fig. 6). Furthermore, in the h = 100 nm system, the dislocation movement is higher than in the h = 50 nm system. It is also notable that the majority of the dislocations in the Al layer are of a stair-rod nature. In the Ni layer, the vast majority of dislocations are Shockley partial dislocations.

While Young’s modulus, observed via MD simulations is mostly independent of the microstructure of the individual layers, the yield strength is strongly affected by microstructure. On the one hand, when the Ni layer is made up of columnar grains, the multilayer is up to twice as strong as in the case where the Ni layer is made up of nanocrystalline grains. This suggests that the columnar grain morphology can significantly strengthen a multilayer system. A reason for this could be the low variability of grain boundary orientations, which prevents shear deformation of the grain boundaries and thus hinders dislocation nucleation. Experimentally, it is very hard to study the influence of grain morphology independently from grain size, distribution of aggregates, and porosity. However, a recent study investigated columnar Cu grains embedded in an amorphous boron grain boundary.39 The study also found an increased strength, which they attributed on the one hand to the strength of the amorphous grain boundaries and on the other hand to the grain boundaries constraining the deformation of the copper columnar grains. Comparison with experimental results, without knowing the microstructure of the experimental multilayers, hints that the Ni layer is made up of nanocrystalline grains in the experiment. Looking at the yield strength, the MD results agree very well with experimental results. The only difference is that while in MD simulations, softening can be observed at bilayer heights below 25 nm, this is not the case in the experiment. While the MD simulations go down to bilayer heights of 5 nm, the minimum bilayer height that was studied in the experiment was 10 nm. However, also at h = 10 nm, there is a significant difference between the MD and experimental results. Beyond uncertainties in experimentally determining h as well as controlling the stoichiometric ratio between Al and Ni atoms at very small bilayer heights, there is another possible explanation; the premixed interlayer in the experimental systems is significantly higher than 2 nm. The yield strength of amorphous AlNi was found to be 1.4 GPa in MD simulations. This might be enough to mask the softening in experimental results, if the interlayer makes up a significant fraction of the entire system. Moreover, the fact that the strain rate is orders of magnitude higher in MD simulations than in experiments, might also play a role. Regarding the Young’s modulus, while the qualitative agreement between MD simulations and experiment is good, there is a clear offset. Likely, the factor that contributes most to the offset of Young’s modulus is the interatomic potential, which slightly underestimates Young’s modulus of Nickel.31 Another factor is the observation that nanoindentation tends to overestimate Young’s modulus of metals, such as nickel, due to pileup.40 

Comparing the equiatomic and equivolumetric systems, it can be observed that there is only a very small difference in both the Young’s modulus and the yield strength. The equivolumetric systems are slightly stronger and stiffer, which can be explained by the higher fraction of Ni (higher fraction of non-columnar grain boundaries). This also suggests that varying the bilayer height h gives access to a wider range of strengths than varying the stoichiometry. However, the combination of the two will lead to an even bigger range of accessible strengths. From h = 100 nm down to h = 50 nm, MD compression simulations confirm the strengthening, which is also observed in the experiment. Figure 4(b) shows that the strengthening approximately follows a h 1 / 2 scaling, which would suggest that the Hall–Petch regime is observed. However, Fig. 4(a), shows that the strengthening also follows a l n ( h ) / h scaling at least as good. Furthermore, both a higher mobility and a higher density of dislocations were observed for larger bilayer heights. While the results do not directly contradict the Hall–Patch behavior, they show that a single hardening regime, based on confined layer slip is at least as likely. Possible explanations for the Hall–Petch effect have been developed based on the observation of an apparent h 1 / 2 scaling, while confined layer slip is based on a single-size effect (the space for dislocation movement, i.e., Mathews critical thickness theory13). This suggests that the h 1 / 2 scaling is simply an empirical relation, which, at appropriate bilayer heights (or grain sizes) emerges from the underlying l n ( h ) / h scaling, as suggested by Li et al.12 For h < 25 nm a softening, which also scales with l n ( h ) / h, can be observed. It can be argued that this is the same size effect, which is observed for hardening at larger bilayer heights. The difference between the fit to σ y = A × l n ( B × h ) / h at h < 15 nm can be explained with a different underlying mechanism. At low bilayer heights, the fraction of atoms in grain boundaries and interfaces becomes significant and scales with 1 / h, combined with the critical thickness, the scaling becomes again l n ( h ) / h, but with a different prefactor. Another explanation of softening that can be found in the literature is that the stability of dislocations decreases with 1 / h.9 However, the simulations in this work do not show dislocations becoming more unstable at lower bilayer heights. Another hypothesis from the literature is that at small bilayer heights, the interface crossing for dislocations is facilitated.41 However, this is only possible when there is no significant premixed region at the interface, which is not true for the MD simulations from this work and also very hard to achieve experimentally.

