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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 pointSlide 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 structureSlide 4:
LATTICE + BASIS = CRYSTAL STRUCTURESlide 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 CELLSlide 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. CubicSlide 9:
SIMPLE CUBIC CRYSTAL a = b = c , α = β = γ = 90Slide 10:
SIMPLE CUBIC CRYSTALSlide 11:
BODY CENTERED CUBIC CRYSTALSlide 12:
Calculation of packing fraction for BCCSlide 13:
A FACE CENTERED CUBIC CRYSTALSlide 15:
THE 14 BRAVIS LATTICESSlide 18:
TRICLINIC CRYSTAL a ≠ b ≠ cSlide 19:
MONOCLINIC CRYSTAL a ≠ b ≠ c Simple cubic Base centered cubicSlide 20:
ORTHORHOMBIC CRYSTAL α = β = γ = 90 Simple cubic Base centered Body centered Face centeredSlide 21:
TETRAGONAL CRYSTAL α = β = γ = 90 a = b ≠ c Simple cubic Body centeredSlide 22:
TRIGONAL CRYSTAL α = β = γ ≠ 90 a = b = c Simple cubicSlide 23:
HEXAGONAL CRYSTAL α = β = 90 , γ = 120 a = b ≠ c Simple cubicSlide 24:
CUBIC CRYSTAL α = β = 90 , γ = 120 a = b ≠ c Simple cubic Body centered Face centeredSlide 25:
DIRECTIONS IN CRYSTALSSlide 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 axesSlide 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 planeSlide 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/VSlide 39:
HEXAGONAL CLOSED PACKED STRUCTURESlide 40:
STRUCTURE OF DIAMONDSlide 41:
STRUCTURE OF ZINC SULPHIDESlide 42:
STRUCTURE OF SODIUM CHLORIDESlide 43:
STRUCTURE OF SODIUM CHLORIDESlide 44:
STRUCTURE OF CESIUM CHLORIDESlide 45:
STRUCTURE OF CESIUM CHLORIDESlide 46:
STRUCTURE OF CESIUM CHLORIDE