Crystal Structure: The internal atomic order of a mineral created by a group of atoms repeated on a lattice. The group of atoms has a certain symmetry that may be reflected in the external symmetry of the crystal (that is the triangular arrangement of CO3 groups is reflected by the 3 fold symmetry of calcite for example). Lattice: A periodic array or repetition of a group of atoms in space. The unit cell or unit pattern is repeated in such a way that the environment around each repeated unit is identical. This is accomplished by a regular shifting or translation of the unit pattern in space. A second way of looking at this is : A lattice is an imaginary pattern of points (i.e. nodes) in which every point has an environment that is identical to that of any other point (node) in the pattern. A lattice has no specific origin and can be shifted parallel to itself. The lattice points or "nodes" may or may not correspond to actual locations of atoms. Most lattice points (nodes) are not actual atomic positions, rather they are geometric points in the structure that have the same angle and distance relationships to the groups of atoms and therefore to the symmetry elements. Thus the lattice comprises the translation component of internal order in a crystal. This component is not reflected in the final exterior form of the crystal but can be seen in the submicroscopic structure of the crystal as revealed by either x-rays or transmission electron microscopy (essentially shooting electrons thru an ultra-thin wafer of the mineral). Translation is also reflected in the patterns of growth of a crystal. A lattice is much like a 3 dimensional axial coordinate system, but it differs in that there is no specific origin, thus all points are measured relative to one another. This is real handy, just in case you’ve never tried to find the molecule at the exact center of a crystal! To put all of this simply, what we are trying to do is simply come up with a series of relationships that describe the ordering of atoms within the crystal. Just as the external symmetry describe the relationship of faces to one another, here we are trying to describe the repetition and relationship of groups of atoms to one another. The five 2-dimensional nets: There are only 5 different possible arrangements of planar lattices that can occur. The arrangement of points on the 2 dimensional lattices or "nets" is a result of the angle between the a and b "axis" directions (the infamous g, that is in English, gamma) and the ratio of the distances along a and b (this should be sounding pretty familiar now). Special cases occur when g = 90 or 60 and when a = b (ring any bells yet?). The lattices are an oblique net (parallelogram), rectangular net, centered rectangular net and diamond net combination (g cannot equal either 90 or 60 for this case), hexagonal net, and square net (see fig. 3.5). Each of the points (or nodes) on the lattice can correspond to symmetry axes, which can in turn be connected by mirror planes. Additional symmetry axes relating the groups of atoms can also be located within the lattice, but are of equal or lower symmetry than those located on the lattice points. An additional symmetry element not found in crystals called glide Planes can also be found within the lattice structure. Glide planes are simply mirror planes with uniform offsets. One last type of symmetry element is called a screw axis. It is like a symmetry axis except that it elevates the lattice a certain amount for each partial turn (think of it as the operation to create a spiral stair case). You don’t have to know what glide planes and screw axes really are, but I just wanted to let you know that they exist.