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For which type of cubic lattice, a = 2r?
In a simple cubic lattice, the side of the solid structure is equal to twice the radius of the atom.
Hence the correct answer is simple cubic.
Additional Information: A cubic lattice is a lattice whose points lie at positions (x,y,z) in the Cartesian three-space, where x, y, and z are integers.
There are three main types of cubic lattices:
1. the simple cubic structure (sc) (also known as primitive cubic)
2. the body-centred cubic structure (bcc)
3. the face-centred cubic structure(fcc)
Packing efficiency of body centred cubic unit cell is:
The packing efficiency of a body-centred cubic unit cell is 68%.
The packing efficiency is the fraction of the crystal (or unit cell) actually occupied by the atoms. It is usually represented by a percentage or volume fraction.
Mathematically Packing Efficiency is:
Number of atoms × volume occupied by 1 share × 100/Total volume of unit cell × 100
Packing efficiency in a unit cell is never 100% because constituent particles are assumed to be:
Packing efficiency can never be 100% because in packing calculations all constituent particles filling up the cubical unit cell 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 a tetrahedral arrangement in the crystal lattice is called tetrahedral void.
HCP structure is present in:
Metals that crystallize in an HCP structure include Cd, Co, Li, Mg, Na, and Zn, and metals that crystallize in a CCP structure include Ag, Al, Ca, Cu, Ni, Pb, and Pt.
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)
Therefore the correct answer is B.
Which of the following shows maximum packing efficiency?
Packing efficiency is defined as the percentage of space occupied by constituent particles packed inside the lattice.
Packing efficiency = Number of atoms × volume occupied by one share × 100/total volume of the unit cell
Packing efficiency in fcc and hcp structures is 74%
The packing efficiency of the body-centred unit cell is 68%.
The packing efficiency of the simple unit cell is 52.4%
Since HCP shows the maximum packing efficiency, the correct answer is A.
The number of atoms in each unit cell in ccp structure is:
In ccp structure or fcc structure, the number of atoms per unit cell is calculated as follows
Thus, in a face-centred cubic unit cell (fcc) or cubic close packing (ccp), we have
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:
In a Body-centred cubic arrangement, there are 8 corners and 1 corner shares 1/8th the volume of the entire cell, so: 8×1/8
8×18 = 1 atom
There is also 1 atom at the centre of the body of the cube. This can’t be shared. So, it will stay as one atom whole: 1 × 1 = 1 atom
Total atoms = 1 + 1 = 2 atoms
So, from this, we can say that the number of atoms in the unit cell of the body-centred cubic crystal is 2.