For which type of cubic lattice, a = 2r?
In simple cubic lattice the side of the solid structure is equal to twice the radius of atom. Hence the correct answer is simple cubic.
Packing efficiency of body centred cubic unit cell is:
The packing efficiency of both types of close packed structure is 74%, i.e. 74% of the space in hcp and ccp is filled. The hcp and ccp structure are equally efficient; in terms of packing. The packing efficiency of simple cubic lattice is 52.4%. And the packing efficiency of body centered cubic lattice (bcc) is 68%.
Packing efficiency in a unit cell is never 100% because constituent particles are assumed to be:
The constituent particles i.e. atoms, molecules and ions are assumed to be spheres.
If r is radius of void and R is radius of the sphere, then for an atom to ocuppy an octahedral void which relation holds true?
Let the radius of the octahedral void be r and radius of the atoms in close-packing be R and the edge length be a.
In the right angle triangle ABC,
AB = BC = a
For the diagonal AC,
Using Pythagoras Theorem we get;
And, AB = 2R
AC = R + 2r + R = 2R + 2r
r = 0.414R
Hence, the relation is r = 0.414R.
Which type of void is represented by the following diagram?
A tetrahedral void is formed when one sphere or particle is placed in the depression formed by three particles.
Definition of Tetrahedral Void: The vacant space or void among the four constituent particles having tetrahedral arrangement in the crystal lattice is called tetrahedral void.
HCP structure is present in:
If r is the radius of the void and R is the radius of the sphere, what is AC in the following diagram?
AC = Diameter of void + (2× Radius of sphere) 》AC = 2r + 2R = 2(R+r)
Which of the following shows maximum packing efficiency?
HCP = 74% packing efficiency
BCC = 68% packing efficiency
Simple cubic = 52.4% packing efficiency
The number of atoms in each unit cell in ccp structure is:
In ccp structure: number of atoms per unit cell is
► 8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom
► 6 face-centred atoms × 1/2 atom per unit cell = 3 atoms
Therefore, the total number of atoms in a unit cell = 4 atoms.
The number of atoms per unit cell in a body centred cubic arrangement is:
For a bcc unit cell, number of atoms per unit cell = (8 *1/8) + 1 = 2