Exploring the transfer of plasticity across Laves phase interfaces in a dual phase magnesium alloy

The mechanical behaviour of Mg-Al alloys can be largely improved by the formation of an intermetallic Laves phase skeleton, in particular the creep strength. Recent nanomechanical studies revealed plasticity by dislocation glide in the (Mg,Al)$_2$Ca Laves phase, even at room temperature. As strengthening skeleton, this phase remains, however, brittle at low temperature. In this work, we present experimental evidence of slip transfer from the Mg matrix to the (Mg,Al)$_2$Ca skeleton at room temperature and explore associated mechanisms by means of atomistic simulations. We identify two possible mechanisms for transferring Mg basal slip into Laves phases depending on the crystallographic orientation: a direct and an indirect slip transfer triggered by full and partial dislocations, respectively. Our experimental and numerical observations also highlight the importance of interfacial sliding that can prevent the transfer of the plasticity from one phase to the other.


Introduction
The mechanical response of composite materials is dependent on the properties of their different phases individually, but also largely on the properties of their interfaces. Lightweight Mg-based composites with a controlled proportion of Al and Ca can be strengthened by the precipitation of a Laves phases skeleton [1]. The reinforcement potential of Laves phases in these alloys is primarily due to their high strength compared to the matrix phase [2]. Laves phases are hard intermetallic phases with a topologically close packed structure arranged in a cubic (C15) or hexagonal (C14 and C36) unit cell [3,4]. The mechanical response of such a dual phase microstructure typically shows plasticity in the Mg matrix and fracture in the hard-intermetallic phase [1,5]. While effectively strengthening the composite, the brittleness of the Laves phase limits the maximum strength and the formability of the composite.
Plasticity in hexagonal Mg-based Laves phases has been observed experimentally at room temperature by means of nano-mechanical testing [2]. In particular, Mg2Ca (C14) micro-pillar compression revealed the activation of basal, prismatic and pyramidal slip systems [2]. Additionally, atomistic simulations with the same phase confirmed that synchroshear dislocations are activated for basal slip [6]. To our best knowledge, one study investigated the properties of interfaces in the similar Mg-Zn2Mg composites [7], and none investigated the transfer of plasticity from the matrix to the Laves phase.
Different Laves phases exhibit different dislocation pinning characteristics as observed for Laves phase reinforced Ti alloys [8]. In case of Mg alloys, Laves phases and their interfaces are strong obstacles for dislocation motion, making Mg alloys containing Laves phases well suited for high temperature applications in which creep resistance is required [9]. However, a lack of slip transfer from α-Mg to Laves phases also results in limited plasticity as displayed by the low ductility of these alloys at room and elevated temperatures [1]. Easier slip transfer is usually associated with more homogenous plastic flow [10] and in case of Mg-Al-Ca alloys, this would presumably result in better bulk plasticity at the expense of creep resistance. The knowledge of slip transfer mechanisms may thus prove essential in designing alloys with a tailored balance between ductility, strength and creep resistance.
Here, we explore the co-deformation of Laves phases with an α-Mg matrix by the combination of experimental and numerical approaches. The surface morphology of a deformed composite is analysed by scanning electron microscopy. Cracks and slip traces are characterised in both, the matrix and the Laves phase skeleton. In parallel, atomistic simulations are performed for a similar composite and several possible orientation relationships are investigated. Numerical nano-mechanical tests and controlled dislocation-interface interactions at the atomic scale enlighten the experimental results.
Finally, we show mechanisms of transfer of plasticity from the Mg matrix to the Laves phase skeleton across the interface.

