The -cristobalite polymorph of SiO 2 has a tetragonal cell with a = 4.971 , b =

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The α-cristobalite polymorph of SiO2 has a tetragonal cell with a = 4.971 Å, b = 6.922 Å, with Si on 2a and O on 4f Wyckoff sites. The Si–O bond length is 1.60 Å and the average O–O distance within tetrahedra is 2.62 Å. The high-pressure stishovite polymorph of SiO2 has the rutile structure (Figure 1.45) with a tetragonal cell of dimensions a = 4.177 Å and c = 2.665 Å, and occupied Wyckoff sites of 2a (Si) and 4f (O). Data for a zeolite A polymorph of SiO2 (LTA) are given in the table accompanying Problem 14.4.

(a) Calculate the theoretical density of each polymorph.

(b) Assuming that Si and O can be treated as hard spheres and that O atoms are in contact in cristobalite, estimate hard-sphere radii for Si and O.

(c) Estimate the volume percent filled by atoms in each polymorph. Comment on your answers.

Figure 1.45

X TiO rutile (ICSD # 9161) P4 /mnm (136) tetragonal a = 4.5941, c= 2.9589 A At. Wyck. x Ti 2a 0 y 0 z 0 O4f

Problem 14.4

Calculate the number of tetrahedral atoms per nm3 for each zeolite framework type listed in the table below.

Name Space group Cell () Im m SOD LTA FAU Pmm ANA Fdm la d RHO Imm 8.9650 11.919 24.34 13.567 14.919 Site TI

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Solid State Materials Chemistry

ISBN: 9780521873253

1st Edition

Authors: Patrick M. Woodward, Pavel Karen, John S. O. Evans, Thomas Vogt

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