### Lattice/Crystal Structures

Lattice Structures

This topic was originally considered for inclusion in this project as a way to explain or define the nomenclature contained in the MyPeriodicTable database and grew from there.

Many of the physical properties of an element or other material are influenced by the crystal’s structure and symmetry. These properties include:

Properties

Absorbtion and reactivity (since chemical reactions occur at or near the surface of solid materials);

Optical properties (such as refractive index and optical transparency);

Surface Tension (varies depending on the density on the surface);

Cleavage (typically occurs parallel to higher density planes).

Background

The terms that are used are largely the result of early work by Auguste Bravais (approx. 1850) and his study of geometry and crystallography.

A crystal is a periodic arrangement of one or more atoms repeated at each lattice point. In general, the lattice systems can be characterized by their shapes according to the relative lengths of the cell edges (a, b, c) and the angles between them (?, ?, ?).

It’s now necessary to define terms used.

Simple (or primitive)
: lattice points on the cell corners only.

Body-Centered (I)
: lattice points on the cell corners with one additional point at the center of the cell.

Face-Centered (F)
: lattice points on the cell corners with one additional point at the center of each of the faces of the cell

Base-Centered (A, B, or C)
: lattice points on the cell corners with one additional point at the center of each face of one pair of parallel faces of the cell.

In three-dimensional space, there are 14 Bravais lattices that are created by combining one of the seven lattice systems (or axial systems) with one of the seven lattice types (or lattice centerings). In general, the lattice systems can be characterized by their shapes according to the relative lengths of the cell edges (a, b, c) and the angles between them (?, ?, ?). The lattice types identify the locations of the lattice points in the unit cell as follows:

The 7 Lattice systems
(from least symetric to most symetric)

 Lattice System Possible Variations Axial Distances (edge lengths) Axial Angles Examples Triclinic Primitive K2Cr2O7, CuSO4.5H2O, H3BO3 Monoclinic Primitive, Base-centred Monoclinic sulphur, Na2SO4.10H2O Orthorhombic Primitive, Body-centred, Face-centred, Base-centred Rhombic sulphur, KNO3, BaSO4 Tetragonal Primitive, Body-centred White tin, SnO2, TiO2, CaSO4 Rhombohedral Primitive Calcite (CaCO3), Cinnabar (HgS) Hexagonal Primitive Graphite, ZnO, CdS Hexagonal Primitive Graphite, ZnO, CdS Cubic Primitive, Body-centred, Face-centred NaCl,

14 Bravais lattices

The volume of the unit cell can be calculated by evaluating a – b * c where a, b, and c are the lattice vectors. The volumes of the Bravais lattices are given below:

 Lattice system Volume