# crystallography

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Published on January 12, 2011

Author: sudharani.kuram

Source: authorstream.com

Slide 1: 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. Slide 2: A space lattice, two possible unit cells, and the environment of a point Slide 3: 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 Slide 4: LATTICE + BASIS = CRYSTAL STRUCTURE Slide 5: 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. Slide 6: UNIT CELL Slide 7: The intercepts a, b, c and interfacial angles α , β and γ constitute the lattice parameters of the unit cell. Slide 8: The seven basic crystal systems are Triclinic Monoclinic 3. Othorhombic 4. Tetragonal 5. Hexagonal 6. Trigonal 7. Cubic Slide 9: SIMPLE CUBIC CRYSTAL a = b = c , α = β = γ = 90 Slide 10: SIMPLE CUBIC CRYSTAL Slide 11: BODY CENTERED CUBIC CRYSTAL Slide 12: Calculation of packing fraction for BCC Slide 13: A FACE CENTERED CUBIC CRYSTAL Slide 15: THE 14 BRAVIS LATTICES Slide 18: TRICLINIC CRYSTAL a ≠ b ≠ c Slide 19: MONOCLINIC CRYSTAL a ≠ b ≠ c Simple cubic Base centered cubic Slide 20: ORTHORHOMBIC CRYSTAL α = β = γ = 90 Simple cubic Base centered Body centered Face centered Slide 21: TETRAGONAL CRYSTAL α = β = γ = 90 a = b ≠ c Simple cubic Body centered Slide 22: TRIGONAL CRYSTAL α = β = γ ≠ 90 a = b = c Simple cubic Slide 23: HEXAGONAL CRYSTAL α = β = 90 , γ = 120 a = b ≠ c Simple cubic Slide 24: CUBIC CRYSTAL α = β = 90 , γ = 120 a = b ≠ c Simple cubic Body centered Face centered Slide 25: DIRECTIONS IN CRYSTALS Slide 26: 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 Slide 27: 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 Slide 33: 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. Slide 34: When the intercept of a plane on any axis is negative, a bar is put on the corresponding Miller index. Slide 35: All equally spaced parallel planes have the same miller index number (h, k, l) Slide 36: The distance between the centres of two nearest neighbouring atoms is called nearest neighbour distance. Slide 37: Coordination number is defined as the number of equidistant nearest neighbours that an atom has in a given structure. Slide 38: 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 Slide 39: HEXAGONAL CLOSED PACKED STRUCTURE Slide 40: STRUCTURE OF DIAMOND Slide 41: STRUCTURE OF ZINC SULPHIDE Slide 42: STRUCTURE OF SODIUM CHLORIDE Slide 43: STRUCTURE OF SODIUM CHLORIDE Slide 44: STRUCTURE OF CESIUM CHLORIDE Slide 45: STRUCTURE OF CESIUM CHLORIDE Slide 46: STRUCTURE OF CESIUM CHLORIDE

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October 17, 2017

October 17, 2017

October 17, 2017

October 17, 2017

October 17, 2017

October 17, 2017

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