Atomic Chain in BCC - # Atoms/Unit Length & Area

[madeinmsia]

i'd like to know what is the number of atoms per unit length for an atomic chain in the [1 1 1] direction of a BCC structure.

i can figure out the unit length, however I'm not sure how many atoms to use. Is it 1/8+1/8+1? That means 1/8s for the two corner atoms and 1 atom for the middle? or is it just 3 atoms?

part of the problem is i cannot find anywhere the meaning of atomic chain in the BCC structure.

likewise, what if i had to find the number of atoms per unit area in the (1 1 1) plane? the area part is easy, but again is the number of atoms 4 or 1/8 * 3 + 1?

 

[Astronuc]

What does one mean by 'atomic chain'? We usually refer to an 'atomic lattice', in which the atoms are located at specific points in a repeated crystal structure.

In a BCC cube, there is one whole atom at the center of the unit cube, and 1/8 atom at each corner of the cube.

 

[madeinmsia]

i'm not sure but that's what i was asked.

so if it's atomic lattice, then i would be right to say the corners are 1/8 and the middle is 1 atom? but isn't the middle atom shared by other diagnoal lattice?

 

[Astronuc]

i'm not sure but that's what i was asked.

so if it's atomic lattice, then i would be right to say the corners are 1/8 and the middle is 1 atom? but isn't the middle atom shared by other diagnoal lattice?

In a sense yes. One could shift the unit cell diagonally in any of the 8 directions of the BCC unit cell, and the corner atom becomes a center atom, and center atom is now a corner atom.

The unit cell is a 3D concept, as opposed to a 2D-plane.

The diagonal length is BCC unit cell is R + 2R + R, where R is the atomic radius, because the corner atoms are tangent to the center atoms. So the cubic unit cell must have a face side length of less than 2R.

http://www.science.uwaterloo.ca/~cchieh/cact/c123/bcc.html

Nice pictures here - http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/metallic_structures.htm

http://genchem.chem.wisc.edu/lab/winss/metal_cells/body_centered_cubic_metals/dim_bbc_unit_cell.htm