orientationdependent

Orientation-dependent describes properties or phenomena that vary with the orientation of a system or measurement relative to a reference direction or frame. In physics, chemistry, and materials science, many properties are not isotropic; they change with direction because of structural anisotropy in molecules, crystals, or assemblies, or due to external fields such as polarization, strain, or magnetic fields.

The dependence is often captured by tensor mathematics. A property that changes with orientation can be described by a tensor, whose components transform under rotation. For simple cases, measurements follow angular laws such as cos^2 theta, where theta is the angle between the measurement axis and a principal material axis. Symmetry considerations of the system restrict which orientation dependencies are allowed.

Examples of orientation-dependent phenomena include optical anisotropy such as birefringence and dichroism, where refractive index or absorption varies with light polarization and propagation direction. In spectroscopy and scattering, cross sections or intensities can depend on the orientation of molecules or crystals relative to the incident beam. In solid-state and materials science, anisotropic conductivity, magnetoresistance, and mechanical properties reflect orientation dependence relative to crystal axes or texture. In chemistry and biology, reaction rates or binding interactions can depend on the relative orientation of reactants or binding partners.

Experimentally, orientation is controlled by rotating samples, aligning crystals, or using polarized probes, and analysis commonly uses symmetry arguments and tensor formalisms to interpret the observed angular variations.