Diffusion and formation energies of adatoms and vacancies on magnesium surfaces
Introduction
Magnesium (Mg) is a hexagonal-close-packed (HCP) metal, and it is the eighth most abundant element in the earth’s crust [1]. Although being close packed like copper or aluminum, HCP metals have lower crystal symmetry. Consequently, surface configurations are less symmetrical than those of, say, copper. This low symmetry may lead to more anisotropic surface diffusion and to more complex mechanisms of surface and step diffusion processes, both of which are interesting and challenging scientifically. Much less is known about surface diffusion of HCP metals than those of face-centered-cubic (FCC) metals such as copper [2]. This lack of scientific understanding is in contrast to the importance of Mg in various applications. With a low density of 1.74 g/cm3 and a high ultimate tensile strength of 250 MPa in alloys, Mg and Mg-based alloys are good candidates for structural materials in automotive and aerospace industries [3]. For comparison, the density of common light aluminum is 2.70 g/cm3, and its tensile strength is typically 40–50 MPa [4]. Due to its low density, Mg particularly in the form of nanostructures is also a candidate for hydrogen storage [5]. The solid form of MgH2 contains 7.6 wt% hydrogen, which meets the 5.0 wt% efficiency target of the automotive industry and the 6.0 wt% US DoE target efficiency for 2010 [6].
The synthesis of Mg nanostructures relies on a fundamental understanding of surface energetics. Physical vapor deposition (PVD) enables the control of material impurity [7] and surface evolution. Using PVD at an oblique angle, Tang et al. have synthesized Mg nanoblades, which help maximize the area of surfaces for hydrogen storage applications [8], [9]. The nanoblades take an inclined angle, which defies the theoretical understanding. Further, sides of the nanoblades are surfaces of high aspect ratio in dimensions, and the authors have suggested that they are of high surface energy planes such as type [8], [9]. However, the crystal orientation of the side surfaces is far from being clear; as an application of the calculation results, we will revisit this issue of crystal orientation near the end of this paper.
Previous studies have shown that surface diffusion, among other factors, dictate the selection of crystal orientations [10], [11]. As a result, it is even possible to design nanostructures of particular crystal orientation and shape through the understanding and use of surface diffusions [12]. Following the same line here, we investigate the diffusion of adatoms and surface vacancies on Mg surfaces using the classical molecular statics method. Based on this investigation we revisit the recent experimental observation of Mg nanoblades, and assess the crystal orientation of their side surfaces. The rest of this paper is organized into three sections. Section 2 covers the simulation methods. Section 3 presents the simulation results and, based on them, the re-analysis of experimental observations of Mg nanoblades. Finally, Section 4 is a summary of conclusions.
Section snippets
Simulation methods
This section starts with a brief description of HCP structures since they are less commonly studied. The presentation continues with descriptions of interatomic potential, simulation cell set up, and the nudged elastic band (NEB) method for diffusion studies.
Shown in Fig. 1a are the four index axes of HCP structures. Figs. 1b–f are five low index (high atomic density) planes; two of them have the same index. Surfaces of low index or high atomic packing density are usually energetically
Simulation results and discussions
This section first presents the simulation results in terms of surface formation energies, formation energies of an adatom and surface vacancy, and the diffusion energy barriers of an adatom and surface vacancy; then discusses the implications of the numerical results to crystal orientations of Mg nanoblades in recent experiments.
As mentioned in the previous section, we consider five low index surfaces of Mg: {0 0 0 1}, , , and . Since each simulation cell contains
Conclusions
Using classical molecular statics method, we have calculated formation energies of defects (adatoms and surface vacancies) and flat surfaces and diffusion energy barriers of the defects on five low index surfaces of Mg. From low to high formation energies, the surfaces are: {0 0 0 1}, , , and . It is particularly noteworthy that the surface is energetically more preferred than the other three surfaces despite being overlooked in the literature. The diffusion
Acknowledgements
The authors gratefully acknowledge the GAANN fellowship from the US Department of Education and National Science Foundation (CMMI-0625602, 0727413 and 0506738). The sponsorship of the US Department of Energy (DE-FG02-04ER46167) has facilitated the participation of HH in this work. We also thank F. Tang and G.-C. Wang for their private discussions about Mg nanoblades fabrication.
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