Updated July 19,
here to go to our main page on material properties
New for July 2010! Isotropy
comes from the Greek iso, for equal (as in isolateral triangles)
and tropos, for direction. Isotropy means that a particular material
property is equal in all directions (X, Y and Z). Anisotropy means
that the material property might vary depending on direction. Anisotropy
can be caused within Angstrom dimensions (in a crystal lattice which
is not uniform in all directions, for example), or at micron dimensions
(where material grain boundaries are oriented in a particular direction),
or at millimeter dimensions (when materials are created in a sandwich
format, such as glass cloth reinforced substrates).
Anisotropy of various properties
is often a result of using "sandwich" materials such as
FR-4 circuit boards. To beat
the food reference to death, a chocolate cake might exhibit different
properties in the radial direction than vertical direction (anisotropy),
but a chocolate chip cookie would not (isotropic), because the chips
are scattered uniformly.
Isotropy and its derivative forms
are all very impressive words, teenage girls should be encouraged
to work it into conversations:
"...and then she goes
'I'm like, totally whatever', and then I'm like, do you mean,
like, that deep sea oil well plugs are anisotropic?", and
she's like, 'whatever'!"
Anisotropic dielectric constant
In microwaves the most typical
discussion of isotropy is around dielectric constant (permittivity).
One example of an anisotropic material is FR-4,
which is a fiberglass laminate. The dielectric constant in Z is
nearly uniform (it's an average of the DK of the epoxy and the glass
fibers), but in X and Y, the electric fields can be concentrated
within a single layer. This is something you need to consider when
you are transitioning between microstrip and CPW on a circuit card:
in microstrip mode, the
fields cut through the entire sandwich, but in CPW
mode, the fields are concentrated in the surface layer of epoxy.
Sapphire is another anisotropic
paper suggests that it ~9.5 in one direction and ~11.5 in the
perpendicular direction (it's actually the lower value in two directions.)
If you are going to design circuits on sapphire, you'll need to
study the effects more than we have, for example, you'll need to
know the difference between r-cut and z-cut crystals. Recommended:
Explore database. If you don't have access, find someone that
Other references to isotropy
conductivity is sometimes anisotropic.
Etching in semiconductor processing
(or MEMS circuits) sometimes
expansion is sometimes anisotropic.
Another use of the word "isotropic"
in microwave engineering refers to antennas.
An isotropic radiator radiates energy in all directions equally.