We study indentation of a nanolayered material consisting of a Si top layer above an Al substrate, using molecular dynamics simulation. We focus on the activity of Si dislocations upon reaching the interface. We find that passage of the dislocations through the interface is possible, if the slip systems of the two crystals are aligned. Upon absorption at the interface, the Si dislocations generate slip which leads to 1-monolayer deep interface pits with well-defined steps; on the Al side dislocations and stacking fault planes are generated, which are pinned to the interface pit. For interfaces with not well aligned slip systems, the passage of dislocations is strongly suppressed. However, still interface pits, albeit with less well defined contours, and stacking fault planes aligned with the interface are created.

The ductile behavior of materials is largely determined by the dislocations that are produced in them and by their behavior.1,2 The interaction of such dislocations with interfaces in the material – surfaces, grain boundaries, etc. – has attracted considerable interest, since it is responsible for a variety of phenomena on the micro- and nanoscale.3 The theoretical elucidation of the mechanisms behind these effects has relied largely on atomistic simulation based on the molecular dynamics (MD) method.4,5

The field of dislocation interactions with grain boundaries was pioneered by MD simulations of van Swygenhoven.6 Later Schiotz and Jacobsen7 found a maximum in the strength of Cu for nanoscopic grain sizes caused by a shift in ductility mechanisms. Yamakov et al.8,9 reported mechanical twinning in the deformation of nanocrystalline Al and built up a two-dimensional stress-grain size deformation-mechanism map for the mechanical behavior of such materials. MD simulations also studied the interaction of dislocations with grain boundaries in detail.10,11

Also the interaction of dislocations with twin boundaries was studied using atomistic simulations.12–15 These investigations exposed how dislocations can penetrate twin boundaries and explained why nanotwinned materials exhibit a favorable combination of strength and ductility.

Several publications studied the interaction of dislocations with bicrystals with a focus on bimetallic layers.16–18 Until now, there seems to be no study of the interaction of dislocations with a metal/ceramic interface.

On the other hand, nanolayered materials based on either two metals19–21 or alternatively on a metal/ceramic composite22–25 become increasingly interesting due to their electrical, magnetic, optical and mechanical properties,23,24 their radiation damage tolerance,21 and strengthening and stiffening efficiencies.26 Therefore it is both timely and relevant to investigate how dislocations interact with a metal/ceramic interface.

Here we use molecular dynamics simulation to study the interaction of dislocations with a hetero-interface. Nanoindentation is used in order to generate dislocations and extend or emit them towards the interface. By way of example, we specialize on the Al-Si system, where Si serves as the hard and less ductile part, while Al is soft and ductile; we note that the Al-Si system features applications in light-weight components such as engine parts or fuel-efficient vehicles.27,28 Indentation into the Si part generates dislocations, and we study the question how the emitted dislocations affect the interface and under which conditions they can be transmitted through the interface.

The simulation system consists of a Si top layer of 14.1 nm thickness above an Al substrate layer of 8.1 nm thickness; the lateral dimensions are 41.3 × 41.3 nm2, see Fig. 1. The Si crystal always has a (100) surface, and the side planes are also {100} planes of the Si cubic diamond (cd) structure. For further use, we introduce a cartesian coordinate system, where the x and y directions are aligned with the [010] and [001] axes of the Si crystallite, respectively, and the z coordinate points normal to the surface.

FIG. 1.

Schematics of the simulation system. Blue: Si; green: Al. The coordinate system used and the system dimensions (in units of nm) are indicated.

FIG. 1.

Schematics of the simulation system. Blue: Si; green: Al. The coordinate system used and the system dimensions (in units of nm) are indicated.

Close modal

For the fcc Al substrate, 3 different orientations are used.

  1. An aligned interface, where the Al crystallite has a (100) interface, and its [010] and [001] axes are aligned with those of the Si crystallite above (so-called cube-on-cube interface29);

  2. A rotated interface, where the Al crystallite is oriented by 45° around the z axis;

  3. A (111) interface with the [12¯1] and the [101¯] along the x and y axes, respectively.

These three systems will be denoted as the Al(100)[010], Al(100)[011], and Al(111)[12¯1] systems, respectively, by using the orientation of the Al interface and the direction aligned with the x axis – i.e. the [010] direction of the Si top layer – as identifiers. Top views of the (unrelaxed) interface structures are presented in Figs. 2a–c.

