Crystal Directions: Finding Basis Vectors

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In summary, the conversation discusses the Wurtzite and Zincblende structure as viewed from a specific direction. The speaker is seeking help on which basis vectors to choose for [1 1 1] and [0 0 0 1]. They suggest that [0 0 0 1] represents three vectors separated by a 120 degree angle in the plane and one vector along the c-axis of the hexagonal crystal. The speaker is unsure of what other system of basis vectors could be chosen to make [1 1 1] match [0 0 0 1]. They clarify that [1 1 1]/[0 0 0 1] represents the direction on the picture in
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I found the following picture of the Wurtzite and Zincblende structure as viewed from a specific direction. I could do with some help on which basis vectors are chosen for either the [1 1 1] or [0 0 0 1]. Now I am pretty sure that the last one refers to a basis where we have three vectors separated by a 120degree angle in the plane and then one vector along the c-axis of the hexagonal crystal. But I don't see what other system of basis vectors you would choose to make [1 1 1] match [0 0 0 1]. Because that's what [1 1 1]/[0 0 0 1] means here right? - that they are reprsenting the direction on the picture in two different bases.
 

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I think they simply mean direction [111] in case of zincblende and [0001] in the case of wurtzite.
 

1. What are basis vectors?

Basis vectors are a set of vectors that are used to describe and define a coordinate system in a vector space. They serve as the building blocks for all other vectors in that space.

2. How are basis vectors used in crystal directions?

In crystallography, basis vectors are used to describe the arrangement of atoms and molecules within a crystal lattice. They represent the relative positions of atoms in the crystal structure and are essential for understanding the physical and chemical properties of crystals.

3. What is the importance of finding basis vectors in crystal directions?

Finding basis vectors allows us to accurately describe the orientation and symmetry of a crystal lattice, which is crucial for studying its structure and properties. It also enables us to predict and understand how the crystal will behave under different conditions.

4. How are basis vectors calculated in crystallography?

Basis vectors are typically calculated using a technique called X-ray crystallography. This involves shooting X-rays at a crystal and analyzing the diffraction pattern produced to determine the positions of atoms within the lattice. These positions are then used to calculate the basis vectors.

5. Can basis vectors change in different crystal directions?

Yes, basis vectors can change in different crystal directions. This is because the arrangement of atoms and molecules within a crystal lattice can vary depending on the direction of observation. Therefore, the basis vectors used to describe the lattice in one direction may be different from those used in another direction.

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