Experiments
A cast Mg-5.21Al-3.18Ca (wt.%) alloy was prepared from raw materials consisting of pure Mg, Ca and Al. The raw materials were molten in an induction furnace and solidified under 15 bar Ar pressure in a steel crucible. The chemical composition was determined through wet chemical analysis.
The samples for microstructural examination were first ground using 4000 SiC emery paper, followed by mechanical polishing using 3 and 1 μm diamond suspension. The mechanically polished samples were then subjected to electrolytic polishing using the AC-II (Struers) electrolyte. Electro-polishing was carried out at ≤ -20 ºC, 15V and for 60 s. Different electrochemical behaviour of the metallic and intermetallic phases resulted in the appearance of a waviness on the sample surface which was then removed by fine polishing with OPU (≈ 40 nm SiO2 colloidal suspension). After fine polishing, the samples were cleaned in an ultrasonic bath followed by light pressing on gently rotating cleaning cloth containing ethanol as a cleaning agent/lubricant. Standard dog bone shaped specimens with a gauge length of 10 mm were deformed in an electromechanical testing machine (ETM) at 170 °C. The specimens were later characterised in a scanning electron microscope (SEM; Zeiss LEO1530) using secondary electron (SE) imaging and electron backscatter diffraction (EBSD) after pre-determined deformation steps of 3 and 5%. An acceleration voltage of 20 kV was used for EBSD and 10-20 kV for SE imaging. The EBSD data were analysed using Channel 5 and Matlab 2018b software. Figure 1 represents an SE image taken from a sample deformed to 3% global strain. It can be seen in the figure that the microstructure consists of two phases, i.e. α-matrix reinforced with an intermetallic Laves phase skeleton. The Laves phase was determined to be C36 ((Mg,Al)2Ca) according to the EDS analysis presented in our earlier work [1]. The same intermetallic phase was also reported by several other researchers in similar alloys, i.e. Suzuki et al. [11] in the Mg-5Al-3Ca alloy and by Luo et al. [12] in AC53 (Mg-4.5Al-3Ca-0.27Mn) alloy. They used transmission electron microscopy (TEM) to confirm their results. In our results, slip lines in the matrix phase are clearly visible and highlighted by blue arrows. Using EBSD-assisted slip line analysis, these slip lines were identified as basal slip traces in the α-Mg matrix. At points where the slip lines interact with the (Mg,Al)2Ca (C36) Laves phase, cracks in the C36 phase can be observed. This is in agreement with our earlier work [1].  Therefore, TEM was performed as part of further studies of the system [13] to identify the orientation relationship of the Mg matrix and the C36 Laves phase. This yielded a "basal plane ‖ prismatic plane (<0001>Mg ⊥ <0001>C36 within ± 13.21 º in the deformed sample)" relationship and identification of basal slip in the Laves phase [13].

Discussion on the experiments
It can be observed in Figure 1 that the cracks in the C36 Laves phase occur at points where slip lines in the α-Mg matrix interact with the Laves phase. Further, it can be seen in Figure 1 that the cracks at points A and B are oriented around 45-50 ° to the globally applied tensile stress direction. Moreover, these cracks in the C36 phase are almost parallel to the basal slip lines in the α-Mg matrix. This indicates that the cracks are developed due to the shearing of the C36 Laves phase by basal slip in the α-Mg matrix. On the other hand, the cracks at points C and D (as can be seen enlarged in the insets of Figure   1) are almost perpendicular to the applied stress direction and correspond probably to brittle fracture of the C36 phase. Figure 2, on the other hand, shows an event where plastic flow is actually transmitted from the α-Mg matrix into the Laves phase. The α-Mg matrix offers significantly lower resistance to dislocations movement as compared to the Laves phases. Specifically, the critical resolved shear stress (CRSS) values for basal, prismatic and pyramidal slip in Mg amounts to ≈ 0.52 MPa [14], ≈ 39 MPa [15] and ≈44 MPa [16], respectively (as determined by macroscopic testing of pure Mg, except in case of [16] where the CRSS for pyramidal slip was determined through micropillar compression). The CRSS values for the Mg phase are much lower than the CRSS values reported for the same slip systems in the C14 Mg2Ca Laves phase, which were determined as ≈520 MPa (basal slip), ≈440 MPa (prismatic slip) and ≈530 MPa (pyramidal slip) by micropillar compression [2] (NB: a direct comparison is impeded by the brittleness of the Laves phase and the size effect encountered in microcompression testing of Mg, resulting in a CRSS for basal slip of the order of ≈ 7 MPa as opposed to 0.52 MPa [14] measured macroscopically [17]). The other Laves phase (C15 Al2Ca phase) in the Mg-Al-Ca system was reported to be even harder than the C14 Mg2Ca Laves phase [18]. As the hexagonal C36 Laves phase is very closely related to the hexagonal C14 Laves phase, we assume here that plastic deformation follows the same mechanisms. Owing to this difference in CRSS; it appears likely that under the application of a tensile stress, slip in the α-Mg matrix is activated first and then at points of severe stress concentrations, for example where slip lines in the Mg phase interact with the Laves phase, plastic flow can be transmitted into the Laves phase. Further, it is possible that at those intersection points of slip in the Mg matrix with the Laves phase, where cracks were observed, some plastic flow has occurred prior to cracking. However, based on post-mortem results only, it is not possible to distinguish cracking with and without prior slip in the Laves phase.

