So the volume of the hcp device cell turns out to be (3/2) √ 3 a 2 chemicaldisplaystyle a^2c, that is certainly 24 √ 2 ur 3displaystyle l^3.
If a = 2 urdisplaystyle a=2r, then its height can become easily determined to be 8 3 adisplaystyle sqrt tfrac 83a, and, as a result, c = 4 2 3 rdisplaystyle d=4sqrt tfrac 23r. Obviously, the advantage of this tetrahedron can be adisplaystyle a. elizabeth., twice the height of the regular tetrahedron whose vertices are usually entertained by (state) the main atom of the lower layer, two adjacent non-central atoms of the same coating, and one atom of the middle level 'resting' on the prior three. The latter is twice the distance between nearby levels, i. Now allow adisplaystyle abe the side duration of the bottom of the prism and cdisplaystyle dbe its height. Each atom touches additional twelve atoms. So the overall number of atoms in the mobile can be 3 + (1/2)×2 + (1/6)×6×2 = 6. Indeed, three are usually the atoms in the center level (inside the prism) in inclusion, for the top and bottom levels (on the bases of the prism), the central atom is definitely propagated with the nearby cell, and each of the six atoms at the vertices can be propagated with additional five surrounding tissues. Right here the unit mobile (equal to 3 primitive unit tissues) is certainly a hexagonal prism containing six atoms (if the particles in the crystal are usually atoms). For the hexagonal close-packed structure the derivation is certainly similar.
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