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.