If we want to make it clear what partial ordering the lattice is based on, we say it is a lattice under. Since a lattice L is an algebraic system with binary operations and, it is denoted by L. Variants on compound cubic lattices are obtained by scaling one of the parent elementary sub-lattices by an integer value of ≥2. A lattice is a poset (L, ) for which every pair of elements has a greatest lower bound and least upper bound. Examples of low-order lattice topologies include (e) elementary cubic, (f) compound cubic, (g) super compound cubic, (h) the Kagome lattice, and (i) the diamond lattice. (e–o) Lattice structures and lattice defects are distinctly different from those in traditional materials science. (a–d) Pertinent length scales in traditional materials science are well established: grains are typically 10–100 µm in size, precipitates 10–100 nm, dislocation spacings 10–100 nm, and solute atoms and vacancies at the sub-nm level. Although these characteristics are relevant to the constituent materials from which lattices are made, descriptions of the lattice structure itself require other concepts.Ĭontrasting elements of structure and defects in traditional materials science and in lattice materials science. : a lattice or work made of lattices Example Sentences the intricate latticework of the fence Recent Examples on the Web Behind latticework beneath the deck of his large house on a dead end street, archaeologists working for police in March 2021 found a soil disturbance about the size of a casket and the presence of human blood, prosecutors said. Some of the important structural characteristics-including crystalline grains, grain and interphase boundaries, dislocations, precipitates, solute atoms, and vacancies-are depicted schematically in Figs. Here, structure encompasses the organization of atoms or molecules relative to one another, often in the form of crystals boundaries between domains of differing orientation and,or composition and defects that disrupt periodic arrangements at length scales ranging from the atomic to the macroscopic. The field of materials science as an academic discipline is founded principally on relationships between processing, structure, and properties (Fig. In establishing relationships between macroscopic properties and lattice structure, questions arise about the nature of structure of lattice materials and how characteristics of structure can be integrated into the materials science paradigm. Lattice materials comprising periodic arrays of interconnected struts have emerged as a new class of engineering materials with potential for use in an incredibly diverse range of applications, including structural biomedical implants, aerospace and naval structures, force protection systems, thermal management, actuation, high-performance running shoes, and photonic and phononic crystals, They can be designed to exhibit unusual properties, including negative thermal expansion, negative Poisson’s ratio, fluid-like elasticity (with an extraordinarily high ratio of bulk to shear moduli), unusually high damping capacity, and negative mass density, When the arrays are large, with individual unit cells being small relative to macroscopic length scales of interest, lattices can be treated effectively as other engineering materials in the sense that their properties can be couched in terms of their volume-averaged response to external stimuli.
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