Titanium dioxide exist in different form of crystal structures like Anatase, Rut

Question

Titanium dioxide exist in different form of crystal structures like Anatase, Rutile and Brookite. The crystal structure and properties of this compound has been well studied by x-ray diffraction and other techniques. Here, you are given the coordinates of a set of Ti and O atoms to create a unit cell of TiO_2 such that the lattice parameters are a =b= about 4.60 A, c = about 2.96 A and alpha = beta = gamma = 90 degree. Draw these points into a coordinate system and label individual Oxygen ion as O1, O2... and individual Ti ion as Ti1, Ti2, Ti3, ..., to show the labelling of each atom clearly. What kind of a unit cell is this - orthorhombic, tetragonal or monoclinic ? What crystal structure is this - Anatase, Rutile or Brookite? How many Ti and O atoms are in one unit cell? Determine the atomic basis vectors of the crystal structure using atom #8 (Ti) as the origin. Is this a primitive cell of the underlying Bravais lattice?

Explanation / Answer

2) Monoclinic Lattice – There are two possible types of monoclinic lattice. They are Primitive and End centred. They have unequal sides and two faces have angles other than 900.

               

Orthorhombic Lattice – Four types of orthorhombic lattice are possible. They are Primitive, End-centred, Body centred and Face centred. They have unequal sides. The Angles between their faces are equal to 900.

                        

3) Rutile is a mineral composed primarily of titanium dioxide, TiO2.

Rutile is the most common natural form of TiO2. Three rarer polymorphs of TiO2 are known:

·         Anatase (sometimes known by the name "octahedrite"), a tetragonal mineral of pseudo-octahedral habit

·         Brookite, an orthorhombic mineral

4) 2 Ti and 4 O are present

5) The unit cell of a crystal structure is the unit of the structure, chosen so that it packs to fill space, and which, translated regularly, builds up the entire structure. The primitive unit cell is the smallest such cell.

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