Bravais lattice from lattice points

In summary, a Bravais lattice is a mathematical representation of a periodic arrangement of points in space, characterized by its lattice points and the symmetry of the arrangement. It can be defined in various dimensions, with each lattice point representing an atom or a group of atoms. The different types of Bravais lattices, including simple, body-centered, face-centered, and hexagonal structures, arise from the combinations of translational symmetry and the geometric arrangement of the points. Understanding Bravais lattices is crucial for studying the properties of crystalline materials and their symmetry.
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GeologistInDisguise
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Homework Statement
Given the orthorhombic unit cell, what is the bravais lattice?

Two atoms of the same kind per unit cell located at 0 1/2 0, 1/2 0 1/2
Relevant Equations
face centering translations: ½ ½ 0 and ½ 0 ½ and 0 ½ ½
body centering translations: ½ ½ ½
base centering translations ½ ½ 0 or ½ 0 ½ or 0 ½ ½
I am confused on how to use these translations to tell what type of unit cell I have. I know that this is not a face centered unit cell because you need 4 total atoms and I only have two. From what I understand, to apply a body centering translation you add or subtract it from the lattice point. From there I am lost. Applying the body centering translation to the first atom results in 1/2 1 1/2. What does this mean? What would it look like if it were body centered? I can't find many examples of this online, and the book I am using does not really provide any examples.
 

FAQ: Bravais lattice from lattice points

What is a Bravais lattice?

A Bravais lattice is a set of infinite, discrete points in space generated by a set of discrete translation operations. It defines the periodic array of points in a crystal structure, where each point has an identical environment. There are 14 unique Bravais lattices in three-dimensional space, classified according to their symmetry properties.

How are lattice points related to a Bravais lattice?

Lattice points are the individual points that make up a Bravais lattice. Each lattice point represents an identical environment within the crystal structure, and the entire lattice can be generated by translating a single lattice point using a set of basis vectors.

What are the basis vectors in a Bravais lattice?

Basis vectors in a Bravais lattice are a set of vectors that define the fundamental repeating unit of the lattice. They are used to translate a single lattice point to generate the entire lattice. In three dimensions, three non-coplanar basis vectors are used.

How many types of Bravais lattices exist in three-dimensional space?

In three-dimensional space, there are 14 distinct types of Bravais lattices. These are categorized into seven crystal systems: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic, each of which can have different lattice types such as primitive, body-centered, face-centered, and base-centered.

What is the significance of Bravais lattices in crystallography?

Bravais lattices are fundamental in the study of crystallography because they describe the geometric arrangement of atoms in a crystal. Understanding the Bravais lattice of a material helps in determining its physical properties, such as symmetry, density, and how it interacts with light and other radiation.

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