Engineering Bravais lattice from lattice points

Thread starter GeologistInDisguise
Start date Oct 18, 2023
Tags

Crystallography Materials science Xrd

AI Thread Summary

Understanding how to apply translations to determine the type of unit cell is crucial in crystallography. The discussion highlights confusion regarding the application of body-centered translations, specifically how to derive the coordinates from lattice points. It is clarified that a face-centered unit cell requires four atoms, while the current scenario only has two, ruling it out. The transformation of the first atom to the coordinates 1/2, 1, 1/2 indicates a body-centered configuration, but further clarification on visual representation is sought. The lack of examples in available resources complicates the understanding of these concepts.

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.