Coordination number

Valence and the Structure of Ionic Crystals

Historically, the concept of valence is a basic tool when studying the chemical interactions of elements. Applied to crystal structures with a framework or ionic type of structure, valence describes the fundamental ability of atoms to form a specific number of bonds.

However, for a full and deep understanding of the architecture of solids, this term alone is insufficient. Classical valence works great when we look at the Periodic Table of Chemical Elements and evaluate the interaction potential of components. But when a substance forms a complex three-dimensional structure, nuances arise that require the introduction of additional characteristics to describe the real picture of the atomic environment and interatomic contacts.

States of Matter Using Sodium Chloride as an Example

To clearly understand the limitations of classical valence, it is advisable to consider the behavior of sodium chloride (formula $NaCl$). If we turn to the Periodic Table, we will see that both sodium ($Na$) and chlorine ($Cl$) are monovalent elements (their valence is equal to I). From the standpoint of traditional rules for writing chemical formulas, writing $NaCl$ is completely correct and fully satisfies the concept of valence: one sodium atom is potentially bonded to one chlorine atom.

However, the spatial organization of this compound changes dramatically depending on its state of aggregation:

• Gaseous phase. If we transfer sodium chloride into the gaseous state, we will indeed find the substance in the form of separate, isolated molecules, where the "one-to-one" principle is observed.
• Solid phase. The situation changes completely when the substance transitions into the solid state. In the solid phase, sodium chloride no longer consists of separate isolated molecules. Instead, atoms line up into an extensive crystal structure—an ionic lattice. In this lattice, the concept of a simple isolated bond ceases to reflect the real state of affairs in space.

Definition of the Coordination Number

It is precisely to characterize the actual, factual number of bonds in complex structures that the concept of coordination number (abbreviated as CN) was introduced into chemistry.

The coordination number is the exact number of atoms that make up the immediate environment of a specific atom under consideration in a molecule or crystal structure. The most important condition is that these surrounding atoms must form chemical bonds with the central atom.

This parameter allows the researcher to understand how densely packed the atoms are and how many actual neighbors each lattice element holds around itself. This is no longer just a theoretical ability to form a bond, but a statement of a physical fact in a specific substance architecture.

Distinction Between Concepts: Valence and Coordination Number

To clearly distinguish between theoretical valence and practical coordination number, it is convenient to analyze the structure of iron chloride ($FeCl_3$).

From the perspective of valence, the analysis is as follows: the central iron atom ($Fe$) is bonded to three chlorine atoms. Since the chlorine atoms in this compound are monovalent, we reasonably conclude that iron is in a trivalent state.

However, if we consider this substance in the solid state and examine its crystal structure diagram, the picture changes. In the crystal lattice, the actual number of neighbors for the iron atom is different. The coordination number of iron in this solid state is 6.

This means that in the real three-dimensional space of a solid crystal, the iron atom is directly surrounded by six atoms with which it forms chemical bonds, despite the fact that its classical valence remains equal to three. This example illustrates why, for an accurate description of solid-state structures, it is necessary to use both terms, understanding the difference between the chemical potential of an element and its real environment.

Briefly: answers to topical questions

Class and exam questions

What else to study on this topic

• Structure of ionic and framework crystal lattices
• Features of the behavior of substances in gaseous and solid phases
• Algorithm for determining the valence of elements using the Periodic Table
• Analysis of crystal structure diagrams using iron chloride as an example

Other topics in the section "Chapter 1. Substances. Properties and Structure"

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