Anisotropy (/ˌænaɪˈsɒtrəpi,ˌænɪ-/) is the structural property of non-uniformity in different directions, as opposed toisotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very differentphysical ormechanical properties when measured along different axes, e.g.absorbance,refractive index,conductivity, andtensile strength.
An example of anisotropy is light coming through apolarizer. Another iswood, which is easier to split along itsgrain than across it because of the directional non-uniformity of the grain (the grain is the same in one direction, not all directions).
In the field ofcomputer graphics, an anisotropic surface changes in appearance as it rotates about itsgeometric normal, as is the case withvelvet.
Anisotropic filtering (AF) is a method of enhancing the image quality of textures on surfaces that are far away and viewed at a shallow angle. Older techniques, such asbilinear andtrilinear filtering, do not take into account the angle a surface is viewed from, which can result inaliasing or blurring of textures. By reducing detail in one direction more than another, these effects can be reduced easily.
A chemical anisotropicfilter, as used to filter particles, is a filter with increasingly smaller interstitial spaces in the direction of filtration so that theproximal regions filter out larger particles anddistal regions increasingly remove smaller particles, resulting in greater flow-through and more efficient filtration.
Influorescence spectroscopy, thefluorescence anisotropy, calculated from thepolarization properties of fluorescence from samples excited with plane-polarized light, is used, e.g., 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.
InNMR spectroscopy, the orientation of nuclei with respect to the applied magnetic field determines theirchemical shift. In this context, anisotropic systems refer to the electron distribution of molecules with abnormally high electron density, like the pi system ofbenzene. This abnormal electron density affects the applied magnetic field and causes the observed chemical shift to change.
Images of a gravity-bound or man-made environment are particularly anisotropic in the orientation domain, with more image structure located at orientations parallel with or orthogonal to the direction of gravity (vertical and horizontal).
Physicists fromUniversity of California, Berkeley reported about their detection of the cosmic anisotropy incosmic microwave background radiation in 1977. Their experiment demonstrated theDoppler shift caused by the movement of the earth with respect to theearly Universe matter, the source of the radiation.[1] Cosmic anisotropy has also been seen in the alignment of galaxies' rotation axes and polarization angles of quasars.
Physicists use the term anisotropy to describe direction-dependent properties of materials.Magnetic anisotropy, for example, may occur in aplasma, so that its magnetic field is oriented in a preferred direction. Plasmas may also show "filamentation" (such as that seen inlightning or aplasma globe) that is directional.
Ananisotropic liquid has the fluidity of a normal liquid, but has an average structural order relative to each other along the molecular axis, unlike water orchloroform, which contain no structural ordering of the molecules.Liquid crystals are examples of anisotropic liquids.
Some materialsconduct heat in a way that is isotropic, that is independent of spatial orientation around the heat source. Heat conduction is more commonly anisotropic, which implies that detailed geometric modeling of typically diverse materials being thermally managed is required. The materials used to transfer and reject heat from the heat source inelectronics are often anisotropic.[2]
Manycrystals are anisotropic tolight ("optical anisotropy"), and exhibit properties such asbirefringence.Crystal optics describes light propagation 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 to crystalline layers). Some materials can have multiple suchoptical axes.
Seismic anisotropy is the variation of seismic wavespeed with direction. Seismic anisotropy is an indicator of long range order in a material, where features smaller than the seismicwavelength (e.g., crystals, cracks, pores, layers, or inclusions) have a dominant alignment. This alignment leads to a directional variation ofelasticity wavespeed. Measuring the effects of anisotropy in seismic data can provide important information about processes and mineralogy in the Earth; significant seismic anisotropy has been detected in the Earth'scrust,mantle, andinner core.
Geological formations with distinct layers ofsedimentary material can exhibit electrical anisotropy;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 the gas andoil exploration industry to identifyhydrocarbon-bearing sands in sequences ofsand andshale. Sand-bearing hydrocarbon assets have highresistivity (low conductivity), whereas shales have lower resistivity.Formation evaluation instruments measure this conductivity or resistivity, and the results are used to help find oil and gas in wells. The mechanical anisotropy measured for some of the sedimentary rocks like coal and shale can change with corresponding changes in their surface properties like sorption when gases are produced from the coal and shale reservoirs.[3]
Thehydraulic conductivity ofaquifers is often anisotropic for the same reason. When calculating groundwater flow todrains[4] or towells,[5] the difference between horizontal and vertical permeability must be taken into account; otherwise the results may be subject to error.
Most common rock-formingminerals are anisotropic, includingquartz andfeldspar. Anisotropy in minerals is most reliably seen in theiroptical properties. An example of an isotropic mineral isgarnet.
