Normal Coordinate Analysis of Benitoite (Batisi 3 O 9 ) and its Constituent Ring
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NORMAL COORDINATE ANALYSIS OF BENITOITE (BaTiSi 3 O9 ) AND ITS CONSTITUENT RING Charles C. Kim*l, M. I. Bell* and D. A. McKeown** "Naval Research Laboratory, Dynamics of Solids Branch, Washington, D.C. 20375-5320 "**Chemistry Dept., Howard University, Washington, D.C. 20059
ABSTRACT The normal modes of vibration and their frequencies are calculated for benitoite, a mineral whose crystal structure (space group D33h) consists of three-membered silicate rings (Si309) linked by Ba+2 and Ti+ 4 ions. The calculation unambiguously assigns the normal modes to the lines in the Raman and infrared spectra and determines the atomic interactions. On the assumption that mode mixings and splittings due to inter-ring interactions are small, the normal frequencies of the isolated ring of C3h symmetry are determined. The identification of normal modes characteristic of three-membered silicate rings may prove to be a valuable guide in the interpretation of the infrared and Raman spectra of amorphous silicates, potentially leading to new information on the ring statistics of these materials. INTRODUCTION Raman spectroscopy has been used to gain insights about the atomic structure of amorphous silicates, or silicate glasses and melts [1,2,3]. Numerous experimental studies of the vibrational spectra of crystalline silicates have been reported [4,5]. Nevertheless, the features in the Raman spectra of amorphous and even crystalline silicates are not well understood physically. More work needs to be done to relate the observed spectra to the dynamics in these materials. We start a series of investigations that address the underlying physics behind the Raman spectra of cyclosilicates which contain one type of isolated three-, four- or six-membered silicate ring. A better understanding of the vibrational spectra of cyclosilicates may be useful in characterizing the vibrational spectra of crystalline and amorphous silicates which contain rings. Furthermore, this knowledge can aid in understanding the vibrational spectra of other silicates with different polymerization of the silicate tetrahedra. 8a Benitoite (BaTiSi 3Og) is a cyclosilicate containing rings of three linked tetrahedra (Si3 Og). It Ti belongs to the space group P6c2 (D'h) and has two formula units per unit cell [6]. Figure 1 shows the crystal structure, where each ring is shown as S composed of tetrahedral units. Each tetrahedron has two bridging oxygen atoms, designated 0(1), X which are shared with two neighboring tetrahedra and two non-bridging oxygen atoms, designated 0(2). The c axis passing through the origin is the axis of three-fold symmetry. Two-fold symmetry axes are perpendicular to the c axis, and pass through the origin, and through the Ba and Ti ions. The two rings are symmetrical with respect to rotation about the two-fold axis. The c axis and FIG. 1. Primitive unit cell of benitoite. one of the two-fold symmetry axes are designated as the z and x axis, respectively. Although the vibrational spectra [7] of benitoite are known, the normal coordinate analysis of be
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