Materials - determining indices for planes. can someone check answers?

In summary, the user posted a problem related to materials engineering and provided their attempt at solving it by defining three different planes. They also asked for feedback on their work.
  • #1
pyroknife
613
3

Homework Statement


I'm not sure if this is the right section, but I also posted in the chemistry section. I'm taking a materials engineering class which involves a lot of chemistry.

I attached the problem.


Homework Equations





The Attempt at a Solution



Plane A: since the plane crosses the origin, I will define the origin to be at x=+1
x=-1 y=1/2 z=3/4
1/x=-1 1/y=2 1/z=4/3
→(-1 2 4/3)→(-3 6 4)

Plane B: x=infinity y=1/4 z=infinity
1/x=0 , 1/y=4 , 1/z=0
→(0 4 0)=(0 1 0)

Plane c: x=infinity y=3/2 z=1
1/x=0 1/y=2/3 1/z=1
→(0 2/3 1)→(0 2 3)


I'm not sure if I did it right. Could someone please check?
 

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  • #2


Thank you for sharing your attempt at solving this problem. I can confirm that your calculations for planes A, B, and C seem to be correct. However, it is always a good idea to double-check your work and make sure all the units and calculations are consistent. Additionally, it would be helpful to see the actual problem or context in which these planes are being used to provide a more thorough evaluation. Keep up the good work in your materials engineering class!
 

1. What is the purpose of determining indices for planes in materials?

The purpose of determining indices for planes in materials is to identify and describe the orientation and arrangement of atoms or molecules within a crystal lattice structure. This information is important for understanding the properties and behavior of materials, such as their mechanical, electrical, and thermal properties.

2. How are indices for planes in materials determined?

Indices for planes in materials are determined using a method called Miller indices. This involves identifying the intercepts of a plane with the crystal's axes, taking the inverse of these intercepts, and then reducing the resulting numbers to their smallest whole numbers. These numbers represent the indices for the plane in the crystal lattice.

3. What factors can affect the determination of indices for planes in materials?

The determination of indices for planes in materials can be affected by factors such as crystal defects, impurities, and crystal growth conditions. These can cause variations in the atomic arrangement and disrupt the regularity of the crystal lattice, making it difficult to accurately determine the indices for planes.

4. How do indices for planes in materials relate to crystallographic directions?

Indices for planes in materials are closely related to crystallographic directions, as they both describe the arrangement of atoms or molecules within a crystal lattice. The indices for a plane can be used to determine the orientation and spacing of crystallographic directions, and vice versa.

5. What are some applications of knowing the indices for planes in materials?

Knowing the indices for planes in materials is important for various applications, such as designing and engineering materials with specific properties, understanding material behavior under different conditions, and identifying and characterizing crystal structures in research and development. It can also help in the production of high-quality materials with controlled crystal orientations for use in electronic devices, optical components, and other advanced technologies.

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