FIG. 2.

Interface structure before (top row) and after (bottom row) relaxation. The Si part has a (100) interface with its [010] axis aligned horizontally. The Al interface has three different orientations: (a) and (d): (100) interface with a horizontal [010] axis; (b) and (e): (100) interface with a horizontal [011] axis; (c) and (f): (111) interface with a horizontal [12¯1] axis. Before relaxation, Al atoms are on fcc (blue) and Si atoms on cd (green) sites. After relaxation, only disordered Si atoms (green), Al interface atoms (blue), hcp (red) and disordered (dark blue) Al atoms are shown. The inserted figures in (e) and (f) zoom into the rectangular areas.

FIG. 2.

Interface structure before (top row) and after (bottom row) relaxation. The Si part has a (100) interface with its [010] axis aligned horizontally. The Al interface has three different orientations: (a) and (d): (100) interface with a horizontal [010] axis; (b) and (e): (100) interface with a horizontal [011] axis; (c) and (f): (111) interface with a horizontal [12¯1] axis. Before relaxation, Al atoms are on fcc (blue) and Si atoms on cd (green) sites. After relaxation, only disordered Si atoms (green), Al interface atoms (blue), hcp (red) and disordered (dark blue) Al atoms are shown. The inserted figures in (e) and (f) zoom into the rectangular areas.

Close modal

The Al and Si lattices have a large misfit; their lattice constants amount to 4.05 and 5.43 Å, respectively. The interfaces are created using the recipe of Noreyan et al.;30 the lateral dimensions are chosen such that they are commensurate for both lattices. In the present case, the lateral length of 41.3 nm fits 76 lattice constants of Si and 102 lattice constants of Al. Note that for the Al(100)[011] and Al(111)[12¯1] systems, the lateral size and thickness of the Al crystallite need to be slightly modified to be commensurate to the Si crystallite.

We employ periodic boundary conditions at the sides of the simulation volume. The bottommost layers (1nm wide) are fixed in order to prevent any rigid-body motion of the entire bicrystal during the indentation process. The next 1 nm at the bottom, as well as at the lateral sides, are thermostatted to 0.01 K via a velocity-scaling algorithm; this procedure is standard in indentation simulations.31,32 Before starting the indentation simulation, the systems are relaxed by energy relaxation; after an anneal at 30 K they are quenched again to temperatures below 1 K; final stresses are below 10 MPa.

The interatomic interactions are modeled with the help of the Al-Si potential by Saidi et al.33 There, the Al-Al interactions follow the well-established embedded-atom model of Mendelev et al.,34 while the Si-Si interactions are based on a modification of the renowned Stillinger-Weber potential.35 The interspecies Al-Si interaction term added by the AEAM potential correctly describes the Al-Si phase diagram and the heat of mixing;33 it also describes Al-Si interfaces satisfactorily.36 

We employ a spherical indenter with radius R = 7 nm. It is initially positioned centrally above the surface, and then moves with constant velocity of 20 m/s down into the bicrystal to a final depth of d = 7 nm. The indenter is modeled by a non-atomistic scheme,37 in which each atom is subject to a purely repulsive potential

V(r)=k(Rr)3,rR,
(1)

where r is the distance between the atom and the center of the indenter; for r > R, the force vanishes. The force constant has been chosen as k = 11.7 eV/ Å3, in agreement with previous studies.36,38

We employ the open-source code LAMMPS39 for the simulations, the Crystal Analysis Tool (CAT)40–42 for identification of crystal defects such as dislocations and OVITO43 for visualization of the simulation results.

Figs. 2d–f display the structure of the interface after relaxation. For the aligned Al(100)[010] interface, Fig. 2d, lattice mismatch leads to a striped interface with an average stripe width of 12 Å. Lines in [011¯] direction are created where the interatomic distance has been increased – up to 3.5 Å, as compared to the nearest-neighbor distance of 2.86 Å in Al – and the bonding correspondingly reduced. Such features are indicative of interface dislocations, i.e., dislocations with their dislocation line lying in the interface plane;29,44 these constitute hence no crystal defects but rather structural properties of the interface itself. They have been identified in several metal/ceramic interfaces.45–48 We provide a detailed view into this structure by zooming into the plane orthogonal to the stripes in Fig. 3. A number of point defects are generated on the Al interface which show up as locally hcp bonded atoms. On the Si side, we observe no point defects, which is plausible since Si is harder than Al.

