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