Crystallographic Formulae

Some useful crystallographic formulas are listed in Table 5.2-1. Table 5.2-1 Some useful crystallographic formulas 

Cosine of the angle between planes with normals, 2 h h2- -k k2- -hh h]h2 + kik2 + hi2+hh/  

Cosine of the angle between planes with normals ni, 2 

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The LTL zeolites have a Si/Al ratio of 3.027. Based upon the crystallographic formula of LTL ([K9(H20)2i][Al9Si27072]), the number of Bronsted acid sites in the LTL with a K/Al = 0.47 is 1.76 mmol/g. In the case of the LTL [0.82], this is 0.57 mmol/g. The LTL zeolites with K/A1>1 have no Bronsted acid sites, and after calcination at elevated temperatures, the excess K is probably present as KOH or K20. Increased amounts of K results in a more basic support, with an increased electron-richness on the support oxygen atoms. ... 

Involving the inversion center one is leaved with the last two possible crystallographic formulae ... 

CeYbjS6 type or F type. The monoclinic cell has the space group P2i/m (Fig. 31.6). There are four kinds of metal sites and the crystallographic formula is (VlIIp)2(VIIo)2(VIo)2(Vro)2Si2 (Rodier et al., 1974). The VIII prismatic sites are always occupied by light rare earths, and the VI octahedral sites by heavy rare earths. But, depending on the nature of the elements, the VII octahedral sites... 

NdYbSj type or H type. The cell is orthorhombic B22i2 (fig. 31.8). Two kinds of metallic sites are present in equal proportion, and the crystallographic formula is (VIIIp)4(VIo)4Si2. (Carre et al., 1974). The only possible chemical formula is RR Ss. Because of the high coordination and the prismatic character of the first sites, they may only be occupied by the lighter lanthanides (Ce to Nd). The VI octahedral sites contain exclusively the last two lanthanides Yb and Lu. 

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