Lattice

Lattice is a term used in various fields of study such as mathematics, physics, and chemistry. It refers to a regular, repeating arrangement of points in space, often visualized as a grid. In mathematics, a lattice is a set of points in a grid-like structure. In physics and chemistry, a lattice is a three-dimensional array of atoms or molecules in a crystalline solid.

Mathematics

In mathematics, a lattice is a set of points in space that form a grid-like structure. This structure is defined by a set of vectors, known as the basis of the lattice, which are used to generate the points in the lattice. The points in a lattice can be represented as integer combinations of the basis vectors.

Lattice theory

Lattice theory is a branch of abstract algebra that studies lattices. In this context, a lattice is a partially ordered set in which every two elements have a unique supremum and infimum.

Physics

In physics, a lattice refers to the arrangement of atoms or molecules in a crystalline solid. This arrangement is often periodic, meaning it repeats in a regular pattern.

Crystal lattice

A crystal lattice is a three-dimensional array of atoms or molecules in a crystalline solid. The structure of a crystal lattice is determined by the arrangement of its atoms or molecules and the nature of the chemical bonds between them.

Chemistry

In chemistry, a lattice is a three-dimensional array of atoms or molecules in a crystalline solid. The structure of a lattice in chemistry is determined by the arrangement of its atoms or molecules and the nature of the chemical bonds between them.

Lattice energy

Lattice energy is a measure of the energy required to separate one mole of a solid ionic compound into its gaseous ions.

See also

• Lattice (order)
• Lattice (group)
• Lattice graph
• Lattice constant
• Lattice (discrete subgroup)

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