FIG. 3.

View of the atomic configuration of Al (blue) and Si (green) atoms in the vicinity of the Al(100)[010] interface. Viewing direction is along [011¯].

FIG. 3.

View of the atomic configuration of Al (blue) and Si (green) atoms in the vicinity of the Al(100)[010] interface. Viewing direction is along [011¯].

Close modal

The rotated interface, Al(100)[011], shows a quite different structure, Fig. 2e, which is characterized by an ordered two-dimensional superstructure, indicative of a two-dimensional interface dislocation pattern; again no Si point defects are formed. The Al(111)[12¯1] interface, finally, shows the most complex structure, Fig. 2f. The Al interface essentially keeps its close-packed (111) geometry with local hexagonal symmetry; however, the lattice mismatch shows up in the variation of the nearest-neighbor distances, which can be particularly well observed in the white spots appearing. For this interface, also defects on the Si side appear; this can be rationalized by the fact that the close-packed Al(111) interface allows less distortion than the (100) interface of the other cases, and hence more stress is exerted on the Si side of the interface. Height variations in this interface amount to around ± 0.6 Å. We note that for all interfaces studied, we did not observe the generation of threading misfit dislocations, in agreement with previous work on this system.30,36

Fcc and cd crystals are similar with respect to the slip systems that can be used for dislocation glide. In both crystal lattices there exist 12 glide systems of the generic form {111}〈110〉.49 The aligned interface, Al(100)[010], therefore also aligns the slip systems of both crystals. We therefore analyze first dislocation interaction with this interface.

Indentation produces dislocations in the Si top layer, which have been characterized well in the past.38,50 Fig. 4 shows that the most prominent one is the perfect 12110 dislocation, which shows up early after indent and develops long shear loops, already at an indentation depth of d = 31 Å. The corresponding partials, 16112, are only generated considerably later, d = 53 Å, and at the interface.

FIG. 4.

Penetration of Si dislocations into Al while indenting the Si top layer to the depths d indicated; aligned Al(100)[010] interface. P1–4 denotes dislocation segments discussed in the text. Top row: dislocations generated in the Si top layer colored according to Burgers vector: 12110 (dark blue), 16112 (green), 13100 (yellow), and others (red). The gray planes indicate the surface, interface and the indent pit. Middle row: Close-up view of the penetrating dislocations and the Al interface atoms. Interface atoms are colored by height, see color bar. Bottom row: View from the Al side showing the Al interface atoms, the dislocations and the stacking faults. Insert at 54.2 Åzooms into rectangular area and demonstrates dislocation interaction, A+C=B, Eq. (2).

FIG. 4.

Penetration of Si dislocations into Al while indenting the Si top layer to the depths d indicated; aligned Al(100)[010] interface. P1–4 denotes dislocation segments discussed in the text. Top row: dislocations generated in the Si top layer colored according to Burgers vector: 12110 (dark blue), 16112 (green), 13100 (yellow), and others (red). The gray planes indicate the surface, interface and the indent pit. Middle row: Close-up view of the penetrating dislocations and the Al interface atoms. Interface atoms are colored by height, see color bar. Bottom row: View from the Al side showing the Al interface atoms, the dislocations and the stacking faults. Insert at 54.2 Åzooms into rectangular area and demonstrates dislocation interaction, A+C=B, Eq. (2).

Close modal

Fig. 4 analyzes in detail the fate of the loop with Burgers vector 12[01¯1¯] created. For further reference we name several of its segments by P1–4, see Fig. 4 top row. Of course, all segments share the same Burgers vector. We note that P1 and P3 glide on the (11¯1) plane, while P2 and P4 glide on the (111¯) plane.

