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Solids are made up of sphere-shaped particles, just as we are. Solid spheres are stacked in various ways to leave as little empty space as possible. The solid’s closed-packed structure is formed by these spheres arranged in various levels. The tightly packed structure is where the crystals develop. A similar close-packed arrangement is formed when spheres in solids are stacked in three dimensions.
Close packed structures close to each other in one dimension is termed packing close to each other in one dimension. Each sphere contacts two of its neighbours, resulting in a coordination number of six.
A two-dimensional close-packed structure [called a crystal plane] is generated when the rows are piled on top of each other. There are two methods to perform this stacking.
It’s possible to arrange the first and second rows of spheres in this way such that they contact each other and are precisely above the spheres in the first row.
In the ABA type, the sphere in the second row might be put in the depression of the first row. Because of this, type 2 of raw material in this coordination no. 6 is distinct from type 1.
Three-dimensional packing: Close packed structures
From a two-dimensional (AAA) square close-packed structure, a three-dimensional close packing.
The second layer and all subsequent layers are constructed so that they are horizontally and vertically aligned on each other, starting with the square tightly packed layer. Thus, their lattice is of the AAA type, as shown above. It’s a primordial unit cell, and that’s all it is.
3D close packing of two-dimensional hexagonal close packing layer:-
Let the spheres be designated as A, and the spaces between spheres are marked as a, b alternately in the tight hexagonal packing of spheres.
Spheres are formed when the second layer is applied in this manner. Find a spot in the first layer’s a void for the b void that was previously occupied since a sphere cannot be put there. C and d voids are the following two categories that we’ll look at. “Tetrahedral Void” refers to an empty triangular space enclosed on all sides by four concentric circles, as in the crystal structure represented by the letter C.
A three-dimensional close packing of the ABAB pattern or a close hexagonal packing is created when a third layer is put over the second layer so that a sphere covers the tetrahedral (c) void.
A good example of hcp is seen in molybdenum and magnesium.
Three-dimensional ABCABC or Cubic Close Packing (CCP) patterns are generated when spheres fill octahedral voids or (d) octahedrons in the second layer. The FCC is a model for it (Face Centred Packing). Various metals, including iron, nickel, and copper, may be found in CCP formations.
Cubic close-packed structure
Cubic packing is arranging spheres in Cartesian space using integer coordinates. Face-centred cubic packing is achieved by arranging close-packed spheres so that the spheres of every third layer overlap one another. Consider stacking six spheres in an equilateral triangle and adding a seventh sphere on top to form a triangular pyramid to understand how the term came about. Make a second grouping of seven spheres and position the two pyramids together, facing each other, side by side.
A mixed oxide’s structure is cubic, and tightly packed (CCP) structure of mixed oxide is cubic close-packed. Oxide ions make up the cubic unit cell of a mixed oxide solution. It is estimated that divalent metal A fills one-fifth of the tetrahedral gaps, and monovalent metal B fills the octahedral spaces in this crystal structure.
Coordination number: Close packed structures
The coordination number is the number of the crystal lattice’s closest (or nearest) neighbours of each component particle.
How to maximise the efficiency of your packing:
The packing efficiency is the proportion of the total space occupied by the particles in the three-dimensional tight packing.
The percentage of the volume that can fit in a container – The percentage of three-dimensional space that is occupied. The packing fraction is a term used to describe the process of packing.
conclusion: Close packed structures
It is simpler to create a three-dimensional structure by stacking two-dimensional square tightly packed planes on top of each other than it is to build it from scratch. Both vertically and horizontally, the spheres are perfectly aligned.
Assuming that the first layer has an A-type arrangement of spheres, the succeeding layers also have an A-type layout. AAA type packing refers to this three-dimensional configuration.
