Isotropic and anisotropic are terms that describe whether or not the properties of materials depend on direction. When a property is the same in all directions, the material is isotropic. When a property varies according to direction, the material is anisotropic. The terms come from the Greek isos (equal) and tropos (way). The an in “anisotropic” means “not.”
Isotropy and anisotropy are important in materials science, optics, astronomy, chemistry, crystallography, and a host of other scientific and engineering disciplines. Properties that are isotropic in some materials and anisotropic in others include refractive index, absorbance, electrical conductivity, tensile strength, Young’s modulus, etc.
Keep in mind, a material may be isotropic for one property, yet anisotropic for another. For example, a piece of polarized glass is isotropic for mechanical properties, yet anisotropic for light filtration. Also, scale is important. For example, the universe is generally isotropic and homogenous with respect to cosmic blackbody radiation, but when you examine regions more closely, you see heterogeneity and anisotropy.
Examples of Isotropic and Anisotropic Materials
An isotropic material has an internal structure that is the same from any direction. So cubic (isometric) crystals and homogeneous amorphous solids are isotropic. Here are examples of isotropic materials:
- Most polymers (e.g. plastic)
- Metals (although many are anisotropic for some mechanical properties; tungsten and aluminum are nearly isotropic)
- Cubic crystals (diamond, halite, fluorite, garnet, spinel)
An anisotropic material has a structure that is different depending on the angle. Plant stems, most crystals and minerals, polycrystalline materials, and composite materials are anisotropic. Here are examples of anisotropic materials:
- Slate (and most sedimentary and metamorphic rocks)
- Most crystals (tourmaline, quartz, beryl, corundum)
- Reinforced concrete
- Muscle fibers
- Nickel and copper single crystals are examples of metals that are anisotropic with respect to mechanical properties.
Isotropic and Anisotropic vs Homogeneous and Heterogeneous
Isotropy and anisotropy are different from homogeneity and heterogeneity. A homogeneous substance has a uniform structure throughout, while a heterogeneous material lacks a uniform composition or structure. Another way of looking at it is that a property is independent of its position within a homogeneous substance, but dependent on position/location in a heterogeneous substance. So, a material can be:
- Isotropic and homogeneous
- Isotropic and heterogeneous
- Anisotropic and homogeneous
- Anisotropic and heterogeneous
For example, a salt crystal (NaCl, halite) is both isotropic and homogeneous. A quartz crystal (SiO2) is anisotropic and homogeneous. Concrete is isotropic, yet heterogeneous. Wood is anisotropic and heterogeneous.
- Courtney, Thomas H. (2005). Mechanical Behavior of Materials (2nd ed.). Waveland Press Inc. ISBN 978-1577664253.
- Newnham, Robert E. (2005). Properties of Materials: Anisotropy, Symmetry, Structure (1st ed.). Oxford University Press. ISBN 978-0198520764.
- Nye, J.F. (1985). Physical Properties of Crystals (1st ed.). Clarendon Press. ISBN:978-0198511656.
- Smoot G. F.; Gorenstein M. V.; Muller R. A. (1977). “Detection of Anisotropy in the Cosmic Blackbody Radiation”. Lawrence Berkeley Laboratory and Space Sciences Laboratory, University of California, Berkeley.
- Tian, Xiaojuan; Itkis, Mikhail E.; et al. (2013). “Anisotropic Thermal and Electrical Properties of Thin Thermal Interface Layers of Graphite Nanoplatelet-Based Composites”. Scientific Reports. 3: 1710. doi:10.1038/srep01710