Misfit dislocation patterns of Mg-Nb interfaces

Abstract

The role of heterogeneous interfaces in improving mechanical properties of polycrystalline aggregates and laminated composites has been well recognized with interface structure being of fundamental importance in designing composites containing multiple interfaces. In this paper, taking the Mg (hexagonal close-packed (hcp))/Nb (body-centered cubic (bcc)) interface as an example, we develop Mg-Nb interatomic potentials for predicting atomic configurations of Mg/Nb interfaces. We systematically characterize interface dislocations of Mg/Nb interfaces with Nishiyama-Wassermann (NW) and Kurdjumov-Sachs (KS) orientation relationships and propose a generalized procedure of characterizing interface structure by combining atomistic simulation and interface dislocation theory, which is applicable for not only hcp/bcc interfaces, but also other systems with complicated interface dislocation configurations. In Mg/Nb, interface dislocation networks of two types of interfaces are significantly different although they originate from partial dislocations of similar character: the NW interface is composed of three sets of partial dislocations, while the KS interface is composed of four sets of interface dislocations - three sets of partial dislocations and one set of full dislocations that forms from the reaction of two close partial dislocations.

Introduction

Magnesium (Mg) and its alloys, benefiting from the lowest weight/volume ratio among all metals have a huge potential in the aerospace and automotive industries [1], [2]. However, Mg and Mg alloys have low ductility and poor formability at room temperature due to scarcity of easy slip systems and the propensity for localized shear via twinning in hexagonal close-packed (hcp) structures [3], [4], [5], [6]. Many techniques, such as non-traditional processing [7], [8], grain refinement [9], [10], [11], nano-spaced stacking faults [12], and alloying with rare earth elements [13], [14], [15] etc., have been applied to tune the relative activity of slip and twinning in Mg and Mg alloys, improving deformability while maintaining high flow strength. Other than these, Mg and Mg alloys can be strengthened through tailoring microstructure of Mg-based composites, such as Mg-metal laminates [16], [17].

Metallic layered composites containing a high density of interfaces show promising enhancement in both strength and ductility [18]. Lu et al. [17] demonstrated that the mechanical strength of Mg/Ti multilayers could achieve a high value of ∼1.5 GPa when the layers are a few nanometers thick. In Mg/Nb, Ham and Zhang [16] found that the mechanical strength of the Mg/Nb multilayers is ∼1.0 GPa. Using transmission electron microscopy (TEM), we have explored that Mg can adopt different crystal structures in layered composites: a hexagonal close-packed structure (hcp-Mg) when the layer thickness of Mg is larger than ∼5 nm and a body-centered cubic structure (bcc-Mg) when the layer thickness is less than ∼5 nm. At small layer thickness, the existence of bcc-Mg layers is ascribed to the lower interface energy of the coherent bcc-Mg/Nb interface (303.7 mJ/m²) compared to coherent and semi-coherent hcp-Mg/Nb interfaces (373 mJ/m² and 624 mJ/m²) [19]. At large layer thickness, the formation of hcp-Mg in thick Mg layers is attributed to the higher bulk energy of bcc-Mg than hcp-Mg [19].

The strength of Mg-metal multilayers reported in the literature above is much greater than that of the majority of Mg alloys reported to date. Along with the improved mechanical properties under various types of mechanical testing [18], [20], [21], [22], the influence of interface structure on mechanical behaviors has been reviewed [23], [24], [25], [26], [27], [28], including that of interface shearing [29], [30], interfacial dislocation nucleation [31], [32], [33], [34], [35], gliding dislocation-interface interaction [36], [37], [38], interfacial dislocation climb [39], [40] and interfacially-driven twinning [41], [42], [43], [44], [45], [46]. To understand the role of Mg-metal interfaces in strengthening as well as plastic deformation, including nucleation and emission of dislocations and twinning from bimaterial interfaces, it is essential to quantitatively characterize the interface structures of Mg-metal multilayers. It is worth mentioning that the misfit dislocation structures that prevail at hcp related layer interfaces have not been investigated in detail and the methodology of identifying such structures is intrinsically linked to mechanical performance of hcp-based nanocomposites. In this paper, we adopt Mg/Nb as a model system to identify interface structure. We first identify the orientation relationships (ORs) of Mg/Nb multilayers by TEM and then we simulate hcp-Mg/Nb interfaces with the empirical interatomic potentials and analyze the dislocation structures of hcp-Mg/Nb interfaces.

