Coordination Number Calculator

Calculate coordination numbers in crystal structures and understand atomic arrangements

Simple Cubic
Atoms at cube corners only
Body-Centered Cubic
Atoms at corners + center
Face-Centered Cubic
Atoms at corners + face centers
Hexagonal Close-Packed
ABAB stacking sequence
6
Coordination Number
1
Atoms per Unit Cell
52%
Packing Efficiency

Understanding Coordination Number

What is Coordination Number?

In chemistry and crystallography, the coordination number of a central atom in a molecule or crystal is the number of atoms, ions or molecules bonded to it. The concept is most commonly applied to coordination complexes and crystal structures.

Crystal Structures
Coordination number describes how many nearest neighbors an atom has in a crystal lattice
Coordination Complexes
In coordination chemistry, it's the number of donor atoms attached to the central metal ion
Chemical Bonding
Affects physical properties like density, melting point, and hardness of materials
Material Science
Helps predict and explain properties of metals, ceramics, and other materials

Common Coordination Numbers

Coordination Number Geometry Examples
2 Linear Ag(CN)2-, HgCl2
3 Trigonal planar BF3, SO3
4 Tetrahedral CH4, ZnCl42-
4 Square planar PtCl42-, Ni(CN)42-
6 Octahedral Fe(CN)64-, CoF63-
8 Cubic CsCl, CaF2

Crystal Structures Guide

Common Metallic Crystal Structures

Metals typically form one of three common crystal structures:

Structure Coordination Number Atoms per Unit Cell Packing Efficiency Examples
Simple Cubic (SC) 6 1 52% Polonium (α-Po)
Body-Centered Cubic (BCC) 8 2 68% Iron (α-Fe), Tungsten, Chromium
Face-Centered Cubic (FCC) 12 4 74% Copper, Aluminum, Gold, Silver
Hexagonal Close-Packed (HCP) 12 6 74% Magnesium, Zinc, Titanium
Ionic Crystal Structures

Ionic compounds form crystal structures based on the relative sizes of cations and anions:

Structure Cation CN Anion CN Examples
Rock Salt (NaCl) 6 6 NaCl, MgO, LiF
Cesium Chloride (CsCl) 8 8 CsCl, CsBr, CsI
Zinc Blende (ZnS) 4 4 ZnS, CuCl, GaAs
Fluorite (CaF2) 8 4 CaF2, UO2, ThO2

Factors Affecting Coordination Number

What Determines Coordination Number?

Several factors influence the coordination number in crystal structures:

  • Size Ratio: The radius ratio of cation to anion determines the maximum number of anions that can surround a cation
  • Electrostatic Forces: Crystal structures tend to maximize attractions between oppositely charged ions
  • Packing Efficiency: Structures with higher coordination numbers generally have higher packing efficiency
  • Bond Type: Covalent, ionic, and metallic bonds have different preferred coordination numbers
  • Temperature and Pressure: Some materials change structure (and coordination number) under different conditions
Frequently Asked Questions
Why do FCC and HCP structures both have coordination number 12?
Both FCC and HCP are close-packed structures with the highest possible packing efficiency (74%). In both structures, each atom is surrounded by 12 nearest neighbors - 6 in the same plane, 3 above, and 3 below. The difference lies in the stacking sequence: FCC has ABCABC stacking while HCP has ABAB stacking.
How does coordination number affect material properties?
Higher coordination numbers generally lead to higher density, higher melting points, and greater hardness. For example, FCC metals (coordination number 12) are typically more ductile than BCC metals (coordination number 8). Coordination number also affects electrical and thermal conductivity in metals.
Can coordination number be fractional?
No, coordination number is always an integer because it counts the number of nearest neighbors. However, in some complex structures or when considering average environments, we might refer to an effective coordination number which could be a non-integer value.