Crystallography in a nutshell
you don't have time or you are not keen to start reading all the
information offered through the menu on the left (or in the table of
contents), here you will find
answers for a few questions that will help you to
understand the beauty and capabilities of this part of science
known as Crystallography:
is Crystallography and what is it for?
crystals we can determine the atomic positions within matter. This can
be applied to crystals made of either living or inanimate matter.
is a branch
of science that examines crystals. Today we know that crystals
are made of matter, atoms, molecules and/or ions that fit together in
repeating patterns, called
unit cells, which like bricks stacked in three
dimensions form the crystals. Inside the unit cells atoms are also
repeated by symmetry operations. These patterns cause the
crystals to show
many sorts of unique shapes which for
thousands of years have drawn
our attention for their colors and outer beauty.
With the crystallographic
tools developed during the 20th century, we
can find out the inner structure of matter, living or inanimate, from
which crystals are formed. To know the inner structure of matter means
to determine the positions of all atoms and how they are linked
together, in many cases forming atomic clusters known as molecules.
The atomic structure
of matter generates knowledge that is used by
biologists, and other scientists. This allows us not only to understand the
properties of matter, but also to modify them for our benefit.
figures on the left
show the molecular structure of penicillin, in
the form of a diagram and its corresponding three-dimensional
shape. Only after the 3D molecular
structure of penicillin was unambiguously determined in
1945 by Dorothy
using crystallography, chemists could start the quick synthesis of this
compound, thus saving millions of lives.
word "crystallography" defines the science that "deals with the shapes
and structures of crystals".
does the word Crystallography comes
The word "crystal" comes from the Ancient Greeks κρνσταλλοσ
= cold + drop), who used the word crystal to refer to
the mineral quartz, meaning both
“ice” and “rock crystal”, that
is cold and
hard. Many minerals have always attracted our attention for its
beautiful shapes and colors. There are references
that relate Sumerians with the use of some mineral crystals in magic
formulas, Chinese in its traditional medicine, and Egyptians that used
crystals as jewels or in powder form for cosmetic purposes.
In its origins,
Crystallography was dedicated exclusively to the study
and description of the external appearance (morphology) of crystals,
time we have found that crystals are ordered matter,
ie, made up of atoms, ions and/or molecules perfectly stacked,
as one can normally see pieces of fruit in a market. This packing is
responsible for the striking forms that crystals normally show
Today Crystallography still deals with crystals, but its interest is
mainly focused on their internal structure, not in their external shape.
and how did crystallography begin as a science?
first historical references to
the use of crystals comes from the Ancient Sumerians (fourth
millennium BC), it was not until the 17th and 18th centuries
when the first scientific hypotheses about the inner nature
of the crystals appeared, and all of them based on the
observation of their
The German Johannes
Kepler (1571-1630) was surprised by the fact that snowflakes
landing on his coat always showed perfect
six-cornered symmetry and never showed five of seven corners. He
explained his observations in terms of the particle packings, as
oranges show in the picture above.
Also based on the observation of crystal morphologies, the
Stensen (1638-1686) and the French mineralogist Jean-Baptiste
Louis Romé de l'Isle (1736-1790), established the
law of constancy of angles between faces of different crystal specimens
of the same species. With all this, René
Just Haüy (1743-1822), another French mineralogist,
commonly styled the Abbé Haüy, concluded that the
crystals were made by the ordered stacking of small bricks, or unit
cells, all of them identical.
years later, during
the nineteenth century,
the mathematical systematization of symmetry concepts
repetition of motifs around a point, as the petals of a flower around
its axis, or the repetition of patterns by translation, gave rise to
the establishment of some mathematical concepts such as:
- the so-called point groups, ie,
groups of symmetry elements (symmetry axes, mirror
planes, etc.) passing through the center of a body, and
In 1830, the German
Friedrich Christian Hessel (1796-1872), using the previous
deductions of René
Just Haüy (1743-1822), and after demonstrating that rotation
axes can only be of orders 2, 3, 4 and 6,
showed that the different possible morphologies of crystals can be
combined to give exactly 32 different combinations of symmetry elements
(the 32 point groups,
also known as crystal classes).
- the concept of lattice, ie,
the repetition rules by which objects or motifs are repeated
by translation in an ordered manner (for example, the drawings in a
In 1848 the French physicist Auguste
Bravais (1811-1863) discovered that in the three-dimensional
space, periodic repetitions by translation can only be made in 14
different modes (the so-called 14
Bravais lattices), as they must to be compatible with the 32
some 50 years
later, the 14 Bravais lattices
and the 32 crystal classes
were the limitations
that the Russian mathematician, crystallographer
and mineralogist S.
