Sphere packing, Chemistry

 

Sphere packing

 

Element structures where chemical bonding is nondirectional are best explained by considering the packing of equal spheres. Close-packed structures are ones that full space most efficiently. In two dimensions this is acquired in a layer with each sphere surrounded hexagonally by six others. Three-dimensional structures are designed by stacking these layers so that the spheres in one layer fall over the hollows in the one below. Having placed two layers, labeled B and A, there are alternative positions for the spheres in the third layer. They could be placed directly over spheres in the first layer A to give a linear sequence denoted ABA. Alternatively, the spheres in the third layer can be placed in positions where there are gaps in layer A; two such spheres labeled C are shown A regular packing based on this latter arrangement should then place the fourth layer directly over layer A, giving a linear sequence denoted ABCA. The simplest three-dimensional close-packed structures are based on these two regular sequences of layer ranks:

 

ABABABAB...gives hexagonal close packing (hcp);

 

ABCABCABC...gives cubic close packing (ccp).

 

These structures are explained respectively. In the ccp arrangement, successive close-packed layers are ranked along the body diagonal of a cube. The unit cell shown is based on a cube with atoms in the face positions, and the structure is also known as face-centered cubic (fcc).

 

 

 

571_Untitled.png

 

 

Fig. 1. Close-packed structures, (a) Stacking of layers showing the sequence ABC (see text); (b) the hcp structure; (c) one unit cell of the fcc structure.

 

In both hcp and fcc structures each sphere is surrounded by 12 others at the same near-neighbor distance. (There are six similar close-packed layer, and three each in the layers above and below.) If the spheres are in contact both structures give 74% filling of space by the spheres, with the remaining 26% outside them. That is the optimum space filling possible with equal spheres. Same types of close-packed structures can be constructed from more complicated sequences of layers such as ABABCABABC..., or even with random sequences. Although these are sometimes achieved, most close-packed structures are of the simple hcp or fcc types.

 

Posted Date: 7/23/2012 12:41:09 AM | Location : United States







Related Discussions:- Sphere packing, Assignment Help, Ask Question on Sphere packing, Get Answer, Expert's Help, Sphere packing Discussions

Write discussion on Sphere packing
Your posts are moderated
Related Questions


Alicyclic compounds - Homocyclic or Carbocyclic These are the compounds that consist of rings of three or more carbon atoms. These resemble along with aliphatic compounds than

Q. What is Electronic Isomerism? Electronic Isomerism: The complex {Co (NH 3 )sNO]Cl 2 exists in two forms. One is black paramagnetic while the other is pink and diamagnetic

The magnetic quantum number for an electron when the value of principal quantum number is 2 can have: (1)3 values (2) values (3)9 values (4)6 values Ans: 3 values

PREPARATIONS OF DIENES

#questio1. Alcohols and amines are both nucleophilic. Explain why this reaction occurs to form Benadryl (diphenhydramine)n..

Which of the following electronic configuration is not possible according to Hund's rule: (1) 1s 2 2s 2                            (2) 1s 2 2s 1              (3) 1s 2

Electron density vs internuclear distance   Electronic density

anode rays properties