As the story goes, one of the most defining
events for crystallography was a mishap.
Rene-Just Haüy, a Parisian priest, had been
invited to look at a friend’s latest acquisition,
a beautiful prismatic calcite crystal. In a
careless moment, the crystal slipped out of
Haüy’s hands and shattered on the floor.
At this time, in 1781, characterizations of
crystals were solely based on their outer
morphology. But Haüy’s mishap led to a
deeper understanding of the essential inner
characteristics of the crystalline state of
matter: periodicity.
On examination of the crystal’s
fragments, Haüy noticed that it “had a
single fracture along one of the edges of the
base… I tried to divide it in other directions
and I succeeded, after several attempts, in
extracting its rhomboid nucleus.” In other
words, Haüy realized that crystals always
cleave along crystallographic planes. In
addition, it was known from previous
discoveries that in a given crystal species
the interfacial angles always have
the same value. Based on these two
clues, Haüy concluded that crystals
must be periodic and composed
of stacks of little polyhedra,
which he called molécules
intégrantes. This theory could
conveniently explain why
all crystal planes are related
by small rational numbers, a
principle we nowadays refer to
as the law of rational indices.
Considering how closely
Haüy’s theory resembles the modern
concept of periodicity, it is a masterpiece
of imagination. But it posed two major
questions. The first one again relates to
outer morphology: What is the complete