UES O12 – ENGINEERING MATERIALS PDF

UES O12 – ENGINEERING MATERIALS Dr. Bhupendrakumar Chudasama Professor School of Physics and Materials Science Thapar Institute of Engineering & Technology Patiala G-253 E-mail: [email protected] (M) +91-9781966136 ...

UES O12 – ENGINEERING MATERIALS Dr. Bhupendrakumar Chudasama Professor School of Physics and Materials Science Thapar Institute of Engineering & Technology Patiala G-253 E-mail: [email protected] (M) +91-9781966136 SYLLABUS  EVALUATON SCHEME Event Marks Sessional – I (Quiz) 10 MST 30 Sessional – II (Tutorials) 05 Sessional – III (Lab: Performance + NB + 10+10+5 = 25 lab quiz) EST 30 Total 100 QUESTIONS ?? Engineering Materials No Engineering without materials School of Physics & Materials Science, THAPAR UNIVERSITY  Classification of Engineering Materials Metals & Alloys Applications: Aluminum, Copper, Gold, silver, Brass, Structure: Concrete, bronze, steel, Furnace, Bridge Magnetic alloys Machines: Engine, Motors, Generators Organic polymers Ceramics & Plastics: PVC, Devices: Transistor, Glasses Polyethylene Lasers, Magnets, Cells Silica, Sodalime glass, Fibres: Nylon, Concrete, cement, Terylene Alumina, Silicon Natural & synthetic carbide rubbers Glass fibre-reinforced plastic School of Physics & Materials Science, THAPAR UNIVERSITY 2  Engineering Materials Performance Materials Engineering Designing the structure to achieve specific properties of materials. Structure Processing Processing Properties Structure Materials Science Properties Investigating the relationship between structure and properties of materials. Performance 3 School of Physics & Materials Science, THAPAR UNIVERSITY  Properties of Materials One of the goal of materials engineering is to select materials with suitable properties for a given application. Mechanical properties A. Elasticity and stiffness (recoverable stress vs. strain) B. Plasticity (non-recoverable stress vs. strain) C. Strength D. Brittleness or Toughness E. Fatigue Electrical properties A. Electrical conductivity and resistivity 4 School of Physics & Materials Science, THAPAR UNIVERSITY  Properties of Materials Dielectric properties A. Polarizability Optical properties B. Capacitance A. Refractive index C. Ferroelectric properties B. Absorption, reflection, transmission D. Piezoelectric properties C. Birefringence (double refraction) E. Pyroelectric properties Magnetic properties Chemical Properties Corrosion A. Paramagnetism B. Diamagnetism C. Ferromagnetism Biological properties A. Toxicity B. bio-compatibility 5 School of Physics & Materials Science, THAPAR UNIVERSITY  Structure of Materials Structure: Internal structure of the material Can be studied at various levels of observations - magnification & resolution are critical Level Notes Macrostructure un-aided eye (resolution 10-4 m) Microstructure optical microscope (1500 X, resolution ~ 10-7 m) Substructure Microscope with much higher magnification & resolution Electron microscope: 105 X Crystal structure Details of atomic arrangement within a crystal X-ray diffraction, Electron diffraction Electronic structure Electrons in outer orbitals of individual atoms Spectroscopic techniques Nuclear structure Using nuclear spectroscopic techniques (NMR) 6 School of Physics & Materials Science, THAPAR UNIVERSITY  Multiple Length Scales Critical in Engineering In Askeland and Phule’s book, from J. Allison and W. Donlon (Ford Motor Company) 7 School of Physics & Materials Science, THAPAR UNIVERSITY  Processing, Structure & Properties Properties depend on structure Annealing T (F) Processing for structural changes Tensile Strength (MPa) Can you correlate structure and Ductility (%EL) strength and ductility? Strength versus Structure of Brass and changes in microstructure Grain size (mm) Annealing T (C) 8 School of Physics & Materials Science, THAPAR UNIVERSITY  Structure-Property interdependence Structure can change property Ex: hardness vs structure of steel 9 School of Physics & Materials Science, THAPAR UNIVERSITY  Optical properties Light transmission of Alumina (Al2O3 / sapphire) single crystal, polycrystals (low and high porosity) Which one is single crystal? Why? These reflect the effects of processing. 