1. The structure
In the context of
this chapter, you will also be invited to visit these sections...
have heard about natural minerals and crystals. We find them
daily without entering a museum. A rock and a mountain are made up
of minerals, as crystalline as a lump of sugar, a bit of porcelain or
a gold ring. However, only occasionally is the size of a crystal large
enough to draw our attention, as is the case of these beautiful
mineral examples of: Diamond
(pure carbon) - Quartz (silicon dioxide) - Scapolite
(aluminium silicate) - Pyrite
Although you can
continue reading these pages without any special difficulty, probably
you would like to know some aspects about the historical
development of our understanding of the crystals. For these readers
we offer some
further notes that can be found through this link.
ancient Greeks identified quartz with
crustallos, or phonetically kroos'-tal-los = cold +
drop), ie, very cold
extraordinary hardness. But the formation of crystals is
not a unique property of minerals; they are also found (but not
necessarily in a natural manner) in the so-called organic compounds,
and even in nucleic acids, in proteins and
A crystal is a material
whose constituents, such as atoms, molecules or ions, are arranged in a
highly ordered microscopic structure. These constituents are held
together by interatomic forces (chemical
bonds) such as metallic bonds, ionic bonds, covalent bonds, van der
Waals bonds, and others.
state of matter is the
state with the highest order, ie, with very high
internal correlations and at the greatest distance range. This
is reflected in their properties: anisotropic and discontinuous.
usually appear as unadulterated, homogenous and with well-defined
geometric shapes (habits)
when they are well-formed.
However, as we say in Spanish, "the habit does not make the
monk" (clothes do not make the man) and their external morphology is
not sufficient to evaluate the
crystallinity of a material.
The movie below shows the process of crystal
of lysozyme (a very stable enzyme) from an aqueous medium. The
duration of the real process, that takes a few seconds on your
corresponds approximately to 30 minutes.
on the left shows a representation of the faces of
a given crystal. If your browser allows the Java
Runtime, clicking on the image will open a new
and you will be able to turn this object. If you do not have this application, you
can still observe the model rotation in continuous mode from
Other Java pop-ups
of faces and forms (habits)
for ideal crystals can be obtained through this
So, we ask
ourselves, what is unique about crystals which distinguishes them from
other types of materials? The so-called microscopic crystal
structure is characterized by groups of ions,
molecules arranged in terms of some periodic
repetition model, and this concept (periodicity)
is easy to understand if we look at the drawings in an carpet,
in a mosaic, or a military parade...
Repeated motifs in a carpet
Repeated motifs in a mosaic
Repeated motifs in a military parade
carefully at these drawings, we will discover that there is always a
fraction of them that is repeated. In crystals, the atoms, ions or
molecules are packed in such a way that they give rise to "motifs" (a
given set or unit) that are repeated every 5 Angstrom, up to the
hundreds of Angstrom (1 Angstrom = 10-8 cm), and
this repetition, in three dimensions, is known as the crystal
lattice. The motif
or unit that is repeated,
by orderly shifts in three dimensions, produces the network
(the whole crystal) and we call it the elementary
cell or unit
cell. The content of
the unit being
repeated (atoms, molecules, ions) can also be drawn as a point
represents every constituent of the motif. For
example, each soldier in the figure above could be a reticular point.
But there are occasions where the repetition is broken, or it is not
exact, and this feature is precisely what distinguishes a crystal
from glass, or in general, from materials called
amorphous (disordered or poorly ordered)...
Planar atomic model of an ordered material
model of glass (an amorphous material)
matter is not entirely ordered or disordered (crystalline
or non-crystalline) and so we can find a continuous degradation of the
degre) in materials, which goes from the perfectly
to the completely disordered (amorphous).
This gradual loss of order which is present in materials is
equivalent to what we see in the small details of the following
photograph of gymnastic training, which is somewhat
ordered, but there are some people wearing pants, other wearing skirts,
some in different positions or slightly out of line...
the crystal structure (ordered) of inorganic materials, the
repetitive units (or motifs) are atoms or ions, which are linked
together in such a way that we normally do not distinguish
isolated units and hence their stability and hardness (ionic
Crystal structure of an inorganic
Where we clearly distinguish
units is in the case of the so-called organic materials, where the
concept of the isolated entity (molecule)
appears. Molecules are made up of atoms linked together.
the links between the molecules within the crystal are very weak (molecular
crystals). Thus, they are generally softer and more
unstable materials than the inorganic ones.
Crystal structure of an organic material:
crystals also contain molecular units (molecules), as
in the organic materials, but much larger. The type of forces
that bind these molecules are also similar, but their packing
in the crystals leaves many holes that are filled with water molecules
(not necessarily ordered) and hence their extreme instability...
Crystal structure of a protein:
The molecular packing produces
very large holes
The different packing modes in crystals lead to the
phases (allotropic phases of the elements) which
confer different properties to these crystals (to
these materials). For example, we all know the
different appearances and properties of the chemical element carbon,
which is present in Nature in two different crystalline forms,
diamond and graphite:
Graphite is black, soft and an
lubricant, suggesting that its atoms must be distributed (packed) in
such a way as to explain these properties. However, diamonds are
transparent and very hard, so that we can expect their
atoms very firmly linked. Indeed, their sub-microscopic
(at atomic level) show us their differences ...
with a very compact structure
showing its layered
structure, each carbon atom is linked to four other ones in the form of
a very compact three-dimensional network (covalent crystals), hence its
extreme hardness and its property as an electric insulator. However, in
the graphite structure, the carbon atoms are arranged in parallel
layers much more separated than the atoms in a single layer. Due to
these weak links between the atomic layers of graphite, the layers can
slide, without much effort, and hence graphite's suitability as a
lubricant, its use for pens and as an electrical conductor.
And speaking about conductors...
The metal atoms in the metallic crystals are structured in such a way
that some delocalized electrons give cohesion to the crystals and are
responsible for their electrical properties.
A slightly different treatment
the so-called quasicrystals...
A quasicrystal is an
"ordered" structure, but not perfectly periodic as the crystals are.
The repeating patterns (sets of atoms, etc.) of the quasicrystalline
materials can fill all available space continuously, but they do not
display an exact repetition by translation. And, as far as symmetry is
concerned, while crystals (according to the laws of classical
crystallography) can display axes of rotation of order 2, 3, 4 and 6
only, the quasicrystals show other rotational symmetry axes, as for
example of order 10
In this website we will
attention to the
quasicrystals. Therefore, if you are interested on it, please go to
where Steffen Weber, in a relatively simple way, describes these
types of materials from the theoretical point of view, and
where some additional sources of information can also be found..Advanced
readers should also consult the
site offered by Paul J, Steinhardt at the University of Princeton.
Nobel Prize in Chemistry 2011 was awarded to Daniel Shechtman
by the discovery of quasicrystals in 1984..
obviously many questions that the reader will ask, having come this
far, and one of the most obvious ones is:
do we know the structure of crystals? This
question, and others, will be answered in following chapters
and therefore we encourage you to