Evgraf Fedorov (1853-1919) and the German mathematician Arthur
Moritz Schoenflies (1853-1928)
used to independently deduce,
between 1890 and 1891, the 230 space groups,
which are the 230 possible ways to restrict distributions of
repetitive structural units of the crystals (atoms, ions and molecules).
However, although these findings on the laws governing the structure of
crystals were very important, they couldn´t help to solve the
fundamental question: what
is the size and shape of molecules inside the crystals? Or
in short, what
positions do atoms occupy in a crystal?
Unfortunately, optical microscopes and visible light are not able to
see such small pieces of matter as scientists imagined atoms to be!
first big step forward: A new light
"look" inside crystals?
discovery of X-rays in 1895.
(Illustration by Alejandro
Martínez de Andrés, CSIC 2014)
The discovery of
X-rays by Wilhelm
the late 19th century completely transformed the old field of
Crystallography, which previously studied the morphology of
crystals, mainly minerals.
Although the discovery of this new "light" gave Röntgen a
popularity, it faded quickly. It took years until the utility of their
amazing "light" was recognized as of medical interest, and even allowed
him in 1901 to won the highest scientific award, the
first Nobel Prize in Physics.
Thanks to that
discovery Crystallography started to become one of the most
for many branches of science, especially for Mineralogy, Physics,
Chemistry, Biology and Biomedicine. This was recently recognized by the
United Nations, declaring 2014
International Year of Crystallography, and celebrating the
centenary of the birth of modern Crystallography...
understand how Crystallography became
an important branch of science, you should continue reading...
Laue showed in 1912 that X-rays are
electromagnetic waves and that crystals have a regular internal
Röntgen's discovery was important for the development of
Crystallography, it was especially due to the experiment conducted in
1912 by Max
von Laue (1879-1960), who convinced by his friend Paul Peter Ewald
decided to demonstrate the undulatory nature of X-rays and discovered
the phenomenon of X-ray diffraction by crystals. He showed that X-rays
are electromagnetic waves with a wavelength of about 10-10
meters and that the internal structure of crystals is regular,
as if they had tiny slits of that order of magnitude, formed by the
distances between atoms.
Indeed, after lighting a crystal of copper sulfate with X-rays Laue
found that a photographic plate showed black spots not only at its
center (as due to the fact that the incident beam passes directly
through the crystal), but also in other places of the photographic
plate, far away
from the center. This result was interpreted as a consequence of the
phenomenon called diffraction,
whereby the X-ray beams scattered by the atoms interfere with each
other inside the crystals and deviate from the central beam.
conducted in 1801 by Thomas Young, in an attempt to discern the wave or
particle nature of light. Young investigated a pattern of interferences
of light coming from a distant source and diffracted by two slits. This
result contributed to the theory of the wave nature of light. Taken
of a wave
experiment, for which he received the Nobel Prize in Physics in 1914,
Laue "killed two birds with one stone". Indeed, after
watching the experimental results he could easily deduce that:
Regardless of the
scientific interest of
these two findings, readers who have arrived to this point will
probably ask themselves:
- crystals behave
slits, with dimensions equivalent to the wavelength of X-rays.
Were Laue's results useful? This and other questions are
diffract X-rays. What is it
In 1914 Max
von Laue (1879-1960) observed that X-rays are scattered in a
peculiar way as they pass through crystals ... he discovered X-ray
diffraction pattern obtained by Max von Laue in 1914 using a crystal of
copper sulfate and scheme on which the Bragg’s based their
interpretation to deduce the internal structure of the crystals from
the diffraction pattern.
Structural knowledge obtained by
Crystallography allows us to produce
materials with predesigned properties, from catalyst for a chemical
reaction of industrial interest, up to toothpaste, vitro ceramic
plates, extremely hard materials for surgery, or certain aircraft
components, just to give some examples of small, or medium sized atomic
or molecular materials. It
did not take long until the Max
von Laue's discovery was recognized as very important. In
fact, in the same year of Laue's experiment, William
Henry Bragg (1862-1942) and his son William Lawrence Bragg (1890-1971)
realized that if atoms inside crystals diffract X-rays and give rise to
a diffraction pattern, this pattern should contain enough information
to extract the relative positions of atoms in the crystal, that is to
go backwards and retrace the path of diffraction. These scientists
interpreted the phenomenon of diffraction with a
simple geometric law: atoms in crystals occupy virtual planes that
behave as mirrors, but reflecting X-rays only for certain angular
positions of incident X-rays (Bragg's law).
