How Can We Visualize the Primitive Vectors of a Basic Cubic Lattice?

In summary, the primitive vectors of the basic cubic lattice in the body centered cubic system are described by the equations provided and can be visualized by connecting two identical lattice points. These vectors translate one-half of a lattice parameter in each direction and can be used to reach the body center starting from a corner atom. This information is helpful for understanding crystal structures.
  • #1
Petar Mali
290
0
Do yoh have some nice picture to show why the primitive vectors of basic cubic lattice are

[tex]\vec{a}_1=\frac{a}{2}(-\vec{e}_x+\vec{e}_y+\vec{e}_z)[/tex]

[tex]\vec{a}_2=\frac{a}{2}(\vec{e}_x-\vec{e}_y+\vec{e}_z)[/tex]

[tex]\vec{a}_3=\frac{a}{2}(\vec{e}_x+\vec{e}_y-\vec{e}_z)[/tex]

Thanks!
 
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  • #3
I'm afraid I don't have a diagram to show you, but it's pretty easy to visualize the primitive vectors by just thinking about it. A primitive vector simply connects two identical lattice points.

So, for instance, the a3 vector translates one-half a lattice parameter in the +x direction, one-half a lattice parameter in the +y direction, and one-half a lattice parameter in the -z direction. If you start at a corner atom in the BCC structure, this will take you to the body center.

I don't know if this helps at all--and it doesn't really answer your question--but it was useful to me when I first learned crystal structures.
 

What is a basic cubic centered lattice?

A basic cubic centered lattice is a type of crystal lattice structure that is characterized by a cube-shaped unit cell with lattice points located at each corner and in the center of each face.

How many lattice points are present in a basic cubic centered lattice?

A basic cubic centered lattice has a total of 8 lattice points per unit cell.

What is the coordination number of a basic cubic centered lattice?

The coordination number of a basic cubic centered lattice is 8, as each lattice point is surrounded by 8 neighboring lattice points.

What is the packing efficiency of a basic cubic centered lattice?

The packing efficiency of a basic cubic centered lattice is 52.4%, meaning that only 52.4% of the total space within the lattice is occupied by atoms or molecules.

What are some examples of materials that exhibit a basic cubic centered lattice?

Some examples of materials that exhibit a basic cubic centered lattice include sodium chloride (salt), copper, and aluminum.

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