First-principles study of rare earth adsorption at -Si 3 N 4 interfaces Gayle S. Painter, 1, * Frank W. Averill, 1,2 Paul F. Becher, 1 Naoya Shibata, 3 Klaus van Benthem, 4,† and Stephen J. Pennycook 1 1 Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 2 Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996-0750, USA 3 Institute of Engineering Innovation, University of Tokyo, Yayoi, Tokyo 113-8656, Japan 4 Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Received 25 August 2008; revised manuscript received 5 November 2008; published 17 December 2008 Structural characterization of rare earth adsorption at surfaces or interfaces of -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 -Si 3 N 4 interface; however the strength of the rare earth–interface bonding is deter- mined by the electronic structure of the nitride surface and the specific adsorbate. This is the principal factor controlling the effects of dopants on the  → phase transformation and on the -Si 3 N 4 grain growth at high temperature as well as the subsequent microstructure of the ceramic. DOI: 10.1103/PhysRevB.78.214206 PACS numbers: 71.55.Jv, 81.05.Je, 68.55.Ln, 73.90.+f I. INTRODUCTION Additions of metallic compounds are widely used in ce- ramic processing to promote densification of the powder compacts during sintering. 1–5 Atoms of the sintering addi- tions often reside largely within regions separating the crys- talline grains. These regions can take the form of disordered amorphous nanometer scale intergranular films IGFs and larger amorphous multigrain pockets that result from the re- action between additives and other constituents during den- sification at elevated temperatures. Some of these species can segregate to grain surfaces and adsorb there according to the chemical driving force and interaction with other atoms in the glass. After densification, these grain-boundary phases are known to greatly influence the resulting microstructure and mechanical properties of ceramics, 6–9 and it is thus im- portant to understand the mechanism and effects of dopant adsorption at internal interfaces. Silicon nitride Si 3 N 4  ceramics have become a model material for basic and applied studies of ceramics 10–13 due to the considerable degree to which they have been character- ized, as well as their importance as structural and electronic materials. Rare earth RE oxide additions are observed to strongly affect the  →  phase transformation, which occurs during densification 14,15 and the anisotropic shape of -Si 3 N 4 grains that grow in the high-temperature sintering stage, 16–22 suggesting that they affect the attachment of nitride growth fragments during Si 3 N 4 crystalline growth and do so with specific surface sensitivity. Since the morphology of the growing grains depends upon RE type and grain aspect ratios are important to fracture toughness of the ceramic, 17 dopant selection provides a way to control the ceramic’s macro- scopic physical properties. It is thus important to obtain a basic understanding of RE adsorption on -Si 3 N 4 prism planes and the reasons for observed differences among the RE series. Until recently 5 little was known about the distribution of rare earths within IGFs mainly due to the difficulties posed for chemical probes by both the very small thickness e.g., 1–2 nm of the IGF and the need to image the RE atoms. Recently RE adsorption at the glass/silicon nitride grain in- terface has been determined through high-angle annular dark-field also known as Z-contrast scanning transmission electron microscopy STEM imaging carried out by three research groups 23–28 generally using samples from the same source. 29 Here, we report first-principles calculations that de- scribe details of the adsorption behavior of La, Lu, and Gd at the prism plane surface of -Si 3 N 4 shown in Fig. 1a. The actual computational models used in this work are pictured in Figs. 1b and 1c. Electronic structure factors that under- lie the observed differences in RE segregation and adsorption behavior are described. Stable interfacial bond sites for spe- cific rare earths are determined by minimizing the total en- ergy of the system through atom relaxations according to calculated forces. The relative binding energies of the REs at different surface sites identify site preferences, and compari- sons of the bond strengths of different rare earths in similar sites give insight into relative adsorption or desorption strengths that relate directly to effects on the phase transfor- mation and grain growth. Finally, analysis of the calculated electronic structure characterizes the nature of the adsorbate/ substrate bond, which has been shown earlier to explain dif- ferences in the effects of RE additions on phase transitions 14 and on grain growth anisotropy. 30 II. METHODS Various theoretical methods have been used 31–35 to model and understand intergranular behavior, motivated by the fact that these nanoscale films effectively control macroscopic ceramic behavior. For problems that require an understand- ing in terms of the electronic structure and bonding, density- PHYSICAL REVIEW B 78, 214206 2008 1098-0121/2008/7821/2142069 ©2008 The American Physical Society 214206-1