biaxial

Biaxial refers to having two axes or two directions along which a property is distinguished. The term is used across science to describe systems with two principal axes of orientation or activity, in contrast to uniaxial or isotropic cases.

In crystallography and optics, a biaxial crystal possesses three distinct refractive indices (n_alpha, n_beta, n_gamma). Light traveling through such a crystal experiences double refraction in most directions, and there are two optic axes along which light propagates with a single refractive index. Biaxial crystals occur in the orthorhombic, monoclinic, and triclinic crystal systems, and their optical properties are often described by a tri-axial indicatrix.

In soft matter, a biaxial nematic phase is a liquid-crystal state in which molecules order along two perpendicular axes, yielding two optical axes and more complex birefringence than in a uniaxial nematic. This phase has been investigated for potential applications in display technology and advanced photonics.

In geometry, a biaxial ellipsoid has three distinct semi-axes a, b, c, and its surface is defined by x^2/a^2 + y^2/b^2 + z^2/c^2 = 1. Such an ellipsoid represents the most general axis-aligned ellipsoid in three dimensions.

In engineering and mechanics, biaxial stress or strain describes loading that acts in two perpendicular directions, typically within a plane, influencing design, analysis, and material behavior.