Igneous rock like granite also shows the anisotropy due to the orientation of the minerals during the solidification process.[6]
Anisotropy is also a well-known property inmedical ultrasound imaging describing a different resultingechogenicity of soft tissues, such astendons, when the angle of thetransducer is changed. Tendon fibers appear hyperechoic (bright) when the transducer is perpendicular to the tendon, but can appear hypoechoic (darker) when the transducer is angled obliquely. This can be a source of interpretation error for inexperienced practitioners.[citation needed]
Anisotropy, inmaterials science, is a material's directional dependence of aphysical property. This is a critical consideration formaterials selection in engineering applications. A material with physical properties that are symmetric about an axis that is normal to a plane of isotropy is called atransversely isotropic material.Tensor descriptions of material properties can be used to determine the directional dependence of that property. For amonocrystalline material, anisotropy is associated with the crystal symmetry in the sense that more symmetric crystal types have fewer independent coefficients in the tensor description of a given property.[7][8] When a material ispolycrystalline, the directional dependence on properties is often related to the processing techniques it has undergone. A material with randomly oriented grains will be isotropic, whereas materials withtexture will be often be anisotropic. Textured materials are often the result of processing techniques likecold rolling,wire drawing, andheat treatment.
Mechanical properties of materials such asYoung's modulus,ductility,yield strength, and high-temperaturecreep rate, are often dependent on the direction of measurement.[9] Fourth-ranktensor properties, like the elastic constants, are anisotropic, even for materials with cubic symmetry. The Young's modulus relates stress and strain when an isotropic material is elastically deformed; to describe elasticity in an anisotropic material,stiffness (or compliance) tensors are used instead.
In metals, anisotropic elasticity behavior is present in all single crystals with three independent coefficients for cubic crystals, for example. For face-centered cubic materials such as nickel and copper, the stiffness is highest along the <111> direction, normal to the close-packed planes, and smallest parallel to <100>. Tungsten is so nearly isotropic at room temperature that it can be considered to have only two stiffness coefficients; aluminium is another metal that is nearly isotropic.
For an isotropic material, where is theshear modulus, is theYoung's modulus, and is the material'sPoisson's ratio. Therefore, for cubic materials, we can think of anisotropy,, as the ratio between the empirically determined shear modulus for the cubic material and its (isotropic) equivalent:
The latter expression is known as theZener ratio,, where refers toelastic constants inVoigt (vector-matrix) notation. For an isotropic material, the ratio is one.
Limitation of theZener ratio to cubic materials is waived in the Tensorial anisotropy index AT[10] that takes into consideration all the 27 components of the fully anisotropic stiffness tensor. It is composed of two major partsand, the former referring to components existing in cubic tensor and the latter in anisotropic tensor so that This first component includes the modified Zener ratio and additionally accounts for directional differences in the material, which exist inorthotropic material, for instance. The second component of this index covers the influence of stiffness coefficients that are nonzero only for non-cubic materials and remains zero otherwise.
Fiber-reinforced or layeredcomposite materials exhibit anisotropic mechanical properties, due to orientation of the reinforcement material. In many fiber-reinforced composites like carbon fiber or glass fiber based composites, the weave of the material (e.g. unidirectional or plain weave) can determine the extent of the anisotropy of the bulk material.[11] The tunability of orientation of the fibers allows for application-based designs of composite materials, depending on the direction of stresses applied onto the material.
Amorphous materials such as glass and polymers are typically isotropic. Due to the highly randomized orientation ofmacromolecules in polymeric materials,polymers are in general described as isotropic. However,mechanically gradient polymers can be engineered to have directionally dependent properties through processing techniques or introduction of anisotropy-inducing elements. Researchers have built composite materials with aligned fibers and voids to generate anisotropichydrogels, in order to mimic hierarchically ordered biological soft matter.[12] 3D printing, especially Fused Deposition Modeling, can introduce anisotropy into printed parts. This is because FDM is designed to extrude and print layers of thermoplastic materials.[13] This creates materials that are strong when tensile stress is applied in parallel to the layers and weak when the material is perpendicular to the layers.
Anisotropic etching techniques (such asdeep reactive-ion etching) are used inmicrofabrication processes to create well defined microscopic features with a highaspect ratio. These features are commonly used inMEMS (microelectromechanical systems) andmicrofluidic devices, where the anisotropy of the features is needed to impart desired optical, electrical, or physical properties to the device. Anisotropic etching can also refer to certain chemical etchants used to etch a certain material preferentially over certain crystallographic planes (e.g., KOH etching ofsilicon [100] produces pyramid-like structures)
Diffusion tensor imaging is anMRI technique that involves measuring the fractional anisotropy of the random motion (Brownian motion) of water molecules in the brain. Water molecules located infiber tracts are more likely to move anisotropically, since they are restricted in their movement (they move more in the dimension parallel to the fiber tract rather than in the two dimensions orthogonal to it), whereas water molecules dispersed in the rest of the brain have less restricted movement and therefore display more isotropy. This difference in fractional anisotropy is exploited to create a map of the fiber tracts in the brains of the individual.
Radiance fields (seeBidirectional reflectance distribution function (BRDF)) from a reflective surface are often not isotropic in nature. This makes calculations of the total energy being reflected from any scene a difficult quantity to calculate. Inremote sensing applications, anisotropy functions can be derived for specific scenes, immensely simplifying the calculation of the net reflectance or (thereby) the netirradiance of a scene.For example, let theBRDF be where 'i' denotes incident direction and 'v' denotes viewing direction (as if from a satellite or other instrument). And let P be the Planar Albedo, which represents the total reflectance from the scene.
It is of interest because, with knowledge of the anisotropy function as defined, a measurement of theBRDF from a single viewing direction (say,) yields a measure of the total scene reflectance (planaralbedo) for that specific incident geometry (say,).
