Ionic Crystal Structures

Introduction

The same empirical formula ratio can occur in different crystal structures. Rock-salt NaCl, CsCl and zinc-blende ZnS are all 1:1 compounds, yet their nearest-neighbor coordination numbers are six, eight and four. Geometry and site occupancy, not formula alone, determine each structure.

Core explanation

In rock-salt structure, one ion type can be viewed as an FCC array and the other occupying all octahedral voids. The FCC conventional cell has four host ions and four octahedral sites, so there are four of each ion, or four formula units. Each cation is surrounded by six anions, and each anion by six cations. NaCl is the named example, though other compounds can adopt the pattern.

In the CsCl structure, one ion type sits at cube corners and the other at the cube body centre in a convenient drawing. Corner contribution is one and body contribution one, giving a 1:1 formula and one formula unit per depicted conventional cube. Each central ion has eight opposite ions at cube corners; each corner ion is surrounded by eight centres from neighboring cubes. The corner and centre are chemically different, so calling this a monatomic BCC lattice is inaccurate even though the geometric positions resemble BCC.

In zinc blende, one ion type forms an FCC array while the other occupies half of its tetrahedral sites. Four FCC hosts and half of eight tetrahedral sites give four guests, again a 1:1 formula with four formula units in the conventional cell. Each Zn has four nearest S and each S four nearest Zn in a tetrahedral arrangement. Bonding in ZnS has significant covalent character, so the “ions in voids” picture is geometric bookkeeping rather than a claim of perfect hard-sphere charges.

The comparison shows three ways to produce AX composition. Coordination number depends on relative size, electrostatic and covalent bonding, pressure and temperature. A larger cation may support more anion neighbors, but radius-ratio rules are only rough guides. Actual structures are measured by diffraction and may change phase under pressure.

When drawing, count nearest opposite ions, not every ion within the whole conventional cell. In CsCl, the centre sees eight corners. In NaCl, a central ion sees six opposite ions along three perpendicular directions. In zinc blende, four opposite ions form a tetrahedron. These geometries also affect material properties and ion transport.

The formula-unit count Z is different for the conventional cells of these structures: NaCl and zinc blende commonly have Z=4, while the standard CsCl-type cube has Z=1. This matters for density: ρ=ZM/(N A Vcell). Using the same Z for every AX salt produces incorrect values despite the same empirical formula.

Step-by-step reasoning

1. Identify which ion forms the host array or corner positions. 2. Count effective ions of each type within the conventional cell. 3. Reduce counts to the empirical formula. 4. Count nearest opposite-ion neighbors for coordination. 5. Keep geometric site language separate from exact bonding character.

Visual explanation

Draw three side-by-side cubes: NaCl with FCC host and octahedral guests, CsCl with distinct corner and body ions, ZnS with FCC host and selected tetrahedral guests. Label 6:6, 8:8 and 4:4 coordination respectively.

Real-world analogy

Three neighborhoods can contain equal numbers of two kinds of residents but seat them differently around each household. A 1:1 population ratio does not specify whether each person has four, six or eight nearest opposite neighbors.

Real-world example

NaCl and CsCl both have 1:1 composition, yet their structures give different coordination and conventional-cell formula-unit counts. A crystallographic result, not the formula alone, establishes which arrangement a sample adopts.

Why?

Why does zinc blende remain 1:1 when only half tetrahedral voids are filled? An FCC array has twice as many tetrahedral sites as host ions; filling half yields one guest per host.

Common misconception

“Every AX ionic solid has NaCl's sixfold coordination.” CsCl and zinc blende are AX examples with eightfold and fourfold coordination in their standard structures.

Worked example

For zinc blende, take four S positions in the FCC conventional cell. Eight tetrahedral sites are available; Zn occupies half, giving four Zn. The count is Zn₄S₄, reducing to ZnS, and Z=4 formula units. Each occupied tetrahedral site has four S neighbors. The formula follows occupancy, while coordination follows local geometry.

Quick check

1. What is the nearest opposite-ion coordination in CsCl structure? Answer: Eight around each ion.

Exam focus

Memorize structures through site occupancy and coordination, not only names. Distinguish CsCl-type corner-body geometry from equivalent-point monatomic BCC.

Advanced insight

Pressure can favor structures with higher coordination by reducing volume, but actual transitions depend on full free-energy balance. Radius ratio alone is therefore not a proof of the stable phase.

Summary

NaCl, CsCl and zinc-blende ZnS all have 1:1 formulas but six-, eight- and fourfold coordination. Their conventional cells differ in formula-unit count and occupied-site geometry. Chemical formula does not uniquely determine structure.

Practice questions

1. How many formula units lie in the conventional rock-salt cell? Answer: Four NaCl units in the standard FCC-based cell. 2. What fraction of FCC tetrahedral sites is occupied in zinc blende? Answer: One half. 3. Why is CsCl not simply a monatomic BCC lattice? Answer: The corner and body positions contain different ion species and are not equivalent lattice points.