Father and son shared the Nobel Prize for Physics in
1915 for demonstrating the usefulness of the phenomenon discovered by
in studying the internal structure of crystals.
The importance of Bragg's work cannot be overstated, for it heralded a
revolution in the scientific understanding of crystals and their atomic
arrangements. This discovery led to many of the most important
scientific achievements of the last century, and these continue to the
present day. To
prove their theory, the Braggs were able to determine
the atomic structure of simple materials such as sodium chloride
(common salt) or the mineral zinc blende (zinc sulfide).
Although in those years these researchers were not able to solve the
structure of more complex materials, over the time Crystallography has
been able to
answer a very large number of fundamental questions on various aspects
of both inanimate and living matter.
thanks to Crystallography we discovered the DNA secrets, the genetic
code. We can increase the resistance of plants against environmental
damage. We are able to understand, modify or inhibit enzymes involved
in fundamental processes of life and important signaling mechanisms
taking place inside of our cells, like cancer. With the structural
knowledge of the ribosome, the largest factory of proteins in our
cells, we can design new antibiotics and modify their structure to
improve the efficiency. We are learning from the structure of certain
components of some viruses to fight bacteria that are highly resistant
to antibiotics, and are able to unravel the subtle defense machinery
that has been developed from these microorganisms, so that we will be
able to fight them with alternative tools.
Atomic and molecular structure of a DNA
can atoms "be seen" with
The interaction of X-rays with
inside the crystals generates a kind of fingerprint known as
diffraction pattern. Therefore, in order to "see" where the atoms are,
we must be able to unravel the information contained in the diffraction
Bragg and W.L.
Bragg’s findings opened
unexpected ways to gain knowledge on the internal structure of
matter. These two researchers were already aware that the right way to
unravel the secrets of crystals was to go backwards,
that is, stepping from the puzzle contained in diffraction pattern to
the atomic positions
in the crystal.
Although we don't claim to reveal all the details on how to solve that
puzzle, we should give some idea about this supposed
understand the difficulty we face, we
need to remember what happens when a crystal is illuminated with
waves pass through a crystal they interfere with each other,
giving rise to waves that deviate from the line defined by the
incident beam. When these new waves reach the photographic plate they
produce a snapshot characteristic of each crystal species (such as a
fingerprint). This is what we call a diffraction pattern.
of how the two waves, shown at the top, add or subtract (depending on
their relative positions), to generate a resultant wave (thick line
below). Animation taken from The
Pennsylvania State University
although we cannot see them with our
eyes, each of these waves is added to (or subtracted from) its neighbors, being reinforced or
decreased, generating a resultant wave, as shown in the figure above.
waves in each direction of diffraction are produced by the
interferences occurring between the waves produced inside the crystal,
a phenomenon entirely dependent on the relative positions of the atoms
in the crystal.
of the diffraction pattern are thus the result of the
arriving at the photographic plate. Each of these resultant waves is
characterized by its amplitude (intensity) and a relative phase with
respect to the remaining ones. In
the figure below two
resultant waves, each one with its own amplitude (intensity) and a
relative phase, generate two separate spots in the diffraction pattern.
The intensity of each spot is proportional to the amplitude of the
corresponding wave, and each wave travels with a different relative
At this point it seems therefore easy to deduce, at least
intensities of the diffraction pattern (= the amplitudes of the waves)
can easily be measured. However, there is no experimental procedure for
measuring the relative phases of the waves!. Therefore, we can now
- If the
resultant waves (each one
with its intensity and phase) that generate the diffraction pattern
depend on the atomic positions in the crystal, reversely, in order to
atomic positions from the diffraction pattern, we will need to know the
intensities and phases of each wave.
- we speak from
solving a puzzle when we describe how to determine a crystal structure,
But, once the intensities of all
are measured, if we are "somehow" able to find out their
phases, there is a simple way (although with some numerical complexity)
that allows us to determine the positions of all atoms in the crystal,
that is, to calculate a three-dimensional picture of the inner
structure of crystal. And
this procedure applies for both living and inanimate matter.
