Abstract
An estimation of category of liquid crystalline (LC) phase based on composite lattices using linear algebra and lattice parameters is proposed. The vector space in three dimensions [Formula: see text] is dissolved in the initial phase into two dimensions [Formula: see text], and one dimension [Formula: see text] subspace in a 3D crystal, respectively, rotate and/or slide between each other during thermal process. In linear algebra, this state is designated as [Formula: see text] composite subspaces of vector. As per linear algebraic approach, [Formula: see text] is not identical with 3D, and the mathematical sign ⊕ indicates addition directly. The phase is represented as [Formula: see text] lattice-based composite phase. Apart from the [Formula: see text] phase, two more mixed phases with [Formula: see text] and [Formula: see text] may also be theoretically studied using linear algebra. Finally, the category of phase is proposed to be analyzed with link to its transition temperature.
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