Tertahadral & Octahedral Voids, HCP & CCP

Concepts of Voids, HCP & CCP Arrangements

Density of unit cell-


Tetrahedral and Octahedral void- 


Tetrahedral Void-
                                                                            
A simple triangular void in a crystal which is surrounded by four spheres is called tetrahedral void.

A tetrahedral void is developed when triangular voids have contact with one sphere either in the upper layer or in the lower layer. Tetrahedral void means the tetrahedral arrangement of spheres.


                                           .  
 Characteristics of tetrahedral void-

(i) Ratio of radii of void and constituent particle is constant.

  r/R = 0.225

(ii) Co-ordination number  of particle present in the void is 4

(iii) Each constituent particle makes two tetrahedron with three spheres above and three spheres below

(iv) No. of tetrahedral voids
   = 2 ×No. of atoms
   = 2× octahedral voids

Relationship B/W  radius of void (r) and radius of atom(R)


Octahedral void- 

The double triangular void which is surrounded by six spheres is called octahedral void. In this void out of the six spheres , four are placed in the same plane touching each other, one sphere is placed from above and the other from below the plane  of these spheres.
Characteristics of octahedral void-

(i) Ratio of radii of void and constituent particle is constant.
   =0.414

(ii) Coordination of particle present in the void is 6

(iii) Size of octahedral void is greater than tetrahedral void

(iv) No. of octahedral void
 = No. of atoms   
 =  1/2  × Tetrahedral void      

Relationship B/W  radius of void (r) and radius of atom(R)


Cubic closed packing (CCP)- 

                                                                              
in this structure atoms are arranged at the corners and at the centres of all the six faces of a cube. 

  
Cubic close packing is more efficient than hcp .The ccp structure has following features- 

(i) Each atom is surrounded by 12 others and is said to have coordination no. 12.

(ii) It has 3 fold axis of symmetry.

(iii) This type of packing give ABC, ABC,ABC………….layers type of arrangement

(iv) CCP arrangement of atoms occupy 74 % of available space

(v) It has four sets of parallel close packed layers, hence the chance for slipping of one layer over the other are more 

Example- Al , Cr , Co , Cu , Ag , Fe et.

Hexagonal closed packing (HCP)- In this arrangement atoms are located at the corners and centre of two parallel hexagons ,three more atoms are placed in a parallel plane  midway between these two planes.

HCP arrangement has following features-

(i) Each atom is surrounded by 12 others and is said to have coordination no. 12.

(ii) It has 6 fold axis of symmetry.

 (iii)This type of packing give AB, AB, AB……..layers type of arrangement

(iv) HCP arrangement of atoms occupies 74 % of the available space.

(v) It has only one set of parallel close packed layers .Hence chance for slipping of one layer over the other is very less.

(v) Fraction of volume available in hcp is = =0.74
Example- Be, Cd, Li ,Mg , Zn etc.


Popular posts from this blog

Basic Concepts of Chemical Crystallography

Image
CHEMICAL CRYSTALLOGRAPHY- A branch of physical science that deals with the study of crystals i.e. their source, classification, properties and structure etc. is called chemical crystallography. A crystalline solid consist of a large number of small units called crystal. A crystal is a solid figure with a definite geometrical shape, flat faces and sharp edges. Crystal lattice and unit cell- “Regular arrangement of constituent particles i.e. atoms, ions or molecules of a crystal in a three dimensional space is called crystal lattice or space lattice.” “The smallest three dimensional portion of a complete space lattice which when repeated over and again in different directions to generate the complete space lattice is called the unit cell”       The situation may be compared with that of a thick wall made up of bricks, where brick is similar to the unit cell and the wall to the complete space lattice. The unit cell may be considered as the fundamenta
Read more

Relation between nearest neighbour distance and radius of atom, Concept of Radius ratio

Image
Relationship between the nearest neighbour distance (d), edge of the unit cell (a) and the radius of the atom (r) (1)Simple cubic unit cell- Distance between nearest neighbour (d) = AB = a Hence for simple cubic (SC)  d = a   and r = a/2 (2)Face centred cubic unit cell-    Distance between nearest neighbour (d) =  AC (Because spheres at the face diagonal are touching each other)    But from  ∆ ABC      AC2 = AB2 + BC2                       Hence        d = a2 + a2                                  d =  2a2                             d =  √2a                             d =a/ √2   Since atomic radius (r = d/2)                                      r=  AC/2 = a/2√2                                                                    Hence for face centred cubic (FCC)  d =a√2         and   r =  a/2√2 (3) Body centred cubic unit cell- The distance between nearest neighbour (d) = 1/2 CD  Since all the spheres at the corners touch the central sphere, so CD
Read more