Drag with the left mouse button to rotate, the center button to zoom, and the right button to move the object.įollow the suggested steps to visualized the structure, which consist of a 6圆圆 array of 216 atoms. The virtual reality display illustrates the packing of atoms in the cubic closest-packed structure. The cubic closest-packed structure has the same packing efficiency, and this value is the highest efficiency For the hexagonal closest-packed structureį = π/(18) 1/2 = 74.05%. The packing efficiency, f, is the fraction of the volume of the unit cell actually occupied by atoms. The volume of an individual atom is V a = 4 π r 3/3 and there are four atoms in the unit cell for theĬubic closest-packed structure, thus the volume occupied by the atoms is 4 V a = 16 π r 3/3. The volume of theįace-centered cubic unit cell, which describes the cubic closest-packed structure, is V = 16(2) 1/2 r 3.
The volume of the unit cell is readily calculated from knowledge of a, b, c, α, β, and γ. How might one characterize the efficiency of the packing of atoms in a crystal? The unit cell for theĬubic closest-packed structure is the face-centered cubic unit cell ( fcc). The sides of the unit cell are all mutually perpendicular, thus α = β = γ = 90 o. In the cubic closest-packed structure, a = b = c = 2 (2) 1/2 r, where r is the atomic radius of the atom. The angles α and β describe the angles between the base and the vertical sides of the
The quantity c is the height of the unit cell. The quantities a and b are the lengths of the sides of the base of the cell and γ is the angle between these two sides. The unit cell is characterized by three lengths and three angles. The entire structureĬan be reconstructed from knowledge of the unit cell. The smallest repeating unit is called the unit cell. In a crystal the atoms are arranged in a regular repeating pattern. This exercise focuses on the cubic closest-packed structure.
The two most efficient packing arrangements are the hexagonal closest-packed structure ( hcp) and the cubic closest-packed structure Metals provide the simplest packing case, because these atoms can generally be regarded as uniform spheres. In order to maximumize intermolecular attractions. Not surprisingly it is not the most efficient way to pack the tennis balls.Īlthough there are a variety of factors that influence how atoms pack together in crystals, atoms generally seek the most efficient packing structure
The resulting packing of the balls is called a Strategy? One could toss all the balls together in a box and shack the box to induce the balls to settle. Suppose you are given a large number of tennis balls and asked to pack them together in the most efficient fashion. Closest-Packed Structures: Cubic Closest-Packed Structure Closest-Packed Structures Efficient Packing of Balls
0 kommentar(er)
