Advanced · 18 min

Growing a crystal: lattice stacking and vacancies

Stack CsCl-type unit cells one by one, then remove ions at random to see how vacancies break perfect periodicity.

Goal

Count ions per unit cell through sharing, link cell-by-cell stacking to real crystal growth, and connect vacancy concentration to growth conditions.

Apparatus and reagents

Saturated alum or copper(II) sulfate solution, a seed crystal on a thread, beaker and filter paper for slow evaporation; the simulation explores lattice defects.

Procedure

Start with one unit cell of the CsCl type: identify the body-centre ion and the eight corner ions.
Increase “cells per edge” to 3: the crystal grows by adding complete unit cells to its faces.
Toggle unit-cell edges and verify the corner sharing: 8 corners × 1/8 = 1 Cl per cell, plus 1 Cs at the centre.
Raise the vacancy slider gradually: note holes appearing anywhere in the bulk, not only at surfaces.

What to observe

Each new unit cell keeps the same motif: periodicity is preserved as the crystal enlarges.
Vacancies show up as isolated missing spheres; a few percent is already visually obvious.
The slider exaggerates defects: equilibrium vacancy fractions at room temperature are astronomically small.

Explanation

Real crystals grow by attaching atoms or ions at kinks and ledges (Kossel–Stranski–TLK picture). Point defects obey thermodynamics: n/N ≈ exp(−ΔGf/2k_BT) for Schottky pairs, so equilibrium vacancies are rare; rapid growth, quenching and impurities raise the real defect content.

History of the experiment

Crystallization is one of the oldest purification arts: salt crystals were already harvested by evaporation in antiquity, and medieval alchemists grew large alum and vitriol crystals in woodcuts' recipes. In the nineteenth century Mitscherlich's 'isomorphism' studies of crystal forms and Pasteur's hand-separated tartrate crystals (1848) turned crystal growth into a serious science. Today seeded, slow-cooling growth of the kind in this lab gives the millimetre-scale single crystals still needed for X-ray diffraction.

Chemists behind it

Louis Pasteur