materialgitter

Materialgitter, literally "material lattice" in German, is a lattice-based representation used in materials science to model the spatial arrangement of atoms, defects, and material properties within solids. As an abstraction, it provides a grid-like framework on which physical fields such as density, composition, displacement, temperature, or electrical potential can be defined and evolved in time.

The lattice can be based on a Bravais lattice with a basis to describe crystalline materials, or it can be a more general grid used in computational models. Lattices may be regular (uniform spacing) or adaptive (varying resolution), and may incorporate defects (vacancies, interstitials, dislocations) or interfaces (grain boundaries). In multi-scale modelling, the materialgitter links atomistic descriptions to continuum fields through mapping rules and homogenization.

Applications include crystal- and defect-diffusion simulations, phase-field models of microstructure evolution, heat and charge transport, and electronic-structure calculations that employ lattice discretizations like tight-binding or k·p methods. It also underpins numerical methods such as finite-difference, finite-element, and lattice-based approaches (e.g., lattice Boltzmann) used to simulate material behaviour.

In practice, a materialgitter is defined by lattice vectors, basis atoms, and connectivity, with boundary conditions and coupling to external drives. It supports visualization and quantitative analysis of spatial correlations, anisotropy, and defect statistics. Terminology varies by community; the concept is widely used but not standardized under a single formal definition.