What is the Relationship Between Lattice Points and Basis Balls?

In summary, a Bravais lattice is a repeating pattern of points in three-dimensional space that describes the arrangement of atoms or molecules in a crystalline solid. It is characterized by its lattice points and unit cell, and there are 14 types classified into seven crystal systems. The basis of a Bravais lattice is a set of atoms or molecules located at each lattice point, which determines the physical and chemical properties of the crystal. In materials science, Bravais lattices are used to study crystal symmetries, diffraction patterns, and predict the behavior of materials.
  • #1
Eth338
1
0
Hi, take a look at the picture from my textbook, specifically the bottom part:

11.png


there are five lattice points, shouldn't that mean that there are also 5 "small basis balls"? Or can they be "shared"? If so, they are not all oriented in the same way - is that not important since there's no special direction?
 
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  • #2
That small sampling of 5 lattice points is not the full lattice. When you fill it out, all of the Basis parts are there.
For example, the 5-point one could have been shown this way:
XxXx
. XxXx
XxXx

or
XxXx
xXxX
XxXx
 

1. What is a Bravais lattice?

A Bravais lattice is a mathematical concept used to describe the arrangement of atoms, molecules, or ions in a crystal. It is a repeating pattern of points in three-dimensional space that represents the basic building block of a crystal structure.

2. How many types of Bravais lattices are there?

There are 14 different types of Bravais lattices, which are classified into seven crystal systems: cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, and rhombohedral.

3. What are the characteristics of a Bravais lattice?

A Bravais lattice is characterized by the length of its unit cell edges, the angles between these edges, and the positions of the lattice points within the unit cell. It is also described by its symmetry elements, such as rotation, reflection, and translation operations.

4. What is the basis of a Bravais lattice?

The basis of a Bravais lattice is a group of atoms, molecules, or ions that occupy the lattice points. The basis determines the chemical and physical properties of the crystal and can vary in size and composition depending on the type of lattice.

5. What is the significance of Bravais lattices in crystallography?

Bravais lattices are important in crystallography because they provide a framework for understanding the arrangement of atoms in crystals. They also allow for the prediction of crystal properties and the classification of different crystal structures based on their lattice types.

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