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

Physical properties - Alkyl nitrites (1) At ordinary temperature it is a gas that can be liquified on cooling to a colourless liquid, (boiling point 17°C) comprising characteri

What are the lattice vacancies The lattice vacancies are a stable feature of metals at all temperatures above absolute zero. By successive jumps of atoms, just like playing Chi

The minimum amount of energy needed for the reaction to takes place is known as threshold energy.

what is made when resorsinol reacts with zinc powder?

oxidation state of p-block elements?

I want to know how to calculate hybridisation of an atom in a given compound like I want to calculate hybridisation of Boron & Oxygen in this boric acid compound H 3 BO 3 I even w

Q. Show the Effect of pressure on chemical equilibrium? Ans. In gases, the pressure is proportional to the number of moles of molecules. Reactions accompanied by a change

Given that dH for the reaction is -92.2 kJ mol-1, which is larger, the total bond dissociation energy of the reactants or the total bond dissociation energy of the products?