When the 12[01¯1¯] loop reaches the interface, it breaks up into two parts (d = 32 Å), while the joining part of P2 sinks in. At d = 53 Å, most of P2 and part of P1 are swallowed by the interface. Shortly later, d = 53.6 Å, sufficient strain has accumulated at the interface to stimulate nucleation of an Al dislocation with Burgers vector 16[11¯2¯] gliding on the (11¯1) plane. Simultaneously, the loop in Si detaches from the indent zone, creating the segment P4. The detached loop quickly moves to the interface (d = 54.2 and 55.2 Å) where it annihilates, punching out a 1-monolayer thick depression with rectangular shape; the sides of this depression can be related to the slip caused by the dislocation segments P1–P4. One might denote this feature an ‘interface island’ in analogy to surface (vacancy or adatom) islands well-known to surface scientists, or as the pit created on the interface by the glide processes.

The dislocations generated in Al feature large stacking fault planes, (11¯1) and (111), see the final shape at d = 55.2 Å. During nucleation, d = 54.2 Å, three dislocations – denoted by A–C in the figure – can be observed, which are connected by the reaction A + C → B, or

16[11¯2¯](A)+16[1¯1¯2](C)13[01¯0](B).
(2)

The perfect dislocation, 12110, at each gliding plane {111}, is split into two partial dislocations, 16112, after reaching the interface. The partial dislocations, 16[11¯2¯] (A) and 16[1¯1¯2] (C), glide first, on (11¯1) and (111), respectively. They lead to stacking faults on the gliding planes. When these two partials meet and interact at the intersection of the (11¯1) and (111) planes, the new partial, 13[01¯0] (B) – known as a stair-rod dislocation – forms. As it gets stuck by the two distinct stacking fault planes induced by the glide of the partial dislocations A and C, it can neither climb nor glide. However, the second partials, 16112, on (11¯1) and (111), stuck in the interface, cannot move into Al. Meanwhile the perfect dislocations on the other two planes (P2 and P3 in Fig. 4) are stopped completely when reaching the interface. Thus, after penetrating the interface, the perfect dislocation loop (on the Si side) evolves into two partials (on the Al side) which induce related stacking faults and a stair rod dislocation.

We conclude that the high stress created in the indentation zone emits dislocation loops towards the Al/Si interface. These are annihilated at the interface punching out 1-monolayer thick interface islands, to which dislocations and stacking fault planes are attached on the Al side. This is equivalent to a transformation of the Si dislocation loop to Al dislocations and hence to a passage of the dislocations through the interface.

Fig. 5 gathers the results obtained for the three interface orientations studied, at full indenter penetration, d = 70 Å. The first row, Figs. 5a–c, gathers the results for the aligned interface, Al(100)[010]. Besides the large interface pit discussed in Sect. III B above, three further similar structures are observed; the interface islands punched out, Fig. 5a, as well as the stacking fault planes and dislocations that passed through the interface to the Al side, Fig. 5c, are clearly seen. The largest interface pit created has dimensions of 63 × 73 Å2, Fig. 4b.

FIG. 5.

Final state of the system after indentation to depth d = 70 Å. The indentation point is in the center of the images in the right and left column. Left column: Top view of the interface showing Al interface atoms colored according to height, see color bar in Fig. 4. Middle column: top view zooming into the rectangular areas of the left column; these areas are also shown as dashed rectangles in the right column. Black line in (e) indicates the position of an Al dislocation buried below the interface. Right column: Side view of the final dislocation structures, colored as in Fig. 4, top row. Dark gray atoms denote Al stacking faults. The three interface orientations are arranged as horizontal rows: (a–c): Al (100) interface with a horizontal [010] axis; (d–f): Al (100) interface with a horizontal [011] axis; (g–i): Al (111) interface with a horizontal [12¯1] axis.

FIG. 5.

Final state of the system after indentation to depth d = 70 Å. The indentation point is in the center of the images in the right and left column. Left column: Top view of the interface showing Al interface atoms colored according to height, see color bar in Fig. 4. Middle column: top view zooming into the rectangular areas of the left column; these areas are also shown as dashed rectangles in the right column. Black line in (e) indicates the position of an Al dislocation buried below the interface. Right column: Side view of the final dislocation structures, colored as in Fig. 4, top row. Dark gray atoms denote Al stacking faults. The three interface orientations are arranged as horizontal rows: (a–c): Al (100) interface with a horizontal [010] axis; (d–f): Al (100) interface with a horizontal [011] axis; (g–i): Al (111) interface with a horizontal [12¯1] axis.

