Finding Hexagonal Crystalline Directions

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In summary, the Miller-Bravais indices for the direction represented by the vector drawn within a unit cell are [11-23], but the answer may be incorrect due to potential misinterpretation of the image or incorrect use of the given equations.
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Seiayyi
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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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Hello?
 

FAQ: Finding Hexagonal Crystalline Directions

1. What exactly are hexagonal crystalline directions?

Hexagonal crystalline directions refer to the specific orientations or paths within a hexagonal crystal structure that exhibit distinct properties and characteristics. These directions are determined by the arrangement of atoms or molecules within the crystal lattice and can affect the physical, mechanical, and chemical properties of the material.

2. Why is it important to find hexagonal crystalline directions?

Finding hexagonal crystalline directions is crucial in understanding the properties and behavior of hexagonal crystals. It allows scientists to predict how the material will respond to external stimuli, such as stress or temperature changes, and aids in the design and development of new materials with desired properties.

3. How can we determine hexagonal crystalline directions?

There are several techniques that can be used to determine hexagonal crystalline directions, such as X-ray diffraction, electron microscopy, and polarized light microscopy. These methods involve analyzing the diffraction patterns or optical properties of the crystal to identify its orientation and symmetry.

4. What are some applications of hexagonal crystalline directions?

Hexagonal crystalline directions have various applications in industries such as aerospace, electronics, and materials science. For example, in aerospace, these directions can be used to design stronger and more lightweight materials for aircraft and spacecraft. In electronics, they are essential in the production of high-performance semiconductors and microchips.

5. Can hexagonal crystalline directions be changed or manipulated?

Yes, hexagonal crystalline directions can be modified through processes such as annealing, alloying, and mechanical deformation. By altering the crystal structure, scientists can control the properties of the material and tailor it for specific applications.

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