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SYSTEM AND TYPES OF LATTICE image, Wigner–Seitz cell, The primitive cell…
SYSTEM AND TYPES OF LATTICE 
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Crystal System
Monoclinic
It comprises three axes where two are at right angles to each other, and the third axis is inclined. All three axes are of different length.
Triclinic
It is the most unsymmetrical crystal system. All three axes are inclined towards each other, and they are of the same length.
Orthorhombic
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Hexagonal
It comprises four axes. The three a1, a2 and a3 axes are all contained within a single plane (called the basal plane) and are at 120°. They intersect each other at an angle of sixty degrees. The fourth axis intersects other axes at right angles.
Cubic
Cubic system is the most symmetrical one out of the seven crystal system. All three angles intersect at right angles and are of equal length.
Tetragonal
It consists of three axes. The main axis varies in length; it can either be short or long. The two-axis lie in the same plane and are of the same length.
Coordination Number
The number of nearest neighbhour(atom,ion,molecule) from its central atom
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Theoretical Density
The voids and pores are the major reasons for the difference between the values of theoretical and experimental density of the composites
The density of metals are the highest because of their large atomic masses and the arrangement are packed.
Primitive cell
The primitive cell in a hexagonal system is a right prism based on a rhombus with an included angle of 120°
Note here that a1 = a2 not equal a3
Later, we will look at the hexagonal close-packed structure, which is this structure with a basis (and is related to the fcc structure).
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Packing Factor
General
In atomic systems, by convention, the APF is determined by assuming that atoms are rigid spheres.
The atomic packing factor of a unit cell is relevant to the study of materials science, where it explains many properties of materials.
In crystallography, atomic packing factor (APF) is the fraction of volume in a crystal structure that is occupied by constituent particles.
Simple Cubic ( SC )
For a simple cubic packing, the number of atoms per unit cell is one. The side of the unit cell is of length 2r, where r is the radius of the atom.
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Face-Centered Cubic ( FCC )
For a face-centered cubic unit cell, the number of atoms is four. A line can be drawn from the top corner of a cube diagonally to the bottom corner on the same side of the cube, which is equal to 4r.
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Body-Centered Cubic ( BCC )
A line that is drawn from one corner of the cube through the center and to the other corner passes through 4r, where r is the radius of an atom.
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Wigner–Seitz cell
A Wigner-Seitz cell is constructed in two dimensions by picking any lattice point and linking it to its near neighbors. The perpendicular bisectors of the connecting lines are built in a second stage. The Wigner-Seitz cell is the space that is enclose. It creates a unit cell, which means it can build the entire lattice without any gaps or overlaps.
The Wigner-Seitz cell of a lattice point is defined as the volume that encloses all points in space which are closer to this particular lattice point than to any other. It can be constructed as depicted below.
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The primitive cell is a unit cell corresponding to a single lattice point, it is the smallest possible unit cell
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If there is a lattice point at the edge of a cell and thus shared with another cell, it is only counted half.
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A lattice vector is a vector joining any two lattice points Any lattice vector can be written as a linear combination of the unit cell vectors a, b, and c: t = U a + V b + W c.
Primitive vector in real space
Primitive vector in real space
Primitive vector in real space
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