Simulations
To explore the atomic-scale details of the slip transfer observed experimentally and to understand the underlying mechanisms, we performed atomistic simulations with semi-empirical potentials. As no reliable potential is available to date that correctly models the plasticity in the ternary Mg-Al-Ca intermetallic phase, we consider here the C14 Mg2Ca Laves phase as surrogate for the C36 (Mg,Al)2Ca Laves phase. Similar to previous experimental [12] and numerical work [7], two different orientation relationships (OR) have been considered in our numerical approach. One with both phases' basal planes parallel, (0001) ! ∥ (0001) "# ! $% , the other with the basal plane of the Mg phase aligned with the prismatic plane of the Mg2Ca, (0001) ! ∥ (112 + 0) "# ! $% , close to the OR we observed by TEM [13].

Numerical methods
Atomistic simulations have been carried out with the classical molecular dynamics code LAMMPS [19].
Interatomic interactions were modelled by the recently developed potential of Kim et al. [20] based on the modified embedded atom method (MEAM). This potential has been specifically optimized to represent both, hexagonal Mg phase and the C14 Mg2Ca Laves phase, and it has been used successfully to model the complex dislocation motion in the basal plane of the C14 Laves phase [6]. This work involves molecular static (MS) and molecular dynamic (MD) simulations. MS simulations were performed by using both conjugate gradient [21] and FIRE [22,23] algorithms, and the configurations were considered optimized for a norm of the global force vector below 10 -8 eV/Å. MD simulations were performed within either the microcanonical (NVE, T0 = 0K) or the canonical (NVT, T0 > 0K) thermodynamic ensemble with a timestep = 1.0 fs. In the NVT ensemble, the temperature was controlled by a Nosé-Hoover thermostat [24] with a damping parameter of 0.1 ps. The atomistic configurations were constructed using Atomsk [25], and visualised and analysed using OVITO [26]. The defects in both, Mg and Mg2Ca phases were evidenced by calculating atomic-level strain tensors at each particle. More specifically, the von Mises local shear invariant, γvM, was estimated from the atomic deformation gradient tensor calculated based on atom displacements [27]. Note that the commonly used structural identification methods, like the common neighbours analysis (CNA) [28], are not adapted to the C14 structure and defects at complex interfaces have been already characterized by such shear invariant based method [29].

Numerical results
We first focus on the OR (0001) ! ∥ (0001) "# ! $% , which forms a composite that exhibits coplanar basal planes. As the objective of the simulation is to study the transfer of slip at the interface from the Mg matrix, the onset of plasticity in the Mg phase is favoured by choosing an angle of 45° with the deformation axis. This maximises the resolved shear stress on the primary (basal) slip planes. The corresponding atomistic sample shown in Figure 3 is made of Mg and Mg2Ca phases separated by an interface perpendicular to the Z-axis, and contains 996,941 atoms. The phases are oriented as follows:   shows the stress-strain curves of our numerical strain-controlled nanomechanical tensile tests at 50K, 500K and 700K. Note, that we also performed compression tests on the same sample, and they produced comparable results. All three curves exhibit a similar profile. First, there is an initially purely elastic co-deformation regime: both phases deform with negligible plasticity limited to surfaces. Then small stress drops indicate the activation of plasticity in the Mg phase by means of dislocation nucleation and glide from the surface or from the interface. Finally, a large stress drop corresponds to the initiation of either fracture at low temperature or slip at high temperature in the Mg2Ca phase, as illustrated by the simulation snapshots in Figure 3b. In all cases, fracture or plasticity in the Mg2Ca phase are initiated from locations where Mg basal slip lines interact with the interface. A closer look at the mechanism is provided in Figure 4 (See also Movie S1), which shows a sequence of snapshots of the     shows a profile that is more staggered than the dynamic deformations, but all tests follow a similar trend. To describe the mechanisms in detail, we will focus on the quasi-static deformation. Figure 5c shows sequences of snapshots of the quasi-static deformation from 1% to 30% compressive strain. The first row shows the entire sample during deformation, evidencing that slip traces form at the surface (See also Movie S2). The second and third rows show only those atoms that have an atomic von Mises shear invariant γvM larger than 0.3. In other words, slip activities are highlighted by hiding atoms that have not undergone significant shear. As a lot of events happened during the deformation, we split the sample in two parts to ease the visualisation: the second and third rows show the Mg and Mg2Ca phases only, respectively (See also Movies S3 and S4). Up to 8% strain, the deformation is purely elastic and no slip events are detected. At 8% strain, a slight drop of the stress occurred (first dashed vertical line in Figure 5b) as the Mg phase shows a strong plastic activity with the nucleation of dislocations and the formation of twins. The Mg2Ca phase is deformed elastically up to 15% strain as the Mg phase continues to deform plastically. At 15% strain, shear events are triggered in the Mg2Ca phase, principally on two approximately orthogonal planes. The shear continues to increase while deforming the sample up to 30%. Note that while the Mg phase appears almost entirely twinned, most of the plastic shear in the Mg2Ca phase is concentrated in the two planes initially activated at 15% strain. A deeper insight in the onset of plasticity in the Mg2Ca phase is given by the kinetics of the mechanism from the dynamic simulation, as shown in Figure 6. Here, the Mg phase appears already largely twinned at a compressive strain of 15% and a time t = 1.98 ns. While maintaining the strain constant, the dynamics is simulated further (snapshots at t = 2.38 ns and t = 3.43 ns, Figure 6a and Movie S5) and evidences the onset of slip at the Mg-Mg2Ca interface in the centre of the pillar. As shown in Figure   6b, the slip event at the interface can be characterized as a non-dissociated prismatic <a> dislocation (See also Movie S6 for the MD counterpart).
The driving force for the onset of plasticity in the Laves phase is unveiled in Figure 7 showing sliced views normal to the glide planes at the onset of Laves phase plasticity.

