Now we want to consider actual crystals and their structures.
the relationship between Bravais lattices and actual crystal structures involves the basis.
We can express this relationship as Bravais lattice + basis → Crystal structure
You can see that the different crystal structures are built on the framework of one of the 14 Bravais lattices and contain a basis consisting of a number of atoms.
In the following sections we group crystal structures in terms of their basis.
This approach may be somewhat different from that which is used to describe structures in introductory materials science classes, but it will help you when we describe the structure factor in Sec. 2.8.
2.4.1 One Atom per Lattice Point
The simplest crystal structures are those in which the basis is one atom located on each lattice point of a Bravais lattice.
(Remember, each atom must be of the same kind.)
Let's consider the crystal structures based on the three cubic Bravais lattices in which each has a basis consisting of one atom.
Using Eq. (9) we obtain for the primitive cubic Bravais lattice: Primitive cubic (cubic P) lattice +one atom → Simple cubic (sc) structure
The sc structure is illustrated in Fig. 18. There is one atom per cell in the sc structure and this atom is located at the origin; i.e., its coordinates are 0,0,0.
(Our choice of the origin of the unit cell is entirely arbitrary, as you will see.)
The simple cubic structure is uncommon; no important metals have this structure.
α-Polonium (Po) is the only element that crystallizes in the simple cubic structure, although some nonequilibrium phases obtained by rapid solidification or mechanical alloying also exhibit this structure. 2015/04/27【引用キャッチコピー抜粋】