The fit to σ y = A × l n ( B × h ) / h, shows that B is around 0.1 for all systems. Using a CLS model for the strength of thin film layers σ y = m × G × b L × l n ( α × L b ),42 with the layer height L a material fitting parameter m, the shear modulus G, the burgers vector b and a core-cutoff parameter α = b / r c o r e with a core cutoff r c o r e. As this study looks at bilayers, L = h / 2. With A = 2 m × b × G, a fraction of the shear modulus, the values obtained from the fits are very reasonable. For the term inside the logarithm, the CLS model predicts B = α 2 b. Using α 10 3 and b 3Å, leads to B 0.5, which is a factor 5 larger than what was obtained from the fit. However, considering that through the nanocrystalline Ni layer as well as the presence of the premixed interlayer, the grains in the Ni layer are smaller than the layer height, the obtained values for B are also reasonable.

Focusing on the underlying mechanisms of the strengthening and softening, observations related to dislocations and their behavior are discussed. At the onset of plasticity (around ϵ = 0.02), no stable dislocations can be observed: however, there are steps in the grain boundaries, which suggest the nucleation of a dislocation, which has likely been absorbed by the grain boundaries between the modeling time steps. The fact that these steps can only be observed in the nickel layer is likely due to the fact that the grain boundaries are not perpendicular to the compression direction in Ni, leading to a shear deformation of the grain boundaries. Furthermore, the grain boundaries themselves show some plastic deformation, via an increase of the order within the grain boundary (more atoms in a hcp configuration). At higher strains, the dislocation density increases, leading to dislocations pinning each other and thus more stable dislocation networks are observed. The majority of dislocations are formed in the Ni layer. This can have multiple reasons. First, it is known that an increasing stacking fault energy, which is higher in Al than in Ni, leads to an increase in normalized strength.43 Furthermore, the nanocrystalline nature of the Ni layer (in contrast to the columnar microstructure in the Al layer) leads to a higher density of grain boundaries as well as a higher variability of grain boundaries. As dislocations nucleate at grain boundaries, and more favorably at grain boundary triple-points,44 this explains the fact that dislocations are largely formed in the Ni layer.

In this work, both equiatomic and equivolumetric Al/Ni multilayer systems with bilayer heights between 5 and 100 nm were investigated via MD uniform uniaxial compression MD simulations. Furthermore, the results were compared with MD simulations with a different microstructure, namely columnar grains instead of nanocrystalline grains in the Ni layer. Finally, the extracted Young’s modulus and yield strength were compared to experimental results and discussed in the context of different hardening and softening theories.

A comparison of the mechanical properties extracted for different microstructures showed that it is essential to use the correct microstructure in order to reproduce experimental results. The mechanical properties of Al/Ni multilayers with nanocrystalline Ni layers showed a very good agreement with the experiment. This emphasizes the importance of a good characterization of experimental systems. On the one hand, this allows for reproducing and extrapolating the results, by employing simulations. On the other hand, this facilitates the explanation of contradicting results obtained in different studies of the apparently equivalent system.

While the bilayer height has a big influence on the mechanical properties, the difference between equiatomic and equivolumetric systems was shown to be very small. Future work should concentrate on extracting the mechanical properties for a wider range of stoichiometries, to better understand its influence.

When looking at the scaling of the hardening, it was shown that the hardening follows both a h 1 / 2 as well as a l n ( h ) / h scaling. While this could simply be interpreted as the Hall–Petch effect, focus on the underlying theory favors l n ( h ) / h scaling, based on a single size effect, caused by the limitation of the dislocation movement [also called confined layer slip (CLS)].

The softening at very small bilayer heights below 25 nm also showed an ln ( h ) / h scaling. This fits the general picture of a single size effect well and the deviation from the scaling at very small bilayer heights is likely based on the increasing fraction of atoms that are part of grain boundaries and interfaces (and not ordered and crystalline within a grain).

The authors have no conflicts to disclose.

Fabian Schwarz: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Ralph Spolenak: Conceptualization (supporting); Formal analysis (supporting); Funding acquisition (lead); Resources (lead); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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