A structure, such as a window, screen, or trellis, made of or containing such a framework. The quantity k n turns out to be the wavenumber of the phonon, i.e. An open framework made of strips of metal, wood, or similar material overlapped or overlaid in a regular, usually crisscross pattern. The potential energy of the entire lattice is the sum of all pairwise potential energies multiplied by a factor of 1/2 to compensate for double counting: 1 2 ∑ i ≠ j V ( r i − r j ) The forces between each pair of atoms may be characterized by a potential energy function V that depends on the distance of separation of the atoms. Magnetic and gravitational forces are generally negligible. These forces may be Van der Waals forces, covalent bonds, electrostatic attractions, and others, all of which are ultimately due to the electric force. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. Since the lattice is rigid, the atoms must be exerting forces on one another to keep each atom near its equilibrium position. In physics, a lattice model is a physical model that is defined on a lattice, as opposed to the continuum of space or spacetime. N is a large number, say of the order of 10 23, or on the order of the Avogadro number for a typical sample of a solid. These particles may be atoms or molecules. The equations in this section do not use axioms of quantum mechanics but instead use relations for which there exists a direct correspondence in classical mechanics.įor example: a rigid regular, crystalline (not amorphous) lattice is composed of N particles. While normal modes are wave-like phenomena in classical mechanics, phonons have particle-like properties too, in a way related to the wave–particle duality of quantum mechanics. Normal modes are important because any arbitrary lattice vibration can be considered to be a superposition of these elementary vibration modes (cf. In classical mechanics this designates a normal mode of vibration.
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