how to calculate packing efficiency in hcp closed packing

Asked by  | 17th May, 2008, 04:36: PM

Expert Answer:

HCP: 6 Packing Atoms; 6 Octahedral Holes; 12 Tetrahedral Holes



·       Take sphere radius = r

·       Work out number of spheres per unit cell. Volume of sphere = (4 π r3) / 3

·       Volume occupied by spheres = number of spheres x (4 π r3) / 3

·       Calculate volume of box

·       Packing efficiency = Volume occupied by spheres / Volume of box

o      Close Packing (12 fold co-ord) – 74% Packing efficiency

o      Body-centred Cubic (BCC) Packing (8 fold co-ord) – 68% Packing efficiency

o      Primitive Packing/Square Packing (6 fold co-ord) – 52% Packing efficiency


Examples of Structures:


NaCl – CCP of Chloride ions with Sodium ions in 100% of OH. (also LiCl, RbI, AgCl)

CaF2 – CCP of Calcium ions with Fluoride ions in 100% of TH - Fluorite structure (also CaCl2)

Li2O – CCP of Oxygen ions with Lithium ions in 100% of TH - Anti-fluorite (also BaCl2)

ZnS (Zinc Blende) – CCP of Sulphide ions with zinc ions in 50% of TH. (also CuCl, AgI)



NiAs – HCP of Arsenic ions with Nickel ions in 100% of OH.

ZnS (Wurtzite) – HCP of Sulphide ions with Zinc ions in 50% of TH.

Answered by  | 20th May, 2008, 07:56: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.