Anisotropy and Crystalline Solids
Name: Neeraj B.
Date: July 2006
Why are crystalline solids anisotropic?
Your question seems to imply that all crystalline solids are
anisotropic. In fact, many crystalline solids are not. Whether
a crystalline solid is anisotropic, or isotropic, depends on
the way the atoms in the crystal are arranged. If the spacing
and arrangement of the atoms in a crystal appears the same in
each of the 3 planes (X, Y, and Z), the crystal is isotropic.
Plain table salt (sodium chloride) which has a lattice
structure called "cubic", is an example of an isotropic
However, if a crystalline solid has a lattice structure whose
atoms are arranged or spaced differently when viewed in any
or all of the 3 planes, that crystal is called anisotropic. A
good example of this is quartz. So to turn the above
statement around to answer your question, those crystalline
solids that are anisotropic, are because when one views the
crystal structure in each of the 3 planes, the spacing and
arrangement of atoms is different in at least 2 of the
They are not always anisotropic. It depends on the symmetry of the
crystal lattice. If the lattice is different in two different
directions, the crystal will be anisotropic. This is because light
passing through the crystal in the different directions will
experience different environments, and hence different refractive indices.
Not all crystalline solids are anisotropic. Two common examples are
NaCl, common table salt, and FeS2, iron pyrite.
There are two potential questions here, related though different. Are
you asking why a single crystal solid has different sized facets, faces,
and features that are not all the same? Or is the question why the
atoms are not bound in a completely symmetric fashion? My guess is the
former, which is related to the latter.
Anyhow, why is a single crystal chunk of metal not symmetric? This is
actually a complicated question in that there are several different
things involved in crystal growth.
First, the conditions on one side of a crystal may not be the same as on
the other sides. This will lead preferentially to atoms bonding on one
surface over another. Availability of atoms (or molecules), catalysts
(something that would help/enable the bonding), defects, impurities,
temperature differences and many other things can cause this. In many,
many instances at least one, if not many, differences will exist over
the surface of a crystal during growth which will cause the facets not
to be exactly the same size. These can also lead to the crystal not
being completely a "single" lattice array of atoms, but to have arrays
tilted at different angles to be stuck together(a polycrystalline material).
If "all things are equal" then the crystal can grow uniformly. Now, it
will still develop facets (faces/surfaces) that reflect the underlying
structure of the crystal. Indeed, the macroscopic angles that you can
measure where the facets meet are a beautiful example of quantum
mechanics and atomic bonding in action. Those angles are the same
angles present on the atomic scale! And the symmetry of the crystal is
the direct result of the symmetry present in how the atoms bond. The
fundamental unit of the crystal, the shape of the building block, will
be present in the crystal.
However, even in a homogeneous environment, where the conditions are the
same everywhere, complex, unusual structures can form. How can this be?
Suppose atoms are being randomly deposited by diffusion onto a symmetric
surface. Once a few atoms deposit themselves near each other on the
surface a bump will form. This bump will stick out further from the
rest of the crystal. The result of this is that atoms will be a little
more likely to hit the bump first than the rest of the crystal. Thus
the bump grows a little faster than the crystal. The bigger it gets,
then the faster it grows relative to the rest of the crystal. This is
how large branches or "arms" can grow out of crystals. It's also how a
snowflake can develop branches instead of just being a hexagon. Such
branching can lead to beautiful, complex structures.
Michael S. Pierce
Materials Science Division
Argonne National Laboratory
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Update: June 2012