Both ccp and hcp are highly efficient lattice; in terms of packing. 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 packing efficiency of simple cubic lattice is 52.4%. And the packing efficiency of body centered cubic lattice (bcc) is 68%.

Packing efficiency can be written as below, Packing efficiency = Volume occupied by 6 spheres ×100 / Total volume of unit cells. Examples are Magnesium, Titanium, Beryllium etc. In body-centered cubic structures, the three atoms are arranged diagonally.

Crystal Structure: Closest Packing

• The most efficient conformation atomic spheres can take within a unit cell is known as the closest packing configuration.
• Densely packed atomic spheres exist in two modes: hexagonal closest packing (HCP) and cubic closest packing (CCP).

Hexagonal

Hexagonal close-packed lattice has the highest packing efficiency of 74%. The packing efficiencies of simple cubic and body-centred cubic lattices are 52.4% and 68% respectively. Was this answer helpful?

– The packing arrangement ABC ABC type in 3 D is equivalent to cubic closed packing (ccp) or face centred cubic (fcc) lattice. – The efficiency of fcc is the highest among all the arrangements, i.e., 74%. – Hence, ABC ABC type arrangement in 3 D​ is the most efficient.

Among the given metals Al occupies hexagonal close-packed (hcp) is having 0.74 packing efficiency and other metals form body-centered cubic (bcc) which has 0.68 packing efficiency.

(i) In a simple cubic lattice the atoms are located only on the corners of the cube. Hexagonal close−packed lattice has the highest packing efficiency of 74%.

The packing efficiency of a crystal structure tells us how much of the available space is being occupied by atoms. It is usually represented by a percentage or volume fraction. Count how many atoms there are per unit cell. Calculate the volume of a single atom and multiply by the number of atoms in the unit cell.

Simple cubic unit cell has least packing efficiency that is 52.4%.

Out of the three types of packing, face-centered cubic (or ccp or hcp) lattice makes the most efficient use of space while simple cubic lattice makes the least efficient use of space.

The highest packing fraction possible is 74.04 % and this is for the FCC lattice. The same value of packing fraction is for the HCP structure as well, which only differs from FCC in that the location of the third layer is different (ababab), but the number of atoms in a given volume is identical in FCC and HCP.

Hint: In the structure of diamond cubic crystal the unit cell present is fcc unit cell. The relation between r and a for diamond is r=√3a8. Complete answer: Packing fraction (P.F), is calculated by volume occupied by the number of spheres in the unit cell divided by volume of a unit cell.

The maximum packing fraction is not a well-defined parameter as it depends on the spatial distribution of the elements, which may depend on the flow history. For uniform spheres it is around 55% if the particles are simply poured in a container and can be increased to 64% by a slight and long vibration.

The relation between edge length (a) and radius of atom (r) for BCC lattice is √3a=4r .

Chromium has BCC structure. Its atomic radius is 0.1249 nm.

Packing Density When the lattice points are inflated gradually, at some point they start to touch each other along the diagonals of the cube. One can now interpret the atoms as close packed spheres with a radius defined geometrically by 4r=√3a 4 r = 3 a ⇔r=√34a ⇔ r = 3 4 a .

What is the atomic radius of a BCC crystal structure? Explanation: Atomic radius is defined as half the distance between the centers of two neighboring atoms. The atomic radius of a simple cube and HCP is a/2 respectively, whereas it is a√2/4 and a√3/4 for FCC and BCC respectively. 17.

1. Which of the following is a point defect in crystals? Explanation: Crystal defects are classified as point defects, line defects, and boundary defects. Point defects include vacancies, impurities, interstitialcies, and electronic defects.

Which of the combinations of crystal structure and their coordination number is (are) correct ? Option (B) is wrong because fcc has 12 coordination no.

seven crystal systems