- the puzzle has
to do directly with the phases of the resulting waves, and why
Representation of the three-dimensional
structure of an organic molecule
the atomic positions in the crystal and the diffraction pattern there
is a holistic relationship. The position of each atom in the crystal
depends on the information existing in the
diffraction pattern (wave intensities and relative phases). Conversely,
the intensity and relative phase of each
diffracted wave, shown as a spot in the pattern, depends on the
position of all atoms in the crystal:
The position of
each atom is
determined by the sum of all diffracted waves (taking into account
their intensities and relative phases). This kind of sum is a holistic
process, ie, the information in every point of the crystal is dependent
on the information existing in the whole diffraction pattern, and vice
versa. It's the same thing as we can say of this arc of stones; the
existence of the arc
depends on each and every one of the stones...
the arc and the stones there is a holistic relationship. The arc
depends on all and everyone of the stones.Image taken from definicionAB
this methodology similar to
an optical microscope?
Although it has been said that
determining the internal structure of
crystals is not an immediate procedure, it resembles the process of
watching a tiny object through an optical microscope. For
example, to see the details of a fly wing (what we cannot
distinguish directly with the naked eye), we put the wing on a slide,
which is illuminated with visible light. Light passing through the wing
is refracted producing various waves (with their intensities and
relative phases) that go through a system of lenses that are able to
these waves (with their intensities and phases) and produce an enlarged
image showing the tiny details of the fly wing.
In what we might call the impossible X-ray microscope,
the object being observed is a crystal that is illuminated with X-rays,
instead of visible light. The waves of "light X” are
by the crystal. But unfortunately, technically speaking there is no
system of lenses able to "combine" diffracted waves of X-rays, with
amplitudes and phases, and therefore we have to be satisfied with the
only thing we can measure on the diffraction pattern: the amplitudes
Only after being able to calculate (somehow) the phases of the
diffracted waves, we will be able to "see" the equivalent enlarged
image of the
optical microscope, that is, the internal structure of the crystal
(=the atomic positions)...
do we use crystals instead
of isolated molecules?
readers will probably wonder why we use crystals (packed molecules) to
"see" atomic positions, rather than using isolated molecules...
answer is quite simple. The interaction of X-rays with matter is very
weak and if we irradiate an isolated molecule with X-rays, we get an
interference pattern which contains very poor scattering information,
making it difficult to reconstruct the structure of molecules from
when a crystal is irradiated, the ordered molecular packing makes the
crystal behave as a very powerful 'amplifier'. The
called diffraction, produce a pattern containing much more information
than the one created by an isolated molecule...
kind of information is contained within a
contains full information, not only about the spatial positions
occupied by all atoms, but also on their thermal vibrational states.
From these positions we can also derive if atoms are bound forming
molecules, and easily calculate all type of geometrical parameters,
including bond lengths, bond angles, etc. In addition, the
structural crystallographic data also show very rich information about
how molecules interact with each other, through attractions or
is even able to distinguish between a
molecule and its mirror image (see left image). These molecules seem to
be the same, but
they are quite different, and so are their properties. Think for
instance on our two hands; they seem to be
"equal", but in reality they are very different; they are not
superimposable, they are mirror images.
Two mirror-image molecules
The three-dimensional shape of a molecule relates to how
the molecule will work in a chemical reaction, in a test tube, or
inside a living being. Once the relationship between the structure and
properties is understood, it is often possible to modify or design new
materials or molecules with specific desired properties.
study the atomic
structure of any material that can build a crystal, from very simple
substances to viruses, proteins or huge protein complexes. But
they also investigate a wide variety of other
materials, such as membranes, liquid crystals, fibers,
liquids, gases and quasicrystals.
In short, the atomic and/or molecular structure that Crystallography
provides contains the most relevant information to understand the
properties of materials, so we can modify them to our benefit.
current macromolecular crystallography includes new X-ray
enhanced remote-accessible capabilities and time-resolved methods to
capture intermediate structures along reaction pathways.
Crystallography allows us to know all
geometrical details (interatomic distances, bond angles, etc.)
of molecules, even for huge
Crystallography provides full details on both molecular
packing and intermolecular interactions.
The structures of most known materials (inorganic, organic,
metal-organic, proteins, enzymes, nucleic acids...) are available
through specialized databases
that are continuously updated.
Even if you do not pretend to know anything more about crystallography,
we hope this summary has clarified some ideas about this powerful and
beautiful branch of modern science.