1 Observations in The Seventeenth Through Nineteenth Centuries
In 1669 Nicolaus Steno studied many quartz crystals and found angles between adjacent prism faces, termed interfacial angles 2 Translational Symmetry
In the previous chapter we discussed symmetry due to rotation, reflection, and inversion. These are all types of point symmetry 3 Unit Cells and Lattices in Two Dimension
What possible shapes can unit cells have 4 Unit Cells and Lattices in Three Dimensions
In two dimensions, patterns are made of unit cells and lattices describe how unit cells and motifs repeat 5 Symmetry of Three Dimensional Atomic Arrangements
In the preceding sections, we discussed the shapes and symmetries of crystals. We now turn our attention briefly to space symmetry 6 Space Groups
When we combine the space group operators in the tables above with the 14 possible space lattices 7 Crystal Habit and Crystal Faces
Why do halite and garnet, both cubic minerals, have different crystal habits 8 Quantitative Aspects of Unit Cells, Points, Lines, and Planes
11.8.1 Unit Cell Parameters and Crystallographic Axes
Earlier in this chapter, we introduced the unit cell parameters a, b, c, α, β, and γ. a 9 Miller Indices
Miller indices were first developed in 1825 by W. Whewell, a professor of mineralogy at Cambridge University 10 The Miller Indices of Planes Within A Crystal Structure
We use Miller indices to describe the orientation of crystal faces, but we also use them to describe planes within a crystal structure. For example 