CHARGE DENSITY ANALYSIS OF b-Si3N4

 

Doug du Boulay,a Nobuo Ishizawa,a and Victor Streltsovb

 

aMaterials and Structures Laboratory, Tokyo Institute of Technology, Nagatsuta, Midori-Ku Japan; b CSIRO HSN, 343 Royal Parade, Parkville VIC 3052, Australia.

(ddb@R3401.msl.titech.ac.jp)



b-Si3N4 is a technologically important material in both the electronics and mechanical fabrications industries, on account of its intrinsic hardness (bulk modulus comparable to diamond) and resistance to oxidation. Despite its widespread use, a minor degree of controversy has persisted as to the true structure of the lattice in the b-phase. Specifically, the existence, or not, of mirror planes normal to the crystallographic 63-screw axes. These mirrors determine whether the structure is centrosymmetric (if they exist) or noncentrosymetric (if they do not).

Using BL-14A of the Photon Factory synchrotron, Tsukuba, Japan, three 0.75A data sets were measured at three different temperatures, 295K, 200K and 150K. Based on that data the authors identified no compelling, reproducible evidence in support of the non-centrosymmetric model. We thus believe that the P63/m symmetry is to be preferred for this material, despite the earlier reports to the contrary by other authors[1-3]. A recent electron microscopy study of b-Si3N4 has subsequently supported these conclusions[4]. Consequently, with greater faith in the experiments, we have used this relatively accurate and largely absorption and extinction free data as a basis for multipole population and topological analyses[5]. These analyses agree largely with more theoretical modelling derived from Density Functional Theory using the Linear Augmented Plain Wave approach as implimented in Wien2k[6].

The results of these analyses are consistent regarding the magnitude and topography of the charge density along the interatomic interactions. The coordination geometries of two independent NSi3 groups is trigonal planar, while that of the SiN4 group is tetrahedral. The three symmetry distinct Si-N bonds exhibit pronounced charge density accumulation near the bond midpoints, characteristic of covalent sp2 and sp3 hybridization schemes for N and Si respectively.

A topological analysis of the electron density revealed the existence of additional (3,-1) critical points at the high symmetry (-6) sites midway along the 2.9A N-N contacts. This feature was reproduced in both the DFT and multipolar models. The magnitude of the Laplacian of the charge density at the N-N critical point is around 20 times smaller than for the other (3,-1) critical points along the N-Si shared electron interactions, with the local electron density at that point around ¼ of that appearing in those N-Si bonds. This could be interpreted as evidence of weak N-N shared electron interactions, i.e. partial covalent bonding. By comparison, all other N and Si bonds are of order 1.73A in length.

 

References

1           Bando, Y. (1983) Acta Cryst. B39, 185-189.

2           Grun, R.(1979) Acta Cryst. B35, 800-804.

3           Schneider, J., Frey, F., Johnson, N. and Laschke, K. (1994), Zeit. fur Krist. 209, 328-333.

4           Tsuda, K. (2002) private communication.

5           Blaha, P., Schwarz, K., Madsen, G.K.H., Kvasnicka, D., and Luitz, J. (2001) WIEN2k, (Karlheinz Schwarz Tech. Universitat Wien, Austria),2001. ISBN 3-9501031-1-2.

6           Stewart, R.F., Spackman, M.A., and Flensburg, C. (1998) VALRAY98.