Two-dimensional systems layered host, layers of sites for

3 Two-dimensional systems layered host, layers of sites for guests 

Many layered compounds are made of close-packed anions, with transition metals in octahedral or trigonal prismatic sites, as shown in Fig. 7.5. Adjacent layers of anions are only weakly coupled together, and so various sizes of guest ions can be inserted between them. The kinds of site between these layers have already been illustrated in Fig. 7.1. 

The structure of layered compounds often can be described by the ABC notation, shown in conjunction with the sites between close-packed layers in Fig. 7.1. Given a close-packed layer of atoms, with atoms at positions we call A, there are three possible places to put the atoms of the next layer directly above the first layer (also in the A positions), or fitted into the interstices of the first layer, either in B or C positions. In this notation, a trigonal prism sandwich is denoted AbA, and an octahedral sandwich is AbC, where the uppercase letters denote the layers of chalcogen or oxygen, and the lowercase letters the layers of transition metal atoms. 

Perhaps the most well known of the lithium intercalation compounds is Li jTiSj. Both Li (for x 1) and Ti are octahedrally coordinated by S (Fig. 7.1) in the ABC notation, the structure is AbC(b)AbC, where the letter in parentheses denote lithium atoms. This structure is also called the IT form, because of its trigonal (T) symmetry and the single layer per unit cell. The electrochemical behaviour of Li in TiSj is described below in connection with staging. 

Li generally occupies octahedral sites in these compounds at low concentrations. But there is only one octahedral site per transition metal in a compound like VScj, and so beyond x = 1 at least some of the Li must occupy tetrahedral sites. Since the tetrahedral sites are above and below the planes of the octahedral sites, the Li-Li repulsion is reduced if the Li already in octahedral sites shift to tetrahedral sites beyond x = 1. Thus the structure goes from AbC(b)AbC at x = 1 to AbC(a,c)AbC at X = 2. That is one way to rationalise why all the Li occupy tetrahedral 

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