Dr. D V N J Jagannadha Rao Associate Professor Gayatri Vidya Parishad College of Engineering (Autonomous) Materials
Metals Ceramics Polymers Oxides, (Plastics) Nitrides, Carbides, Glasses, Thermoplastic Thermoset Rubber Ferrous Cast Nonferrous (Elastomer) Graphite, Acrylics, Epoxies, iron, Steel, Aluminum, Poly- Diamond, PVC, Phenolics, Stainless steel, Titanium, etc. urethanes Copper, etc. etc.
Composites-reinforced plastics, metal or ceramic matrix, laminates, others. Semiconductors-Silicon, Germanium, Gallium phosphor, other. Biomaterials-biocompatible materials, Co-Cr-Mo, Co-Ni-Mo metal alloys (for hip) (+) Cations in a ‘sea’ of (-) electrons.
The movement of these electrons makes metals good conductors of heat and electricity. Metals are Malleable. Metals are Ductile Metals have High Melting points and Boiling Points.
BCC ◦ α-iron, chromium, tungsten, tantalum, molybdenum, niobium FCC ◦ γ-iron, aluminium, copper, silver, gold HCP ◦ Zinc, beryllium, cadmium, magnesium, titanium, zirconium The fractional amount of volume or space occupied by atoms in an unit cell is called as Atomic Packing Factor (or) Atomic density packing APF = Volume of atoms in unit cell ------Volume of the unit cell • Rare due to low packing density (only Po has this structure) • Close-packed directions are cube edges.
• Coordination # = 6 (# nearest neighbors)
Click once on image to start animation (Courtesy P.M. Anderson)
11 Volume of atoms in unit cell* APF = Volume of unit cell
*assume hard spheres
• APF for a simple cubic structure = 0.52
volume atoms atom 4 a p 3 unit cell 1 (0.5a) 3 R=0.5a APF = a 3 volume close-packed directions unit cell contains 8 x 1/8 = 1 atom/unit cell
12 • Atoms touch each other along face diagonals. --Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing.
ex: Al, Cu, Au, Pb, Ni, Pt, Ag • Coordination # = 12
Adapted from Fig. 3.1, Callister & Click once on image to start animation Rethwisch 8e. (Courtesy P.M. Anderson) 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8
13 • APF for a face-centered cubic structure = 0.74 maximum achievable APF
Close-packed directions: length = 4R = 2 a 2 a Unit cell contains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell a Adapted from Fig. 3.1(a), Callister & atoms 4 volume Rethwisch 8e. p 3 unit cell 4 ( 2 a/4 ) atom 3 APF = volume a 3
unit cell 14 • Atoms touch each other along cube diagonals. --Note: All atoms are identical; the center atom is shaded differently only for ease of viewing. ex: Cr, W, Fe (), Tantalum, Molybdenum • Coordination # = 8
Adapted from Fig. 3.2, Click once on image to start animation Callister & Rethwisch 8e. (Courtesy P.M. Anderson) 2 atoms/unit cell: 1 center + 8 corners x 1/8
15 • APF for a body-centered cubic structure = 0.68
3 a
a
2 a
Close-packed directions: R length = 4R = 3 a a
atoms 4 volume p 3 unit cell 2 ( 3 a/4 ) 3 atom APF = volume a 3 unit cell 16 • ABAB... Stacking Sequence
• 3D Projection • 2D Projection
A sites Top layer c B sites Middle layer
A sites Bottom layer
a Adapted from Fig. 3.3(a), Callister & Rethwisch 8e.
• Coordination # = 12 6 atoms/unit cell
• APF = 0.74 ex: Cd, Mg, Ti, Zn
• c/a = 1.633
17 COMPARISON OF CRYSTAL STRUCTURES
Crystal structure coordination # packing factor close packed directions
Body Centered Cubic 8 0.68 body diagonal
Face Centered Cubic 12 0.74 face diagonal
Hexagonal Close Pack 12 0.74 hexagonal side Crystallization of Metals
Crystallization or solidification is the process of transition from liquid to solid state. When the molten metal is cooled ,the whole mass does not solidify instantaneously. It compromises two steps : Nucleation - Formation of tiny stable solid particles from liquid. Growth - The growth of nuclei into crystal and the formation of the grain structure . DETERMINATION OF GRAIN SIZE To determine grain size have these methods 1. COMPARISION METHOD 2. INTERCEPT METHOD OR HEYN METHOD 3. Jeffries Method COMPARISON METHOD : The ASTM has devised standard comparison charts(ASTM E112-63) with different grain sizes. Each is assigned grain size number(n) ranging 1 to 10 based on the following relation N = 2n-1 Where N = avg number of grains per square inch at a magnification of 100x .
