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Anisotropy, as opposed to isotropy, is also used to describe situations where properties vary systematically, depending on direction. As already seen for the anisotropy we can have various definitions depending on the field of interest.

Anisotropy, in materials science, represents the directional dependence of a material on a physical property. This is a fundamental characteristic for material selection in engineering applications. Tensor descriptions of material properties can be used to determine the directional dependence of the property in question. For single-crystal materials, anisotropy is associated with crystal symmetry in the sense that more symmetrical crystal types have fewer independent coefficients in the tensor description of a given property.

In Chemistry we have the following definitions:

  • A chemical anisotropic filter, used to filter particles, is a filter with smaller and smaller interstitial spaces in the direction of filtration so that the proximal regions filter out larger particles and the distal regions remove smaller and smaller particles, resulting in higher flux and more efficient filtration.
  • In nuclear magnetic resonance (NMR) spectroscopy, the orientation of nuclei with respect to the applied magnetic field determines their chemical shift. In this context, anisotropic systems refer to the electronic distribution of molecules with abnormally high electron density, such as the π-system of benzene. This abnormal electron density affects the applied magnetic field and causes the observed chemical shift to change.
  • In fluorescence spectroscopy, fluorescence anisotropy, calculated from the polarization properties of fluorescence from samples excited with in-plane polarized light, is used, for example, to determine the shape of a macromolecule. Anisotropy measurements reveal the average angular displacement of the fluorophore that occurs between absorption and subsequent emission of a photon.

In Physics we have the following definitions:

  • Physicists use the term anisotropy to describe direction-dependent properties of materials. Magnetic anisotropy, for example, can occur in a plasma so that its magnetic field is oriented in a preferred direction. Plasmas can also exhibit “filaments” (such as those seen in a lightning bolt or plasma globe) that are directional.
  • An anisotropic liquid has the fluidity of a normal liquid, but has an average structural ordering with respect to each other along the molecular axis, unlike water or chloroform, which contain no structural ordering of molecules. Liquid crystals are examples of anisotropic liquids.
  • Some materials conduct heat isotropically, i.e., regardless of spatial orientation around the heat source. Heat conduction is most commonly anisotropic, which necessarily implies detailed geometric modeling of materials to manage heat flow. The materials used to transfer and dissipate heat from its source into electronics are often anisotropic.
  • Many crystals are anisotropic to light (optical anisotropy) and exhibit properties such as birefringence. Crystal optics describes the propagation of light in these media. An “axis of anisotropy” is defined as the axis along which isotropy is broken (or an axis of symmetry, such as normal and crystalline layers). Some materials may have more than such optical axes.

In Geophysics and Geology we have the following definitions:

  • Seismic anisotropy is the variation of seismic wave velocity with direction. Seismic anisotropy is an indicator of long-range order in a material, where features smaller than the seismic wavelength (e.g., crystals, cracks, pores, layers, or inclusions) have a dominant alignment. This alignment leads to a directional change in wave velocity elasticity. Measuring the effects of anisotropy in seismic data can provide important information about the Earth’s processes and mineralogy; significant seismic anisotropy has been detected in the Earth’s crust, mantle, and inner core.
  • Geologic formations with distinct layers of sedimentary material can exhibit electrical anisotropy; the electrical conductivity in one direction (e.g., parallel to a layer), is different from that in another (e.g., perpendicular to a layer). This property is used in oil and gas exploration to identify hydrocarbon-containing sands in sand and shale sequences. Hydrocarbon resources that contain sand have high resistivity (low conductivity), while shales have lower resistivity. Formation evaluation tools measure this conductivity/resistivity and the results are used to help find oil and gas in wells. The mechanical anisotropy measured for some of the sedimentary rocks such as coal and shale can change with corresponding changes in their surface properties such as sorption when gases are produced from coal and shale deposits.
  • The hydraulic permeability of aquifers is often anisotropic for the same reason. When calculating groundwater flow, the difference between horizontal and vertical permeability must be taken into account, or the results may be subject to error.
  • The most common rock-forming minerals are anisotropic, including quartz and feldspar. Anisotropy in minerals is most reliably observed in their optical properties. An example of an isotropic mineral is garnet.

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