Simple shear of dislocation pile-up
To gain detailed and well-defined insights into the mechanisms of interfacial plasticity, it is common to use carefully controlled two dimensional atomistic setups [31][32][33]. Such approaches include infinite straight dislocations with controlled character, semi-infinite planar interfaces and controlled stress states. In our work, we consider a quasi-2D bi-crystal slab made of the Mg phase and the C14-Mg2Ca phase with the OR (0001) ! ∥ (0001) "# ! $% and the OR (0001) ! ∥ (112 + 0) "# ! $% . Figure 8a shows the Mg-Mg2Ca atomistic composite sample, with periodic boundary condition (BC) along the X and Y axes.
The OR (0001) ! ∥ (112 + 0) "# ! $% is chosen as an example, but we observed identical results for the OR (0001) ! ∥ (0001) "# ! $% . 2D BC are applied along the Z axis (red layers in Figure 8a). From 1 to 20 infinite straight basal edge dislocations are inserted in the centre of the simulation within the Mg phase. The dislocations are successively inserted by using Atomsk [25]. The system is relaxed by MS (see section 3.1) and deformed by quasi-static simulations as described in the following. A strain )* is applied on the sample by homogeneously displacing all the atoms, followed by a complete relaxation of the system by MS. To maintain the deformation during the minimization, a force is applied in the Z direction on each atom that belong to the 2D BC, and defined by = 5 )* . * +++ 8 ( . ) ⁄ with * +++ being the average shear modulus of the sample for the particular orientations, the surface area along the Z direction and the number of atoms in the 2D BC. We investigated the influence of temperature on the behaviour we report above. The two dimensional set up with a pile-up of four dislocations has been deformed at finite temperatures within the canonical ensemble (NVT) at a shear rate of 10 8 s -1 . Figure 8b shows the stress-strain curves of these deformation tests at 300K and 700K in green and light blue, respectively. Similar to the quasi-static simulations, the stress drops correspond to the nucleation of defects in the Mg phase or to the failure of the interface.
No transfer of slip from the Mg to the Mg2Ca phase is observed (See also Movie S7). The behaviour presented above appears thus independent of the temperature.

Discussion on the simulations
The numerical deformation tests we present in this work show slip transmission across the Mg-Mg2Ca interface. We identified two regimes depending on the orientation relationship. When the basal planes of the matrix are aligned with the basal planes of the Laves phase, a direct slip transmission can occur.
It consists of the accumulation of matrix <a> basal full dislocations at the interface, that directly trigger the nucleation of a partial synchroshear dislocation on the basal planes of the Laves phase. The temperature dependency indicates that this mechanism is thermally activated, similar to the propagation of the synchroshear dislocation in bulk Laves phases [6,30,34]. On the other hand, when the basal planes of the matrix are aligned with the prismatic planes of the Laves phase, an indirect transmission can occur. It consists of the local accumulation of shear stress within the interface plane, the resulting torsion indirectly triggering the nucleation of a full non-dissociated <a> dislocation on the prismatic plane of the Laves phase. This mechanism seems thus to be strongly facilitated by deformation twinning in the matrix.
These two regimes for slip transmission can be, however, entirely inhibited by interfacial sliding. In particular, when the applied load favoured sliding within planes parallel to the interface plane, local sliding of the atoms at the interface appears to release sufficient internal stress to prevent the nucleation of dislocations in the Laves phase.