Close modal

For the rotated interface, Figs. 5d–f, no clearly localized interface pits are created; however, still depressions are observed, in which the interface is lowered by up to 2 Å. These depressions are now, however, irregularly shaped, see Fig. 5e; their sides are not linear. This is a consequence of the misaligned slip systems in the two crystals, which do not allow for straight atom transfer through the interface. Still, one dislocation developed in the Al part with Burgers vector 16112; it is denoted by the dashed black line in Fig. 5e and highlighted by the rectangle in Fig. 5f. Note that it does not form on the boundary of the depression – as it was the case for the aligned interface – but rather cuts through its interior. The atomic structure in the depressions looks strongly disturbed from the original Al lattice sites; this is caused by the complex geometry of the slip systems of the two crystals meeting at the interface.

For the Al(111) interface, Figs. 5g–i, the interface pits again look more strongly localized, with sharp delineations at the inner and extended but more diffuse boundaries towards the outside. Now the hexagonal structure of the fcc Al(111) interface remains intact to a higher degree than the fcc (100) interface in the rotated case, Fig. 5e. This is due to the dense packing of the (111) interface plane which makes it harder and less prone to in-plane deformations. Stacking fault planes are generated immediately at the interface, Fig. 5i, which accommodate the strain inside the interface plane, such that no dislocations are generated in Al in this case. The stacking fault planes are parallel to the (111) interface and have irregular shapes. Three larger stacking fault planes are observed – the largest one with an area of 765 Å2 and thus a factor of 6 smaller than the pit created for the aligned interface – as well as a multitude of smaller defects.

We conclude that aligned slip systems on both sides of the interface allow for the easiest passage of dislocations though the interface. For the other surfaces, generation of dislocations and stacking faults is strongly suppressed. For the rotated interface, only one Al dislocation was formed; for the (111) interface, stacking fault planes parallel to the interface are generated. These defects are all created when Si dislocations induce slip at the interface.

In our study, we observe that dislocations can penetrate a metal/ceramic interface, but only for special crystal orientations, and at the cost of strong shrinking and trapping close to the interface. On the other hand, it has been reported that perfect dislocations can penetrate metal/metal interfaces successfully.16,19,51 In these cases, the dislocation density on one metal side is high as it is induced by a large crystal deformation. In such a situation it is possible for dislocations to penetrate the interface completely. In contrast, in ceramics such as in the Si crystal studied here, the dislocation density is low due to the high ceramic hardness. This – apart from the obvious lattice mismatch between the two crystal lattices – is the reason underlying the poor penetrability of ceramic/metal interfaces for dislocations.

In this study we used nanoindentation of a nanolayered material to investigate the behavior of dislocations that are driven by stress gradients against a hetero-interface. Focusing on the Si-Al interface we found that an interface with aligned slip systems – such as the Al(100)[010] system – allows for passage of the dislocations from the Si to the Al crystallite. Such a passage is accompanied by the disappearance of the Si dislocation loops upon reaching the interface; at the interface a 1-monolayer deep depression is punched out. The interface pit has sharp rectangular sides, which reveal that the depression is formed by regular dislocation glide through the interface.

In contrast, when the slip systems of the two crystallites are not aligned – for example for the Al(100)[011] system – dislocation passage is strongly suppressed. When Si dislocations reach the interface, irregularly shaped depressions form, which are, however, not as localized as in the first case, but strongly spread out laterally. The strain caused by the Si dislocations reaching the interface leads to local disorder in the interface plane rather than to the generation of Al dislocations.

In another case – the Al(111)[12¯1] system – the interface features generation of stacking fault planes oriented parallel to the interface. This relieves the strain and no dislocations are formed in the Al substrate.

Simulations were performed at the High Performance Cluster Elwetritsch (RHRK, TU Kaiserslautern, Germany). We acknowledge the financial support of the Deutsche Forschungsgemeinschaft via the IRTG 2057.

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