Crystal Structure

[Luckygamer]

During the summer I've been studying chemistry by myself to prepare myself for college. I'm currently stuck on the topic of crystal structure. The book is trying to explain graphing the structures on a coordinate plane and finding interatomic distances between the atoms using Angstroms. It's pretty confusing can anyone help explain?

[cypress]

Sure, if you can be more specific. I assume you understand the unit of measure but you are having difficulty with the trigonometry and geometrics, or spacial relationships.

Edited June 23, 2010 by cypress

[Horza2002]

Angstoms are a unit of measure used in chemistry because a lot of lenghts happen to be on that order. It is x10^-10 of a metre

[Luckygamer]

Okay, well here's one specific problem from the book.

 

The metal iron is cubic, with a = 2.86 Angstroms, and with two iron atoms in the unit cube at 0,0,0 and 1/2,1/2,1/2. How many nearest atoms does each iron atom have and how far away are they?

 

It has me pretty stumped. I'm not sure whata is supposed to represent and I don't even know where to begin to solve this problem.

 

Thanks for the help.

[Horza2002]

a is usually the length of the unit cell and the numbers are the coordinates which indicate the position of the atom within the unit cell. You should then be able to imply use pythagaros therom to work out the distances between the atoms.

[cypress]

Right, but since Luckygamer seems to be stumped from the beginning it may be best to back up one step and begin by understanding from the description what is the geometry of the crystal and the spacial relationships of the atoms to each other.

 

So, if you start by drawing the shape of the structure and then place the two atoms as described perhaps that would help you see the structure.

[Horza2002]

Well seeign as it says its a cube draw a cube with length a and then choose a corner to be the origin. Then place the second atom at the cooridinate 0.5, 0.5, 0.5....once youve done that you should then be able to work out the distance between them using Pythagorus theroum

[Luckygamer]

Well the book's solution says that each atom is surrounded by seven atoms (the corner's of the cube). Then it says the square of the interatomic distance = (a/2)[math]^{2}[/math] + (a/2)[math]^{2}[/math] + (a/2)[math]^{2}[/math] or [math]\sqrt{3}[/math] a/2 thus the distance between the atoms is 2.48 Angstroms and the metallic radius of iron to be 1.24 Angstroms.

 

I understand the math I'm just not sure where they got the equation for it. Your help has been extremely useful, if I can figure out this last bit I think I'll be ok.

[cypress]

The book should have said each atom is surrounded by eight atoms....

 

Think more about the geometry that is implied by the description. Can you visualize it? Draw it out as a three dimension sketch and you should begin to see which atoms are touching. Hint: The atoms at the eight corners of a cube are not touching each other.....

Edited June 26, 2010 by cypress
added more detail

[Luckygamer]

The problem has been solved. Thanks for all the help! I'm sure I'll have another question soon.