Properties of engineering materials Chapter 3 materials Metals

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Properties of engineering materials Chapter 3 -

Properties of engineering materials Chapter 3 -

materials • • • Metals (ferrous and non ferrous) Ceramics Polymers Composites Advanced (biomaterials,

materials • • • Metals (ferrous and non ferrous) Ceramics Polymers Composites Advanced (biomaterials, semi conductors) Chapter 3 - 2

Properties • • • Optical Electrical Thermal Mechanical Magnetic Deteriorative Chapter 3 - 3

Properties • • • Optical Electrical Thermal Mechanical Magnetic Deteriorative Chapter 3 - 3

The Structure of Crystalline Solids - Crystalline : atoms/ crystals - Non crystalline or

The Structure of Crystalline Solids - Crystalline : atoms/ crystals - Non crystalline or amorphous - Solidification? Chapter 3 - 4

Packing of crystals: Non dense =random Dense = regular Chapter 3 - 5

Packing of crystals: Non dense =random Dense = regular Chapter 3 - 5

Unit cell and lattice parameters • Unit cell : small repeated entities • It

Unit cell and lattice parameters • Unit cell : small repeated entities • It is the basic structural unit or building block of the crystal structure • Its geometry is defined in terms of 6 lattice parameters: 3 edges length (a, b, c) 3 interaxial angles Chapter 3 - 6

Unit cell parameters Chapter 3 - 7

Unit cell parameters Chapter 3 - 7

Chapter 3 - 8

Chapter 3 - 8

Metallic crystals • 3 crystal structures: – Face-Centered Cubic FCC – Body-Centered Cubic BCC

Metallic crystals • 3 crystal structures: – Face-Centered Cubic FCC – Body-Centered Cubic BCC – Hexagonal close-packed HCP • Characterization of Crystal structure: – Number of atoms per unit cell – Coordination number (Number of nearest neighbor or touching atoms) – Atomic Packing Factor (APF) : what fraction of the cube is occupied by the atoms Chapter 3 - 9

The Body-Centered Cubic Crystal Structure • Coordination no. = ? • Number of atoms

The Body-Centered Cubic Crystal Structure • Coordination no. = ? • Number of atoms per unit cell = ? ? • what fraction of the cube is occupied by the atoms or Atomic packing factor Chapter 3 - 10

The Body-Centered Cubic Crystal Structure Chapter 3 - 11

The Body-Centered Cubic Crystal Structure Chapter 3 - 11

APF = 0. 68 solve ? Relation between r and a Chapter 3 -

APF = 0. 68 solve ? Relation between r and a Chapter 3 - 12

Solution Chapter 3 - 13

Solution Chapter 3 - 13

The Face-Centered Cubic Crystal Structure • Coordination no. = ? • Number of atoms

The Face-Centered Cubic Crystal Structure • Coordination no. = ? • Number of atoms per unit cell = ? ? • what fraction of the cube is occupied by the atoms or Atomic packing factor Chapter 3 - 14

The Face-Centered Cubic Crystal Structure Chapter 3 - 15

The Face-Centered Cubic Crystal Structure Chapter 3 - 15

APF = 0. 74 solve ? Relation between r and a Chapter 3 -

APF = 0. 74 solve ? Relation between r and a Chapter 3 - 16

Solution Chapter 3 - 17

Solution Chapter 3 - 17

The Hexagonal Close-Packed Crystal Structure Chapter 3 - 18

The Hexagonal Close-Packed Crystal Structure Chapter 3 - 18

HCP • The coordination number and APF for HCP crystal structure are same as

HCP • The coordination number and APF for HCP crystal structure are same as for FCC: 12 and 0. 74, respectively. • HCP metal includes: cadmium, magnesium, titanium, and zinc. Chapter 3 - 19

Examples Chapter 3 - 20

Examples Chapter 3 - 20

Polymorphism Chapter 3 - 21

Polymorphism Chapter 3 - 21

Crystallographic Points, Directions, and Planes Chapter 3 - 22

Crystallographic Points, Directions, and Planes Chapter 3 - 22

POINT COORDINATES Point position specified in terms of its coordinates as fractional multiples of

POINT COORDINATES Point position specified in terms of its coordinates as fractional multiples of the unit cell edge lengths ( i. e. , in terms of X a b and c) Z 1, 1, 1 0, 0, 0 Y Chapter 3 - 23

Solve point coordinates (2, 3, 5, 9) Chapter 3 - 24

Solve point coordinates (2, 3, 5, 9) Chapter 3 - 24

solution Chapter 3 - 25

solution Chapter 3 - 25

Crystallographic directions 1 - A vector of convenient length is positioned such that it

Crystallographic directions 1 - A vector of convenient length is positioned such that it passes through the origin of the coordinate system. Any vector may be translated throughout the crystal lattice without alteration, if parallelism is maintained. 2. The length of the vector projection on each of the three axes is determined; these are measured in terms of the unit cell dimensions a, b, and c. 3. These three numbers are multiplied or divided by a common factor to reduce them to the smallest integer. 4. The three indices, not separated by commas, are enclosed as [uvw]. The u, v, and w integers correspond to the reduced projections along x, y, and z axes, respectively. Chapter 3 - 26

Example Chapter 3 - 27

Example Chapter 3 - 27

Solution Chapter 3 - 28

Solution Chapter 3 - 28

Z [0 1 0] [1 0 1] Y X Chapter 3 - 29

Z [0 1 0] [1 0 1] Y X Chapter 3 - 29

Planes ( miller indices) 1 - If the plane passes through the selected origin,

Planes ( miller indices) 1 - If the plane passes through the selected origin, either another parallel plane must be constructed within the unit cell by an appropriate translation, or a new origin must be established at the corner of another unit cell. 2. At this point the crystallographic plane either intersects or parallels each of the three axes; the length of the planar intercept for each axis is determined in terms of the lattice parameters a, b, and c. 3. The reciprocals of these numbers are taken. A plane that parallels an axis may be considered to have an infinite intercept, and, therefore, a zero index. 4. If necessary, these three numbers are changed to the set of smallest integers by multiplication or division by a common factor. 5. Finally, the integer indices, not separated by commas, are enclosed within parentheses, thus: (hkl). Chapter 3 - 30

example Chapter 3 - 31

example Chapter 3 - 31

Solution Chapter 3 - 32

Solution Chapter 3 - 32

Example : solve Z Y X Chapter 3 - 33

Example : solve Z Y X Chapter 3 - 33

solve z c z a c b y x a x b y Chapter

solve z c z a c b y x a x b y Chapter 3 - 34

Crystallographic Planes z example 1. Intercepts 2. Reciprocals 3. Reduction a 1 1/1 1

Crystallographic Planes z example 1. Intercepts 2. Reciprocals 3. Reduction a 1 1/1 1 1 4. Miller Indices (110) example 1. Intercepts 2. Reciprocals 3. Reduction a 1/2 1/½ 2 2 4. Miller Indices (100) b 1 1/1 1 1 c 1/ 0 0 c b a x b 1/ 0 0 c 1/ 0 0 y z c a b x Chapter 3 - 35 y

Crystallographic Planes z example 1. Intercepts 2. Reciprocals 3. Reduction 4. Miller Indices a

Crystallographic Planes z example 1. Intercepts 2. Reciprocals 3. Reduction 4. Miller Indices a 1/2 1/½ 2 6 (634) b 1 1/1 1 3 c c 3/4 1/¾ 4/3 4 a x b y Chapter 3 - 36

Chapter 3 - 37

Chapter 3 - 37