Question

The ceramic compound TiC is even harder than martensite. It is Therefore very valuable as a utting tool in industry. TiC is cubic. The sketch shows the atom arrangement on the (100), (110), and (001) planes (facial planes). The center-to-center distance between the closest titanium and carbon atoms is 2.16 A (0.216nm). (section 11.1 through 11.3). a) Is the arrangement of the titanium atoms in the structure simple cubic, BCC, or FCC? b) What is the coordination number for titanium in this unit cell? c) what id the unit cell volume in cubic angstroms? d) What is the closest cneter-to center approach of teo titanium atoms in angstroms? Each titanium atom is related to how many other titanium atoms at this same distance?

Answer 1

a) As the atom arrangements are on the (100), (110), and (001) planes (facial planes) That's why the arrangement of the titanium atoms in the structure is simple cubic lattice.

b) The coordination number for titanium in this unit cell is Six(6). As the arrangement is Simple primitive cubic lattice.

c) The unit cell volume in cubic TiC is, V = (2r)³ = (2.16 A)³= 10.08 A³ [A= angstroms]

As 2r= The center-to-center distance between the closest titanium and carbon atoms = 2.16 A (0.216nm)