10 School of Physics & Materials Science, THAPAR UNIVERSITY Structure – Property Correlation School of Physics & Materials Science, THAPAR UNIVERSITY  Crystal Structure School of Physics & Materials Science, THAPAR UNIVERSITY 1  Crystal structure It is about specific arrangement of atoms. More precisely, it is about how atoms are arranged in a solid for given process conditions such as pressure and temperature. Importance Properties of materials are directly related to their crystal structure - Magnesium and beryllium, having one crystal structure, are much more brittle than gold and silver that have another crystal structure. - A knowledge of the crystal structure for iron helps us understand transformations that occur when steels are heat treated to improve their mechanical properties. - Specific arrangement of the silicon and oxygen atoms in quartz give rise to the property of peizoelectricity. understand ing of relationsh ips between  designing of materials     crystal structure, compositio n & properties  with desired properties  School of Physics & Materials Science, THAPAR UNIVERSITY Structure of materials Do all solids have same (or similar) crystal structure? No. Evident from variation in physical properties of solids. For example: Glass does not show a sharp melting point (it softens first, and gradually becomes a viscous fluid, while metal like copper shows a sharp transition temperature. Materials are of two types: Crystalline & Non-crystalline Non-crystalline solid: Atom are not situated in an orderly, repeating pattern. i.e. glass , rubber, plastic etc. Crystalline solid: Atoms are spatially arranged in an orderly, repeating pattern extending in all three dimension. i.e. Copper, NaCl School of Physics & Materials Science, THAPAR UNIVERSITY  Structure of materials From Materials Science and Engineering: An Introduction (8th Edition), By W. D. Callister, Jr. & D. G. Rethwisch School of Physics & Materials Science, THAPAR UNIVERSITY  Space lattice Space Lattice – A blue print An infinite array of points where every point has surrounding identical to that of every other point. 1D Lattice If all points must have identical surrounding, there should be one more to the left and one to the right This would lead to an infinite number of points   Starting with a point the lattice translation vector can generate the lattice School of Physics & Materials Science, THAPAR UNIVERSITY 5 2D lattice                                                                                      b               a      Two distances: a, b b                  a There are three lattice parameters which describe this lattice One angle:  Two basis vectors generate the lattice = 90 in the current example School of Physics & Materials Science, THAPAR UNIVERSITY 6  2D lattice Not fundamental translational vectors, because all points of lattice can not be generated by these two vectors. School of Physics & Materials Science, THAPAR UNIVERSITY 7  Space lattice & crystal structure Space lattice is a blue print of points arranged in space. But, real crystals are about atoms! We assign one or group of atoms per lattice point to form the structure. The frame of atoms is called BASIS. A space lattice is combined with a basis to generate a crystal structure. Space lattice + basis  crystal structure Example Crystal structure of Cu is generated as: FCC space lattice + 1 Cu atom