Mg/Nb multilayers with individual layer thickness of 50 nm were prepared by magnetron sputtering. Cross-sectional TEM analysis shows that hcp-Mg/Nb multilayers adopt (0001)||{110} interfaces (Fig. 1 ). Selected area diffraction (SAD) patterns of Mg/Nb multilayers indicate two ORs between hcp-Mg and Nb layers: (0001)||($01\overline{1}$)||interface with <$2\overline{1}\overline{1}$ 0>||<111> and (0001)||($01\overline{1}$)||interface with <$2\overline{1}\overline{1}$ 0>||<100>. From a crystallographic viewpoint, <$2\overline{1}\overline{1}$ 0> in hcp structure is equivalent to <110> in face-centered cubic (fcc) structure and (0001) plane is equivalent to (111) in fcc structure. We refer the first OR to the Kurdjumov-Sachs (KS) OR and the second to the Nishiyama-Wassermann (NW) OR in terms of the KS and NW ORs in fcc/bcc systems.

KS and NW interface structures in fcc/bcc systems, such as Cu/Nb multilayers, have been systematically investigated [47], [48]. Atomic planes around the interface have a stacking sequence … ABCABC|ABAB …, where the symbol “|” indicates the position of the interface plane. ABCABC ahead of “|” shows the stacking sequence of close-packed (111) planes in a fcc structure, and ABAB after “|” shows the stacking sequence of close-packed (110) planes in a bcc structure. We note that the first (110) plane in the bcc structure stacks in the normal stacking sequence of (111) planes to achieve a low-energy configuration. When replacing the fcc structure with an hcp structure to form a hcp/bcc interface, the stacking sequence near the hcp/bcc interface is no longer unique. Since hcp {0001} planes are stacking with a sequence … ABAB …, the hcp/bcc system could possibly have two stacking sequences of atomic planes around the interface, either … ABAB|CACA … or … ABAB|ABAB …, where ABAB ahead of “|” is the stacking sequence of (0001) planes in a hcp structure. In the former case CACA after “|” shows the stacking sequence of (110) planes in a bcc structure. The first (110) plane from the interface occupies a C-plane in terms of ABC stacking in a fcc structure. The interface is thus referred as a normal fcc structure (FCC). In the latter case, ABAB after “|” exhibits the stacking sequence of (110) planes in a bcc structure, the first (110) plane from the interface occupies the A-plane in terms of ABC stacking in a fcc structure, forming a stacking faulted structure at interface. The interface is thus referred as a stacking faulted structure (SF).

To analyze the misfit dislocation structures of hcp-Mg/Nb interfaces with KS and NW ORs, we first calculated the generalized stacking fault interface energy of coherent hcp/bcc interfaces and found two low-energy coherent interfaces, …ABAB|CACA … (FCC) and … ABAB|ABAB … (SF). The two coherent interfaces can interchange from one to the other by interface shear associated with interface dislocations. Secondly, we characterized misfit dislocation patterns of the KS and NW interfaces by atomically informed Frank-Bilby (AIFB) theory [47], [48], [49]. We found that both interfaces are initially composed of two coherent structures (FCC and SF) and three sets of partial dislocations, which is similar to that found in fcc/fcc interfaces, but that for the KS case of Mg/Nb, two sets of partial dislocations in close proximity to one another react to form full dislocations, increasing the complexity of characterizing these interface dislocations.

Correspondingly, this article is organized as follows. We describe essential details of atomistic simulations and interface characterization techniques in Section 2. In Section 3, we define reference lattices (commensurate/coherent dichromatic pattern (CDP) or Rotated CDP (RCDP)) [47], [48], [49] for Mg/Nb interfaces and possible Burgers vectors in the two lattices. Afterwards, we characterize misfit dislocations of Mg/Nb interfaces by using AIFB theory. We conclude that both NW and KS Mg/Nb interfaces originally are comprised of two types of coherent interfaces separated by three sets of partial dislocations, whereas two sets of near-parallel partial dislocations in KS interface react, forming four sets of interface dislocations. Finally, we generalize procedures of characterizing interface dislocation structures.