Discussion on experimental and simulation results
In this work, experimental and numerical approaches were combined to investigate the plasticity and co-deformation of Mg-Laves phase composites. As discussed in the previous sections, the stress required to activate plasticity in the Mg phase is significantly lower than that required in case of the

Slip transfer from α-Mg to Laves phase
Alternatively, simulations also confirm that, at the same stress concentration points (where basal slip lines in the α-Mg matrix interacts with the Laves phase), plasticity may be transmitted to the Laves phase, especially at elevated temperatures (500K and 700 K, see Figure 3 and Figure 4). We further showed that the basal <a> slip in the α-Mg matrix activates plasticity in the Laves phase through synchroshear dislocations within the basal planes. Similar results were again also obtained in our experiments, where plasticity from the α-Mg phase can be seen transmitted to the Laves phase ( Figure   2) at the stress concentration points. As TEM further confirmed the occurrence of basal slip in the Laves phase, it shows the prime importance of the synchroshear mechanism for this phase.
In some cases (for the orientation relationship (0001) ! ∥ (112 + 0) "# ! $% ), the slip event in the Mg2Ca activated from the interface, was based on non-dissociated prismatic <a> dislocations. In agreement with this, observations of prismatic slip during nano-indentation have also been made by Zehnder et al. [2]. In fact, the CRSS for 1 st order prismatic slip (≈440 MPa) was reported to be lower compared with basal slip (≈520 MPa) at room temperature [2].

Interfacial sliding at the α-Mg-Laves phase interfaces
Our atomistic results suggest that interface sliding can prevent the transfer of matrix slip to the Laves phase. Interfacial sliding is primarily achieved by the absorption of dislocations at the interface. This is in agreement with earlier experimental observations, where interfacial sliding of Mg-Laves phase interfaces has been reported [35,36].
However, unfortunately we have not been able to provide an experimental correlation between slip transfer or local interfacial sliding and the local stress state and orientation relationship, as the number of events we observed remained limited. Nonetheless, our simulations show that the slip transfer mechanism depends on the interfacial orientation and can be inhibited for particular geometries, even at high temperature (see Figure 8). This highlights the importance of considering local strain distributions and local interfacial geometries to predict slip transfer at phase boundaries.
Experimentally, these insights may help guide future experiments to target specific orientation relationships and to investigate the thermal activation of interface-dominated deformation by nanomechanical testing. In this way, simulations and experiments will directly benefit from each other to unravel the co-deformation mechanisms of the two phases.

Conclusions
In this work, we combined experimental and numerical approaches to investigate the plasticity and co-deformation of Mg-Laves phase composites. From this work we conclude that: • The mechanisms of co-deformation, namely cracking, slip transmission and interfacial sliding as a result of slip activity in the Mg phase, are in agreement for simulation and experiment in that they are observed in both.
• For slip transfer, the Laves phase deforms on those planes identified previously in experiments and simulations, the prismatic and basal planes. The simulations reveal that this should occur by synchroshear on the basal plane and non-dissociated <a> dislocation on the prismatic plane.
• In the case of interfacial sliding, we found that dislocations are absorbed into the interface in the simulations. An insight that may be validated experimentally by targeted deformation and transmission electron microscopy in the future.
• Overall, our simulations reveal that the active co-deformation mechanism depends on the interfacial orientation. This highlights the importance of considering local strain distributions and local interfacial geometries to predict slip transfer at phase boundaries.
More work has to be performed to understand the full extent of slip transfer at such complex interfaces. In particular, our numerical results suggest that this transfer might be thermally activated, but this remains to be confirmed by dedicated experiments. The findings we present here on the transfer of slip across Laves phase interfaces in Mg alloys pave the way for in-depth investigations of the plasticity in such complex lightweight composite. More generally, understanding how the plasticity is transferred at phase boundaries opens up exploration paths for composites with tailored mechanical properties.