How Atoms Pack

Does It Matter How Atoms ?




How atoms pack produce their properties. Properties like density. conductivity, melting point, and heat capacity.



For example with metals, how atoms pack controls how ductile, malleable, and how resistant to shock. 




Similarly, ionic compounds form ceramics to make super conductors, nanoparticles, and quantum dots. Further, these depend on surface science, which involves how atoms pack.




Atoms Pack As Spheres


Imagine atoms as simple spheres. They begin like a collection of  a loose bag of marbles. 




Two Dimensional Atoms Pack




Spheres follow a set of rules when they pack. First. they press as close as possible. Each sphere has the most number of contacts.




atoms pack in two dimensions

Figure 1: Two possible arrangements  in two dimensions shows orange central atoms. The blue atoms in the square packed atoms are the closest contacts. The purple atoms in the close packed atoms indicate neighbors.


Put them together to fit the maximum number of spheres in a square. 


This results in two ways to place the spheres become possible, Figure 1.



This causes the spheres to adopt a square packed array or a close packed arrangement.


How Square Atoms Pack




In the case of square packed atoms, each atom touches four atoms. You might think this makes the most efficient way. However, pay attention to the empty space between the atoms.



This results in makes the packing efficiency 79%. 




How Hexagonal Atoms Pack



Circles pack more efficiently if the next row nestles into the gap where two circles in the first row touch.



As a result, this allows each atom to touch six neighbors. Therefore the  atoms use 91% of the unit cell’s volume. 



Three Dimensional Atoms Packed



In addition, the three dimensional structure of a crystal emerges as more layers take their place.


The Second Layer Atoms Packed




second row in 3d atom packing

Figure 2: The second layer sits in the depression created where atoms touch. This repeats the pattern of the first layer. The position of the atoms shift from one level to the next.

Furthermore, the second layer packs in the depression made when atoms touch in the first layer, Figure 2.








As a result, the pattern made in the in the first layer repeats in the second layer. This causes the atoms to shift. It creates depressions where the spheres touch.


Third Layer Atoms Packed




To continue, the latent structure of a crystal structure expresses becomes apparent when the third layer adds, Figure 3.


add 3rd layer to atoms pack

Figure 3: The three structures result from atom packing. One structure comes from cubic packing. Two structures arise from close packing: hexagonal close packing, and cubic close packing.

The third layer of atoms fit into the depressions created where atoms touch.



Cubic Packed Atoms



The cubic packed structure produces the same pattern in the third layer.


This means spheres in the third level rest over empty space where atoms on the first layer meet.




Close Packed Atoms



two ways to place third layer of atoms in close packed spheres

Figure 4: Close packed atoms add a third layer  in one of two ways. The new layer can be directly above atoms on the second layer or placed above the grooves of the first layer.


In contrast, close packed atoms have two ways to place the third layer, Figure 4.



Hexagonal Close Packed Atoms



The first way puts atoms in the groove directly above atoms of the first layer. This creates a hexagonal close packed structure, (hcp).







Cubic Close Packed Atoms



To continue, the second way puts the atoms in a groove directly above a groove in the first layer. This results in a cubic close packed structure, (ccp).


The Three Most Common Way Atoms Pack



Consequently, these three ways atoms pack form the majority of crystal structures. Knowing these three forms the basis of the properties of metals and ionic solids.




Atoms Pack In Unit Cells





equivalence of atom packing and unit cells

Figure 5: Atom packing schemes translated into unit cells. Cubic packed atoms produce body centered-cubic unit cells. Cubic close packed structures form face-centered cubic packed unit cells. Hexagonal close packed atoms results in hexagonal unit cells.

Generally speaking, you often find the structure of solids expressed in terms of their unit cells, Figure 5.



Body Centered Cubic



First of all, cubic packing makes a body-centered cubic unit cells. A central atom occupies space within a cube. 


Every corner atom accounts for 1/8 of an atom. The atom at the center contributes 1 atom. This results in a total of 2 atoms in a bcc unit cell








Face Centered Cubic



Next, cubic close packed atoms make a face-centered cubic packed unit cell. Each corner has an atom. The face has an atom at the center of each face.



Consequently, every atom on a corner adds 1/8 of an atom. Each atom at a face adds 1/2 of an atom. There is a total of 3 atoms in each unit cell.



Hexagonal Packing




exploded view of hexagonal unit cell
Figure 6: The hexagonal unit cell in a space filling model and atoms shown as smaller points to emphasize the atoms 

Finally, hexagonal close packed atoms form a hexagonal unit cell. This takes into account the hexagonal surfaces. The interior triangle of atoms reside inside the unit cell, Figure 6.


In that vein, each edge atom contributes 1/6 of an atom. Each central on the face adds 1/2 an atom. The three interior atoms give 3 atoms.



Therefore, a hexagonal unit cell contains 6 atoms.






To sum up what this means:


  • Common unit cells result from how atoms pack


  • The three most important structures come from cubic packing, cubic close packing, and hexagonal close packing.


  • Cubic packed atoms produce a body-centered cubic unit cell.


  • The way close packed atoms get placed on top of the second row creates two possible close packed structures.


  • Cubic close packing produces face-centered cubic unit cells.


  • Hexagonal close packing generates hexagonal unit cells.