Understanding Miller Indices to Interpreting Crystal Planes

  • Context: Undergrad 
  • Thread starter Thread starter _Andreas
  • Start date Start date
  • Tags Tags
    Indices
Click For Summary

Discussion Overview

The discussion revolves around understanding Miller indices and their application in interpreting crystal planes, particularly how to derive coordinates from given indices and vice versa. It touches on theoretical aspects, practical applications, and challenges faced by participants in visualizing and utilizing these indices in crystallography.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion regarding how to visualize the intercepts of a plane with a given Miller index, such as (233).
  • Another participant discusses the significance of Miller indices in relation to the directional properties of solids, citing applications in stress and strain, piezoelectricity, X-ray diffraction, and semiconductor device physics.
  • A participant seeks clarification on how to derive the coordinates (3,2,2) from the Miller index (233), noting that while they can convert coordinates to indices, the reverse process is challenging.
  • Several participants suggest a tutorial link for further guidance, although one participant reports an error when attempting to access it.
  • A repeated request for clarification on deriving indices from coordinates indicates ongoing confusion and a desire for a more comprehensive understanding.

Areas of Agreement / Disagreement

Participants generally agree on the importance of Miller indices in crystallography and their practical applications. However, there remains disagreement and confusion regarding the process of converting between Miller indices and coordinates, with no consensus on a clear method presented in the discussion.

Contextual Notes

Participants express limitations in their understanding of the relationship between Miller indices and crystal coordinates, highlighting a potential gap in instructional resources or clarity in existing materials.

Who May Find This Useful

This discussion may be useful for students and researchers in materials science, crystallography, and semiconductor physics who are grappling with the concepts of Miller indices and their applications in crystal structure analysis.

_Andreas
Messages
141
Reaction score
1
They confuse me. If someone tells me a plane has the index, say (233), it's very difficult for me to see where it intercepts the crystal axes. What are they good for?
 
Physics news on Phys.org
The properties of a solid differ depending on directions in the crystal structure. Some examples:
Stress and strain (you can apply a squeezing force along one axis and see bulging or contraction along another)
Piezoelectricity
Xray diffraction
Wave propagation
The most important practical applications of Miller indices are in semiconductor device physics. Look at any semiconductor research article and you'll see the parameter or measurement under discussion is indexed to a direction like (100) in Silicon.
 
Thanks.

But let's go back to the plane with index (233). I want to draw it in a coordinate system with the crystal axes a, b, and c. I know from my textbook that its coordinates in this coordinate system are (3,2,2) (that is, the plane intercepts the axes at 3a, 2b and 2c). But how do I get this information if I only know the index? I know how to get the index from knowing the coordinates, but vice versa seems to be more difficult.
 
Last edited:
try this tutorial...

https://www.physicsforums.com/showthread.php?t=110233
 
Last edited by a moderator:
Dr Transport said:
try this tutorial...

https://www.physicsforums.com/showthread.php?t=110233


i am getting a n error message whew i want to open this
 
Last edited by a moderator:
_Andreas said:
Thanks.

But let's go back to the plane with index (233). I want to draw it in a coordinate system with the crystal axes a, b, and c. I know from my textbook that its coordinates in this coordinate system are (3,2,2) (that is, the plane intercepts the axes at 3a, 2b and 2c). But how do I get this information if I only know the index? I know how to get the index from knowing the coordinates, but vice versa seems to be more difficult.

do the same thing for vice versa also
 

Similar threads

Undergrad Miller indices for hexagonal crystal systems
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad Understanding Ewald's sphere in the context of X-Ray diffraction
  • · Replies 3 ·
Replies
3
Views
6K
Graduate Miller Indices of Simple Cubic Lattice
  • · Replies 2 ·
Replies
2
Views
10K
Undergrad Miller indices and periodic boundary conditions
  • · Replies 0 ·
Replies
0
Views
3K
Undergrad Why the reflected angle is the same as incident in x-ray diffraction?
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad How can phonons "travel" if they are excitations of normal modes?
  • · Replies 7 ·
Replies
7
Views
4K
Graduate What, physically, are the Miller planes of a crystal?
  • · Replies 8 ·
Replies
8
Views
5K
Undergrad Standard crystallographic notation confusion
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Rotating birefringent calcite crystals: precession of image?
  • · Replies 7 ·
Replies
7
Views
2K
HCP miller indices in Orthogonal coordinate system
  • · Replies 4 ·
Replies
4
Views
7K