Atomistic Simulation of the Surface Energy of Spinel MgAl₂O₄

Abstract

Atomistic simulations with atomic potentials including anion polarizibility have been performed for the low-index surfaces of spinel MgAl 2 O 4 with various terminations. The calculations show that for the most stable surface the surface energy is 2.27 J/m 2 for the {100}, about 2.85 J/m 2 for the {110}, and 3.07 J/m 2 for the {111} orientation. The ratio between the experimental values to the calculated relaxed surface energies is about 1.5. Strong surface relaxation was found for the {110} and {111} orientation but only moderate surface relaxation for the {100} surface.S URFACE energy is an important parameter of ceramic materials.It controls many chemical and physical processes and properties, such as sintering, mass loss, adherence, crack nucleation and growth, catalysis, sensing, etc. A precise knowledge of this quantity would be very useful in predicting and optimizing processing and properties of ceramic materials. 1 For example, in the fracture process of brittle materials surface energies play an important role according to the Griffith criterion. 2 The fracture of MgAl 2 O 4 has been a subject of several investigations. 3-8 Stoichiometric spinel MgAl 2 O 4 is a brittle single crystal, which exhibits plastic flow only at elevated temperature. 3 Stewart and Bradt 4 studied the fracture of single-crystal, stoichiometric MgAl 2 O 4 for the low-index planes and found that the fracture toughness at room temperature is 1.18, 1.54, and 1.90 MN⅐m Ϫ3/2 for {100}, {110}, and {111}, respectively. They also estimated the surface energy to be 3.57 J/m 2 for {100}, 4.07 J/m 2 for {110}, and 4.85 J/m 2 for {111}. 5,6 Early theoretical calculations by Mishra and Thomas 9 indicated that surfaces parallel to the {111} plane are of the lowest energy for spinel MgAl 2 O 4 , in contrast to the experimental data. 4 -6 Recently Davies et al. performed atomistic simulations for the low-index surfaces of spinel MgAl 2 O 4 , but their calculations were limited to certain terminations with half anion/cation occupation. 10

Effects of substrate orientation on aluminum grown on MgAl2O4 spinel using molecular beam epitaxy

“…This explanation is consistent with the low stacking fault energy for fcc materials [11,13,16]. A second possible source of twin formation is related to the presence of sub-monolayer steps on the oxygen-terminated (1 1 1) spinel substrate surface [9,17]. The oxygen planes exposed by sub-monolayer steps are inequivalent to the oxygen planes on a surface with only full monolayer steps and may therefore support nucleation of Al with a reversed stacking sequence, which in turn would lead to twin boundaries in the Al layer as growth proceeds.…”

“…This lattice mismatch of less than 0.25% not only makes epitaxial Al thin film growth possible, but significantly simplifies the atomic structure at the metal/oxide interface so that this system can be readily studied using present theoretical models [2]. For Al-on-MgAl 2 O 4 systems, the orientation of spinel substrates is considered to be a critical parameter impacting the Al/spinel interface properties due to the surface energy difference [9]. However to date, little research has been done to study Al thin films grown on spinel substrates as a function of substrate orientation.…”

Effects of phosphorus and saccharide on size, shape, and reducibility of Fischer–Tropsch catalysts for slurry phase and fixed-bed reactions

“…As shown in Fig. 12d-e, most of crystals resembled spheres or hexagons, which were believed to grow selectively at specific facets, minimizing their surface energies [46][47][48]. This selective and regular growth of the cobalt oxide crystals seemed to exert a positive impact on hydrocarbon growth by providing more stable active sites on the catalytic surface.…”

Configurational and energy study of the (100) and (110) surfaces of the MgAl2O4spinel by means of quantum mechanical and empirical techniques

“…This finding is in agreement with the previous ones. [12][13][14] Always concerning the configurational analysis, it is advisable to treat the crystal surface as a crystallographic entity and not exclusively as a chemical system lacking of whatever symmetry. As a matter of fact, when a crystal face is studied, it is fundamental to specify the symmetry elements preserved, if any, in the different surface configurations, as well as the cell parameters of the 2D cell considered.…”

“…[12][13][14] In all of these works, only stoichiometric surfaces (that is surface reconstructed to cancel out the dipole moment) were taken into account and a restricted number of (100) surface configurations were analyzed; unfortunately, in these papers there are not sufficient information and detailed figures that allow to understand and analyze the structure of the surface configurations. In detail, van del Laag et al 12 have described only two surface configurations (Mg-and Al-terminated), whereas Fang et al 13 In this paper, we will deal with stoichiometric surfaces at 0K in vacuum and we will show that the number of surface configurations detected in the previous papers is not sufficient to give a correct description of the structural complexity of a crystal face of MgAl 2 O 4 spinel. Furthermore, we will also show that the surface energy value of the more stable Al-O-terminated configuration found in the present work is noteworthy lower than those previously published.…”