Finding Hexagonal Crystalline Directions

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SUMMARY

The discussion focuses on determining the Miller-Bravais indices for a specific direction within a hexagonal unit cell. The user applied the equations from "Materials Science & Engineering: An Introduction" by Callister, 8th Edition, and derived values for a1, a2, and c as 1/2, resulting in u'=1, v'=1, and w'=1. However, the calculated direction of [11-23] was identified as incorrect, prompting the user to seek clarification on their interpretation of the image and the application of the equations.

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  • Understanding of Miller-Bravais indices
  • Familiarity with hexagonal crystal structures
  • Proficiency in vector mathematics
  • Knowledge of materials science principles
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  • Review the derivation of Miller-Bravais indices in hexagonal systems
  • Study the application of vector mathematics in crystallography
  • Examine the differences between cubic and hexagonal unit cells
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Homework Statement



What are the Miller-Bravais indices for the direction represented by the vector that has been drawn within a unit cell?

fc2rkn.jpg


Homework Equations



u = 1/3(2u' - v')
v = 1/3(2v' - u')
t = -(u+v)
w = w'

Equations from this book: Materials Science & Engineering an Introduction by Callister, 8th Edition

The Attempt at a Solution



From the image, I got that the values of a1, a2, and c are respectively: 1/2, 1/2, 1/2. Then multiplying by 2 to get integer values, I have u'=1, v'=1, and w'=1. Working everything out with the given equations, I from that the direction should be [11-23] but my answer turned out to be wrong.

I'm not sure if I'm interpreting the image incorrectly or if I'm not using the equations correctly.
 
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