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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 threespace, 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 bodycentred cubic structure (bcc)
3. the facecentred cubic structure(fcc)
The packing efficiency of a bodycentred cubic unit cell is 68%.
Explanation:
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 closepacking 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;
Also,
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.
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.
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 bodycentred 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 facecentred cubic unit cell (fcc) or cubic close packing (ccp), we have
8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom
6 facecentred 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 Bodycentred 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 bodycentred cubic crystal is 2.
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