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Solid State
Solids can be classified into 2 based on the nature of order in the arrangements of their constituent’s particles.
Crystalline solid | Amorphous solid |
1. The constituent particles are arranged in a regular fashion containing short-range and long-range order. The long-range order means the atoms or ions, or molecules, are arranged regularly, and this symmetrical arrangement extends throughout the crystal length. | 1. The constituent particles are not arranged in any regular fashion. There may be some short-range order only and has completely random particle arrangements, i.e. no regular arrangement, no shape of its own. |
2. They have a sharp melting point | 2. They melt over a range of temperatures. |
3. They are Anisotropic, i.e. properties like electrical conductivity, thermal expansion, etc., have different values in different directions. | 3. They are Isotropic, i.e., properties like electrical conductivity, thermal expansion, etc. have the same value in different directions |
4. They undergo a cleavage. Therefore, they are considered as True Solid. | 4. They undergo an irregular cut. They are also Supercooled Liquid or Pseudo Solid. |
5. | 5. |
6. Examples-Quartz, Diamond, NaCl, ZnS, CsCl, Boron Nitride etc. | 6. Examples- Glass, Rubber, Plastics etc. |
Unit Cells
Certain properties of a solid depend only on the constituents of the solid and the pattern of arrangement of these constituents. The smallest amount of the solid whose properties resemble the properties of the entire solid irrespective of the amount taken is called a unit cell. It is the smallest repeating unit of the solid. Any amount of the solid can be constructed by simply putting as many unit cells as required.
In a 3-dimensional space lattice, to specify a unit cell we need the values of three vectors which give three distances along the three axes and three angles as shown in the figure below:
Primitive Cubic Unit Cell
In the primitive cubic unit cell, the lattice points are the corners of the cube. This implies that the atoms are present only at the corners of the cube. Each atom at the corner of the unit cell is shared by eight unit cells. Therefore, the volume occupied by a sphere in a unit cell is just one-eighth of its total volume. Since there are eight such spheres, the total volume occupied by the spheres is one full volume of a sphere. Therefore, a primitive cubic unit cell has effectively one atom.
Packing Fraction
It is defined as the ratio of the volume occupied by the spheres in a unit cell to the volume of the unit cell
Thus, Void Fraction = (1 – Packing fraction).
Since adjacent atoms touch each other, the edge length of the unit cell 'a' is equal to 2r, where r is the radius of the sphere. Therefore, the Packing fraction (PF) is:
This implies that 52 % of the volume of a unit cell is occupied by spheres
Void Fraction (VF) is approximately equal to 0.48.
Body-Centred Cubic Unit Cell
In a body-centered cubic unit cell, the lattice points are the corners and body centre of the cube. That is the atoms are present at all the corners and at the body centered position. Thus, the effective number of atoms in a Body centred Cubic Unit Cell is 2 (One from all the corners and one at the centre of the unit cell).
The Packing Fraction in this case is:
The void fraction (VF) is approximately equal to 0.32.
Face Centered Cubic Unit Cell
In FCC unit cells, the lattice sites are corners and face centres. That is in face centred cubic unit cell, the atoms are present at the corners and the face centres of the cube. The effective number of atoms in FCC is 4 (one from all the corners, 3 from all the six face centres since each face centred atom is shared by two cubes).
Void Fraction (VF) is approximately equal to 0.26.
Density of Crystal Lattice
The density of crystal lattice is the same as the density of the unit cell which is calculated as:
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