Coordination Number (CN) is a fundamental concept in crystallography. It defines the number of nearest neighboring atoms surrounding an atom in a crystal lattice.

Understanding CN is essential because it influences metal density, ductility, slip systems, and mechanical strength, all of which are important for engineering applications and competitive exams.

Definition

Coordination Number (CN)

The coordination number is the number of nearest neighbor atoms that are in direct contact with a central atom in a crystal structure.

Core Concept Explanation

Every atom in a crystal is surrounded by other atoms at the shortest distance (nearest neighbors).
CN depends on crystal type and packing efficiency.
Higher CN → more closely packed → usually higher ductility and density.
Lower CN → less densely packed → usually harder and less ductile.

Coordination Numbers for Common Crystal Structures

Crystal Structure	Coordination Number (CN)	Notes	Example Metals
Simple Cubic (SC)	6	Least densely packed	Polonium
Body-Centered Cubic (BCC)	8	Moderately packed	α-Iron, Chromium, Tungsten
Face-Centered Cubic (FCC)	12	Closest-packed, high ductility	Aluminium, Copper, Nickel, Gold
Hexagonal Close-Packed (HCP)	12	Closest-packed, less ductile than FCC	Magnesium, Zinc, Titanium

Relationship Between CN and Properties

High CN (12) → metals are densely packed, ductile, good conductivity → FCC, HCP
Moderate CN (8) → metals are stronger, less ductile → BCC
Low CN (6) → metals are loosely packed, harder → SC

CN is directly related to slip systems, which determines metal deformation under stress.

Importance in Engineering

Helps predict mechanical properties: strength, ductility, malleability
Influences slip planes and slip directions in metals → critical for metal forming
Guides material selection for structural, electrical, and aerospace applications
Assists in calculating packing efficiency and density

Exam-Focused Points

CN = number of nearest neighbor atoms surrounding a central atom.
SC → CN = 6
BCC → CN = 8
FCC → CN = 12
HCP → CN = 12
Higher CN → closer packing → higher ductility

Common Exam Traps

Confusing CN of BCC (8) with FCC/HCP (12)
Assuming SC is ductile (CN = 6 → low ductility)
Forgetting CN is related to nearest neighbors, not total atoms in unit cell

Example Competitive Exam Questions

What is coordination number?
Answer — Number of nearest neighbor atoms surrounding a central atom.

Coordination number of BCC?
Answer — 8

Coordination number of FCC?
Answer — 12

Coordination number of HCP?
Answer — 12

Coordination number of SC?
Answer — 6

Quick Revision

Coordination Number = nearest neighbors around an atom
SC = 6, BCC = 8, FCC = 12, HCP = 12
Higher CN → denser packing, higher ductility
CN affects mechanical properties, slip systems, and material selection

Unit 3.7: Coordination Number