Unit cell,crystal structure,Primitive cell and Bravais lattice.

1. A unit cell,is one that we repeat to form a perfect single crystal.A unit cell,must be same to the other unit cell : See figure below ,for unit cell in 2D

Figure 1

example a unit cell

 

Figure 2

example of unit cell that construct a full crystal.Observe carefully the repeating pattern of the unit cell.

 

Figure 3

its not necessary for us to construct unit cell starting from the left/right most side 

 Figure 4
we can also construct sets of unit cell by using this way

2. Crystal structure = crystal lattice ( kekisi ) + basis ( a group of atoms that describe crystal structure ).See figure 5

Figure 5

3. Primitive cell ,it is a simple cell ( simple cubic).See figure 6 :

Figure 6

4. Non primitive cell,example,Face CC,Body CC etc (see figure 7 and 8)

 Figure 7

Figure 8

  5.Bravais ( the name of the founder Auguste Bravais ) concluded that,there are only 14 possible space lattice.There are :

     

    Now,we will go 1 by 1,to see the properties of the bravais lattice.From all the     structures given above,we may categorized it into several group,

    a. Cubic crystal - simple cubic,body centered cubic (BCC),Face centered cubic (FCC)

    b. Tetragonal crystal - Simple tetragonal,body centered tetragonal

    c.  Orthorhombic crystal - Simple orthorhombic,BCC orthorhombic,FCC orthorhombic,End centered orthorhombic

    d.  Hexagonal crystal - Simple hexagonal

    e.  Rhombohedral crystal - Simple rhombohedral

    f.  Monoclinic crystal - Simple monoclinic,end centered monoclinic

    g. Triclinic crystal - Simple triclinic

Now,consider the vector a,b and c (refer figure below) is applicable for  not only  simple cubic,but also for the rest of bravais crystals.

 1.cubic crystal, a = b = c,
where angle alpha (angle between vector c and b),beta (angle between a and c ),gamma (angle between vector a  and b )= 90


2.Tetragonal crystal, a = b # c / 
   alpha = beta = gamma = 90 


3.Orthorhombic crystal, a # b # c / 
   alpha = beta = gamma = 90

4.Hexagonal crystal,a = b # c /
   alpha = Beta = 90,while gamma = 120


5.Rhombohedral crystal,a = b = c
   alpha # beta # gamma # 90


6.Monoclinic crystal,a # b # c
   alpha # 90, beta & gamma = 90


7.Triclinic crystal,a # b # c
    alpha # beta # gamma # 90