u1 Slide 24 u1 user, 6/10/2020 Line intercept method : This is one of the most commonly used methods. Number of grains intersecting a given length of a random line is counted. Grain size D = Length of the line/no of grains intersected by it gives grain diameter. Crystal Imperfection or Defects Crystals are rarely perfect. They contain large number of defects (imperfections) which Influence the behavior of metals. Because of these defects, the actual strength of metal is much less than the theoretical strength. Crystal defects are classified as : 1. Point Defects 2. Line defects 3. Surface defects 4. Volume defects Point Defects : Are highly localized disruption of the lattice involving one or just few atoms. These are regarded as zero dimensional defects. Some of the important defects are VACANCY DEFECT INTERSTITIAL DEFECT SUBSTITUTIONAL DEFECT . Vacancy Defect : An atom missing from regular lattice position. • These defects are caused due to imperfect packing during original crystallization or may Be Arise from thermal vibration of atoms at elevated temperature. In vacancies you have other types of effects such as Frenkel defect and Schottky defect. Frenkel defect: If a ion displaced from the normal lattice point to an interstitial site ,then the defect is called as Frenkel defect. Schottky defect : The removal of positive ion (to create vacancy) must be counter balanced by the removal of negative ion in order to maintain neutrality. The pair of vacancies by removal of positive ion and negative ion is called Schottky defect.
Frenkel defect Schottky defect Interstitial Defects : Is formed when an extra atom is inserted into the lattice at a normally occupied site(intersticies).
Substitutional defects : Occurs when an atom in a lattice is replaced (substituted) by other different atom which may be impurity or deliberately alloying element.
Interstitial Defect Substitutional defects 2.Line defects : The defects, which take place due to dislocation or distortion of atoms along a line, in some direction are called as ‘line defects’. Line defects are also called dislocations. In the geometric sense, they may be called as ‘one dimensional defects’. Dislocations are produced during crystallization, but more commonly originate during deformation. Most significant defects that are going to reduce strength of metal. The two types of dislocations are, 1. Edge dislocation 2. Screw dislocation EDGE DISLOCATION SCREW DISLOCATION
In this dislocation, the atoms are displaced in two separate planes parallel to each other. It forms a spiral ramp around the dislocation. The Burgers Vector is parallel to the screw dislocation line. Speed of movement of a screw dislocation is lesser compared to edge dislocation. Normally, the real dislocations in the crystals are the mixtures of edge and screw dislocation. ◦ Indices are written in square brackets without commas (ex: [hkl]) ◦ Negative values are written with a bar over the integer. Ex: if h<0 then the direction is [hkl] Crystallographic Planes ◦ Identify the coordinate intercepts of the plane the coordinates at which the plane intercepts the x, y and z axes. If a plane is parallel to an axis, its intercept is taken as . If a plane passes through the origin, choose an equivalent plane, or move the origin ◦ Take the reciprocal of the intercepts ◦ Clear fractions due to the reciprocal, but do not reduce to lowest integer values. ◦ Planes are written in parentheses, with bars over the negative indices. Ex: (hkl) or if h<0 then it becomes ex: plane A is parallel to x, and intercepts y and z at 1, and therefore is the (011). Plane B passes through the origin, so the origin is moved to O’, thereby making the plane the (112)
Crystallographic Planes ◦ Identify the coordinate intercepts of the plane the coordinates at which the plane intercepts the x, y and z axes. If a plane is parallel to an axis, its intercept is taken as . If a plane passes through the origin, choose an equivalent plane, or move the origin ◦ Take the reciprocal of the intercepts
Elastic modulus Poisson’s ratio Yield strength Ultimate tensile strength Compressive strength Hardness Toughness Creep resistance Corrosion resistance Fatigue strength