Bravais lattice from lattice points

Engineering
Thread starter GeologistInDisguise
Start date Oct 18, 2023
Tags

Crystallography Materials science Xrd

Oct 18, 2023

GeologistInDisguise

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.

Related to 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.