Unit Cell to Lattice

FROM UNIT CELL TO LATTICE

If we take the square unit cell S2 and stack it, we produce this square lattice. Notice that once we begin stacking the unit cells, we never change the orientation of any subsequent unit cells as they stack. In other words, once the orientation of a unit cell is determined, all unit cells within that lattice have the same orientation.

The hexagonal unit cell H1 gives a different arrangement of circles.

In the figures below we have created lattices from unit cells. It is the stacking which creates lines and cavities which are not immediately obvious from looking at the unit cells.

S1 unit cell S1 lattice

We can look at the S1 lattice as alternating staggered rows of solid and empty circles - both horizontally and vertically.

We can also see it as diagonal rows of alternating circles.

S3 unit cell S3 lattice
We can see lattice S3 as different diagonal lines of atoms, or horizontal rows, or vertical columns. If we rotate the entire lattice 90 degrees we see an identical pattern. This is a property of a square lattice.

H1 lattice

In the H1 lattice we can view the structure as parallel lines of circles along the X - axis, each line staggered from the next.

If we rotate the entire lattice 60 degrees or 120 degrees we see an identical pattern. This is because the unit cell is hexagonal.

H3 lattice

In the H3 lattice, the pattern of lines is the same (every 60 degrees), but each line contains the repeating sequence (pink- purple-purple).

Click here to go to the next page. Structure of Crystals Crystal Lattices Unit Cells

From Unit Cell to Lattice

From Lattice to Unit Cell Stoichiometry Packing & Geometry Simple Cubic Metals Close Packed Structures Body Centered Cubic Cesium Chloride Sodium Chloride Rhenium Oxide Niobium Oxide Except as otherwise noted, all images and movies are owned and copyright by Dr. Barbara L. Sauls and Dr. Frederick C. Sauls 1998. Contact the owners for individual permission to use. barbarasauls@kings.edu