per lattice point FCC crystal of Cu School of Physics & Materials Science, THAPAR UNIVERSITY 8  Crystalline materials: Unit cell Building block: A cube Unit Cell The basic structural unit of a crystal structure. Its geometry and atomic positions define the crystal structure. School of Physics & Materials Science, THAPAR UNIVERSITY 9  Unit cells & Unit vectors School of Physics & Materials Science, THAPAR UNIVERSITY 10 Unit cells – 7 crystal structures School of Physics & Materials Science, THAPAR UNIVERSITY 11 Unit cells – 7 crystal structures 12 School of Physics & Materials Science, THAPAR UNIVERSITY  Unit cell types Primmitive 13 School of Physics & Materials Science, THAPAR UNIVERSITY  Unit cell types 14 School of Physics & Materials Science, THAPAR UNIVERSITY  Unit cell types Face - centered 15 School of Physics & Materials Science, THAPAR UNIVERSITY  Unit cell types 16 School of Physics & Materials Science, THAPAR UNIVERSITY 7 crystal systems, 14 Bravais Lattices 1. Simple 2. Body centered 3. Face centered 1. Simple 1. Simple 2. Body centered 17 School of Physics & Materials Science, THAPAR UNIVERSITY 7 crystal systems, 14 Bravais Lattices 1. Simple 1. Simple 2. End-centered 3. Body centered 4. Face centered 1. Simple 2. End centered 1. Simple 18 School of Physics & Materials Science, THAPAR UNIVERSITY End Centered Cubic Structure School of Physics & Materials Science, THAPAR UNIVERSITY 19 No. of atoms & Coordination no. 20 School of Physics & Materials Science, THAPAR UNIVERSITY Atomic packing factor (APF) 21 School of Physics & Materials Science, THAPAR UNIVERSITY Cubic crystal system -FCC Face-centered cubic (FCC) structure Al, Ag, Cu, Au, Pb 22 School of Physics & Materials Science, THAPAR UNIVERSITY FCC structure 23 School of Physics & Materials Science, THAPAR UNIVERSITY APF in FCC structure 24 School of Physics & Materials Science, THAPAR UNIVERSITY Coordination no. FCC structure 25 School of Physics & Materials Science, THAPAR UNIVERSITY Cubic crystal system -BCC Body-centered cubic (FCC) Cr, Fe, Mo, Ta 26 School of Physics & Materials Science, THAPAR UNIVERSITY No of atoms in BCC structure 27 School of Physics & Materials Science, THAPAR UNIVERSITY APF in BCC structure 28 School of Physics & Materials Science, THAPAR UNIVERSITY Coordination number in BCC crystals 29 School of Physics & Materials Science, THAPAR UNIVERSITY Comparison of BCC & FCC BCC FCC 30 School of Physics & Materials Science, THAPAR UNIVERSITY 1  2 Showing 3 unit cells and the rhombic prism UC  HEXAGONAL CLOSED PACKED STRUCTURE It consists of three layers of atoms. The bottom layer has six corner atoms and one face centered atom. The middle layer has three full atoms. The upper layer has six corner atoms and one face centered atom. Each and every corner atom contributes 1/6 of its part to one unit cell. The number of total atoms contributed by the corner atoms of both top and bottom layers is 1/6  12 = 2. School of Physics & Materials Science, THAPAR UNIVERSITY 3 HEXAGONAL CLOSED PACKED STRUCTURE The face centred atom contributes 1/2 of its part to one unit cell. Since there are 2 face centred atoms, one in the top and the other in the bottom layers, the number of atoms contributed by face centred atoms is 1/2 2 = 1. Besides these atoms, there are 3 full atoms in the middle layer. Total number of atoms present in an HCP unit cell is 2+1+3 = 6. School of Physics & Materials Science, THAPAR UNIVERSITY 4 HEXAGONAL CLOSED PACKED STRUCTURE ATOMIC RADIUS (R) Consider any two corner atoms. Each and every corner atom touches each other. Therefore a = 2r. i.e., The atomic radius, r = a/2 a a School of Physics & Materials Science, THAPAR UNIVERSITY 5 HEXAGONAL CLOSED PACKED STRUCTURE CO-ORDINATION NUMBER (CN) The face centered atom touches 6 corner atoms in its