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Isotropy and anisotropy

Updated July 19, 2010

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 material. This 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: search IEEE Explore database. If you don't have access, find someone that does.

### Other references to isotropy

Thermal conductivity is sometimes anisotropic.

Etching in semiconductor processing (or MEMS circuits) sometimes performs anisotropically.

Thermal 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.

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