Understanding HCP Crystal Structure: Confusion with Coordinates of Center Atom

In summary, the conversation discusses the coordinates for the center atom in a hexagonal close-packed structure, specifically in relation to the unit cell and origin. The coordinates are found using trigonometry and there is a slight difference in convention for the unit cell's position.
  • #1
DollarBill
44
0
Considering only the 4 lower-right atoms (one unit cell), I'm somewhat confused as to why the coordinates for the center atom (b) is (1/3, 2/3, 1/2) with respect to (a1, a2, c).

c is pretty self explanatory, but I don't quite get the other 2. I think one of my main confusions is where the origin is being taken when considering just one unit cell.

[PLAIN]http://img856.imageshack.us/img856/2272/hexagonalclosepackedstr.gif

Thanks
 
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  • #2
hcpcoord.png


The triangle drawn has side length a. From simple trigonometry you can find that the center of an equilateral triangle is 1/3 of the way from a side along the perpendicular. The total height is a*cos(30). Then x and y give you the 2/3*a and 1/3*a you are looking for. Actually I chose the unit cell opposite to how you did. So mine is 2/3, 1/3, 1/2 instead of 1/3, 2/3, 1/2. But that's just convention.
 
  • #3
That definitely cleared it up -- can't believe I didn't get it before. Thanks!
 

1. What is the HCP crystal structure?

The HCP (Hexagonal Close-Packed) crystal structure is a common arrangement of atoms in a solid material. In this structure, the atoms are closely packed together in a hexagonal lattice, with each atom surrounded by six others.

2. How is the HCP crystal structure different from other crystal structures?

The HCP crystal structure is unique because it has two different types of layers: a hexagonal layer and a triangular layer. This results in a more compact structure compared to other crystal structures, such as the FCC (Face-Centered Cubic) or BCC (Body-Centered Cubic) structures.

3. What materials have the HCP crystal structure?

Some common materials with the HCP crystal structure include metals such as magnesium, titanium, and zinc, as well as some non-metals like graphite and cadmium. Many minerals, such as quartz and mica, also have an HCP crystal structure.

4. How does the HCP crystal structure affect the properties of a material?

The HCP crystal structure can greatly influence the properties of a material. For example, materials with an HCP structure tend to have high strength and ductility, making them ideal for use in structural applications. They also tend to have high melting points and good thermal and electrical conductivity.

5. Can the HCP crystal structure change under different conditions?

Yes, the HCP crystal structure can change under different conditions, such as changes in temperature or pressure. These changes can result in different crystal structures, known as polymorphs, which can have different properties. For example, carbon can exist as both graphite and diamond, which have different crystal structures and properties.

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