plane. The middle layer has 3 atoms. There are three more atoms, which are in the middle layer of the unit cell. Therefore the total number of nearest neighbours is 6+3+3=12. School of Physics & Materials Science, THAPAR UNIVERSITY 6 HEXAGONAL CLOSED PACKED STRUCTURE ATOMIC PACKING FACTOR (APF) v APF = V v = 6  4/3 r3 a Substitute r = , 2 v = 6  4/3  a 3 8 v = a3 School of Physics & Materials Science, THAPAR UNIVERSITY 7 HEXAGONAL CLOSED PACKED STRUCTURE C a O 30  A 30  A X O B School of Physics & Materials Science, THAPAR UNIVERSITY 8 HEXAGONAL CLOSED PACKED STRUCTURE AB = AC = BO = ‘a’. CX = where c height of the hcp unit cell. Area of the base = 6  area of the triangle – ABO = 6  1/2  AB  OO Area of the base = 6  1/2  a  OO In triangle OBO O ' OB  30 School of Physics & Materials Science, THAPAR UNIVERSITY 9 HEXAGONAL CLOSED PACKED STRUCTURE cos30º = OO ' OO '  BO a  OO = a cos 30º = 3 2 a Now, substituting the value of OO, 1 3 Area of the base = 6   a  a 2 2 = 3 3a 2 2 V = Area of the base × height School of Physics & Materials Science, THAPAR UNIVERSITY 10 HEXAGONAL CLOSED PACKED STRUCTURE V =3 3a  c 2 2 APF = v a 3  2 V 3 3 a c 2a 3 = 2 2 3 3a c 2 a  APF = 3 3 c School of Physics & Materials Science, THAPAR UNIVERSITY 11  CALCULATION OF c/a RATIO In the triangle ABA, A ' AB  30 AA ' Cos 30º = AB AA = AB cos 30º = a 3 2 2 2 3 But AX = AA = a 3 3 2 a i.e. AX = 3 School of Physics & Materials Science, THAPAR UNIVERSITY 12  CALCULATION OF c/a RATIO In the triangle AXC, AC2 = AX2 + CX2 Substituting the values of AC, AX and CX, 2  a  2 c a2 =  3     2 2 2 a c a2   3 4 c2 a2  a  2 4 3 School of Physics & Materials Science, THAPAR UNIVERSITY 13  CALCULATION OF c/a RATIO c2 2  1  a 1   4  3 c2 8  a2 3 c 8  a 3 Now substituting the value of to calculate APF of an hcp unit cell, School of Physics & Materials Science, THAPAR UNIVERSITY 14 HEXAGONAL CLOSED PACKED STRUCTURE 2 3 APF = 3 3 8 2 3 = 3 3 2 2   APF =  0.74 3 2 Packing Fraction =74% School of Physics & Materials Science, THAPAR UNIVERSITY 15  PROBLEMS Worked Example Zinc has HCP structure. The height of the unit cell is 4.935Å. Find (i). How many atoms are there in a unit cell? and (ii). What is the volume of the unit cell ? Height of the unit cell, c = 4.935Å = 4.935 × 10-10m In HCP structure, the number of atoms present in the unit cell is 6. c 8 We know that, the ratio  a 3 3 3 a = c , , a = 4.935 × a = 3.022 Å 8 8 School of Physics & Materials Science, THAPAR UNIVERSITY 16 No. of atoms in HCP structure Contributes ½ (2 x ½ = 1) Contributes 1/6 (12 x 1/6 = 2) Contributes 1 (3 x 1 = 3) Total = 6 Coordination number = 12 Atomic packing factor = 0.74 17 School of Physics & Materials Science, THAPAR UNIVERSITY  MILLER INDICES Miller Indices Miller Indices Directions Planes Lattices Crystals Note: both directions and planes are imaginary constructs Vector r passing from the origin to a lattice point: r = r1 a + r2 b + r3 c a, b, c → fundamental translation vectors School of Physics & Materials Science, THAPAR UNIVERSITY Miller Indices for directions                                   (4,3)                                                                     (0,0)                  5a + 3b                                   b                  a Miller indices → School of Physics & Materials Science, THAPAR UNIVERSITY  [110] Coordinates of the final point  coordinates of the initial point Reduce to smallest integer values School of Physics & Materials Science, THAPAR UNIVERSITY Family of directions Index Number in the family for cubic lattice → 3x2=6 → 6 x 2 = 12 → 4x2=8 Alternate Symbol symbol [] → Particular direction [[ ]] → Family of directions School of Physics & Materials Science, THAPAR UNIVERSITY Miller indices for planes 22 Procedure when plane is given 1. 2. 3. 4. 5.  