SPACE LATTICE A space lattice is defined as an infinite array of points in three dimensions in which every point has surroundings identical to that of every other point in the array.

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A space lattice, two possible unit cells, and the environment of a point

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UNIT CELL The unit cell is the smallest unit which, when repeated in space indefinitely, generates the space lattice. BASIS A group of atoms or molecules identical in composition is called the basis. Lattice + basis crystal structure

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LATTICE + BASIS = CRYSTAL STRUCTURE

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UNIT CELL The unit cell is defined as the smallest geometric figure, the translational repetition of which in all over the three dimensions gives the actual crystal structure.

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UNIT CELL

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The intercepts a, b, c and interfacial angles α , β and γ constitute the lattice parameters of the unit cell.

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The seven basic crystal systems are Triclinic Monoclinic 3. Othorhombic 4. Tetragonal 5. Hexagonal 6. Trigonal 7. Cubic

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SIMPLE CUBIC CRYSTAL a = b = c , α = β = γ = 90

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SIMPLE CUBIC CRYSTAL

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BODY CENTERED CUBIC CRYSTAL

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Calculation of packing fraction for BCC

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A FACE CENTERED CUBIC CRYSTAL

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THE 14 BRAVIS LATTICES

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TRICLINIC CRYSTAL a ≠ b ≠ c

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MONOCLINIC CRYSTAL a ≠ b ≠ c Simple cubic Base centered cubic

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ORTHORHOMBIC CRYSTAL α = β = γ = 90 Simple cubic Base centered Body centered Face centered

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TETRAGONAL CRYSTAL α = β = γ = 90 a = b ≠ c Simple cubic Body centered

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TRIGONAL CRYSTAL α = β = γ ≠ 90 a = b = c Simple cubic

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HEXAGONAL CRYSTAL α = β = 90 , γ = 120 a = b ≠ c Simple cubic

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CUBIC CRYSTAL α = β = 90 , γ = 120 a = b ≠ c Simple cubic Body centered Face centered

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DIRECTIONS IN CRYSTALS

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MILLER INDICES Miller indices are symbolic vector representation of an atomic plane in a crystal lattice and are defined as the reciprocals of the fractional intercepts which the plane makes with the crystallographic axes

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PROCEDURE FOR FINDING MILLER INDICES Find the intercepts of the desired plane on the three coordinate axes. Let these be (pa, qb , rc ). Express the intercepts as multiples of the unit cell dimensions or lattice parameters i.e.,(p, q, r). Take the ratio of reciprocals of these numbers i.e., 1/p, 1/q, 1/r. Convert these reciprocals into whole numbers by multiplying each with their L. C. M to get the smallest whole number. This gives the Miller indices (h k l) of the plane

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When a plane is parallel to any axis, the intercept of the plane on that axis is infinity. Hence its miller index for that axis is zero.

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When the intercept of a plane on any axis is negative, a bar is put on the corresponding Miller index.

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All equally spaced parallel planes have the same miller index number (h, k, l)

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The distance between the centres of two nearest neighbouring atoms is called nearest neighbour distance.

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Coordination number is defined as the number of equidistant nearest neighbours that an atom has in a given structure.

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Atomic packing factor is the ratio of volume occupied by the atoms in an unit cell (v) to the total volume of the unit cell (V). Packing factor = v/V

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HEXAGONAL CLOSED PACKED STRUCTURE

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STRUCTURE OF DIAMOND

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STRUCTURE OF ZINC SULPHIDE

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STRUCTURE OF SODIUM CHLORIDE

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STRUCTURE OF SODIUM CHLORIDE

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STRUCTURE OF CESIUM CHLORIDE

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STRUCTURE OF CESIUM CHLORIDE

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STRUCTURE OF CESIUM CHLORIDE

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