
#1
Nov608, 11:51 AM

P: 11

Hey All..
I'm having some problems trying to understand the tetrahedral and octahedral sites in face centered cubic (fcc) and body centered cubic (bcc). It is hard to visualise the structures in 3D.. I wanted to know how to find out the positions per unit cell for the tetrahedral and octahedral in both fcc and bcc.. For the tetraheral fcc = 8 tetrahedron per unit cell bcc = 12 tetrahedron per unit cell The bcc is worked out (6*4)/2 = 12 For the octrahedral fcc = 4 octrahedron per unit cell bcc = 6 octrahedron per unit cell The fcc is worked out (12/4)+1 = 4 The bcc is worked out (12/4)+(6/2) = 6 Although I have the soultions I'm still confused how they are worked out to the above answers..I have attached a picture.. hope someone can help Thank you 



#2
Nov608, 02:41 PM

Emeritus
Sci Advisor
PF Gold
P: 11,154

First, count the number of sites (small open circles, in the attached pictures) of each kind. In the FCC there are two kinds of octsites, marked in red and white. Do you understand why they are different?
Next, you look at each kind and determine whether or not the site is entirely contained within the unit cell. In the above example, only one kind of site is. Which one? Whenever a site is shared by more than one unit cell, you need to figure out how many unit cells it is shared between. The white octsites on the FCC live on the unit cell edges. How many unit cells share each such edge? Divide the number of shared sites of each type by the number of unit cells that share it*, to get the number per unit cell. * Note: This division assumes that the site is shared equally by each of the unit cells involved in the sharing. This is often the case (determine by inspection from symmetry), but need not always be. 



#3
Nov708, 11:34 AM

P: 11

My understanding of the topic is very brief so bare with me.. Firstly I'm not sure about the difference between the red and white.. The FCC e.g. you have given is an octahedral site From my understanding of per unit cell for fcc is 4 and bcc is 2.. the way i know this is by counting the solid spheres as in the attached pic.. Thank you 



#4
Nov708, 11:59 AM

Emeritus
Sci Advisor
PF Gold
P: 11,154

crystal structuresDo you know what an interstitial site (or void) is? That's where you need to start before you can count them. 



#5
Nov708, 01:51 PM

P: 11





#6
Nov708, 04:40 PM

P: 11

maybe the question should be how do you find the number of voids for tetrahedral/octahedral around sphere...?
(but then why are there 12 white circles in the fcc...and not 6 whereas the tetrahdral there are 8..) arghh i'm confusing myself!! not sure if i'm making sense sorry 



#7
Nov708, 06:38 PM

Emeritus
Sci Advisor
PF Gold
P: 11,154

No, the interstitials we are talking about here are not defects  they are the spaces between the atoms that occupy lattice sites. The geometry of atoms surrounding the void determines whether you call it a tetrahedral void or an octahedral void.
You seem to be pretty confused. You need to start from the beginning here. Do you have a textbook? See also: http://ww1.iucr.org/comm/cteach/pamphlets/5/node1.html 



#8
Nov808, 10:44 AM

P: 11

No I don't have a textbook just some notes..but I need to understand the basics before I move on to different structures rock salt, zinc blende etc.. I have also come across this a few times in internet searches (from the link).. "the particular sphere being considered covers a triangular void in the layer above it and another in the layer below it. Thus two more tetrahedral voids surround the spheres. This results in 2 * 3 + 1 + 1 = 8 tetrahedral voids and 2 * 3 = 6 octahedral voids surrounding the sphere. Since a tetrahedral void is shared by four spheres, there are twice as many tetrahedral voids as there are spheres. Similarly, since an octahedral void is surrounded by six spheres, there are as many octahedral voids as there are spheres" maybe a picture of this may help me understand it better.. 



#9
Nov808, 01:17 PM

P: 11

but now I'm still confused on the 2*3=6 octahedral voids and 2*3+1+1=8 tetrahedral voids.. lol sorry 



#10
Nov1308, 10:39 AM

P: 11

How to you determine no. of octahedral/tetrahedral voids around sphere..
(2*3=6 oct, 2*3+1+1=8 tet) What is the best way to visualise this? 



#11
Nov1308, 05:22 PM

P: 11

Hey All..
I found the answer I worked it out... found a useful site so thought I will share :) Very good for crystal structures.. exactly what I needed to help visualise the stuff.. Heres the link: http://firstyear.chem.usyd.edu.au/ca...te.shtml?tab=2 The answer to my question above.. Voids around sphere for tetrahedral/octahedral I have attached a picture.. 



#12
Nov1308, 06:16 PM

Emeritus
Sci Advisor
PF Gold
P: 11,154

Sorry, I forgot to get back to this thread. Glad you found what you needed.




#13
Nov1508, 03:00 PM

P: 11

Thanks for your reply :)
No need to apologise.. Your help was much appreciated. 


Register to reply 
Related Discussions  
crystal structures question  Materials & Chemical Engineering  1  
Crystal Structures in Metals  Atomic, Solid State, Comp. Physics  3  
Crystal Lattice Structures  Computing & Technology  1  
Symmetry in crystal structures please help!!!  Introductory Physics Homework  0  
Symmetry in crystal structures please help!!!  Atomic, Solid State, Comp. Physics  0 