ENGINEERING REQUIREMENTS OF MATERIAL Fabrication Requirements Service Requirements

ENGINEERING REQUIREMENTS OF MATERIAL Fabrication Requirements Service Requirements Economics Requirements

Properties of Materials Performance Requirements Material’s Reliability Factors affecting the selection of engineering materials Safety Physical Attributes Environments condition Availability Disposability and Recyclability Economic Factors

Structures of Metals 3

Crystal Structures ØCrystalline ØNoncrystalline.

Materials Crystalline Material Noncrystalline Material Atom or molecules are arranged in a very regular and orderly fashioned in three dimension pattern. Atom or molecules are arranged in irregular manner. They are also known as Amorphous materials. Strength of the materials are comparatively high. Strength of the materials are lower than crystalline materials. Examples are metals & alloys. Examples are Glass, Wood, Plastics, Rubbers etc. Fig. Showing disordered arrangement of non crystalline solid. Fig. shows highly ordered arrangement of crystalline solid.

Quartz: crystalline Si. O 2 Long-range order Glass: amorphous Si. O 2 Only short-range order

Space lattices Ø Atom presents in any crystalline material are arranged in a regular three dimensional repeating pattern. this pattern is known as space lattice or crystal lattice.

Space lattices The point of interaction of lines are called lattice point.

Unit cell Ø A unit cell is the smallest geometrical figure the repetition of which in three dimensions will give the actual crystal structure. Ø A unit cell is a building block of a crystal. the crystal consist of unit cell of stacked tightly together. Ø Each identical in shape, size and orientation with each other.

Unit cell Ø A unit cell is completely defined by Ø six lattice parameters. Ø a, b, c , a, b, g As shown in figure. Ø The lattice parameter of a unit cell are its characteristics intercept ( a, b, c ) and interfacial angles (a, b, g ) Unit Cells and Unit Cell Vectors

Crystal System Ø There are seven crystal systems depending upon the lattice parameters of the unit cell. Ø Each crystal system can be defined in terms of intercepts a, b, c and angles , a, b, g between them. Ø Many of the seven crystal systems have variations of the basic unit cell. Ø A French crystallographer A. J. Bravais showed that 14 standard unit cells could describe all possible lattice networks.

Lattice parameter relationship & Figure showing Unit cell Geometries for the seven crystal systems.

Bravais Lattices

Crystal structure for metallic elements Ø Most metals crystallize in relatively simple crystal structures as under. § Simple cubic Structure Example –Polonium § Body centred cubic structure (BCC) Examples –Cr, V, Mo, Mn etc. § Face centred cubic structure (FCC) Examples –Al, Cu, Ni, Au, Ag, Pb etc. Hexagonal close-packed (HCP or CPH) structure. Examples –Mg, Zn, Co etc. . §

1. Simple cubic structure (SC) Ø One atom is located at each of the corners of the cube. Ø Therefore , it contains eight atoms at the corners which are shared by the adjoining eight cubes. Ø Hence the share of each cube=1/8 th of each corner atom Ø Total no. of atom/unit cell =1/8 x 8 corners =1 atom

Atomic Radius Ø Considering atoms to be spherical in shape and in contact in a crystal. Ø Atomic radius can be defined as half the distance between the centers of two neighboring atoms. Atomic Radius of a Simple Cubic Structure: Ø In fig. One atom is at each of the corner of the cube. Ø If ‘a’ is lattice parameter i. e. length of the cube edge and ‘r’ is the atomic radius. Then, Ø a=2 r Ø r=a 2

Atomic Packing Factor: Ø The packing of atoms in a unit cell of the crystal structure of a material is known as atomic packing. APF = Volume of atoms in unit cell Volume of unit cell

Atomic Packing Factor of simple cubic structure: APF = (No. of atoms/unit cell) x (Volume of one atom) Volume of unit cell a R=0. 5 a close-packed directions contains 8 x 1/8 = 1 atom/unit cell • APF for a simple cubic structure =p/6 = 0. 52 20

2. Body Centred Cubic structure (BCC) Ø One atom is located at each of the corners of the cube and one atom at the centre of body. Ø Therefore , it contains nine atoms. 2 atoms/unit cell: 1 center + 8 corners x 1/8

Atomic Radius of a BCC Structure: Ø If ‘a’ is lattice parameter i. e. length of the cube edge and ‘r’ is the atomic radius. Ø From the figure, 2 2 2 Ø AE = AB +BE 2 2 Ø =a+a 2 Ø = 2 a 2 2 2 Ø AF = AE +EF Ø = 2 a 2+ a 2 Ø = 3 a 2 Ø AF = a 3 ØAnd also, ØAF =R+2 R+R =4 R Ø 4 R = a 3 ØR = a 3 4

Atomic Packing Factor of BCC structure: - Adapted from Fig. 3. 2, Callister 6 e. • APF for a body-centered cubic structure = p 3/8 = 0. 68

3. Face Centred Cubic structure (FCC) Ø One atom is located at each of the corners of the cube and one atom at the centre of each of the six faces of the cube. Ø The face centred atom is located at the intersection of the diagonal of the face. 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8

Atomic Radius of a FCC Structure: Ø If ‘a’ is lattice parameter i. e. length of the cube edge and ‘r’ is the atomic radius. Ø Then considering a triangle, 2 2 2 Ø (4 R) = a +a 2 2 Ø 16 R = 2 a Ø R = 2 a/4

Atomic Packing Factor of FCC structure: - Adapted from Fig. 3. 1(a), Callister 6 e. • APF for a body-centered cubic structure = p/(3 2) = 0. 74

3. Hexagonal close packed structure (HCP) Ø 1. 2. 3. The HCP structure consist of: One atom at each corner of the hexagon. One atom each at the centers of the two hexagonal faces (basal planes) Three atoms in the form of a triangle midway between the two basal planes.

3. Hexagonal close packed structure (HCP) Ø § § § The unit cell of the HCP contains: 12 atoms at the corners x 1/6 =2 atoms. 2 face centred atoms x ½ = 1 atom. 3 middle layer atoms = 3 atoms. Total atom in H. C. P. = 6 atoms.