A crystallography problem using 3D geometry

In summary, the stacking sequence of three planes can be altered to form the hexagonal close packed structure by sliding the third plane by the vector r over the second. If the planes in the fcc structure are all (111) planes, the translation vector r can be expressed as (1/3)a + (2/3)b in terms of unit vectors [100], [010], and [001] of the fcc lattice.
  • #1
hzx
3
0

Homework Statement


Three close-packed planes of atoms are stacked to form fcc lattice. The stacking sequence of the three planes can be altered to form the hexagonal close packed structure by sliding the third plane by the vector r over the second. If the planes in the fcc structure are all (111) planes, what is the translation vector r in terms of unit vectors [100], [010], and [001] of the fcc lattice?

Homework Equations


PMC4501222_fpsyg-06-00927-g0006.png
PMC4501222_fpsyg-06-00927-g0006.png

The Attempt at a Solution


Unit vectors [100], [010], and [001] of the fcc lattice can be expressed as a, b, and c (any arbitrary origin point O would work).
The problem can be converted to finding relative position of one atom from hcp from an arbitrary origin point O defined using fcc lattice.
 

Attachments

  • PMC4501222_fpsyg-06-00927-g0006.png
    PMC4501222_fpsyg-06-00927-g0006.png
    33.5 KB · Views: 483
Physics news on Phys.org
  • #2
We know that hcp is formed by stacking two identical lattices with a relative shift of (1/3)a + (2/3)b from one lattice to the other.Therefore, translation vector r = (1/3)a + (2/3)b.
 

Related to A crystallography problem using 3D geometry

1. What is crystallography and how does it relate to 3D geometry?

Crystallography is a scientific field that studies the arrangement of atoms in crystals. It involves using techniques such as X-ray diffraction and 3D geometry to determine the structure of crystals and how their atoms are arranged in a 3-dimensional space.

2. What is a crystallography problem using 3D geometry?

A crystallography problem using 3D geometry is a problem that involves using principles and techniques from both crystallography and 3D geometry to determine the structure of a crystal. This may include determining the unit cell, symmetry elements, and atomic positions of the crystal.

3. What tools or techniques are commonly used to solve crystallography problems using 3D geometry?

Some common tools and techniques used to solve crystallography problems using 3D geometry include X-ray crystallography, neutron diffraction, electron microscopy, and computer simulations. These techniques allow scientists to analyze the diffraction patterns of crystals and determine their structure in 3D space.

4. How is crystallography using 3D geometry important in scientific research?

Crystallography using 3D geometry is important in scientific research because it allows scientists to understand the structure and properties of materials at the atomic level. This can have implications in fields such as chemistry, materials science, and biology, and can help in the development of new technologies and materials.

5. What are some real-world applications of crystallography problems using 3D geometry?

Crystallography problems using 3D geometry have numerous real-world applications, including drug design, protein structure determination, and the development of new materials. They are also used in industries such as pharmaceuticals, biotechnology, and nanotechnology to understand the properties of materials and improve their functionality.

Similar threads

Crystallography; from hcp to fcc
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Packing fraction of spheres in a HCC structure
    • Introductory Physics Homework Help
Replies
8
Views
2K
Electron Diffraction Intensity and Reciprocal Lattic
    • Introductory Physics Homework Help
Replies
1
Views
1K
Calculate the packing fraction of an FCC pyramid
    • Introductory Physics Homework Help
Replies
4
Views
7K
A What is the Structure of Gallium Oxide?
    • Classical Physics
Replies
1
Views
754
B Reprise: Calculate the distance between two points without using a coordinate system
    • General Math
Replies
1
Views
341
I Why does (100) and (010) have the shortest reciprocal lattic
    • Atomic and Condensed Matter
Replies
1
Views
1K
Determining equations for tension in 3D statics problem.
    • Introductory Physics Homework Help
Replies
2
Views
5K
What is the exact definition of an octahedral hole in an ionic solid?
    • Chemistry
Replies
2
Views
898
Coordination in a zincblende lattice
    • Introductory Physics Homework Help
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top