23 Remember Atom is in 0-D Direction is in 1-D Plane is in 2-D Crystal is in 3-D A plane cannot pass through the origin. If such as case arises, either shift the plane or shift the origin  24 Z Y O X 1 Choose origin Y 2 Find intercepts on the 1,∞,∞ respective axis 3 Take reciprocal 1,0,0 4 Clear fractions -- 5 Enclose in () (100)  25 Z Y O X 1 Choose origin Y 2 Find intercepts on the 1,1,∞ respective axis 3 Take reciprocal 1,1,0 4 Clear fractions -- 5 Enclose in () (110)  26 Z Y O X 1 Choose origin Y 2 Find intercepts on the 1,1,1 respective axis 3 Take reciprocal 1,1,1 4 Clear fractions -- 5 Enclose in () (111)  27 Z Y X O 1 Choose origin Y 2 Find intercepts on the -1,-1, ∞ respective axis 3 Take reciprocal -1,-1, 0 4 Clear fractions -- 5 Enclose in () (110) O’  28 Z Y X O 1 Choose origin Y 2 Find intercepts on the ∞,1/2,∞ respective axis 3 Take reciprocal 0,2,0 4 Clear fractions -- 5 Enclose in () (020) Intercepts → 1   Intercepts → 1 1  Plane → (100) Plane → (110) Family → {100} → 6 Family → {110} → 12 Intercepts → 1 1 1 Plane → (111) Family → {111} → 8 (Octahedral plane) School of Physics & Materials Science, THAPAR UNIVERSITY  Miller Indices for planes (0,0,1) (0,3,0) (2,0,0)  Find intercepts along axes → 2 3 1  Take reciprocal → 1/2 1/3 1  Convert to smallest integers in the same ratio → 3 2 6  Enclose in parenthesis → (326) School of Physics & Materials Science, THAPAR UNIVERSITY  31 Procedure when MI is given 1. 2. 3. 4.  32 Draw (112) plane Z Y X O 1 Choose origin Y 2 Take reciprocal of the MI 1, 1, 1/2 given 3 Mark the intercepts on Y respective axis 4 Join the intercepts -- 33  34 Lattice parameter a d hkl  h2  k 2  l 2 d-spacing (distance between two planes) Miller indices for that plane  35 Hexagonal crystals → Miller-Bravais Indices a3 Intercepts → 1 1 - ½  Plane → (1 12 0) (h k i l) i = (h + k) a2 a1 The use of the 4 index notation is to bring out the equivalence between crystallographically equivalent planes and directions School of Physics & Materials Science, THAPAR UNIVERSITY Examples to show the utility of the 4 index notation a3 a2 a1 Intercepts → 1 -1   Intercepts →  1 -1  Miller → (1 1 0 ) Miller → (0 1 0) Miller-Bravais → (1 1 0 0 ) Miller-Bravais → (0 11 0) School of Physics & Materials Science, THAPAR UNIVERSITY Examples to show the utility of the 4 index notation a3 a2 a1 Intercepts → 1 1 - ½  Intercepts → 1 -2 -2  Plane → (2 11 0 ) Plane → (1 12 0) School of Physics & Materials Science, THAPAR UNIVERSITY Intercepts → 1 1 - ½ 1 Plane → (1 12 1) Intercepts → 1   1 1 Plane → (1 01 1) School of Physics & Materials Science, THAPAR UNIVERSITY FCC: Linear Density Number of atoms Linear Density of Atoms  LD = Unit length of direction vector ex: linear density of Al in direction a = 0.405 nm # atoms a 2 LD   3.5 nm1 Adapted from Fig. 3.1(a), length 2a Callister & Rethwisch 8e. School of Physics & Materials Science, THAPAR UNIVERSITY 40 P 3.53 (a): Linear Density for BCC Calculate the linear density for the following directions in terms of R: a. b. c. School of Physics & Materials Science, THAPAR UNIVERSITY  Planar Density of (100) Iron Solution: At T < 912ºC iron has the BCC structure. 2D repeat unit (100) 4 3 a R 3 Adapted from Fig. 3.2(c), Callister & Rethwisch 8e. Radius of iron R = 0.1241 nm atoms 2D repeat unit 1 1 atoms atoms 19 Planar Density = = 2 = 12.1 = 1.2 x 10 area a2 4 3 nm 2 m2 R 2D repeat unit 3 School of Physics & Materials Science, THAPAR UNIVERSITY 42 P 3.55 (a): Planar Density for BCC Derive the planar density expressions for BCC (100) and (110) planes in terms of the atomic radius R. School of Physics & Materials Science, THAPAR UNIVERSITY  Planar Density of BCC (111) Iron Solution (cont): (111) plane 1 atom in plane/ unit surface cell 2a atoms in plane atoms above plane atoms below plane 3 h a 2 2  4 3  16 3 2 area  2 ah  3 