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
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)