Understanding Miller Indices: A Guide to Interpreting Crystal Planes

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In summary, the conversation discusses the difficulty in understanding the coordinates of a plane with a given index in a crystal structure. The properties of a solid can vary depending on directions in the crystal structure, such as stress and strain, piezoelectricity, X-ray diffraction, and wave propagation. Miller indices are important in semiconductor device physics, and many research articles use them to discuss specific parameters or measurements. However, determining the coordinates of a plane from its index can be challenging. A suggested tutorial is provided as a resource for further understanding.
  • #1
_Andreas
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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?
 
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  • #2
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.
 
  • #3
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.
 
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  • #4
try this tutorial...

https://www.physicsforums.com/showthread.php?t=110233 [Broken]
 
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  • #5
Dr Transport said:
try this tutorial...

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


i am getting a n error message whew i want to open this
 
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  • #6
_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
 

1. What are Miller indices?

Miller indices are a notation system used to describe the orientation of crystal planes within a crystal lattice. They are represented by three integers (hkl) that indicate the intercepts of the plane with the crystal axes.

2. How are Miller indices determined?

Miller indices are determined by taking the reciprocals of the intercepts of a plane on the crystal axes and then reducing the resulting numbers to the smallest set of integers. The numbers are then enclosed in parentheses, with no commas separating them.

3. What is the significance of Miller indices?

Miller indices are significant because they allow for a standardized way of describing crystal planes and their orientation within a crystal lattice. This information is important for understanding the properties and behavior of crystals, and is essential in the study of crystallography.

4. How can Miller indices be used to determine the symmetry of a crystal?

Miller indices can be used to determine the symmetry of a crystal by examining the pattern of planes and their orientations within the crystal lattice. The symmetry of a crystal can be determined by comparing the Miller indices of equivalent planes and identifying any patterns or repetitions.

5. Are there any limitations to using Miller indices?

There are a few limitations to using Miller indices. One limitation is that they can only be used for crystals with a regular lattice structure. Another limitation is that they do not account for the size or shape of the crystal, only the orientation of the planes within it. Additionally, Miller indices cannot be used to describe planes that do not intersect with the crystal axes.

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