The most dense packing of hexagons is the arrangement of atoms and the array of points in the crystal structure. Among all kinds of densest packing, hexagonal densest packing is a kind of symmetry.

Face-centered cube is the most densely packed cubic unit cell with face-centered type due to symmetry. The 14 atoms involved in a unit cell belong to four layers: one vertex is layer A, the three atoms closest to the face center and three vertices belong to layer B, the next six atoms belong to layer C, and the other vertex is opposite to the vertex of layer A, which is in the next cycle.

2. Different coordination numbers

The closest packing coordination number of a hexagon is 12. The space utilization rate is high, about 74%.

The closest packing coordination number of face-centered cube is 14.

Extended data:

Hexagonal densest packing (abbreviated as hcp, also called A3 type) generally takes one third of the hexagonal cone when taking the unit cell, which belongs to hexagonal crystal system, and the acute angle of the bottom diamond must be 60. The stacking method of hcp is to stack the third layer on the close-packed double layer. Another way is that the center of the ball is opposite to the center of the first layer, and the fourth layer is opposite to the second layer, so it is ABABAB. These two layers are stacked in a periodic and repetitive manner.

Spatial structure diagram:

This stacked hexagonal pyramid crystal involves 17 atoms, one atom at each vertex, one atom at each bottom and three atoms inside the crystal.

Therefore, the atomic number of each hexagonal pyramid crystal is:12 *1/6+2 *1/2+3 = 6, so the atomic number of the unit cell is 65438+ 0/3 of the atomic number of the hexagonal pyramid crystal, so the atomic number of the unit cell is 6 *1/.

In order to obtain strong force, many simple substances, especially metal simple substances, often use the densest filler.

The densest basic substance in the six surfaces is:

Beryllium and magnesium

Titanium, cobalt, zinc, zirconium, technetium, ruthenium, cadmium, hafnium, rhenium, osmium

Scandium, yttrium, lanthanum, praseodymium, neodymium, promethium, gadolinium, terbium, dysprosium, holmium, erbium and thulium.

The most dense simple materials with a face-centered cube is:

Calcium and strontium

Aluminum, lead

Neon, argon, krypton, xenon

Nickel, copper, rhodium, palladium, silver, iridium, platinum, gold

Cerium, ytterbium, actinium, thorium

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