STRUCTURE OF SOLID MATERIALSCLASSIFICATION 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 CELLLATTICE 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 NUMBERNo. of equally spaced nearest neighbours that each atom has in a

given crystal structure

ATOMIC PACKING FACTORRatio 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 = 0.74

4R a

a

CRYSTAL STRUCTURE- EXAMPLES

STRUCTURE METALS

BCC Molybdenum, Tantalum, Tungsten, Chromium, alpha iron

FCC Copper, Aluminum, Silver, gold

HCP Cadmium, Cobalt, Titanium (α), Zinc

HCPHCP

Knowledge of crystal structure

For computing theoretical density ρ

AcNV

nA

Where n = number of atoms associated with each unit cellA = Atomic weightVc= volume of the unit cellNA= Avogadro’s number (6.023 X 1023 atoms/mol)

Eg: Copper- FCC - atomic radius = 0.128nm (1.28A0) Atomic weight= 63.5g/mol

Here, n = 4, A= 63.5 ; for FCC, Vc = a3 ; a = 2R √2,

ρ = 8.89 g/cm3

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

X Y ZPROJ. a/2 b 0ca=b=c 1/2 1 0reduction 1 2 0

Crys. Direction: [1 2 0]

• 1 [1 0 0]

• 2 [1 1 0]

• 3 [1 1 1]

3

12

INDICES: [1 1 1]

INDICES: [ 2 0 1 ]

INDICES: [1 0 1]

NOT as [ 1 0 -1]

INDICES: [1 1 1 ]NOT as [ 1 -1 1]

INDICES: [1 0 1 ] NOT as [ 1 0 -1]

INDICES: [1 1 1 ] NOT as [ 1 -1 1]

SIMILARLY, THE CRYSTALLOGRAPHIC PLANES ARE ALSO INDICATED .

Eg: (2 0 1)