STRUCTURE OF SOLID MATERIALS CLASSIFICATION OF SOLIDS SOLIDS CLASSIFIED AS CRYSTALLINE, AMORPHOUS OR A COMBINATION OF THE TWO. CRYSTALLINE - BUILT UP OF CRYSTALS OF SIMILAR/VARYING SIZES CRYSTAL AS LARGE TO FORM A COMPLETE BODY- SINGLE CRYSTAL AMORPHOUS - MOLECULES AS BASIC STRUCTURAL UNIT; PRINCIPAL CHARACTERISTIC MORE OR LESS DISORDERED; NO REGULARITY OF ARRANGEMENT- LOWER IN DENSITY

CRYSTALLINE SOLIDS During solidification, atoms arrange themselves into ordered, repeating, 3 – dimensional pattern Such structures called Crystals. Or, Crystal is said to have formed whenever atoms arrange themselves in an orderly 3- D pattern Rows can be identified – in various directions- along which atoms are regularly spaced.

SCHEMATIC REPRESENTATION OF CRYSTAL LATTICE Eg: all metals, salts, many oxides & certain plastics Axes of this lattice are three lines at right angles to one another Lines that make up the lattice are parallel to the axes and equally spaced along them Atoms of a single cubic crystal occupy the lattice points- at intersections of the lines Atoms oscillate about fixed locations and are in dynamic equilibrium, rather than statically fixed.

Three dimensional network of imaginary lines connecting the atoms called SPACE LATTICE Smallest unit having the full symmetry of the crystal called- UNIT CELL LATTICE PARAMETERS- edges of unit cell and angles

14 possible different networks of lattice points All crystals based on these possible space lattices BRAVAIS LATTICES

Body Centered Cubic (BCC) Face Centered Cubic (FCC) Hexagonal Close Packed (HCP/CPH)

BODY CENTERED CUBIC Atoms at corners, one at geometric centre of volume, total-9 atoms Each corner atoms shared by 8 adjacent cubes No. of atoms/cell= 2

FACE CENTERED CUBIC Atoms at corners, one atom at centre of each face Each face atom shared by one adjoining cube No. of atoms/ cell = 4

HEXAGONAL CLOSE PACKED Basic unit cell is hexagonal prism Three atoms in the form of triangle midway between the two basal planes. When 6 equilateral triangles considered, 3 atoms on alternate triangles Total 17 atoms

COORINATION NUMBER No. of equally spaced nearest neighbours that each atom has in a given crystal structure

ATOMIC PACKING FACTOR Ratio of volume of atoms to volume of unit cell no. of atoms /unit cell X volume of atom Volume of unit cell Centre and corner atoms touch one another along cube diagonal. a and R are related through a = 4R/ √ 3 Thus,in BCC, a = 4R/√3 and APF = 0.68

For FCC, a = 2R√2 APF = 0.74 Similarly, For HCP, APF = R a a

CRYSTAL STRUCTURE- EXAMPLES STRUCTURE METALS BCCMolybdenum, Tantalum, Tungsten, Chromium, alpha iron FCCCopper, Aluminum, Silver, gold HCPCadmium, Cobalt, Titanium (α), Zinc

HCP

Knowledge of crystal structure For computing theoretical density ρ Where n = number of atoms associated with each unit cell A = Atomic weight Vc= volume of the unit cell N A = Avogadro’s number (6.023 X atoms/mol) Eg: Copper- FCC - atomic radius = 0.128nm (1.28A 0 ) Atomic weight= 63.5g/mol Here, n = 4, A= 63.5 ; for FCC, Vc = a 3 ; a = 2R √2, ρ = 8.89 g/cm 3 The value from tables is 8.94 g/cm3

CRYSTALLOGRAPHIC DIRECTIONS A LINE BETWEEN TWO POINTS, OR A VECTOR. STEPS IN DETERMINING THE 3 DIRECTIONAL INDICES: 1.A vector of convenient length is positioned such that it passes through the origin of the coordinate system. Any vector can be translated without alteration, if parallelism maintained. 2.The length of the vector projection – on each of 3 axes- is determined, measured in terms of unit cell dimensions 3.These 3 nos. are multiplied/divided by common factor to reduce to smallest integer values 4.3 indices- not separated by commas, are enclosed in square brackets– each corresponds to reduced projections along x, y and z axes. Both +ve and -ve coordinates can exist. –ve represented by a bar over index

X Y Z XYZ PROJ. a/2b0c a=b=c 1/210 reduction 120 Crys. Direction : [1 2 0]

1 [1 0 0] 2 [1 1 0] 3 [1 1 1] 3 1 2

INDICES: [1 1 1]

INDICES: [ ]

INDICES: [1 0 1] NOT as [ ]

INDICES: [1 1 1 ] NOT as [ ]

INDICES: [1 0 1 ] NOT as [ ] INDICES: [1 1 1 ] NOT as [ ] SIMILARLY, THE CRYSTALLOGRAPHIC PLANES ARE ALSO INDICATED. Eg: (2 0 1)