Properties of engineering materials

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

Properties Optical Electrical Thermal Mechanical Magnetic Deteriorative

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

Packing of crystals: Non dense =random Dense = regular

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

Unit cell parameters

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

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

The Body-Centered Cubic Crystal Structure

APF = 0.68 solve ? Relation between r and a

Solution

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

The Face-Centered Cubic Crystal Structure

APF = 0.74 solve ? Relation between r and a

Solution

The Hexagonal Close-Packed Crystal Structure

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.

Examples

Polymorphism

THEORETICAL DENSITY

Crystallographic Points, Directions, and Planes

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

Solve point coordinates (2,3,5,9)

solution

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.

Example

Solution

Z Y X [0 1 0] [1 0 1]

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).

example

Solution

Example : solve Z Y X

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

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

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

FCC Stacking Sequence repeated every third plane

(HCP) repeated every second plane

Polycrystals • Most engineering materials are polycrystals. 1 mm

The various stages in solidification of polycrystalline materials. Polycrystalline crystalline solids composed of many crystals or grains. Various stages in solidification: Small crystallite nuclei Growth of the crystallites; of obstruction of some grains that are adjacent to one another is also shown. c. Upon completion of solidification, grains that are adjacent to one another is also shown. d. Grain structure as it would appear under the microscope.

Anisotropy Physical properties (e.g., Elastic modulus, index of refraction) of single crystals of some substances depend on crystallographic direction in which measurements are taken (i.e., anisotropy). It results from variation of atomic or ionic spacing with crystallographic direction. Isotropic materials: Substances in which measured properties are independent of the direction of measurement.

X – ray diffraction

X ray diffraction

BCC crystal structure, h+ k+ l must be even Case study: explain why? Group of four . Dead line: 30/12/ 2015 BCC crystal structure, h+ k+ l must be even FCC, h, k, and l must all be either odd or even

Linear and Planar Densities Atomic linear density: LD = number of atoms centered on direction vector / length of direction vector Planar density: Fraction of total crystallographic plane area that is occupied by atoms (represented as circles). PD = number of atoms centered on a plane / area of plane Linear and planar densities are important for deformation

Indices?

notes for cubic crystals Planes having the same indices, irrespective of the order and sign are equivalent. For example, both (123) and (312) belong to the family ( 123)