First-principles study of rare earth adsorption at $\ensuremath{\beta}{\text{-Si}}_{3}{\text{N}}_{4}$ interfaces

First-principles study of rare earth adsorption at $β {-Si}_{3} N_{4}$ interfaces

Gayle S. Painter, Frank W. Averill, Paul F. Becher, Naoya Shibata, Klaus van Benthem, and Stephen J. Pennycook

Phys. Rev. B 78, 214206 – Published 17 December 2008

Abstract

Structural characterization of rare earth adsorption at surfaces or interfaces of $β {-Si}_{3} N_{4}$ grains within silicon nitride ceramics has recently been reported by three different groups using $Z$ -contrast scanning transmission electron microscopy (STEM) imaging. Here we report the electronic structure basis for these observations and discuss the origin of similarities and differences among the lanthanides characterized in that work. Along with the features that are well described by a first-principles cluster and surface slab models, we identify those differences in the experiment and theory that warrant further investigation. Stereochemical bonding factors are found to determine adsorption site preferences as opposed to ionic size effects. The set of possible bond sites is a characteristic of the $β {-Si}_{3} N_{4}$ interface; however the strength of the rare earth–interface bonding is determined by the electronic structure of the nitride surface and the specific adsorbate. This is the principal factor controlling the effects of dopants on the $α \to β$ phase transformation and on the $β {-Si}_{3} N_{4}$ grain growth at high temperature as well as the subsequent microstructure of the ceramic.

Received 25 August 2008

DOI:https://doi.org/10.1103/PhysRevB.78.214206

Authors & Affiliations

Gayle S. Painter^1,*, Frank W. Averill^1,2, Paul F. Becher¹, Naoya Shibata³, Klaus van Benthem^4,†, and Stephen J. Pennycook¹

¹Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
²Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996-0750, USA
³Institute of Engineering Innovation, University of Tokyo, Yayoi, Tokyo 113-8656, Japan
⁴Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*Deceased.
^†Present address: Department of Chemical Engineering and Materials Science, University of California at Davis, Davis, California 95616, USA.

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Vol. 78, Iss. 21 — 1 December 2008

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Figure 1
(a) The $β {-Si}_{3} N_{4}$ crystal structure viewed slightly off normal to the basal plane and across the edge of the $[11 \bar{2} 0]$ prism plane terminating with N atoms and one adsorbed RE atom in each surface unit cell. The actual computational models used in this work are pictured in parts (b) and (c). The inset of (a) is an atomic cluster model of this interface shown with a RE adsorbate. (b) The $β {-Si}_{3} N_{4}$ model surface with an adsorbed RE within each surface unit cell along the prism plane. Also shown are the atoms underneath the surface which are included in the VASP surface slab calculations as well as the local coordinate system for that model. The horizontal slice shown here is infinitely replicated in the $z$ direction. (c) Side and top views of the 23 atom cluster model of the surface with its local coordinate system. The 1.06 nm length of the cluster gives the scale of the system. The $x$ direction is the $[10 \bar{1} 0]$ of the $β {-Si}_{3} N_{4}$ lattice, the $y$ direction represents the $[11 \bar{2} 0]$ and the $z$ direction the [0001].Reuse & Permissions
Figure 2
(a) Surface decoration pattern of RE atom adsorbed on the nitride prism plane (all in $z = 0$ plane). The coordinate system is defined in Fig. 1. RE absorption sites $A$ and $B$ are stable RE equilibrium sites in the atom cluster and surface slab models. Site $M$ is an unstable equilibrium in these models and has only been observed experimentally in the case of La and not in Gd or Lu. It is hypothesized in the text that for La, site $M$ may be stabilized by the interaction of that RE with the IGF. (b) Free energy (eV) of the surface unit cell in the surface slab model as a function of the $x$ coordinate $(Å)$ of the La atom as La moves in the $z = 0$ plane above the grain surface. The relative stabilities of sites $A$ , $B$ , and $M$ in this model can be clearly seen.Reuse & Permissions
Figure 3
Comparison of aberration corrected STEM images of RE adsorption at the prism planes of $β {-Si}_{3} N_{4}$ grains in silicon nitride ceramics and theory. In (a) Gd is the RE additive (as an oxide) and in (b) the RE is Lu. The array of hexagonal spots in the lower half of each panel originates from Si atom columns along the crystal $c$ axis. The top row of Si (and terminal N) atoms is superimposed by translated atomic cluster models showing calculated RE adsorbates. The two bright spots that repeat with the period of the surface in the images correspond to RE in the pair of calculated stable $A$ and $B$ sites in the surface unit cell. These define the interface with the amorphous intergranular film that extends out and terminates on an adjacent grain interface with random orientation.Reuse & Permissions
Figure 4
Perspective view of primary adsorption sites $A$ and $B$ for $RE = La$ defined by single-bonded anion pair on the $(11 \bar{2} 0)$ prism plane of $β {-Si}_{3} N_{4}$ . Site $A$ binding energy is stronger than that at $B$ due to coordination factor: threefold RE-N bond set (2.2, 2.2, 2.6) of $A$ versus that of (2.3, 2.3, 2.9) of $B$ , all in $Å$ . The added bond strength of site $A$ appears to come from the N at $2.6 Å$ (i.e., N1) which has an unsaturated third bond to give to the RE, whereas the comparable N at $2.9 Å$ (i.e., N4) from $B$ is fully saturated.Reuse & Permissions
Figure 5
(Color) Atom cluster model SCPW charge deformation densities for La adsorbed at the $A$ interfacial site. In (a) the plane of the contours passes through the La atom (see Fig. 4) and the N atoms N1 and N2 are located at 2.6 and $2.2 Å$ , respectively, from the La. In (b) the plane passes through the La atom and both N at $2.2 Å$ (N2 and N3). The violet contour is the zero level contour and successive contours differ by $\pm 0.004 units$ . The cutoffs for contours occur at $- 0.02$ and $+ 0.016$ . The line curves at the top and right sides are values along the intersecting cuts shown in the figures. The La atom bonds to the interface by transferring charge from its bond region to the nearby N atoms which in turn form directed $s p$ bonds toward La. The especially large strength of the La bond to N2 and N3 is evidenced by the large charge transfer from La and the large directed $s p$ bonds on N2 and N3.Reuse & Permissions

Physical Review B

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First-principles study of rare earth adsorption at $β {-Si}_{3} N_{4}$ interfaces

Gayle S. Painter, Frank W. Averill, Paul F. Becher, Naoya Shibata, Klaus van Benthem, and Stephen J. Pennycook

Phys. Rev. B 78, 214206 – Published 17 December 2008

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First-principles study of rare earth adsorption at β-Si3N4 interfaces

Gayle S. Painter, Frank W. Averill, Paul F. Becher, Naoya Shibata, Klaus van Benthem, and Stephen J. Pennycook

Phys. Rev. B 78, 214206 – Published 17 December 2008

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First-principles study of rare earth adsorption at $β {-Si}_{3} N_{4}$ interfaces