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Name: Neeraj B.
Status: Other
Grade: Other
Location: India
Country: India
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 crystal.

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 planes.

Bob Wilson.

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.

Richard Barrans

Not all crystalline solids are anisotropic. Two common examples are NaCl, common table salt, and FeS2, iron pyrite.

Vince Calder

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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