a  3  2 R   R atoms  3  3 2D repeat unit 1 atoms = atoms Planar Density = = 7.0 0.70 x 1019 nm 2 m2 area 16 3 2 R 2D repeat unit 3 School of Physics & Materials Science, THAPAR UNIVERSITY 44 P 3.54 (a): FCC Derive planar density expressions for FCC (100), (110), and (111) planes. School of Physics & Materials Science, THAPAR UNIVERSITY  1 Linear and Planar density  2 YES The density of atoms along a direction called as linear density The density of atoms in a plane called as planar density Remember 3 o Only atoms whose center of mass lies on the plane has to be count. o In the BCC crystal, the (111) plane partially intersects the atom at the body center (½,½,½). This atom has to be excluded from the calculation.  4 LD = No. of atoms along a particular direction (1D) No. of atoms along a direction LD  Unit Length  5 o Y o Y X X LD = 1/a LD = 1/a√2  6 Z O O O Y X LD = 1/a LD = 1/a√2 LD = 1/a√3  7 Structure LD LD LD SC 1/a 1/a√2 1/a√3 BCC FCC  Linear Density: BCC and FCC 8 Structure LD LD LD BCC 1/a 1/a√2 2/a√3 FCC 1/a 2/a√2 1/a√3  9 No. of atoms lying in a plane PD  Area of the plane  10 Z a Y O a X Structure PD PD PD sc 1/a2 1/a2√2 1/√3 a 2  11 Z 2a Y O 1 x3 X PD  6 1 3 xa 2 xa 2 2 Area of equilateral triangle =1/2*b*h  12 (100) (110) (111) SC a 2a 2a FCC a a 2a 2a BCC a 2a 2a  13 Structure PD (100) PD (110) PD (111) SC 1/a2 1/a2√2 1/a2√3 BCC FCC  X-RAY DIFFRACTION BRAGG’s Deviation = 2θ EQUATION Ray 1 Ray 2 θ θ θ θθ d ▪ The path difference between ray 1 and ray 2 = 2d Sinθ ▪ For constructive interference: nλ = 2d Sinθ School of Physics & Materials Science, THAPAR UNIVERSITY Generation of X- rays ❑ X-rays can be generated by decelerating electrons. ❑ Hence, X-rays are generated by bombarding a target (say Cu) with an electron beam. ❑ The resultant spectrum of X-rays generated (i.e. λX-rays versus Intensity plot) is shown in the next slide. The pattern shows intense peaks on a ‘broad’ background. ❑ The intense peaks can be ‘thought of’ as monochromatic radiation and be used for X-ray diffraction studies. Beam of X- Targe electrons t rays An accelerating (or decelerating) charge radiates electromagnetic radiation School of Physics & Materials Science, THAPAR UNIVERSITY Mo Target impacted by electrons accelerated by a 35 kV potential shows the emission spectrum as in the figure below (schematic) X-ray sources with different λ for doing XRD studies Target λ Of Kα Metal radiation (Å) Mo 0.71 Cu 1.54 Co 1.79 Fe 1.94 Cr 2.29 The high intensity nearly monochromatic Kα x-rays can be used as a radiation source for X-ray diffraction (XRD) studies ⮚ a monochromator can be used to further decrease the spread of wavelengths in the X-ray School of Physics & Materials Science, THAPAR UNIVERSITY  ▪ Bragg’s equation is a negative law ⮚ If Bragg’s eq. is NOT satisfied → NO reflection can occur ⮚ If Bragg’s eq. is satisfied → reflection occur. Might be observed too. ▪ Diffraction = Reinforced Coherent Scattering Reflection versus Scattering Reflection Diffraction Occurs from surface Occurs throughout the bulk Takes place at any angle Takes place only at Bragg angles ~100 % of the intensity may be reflected Small fraction of intensity is diffracted X-rays can be reflected at very small angles of School of Physics & Materials Science, THAPAR UNIVERSITY ▪ nλ = 2d Sinθ ▪ n is an integer and is the order of the reflection ▪ For Cu Kα radiation (λ = 1.54 Å) and d110= 2.22 Å n Sinθ θ 1 0.34 20.7º First order reflection from (110) Second order reflection from (110) 2 0.69 43.92º Also written as (220) School of Physics & Materials Science, THAPAR UNIVERSITY  Crystal Structure Determination: THE POWDER METHOD School of Physics & Materials Science, THAPAR UNIVERSITY  Cryst al Intensity → 0 9 18 Diffraction 0 angle (2θ) 0 → Monoatomic gas Liquid / Amorphous solid Intensity Diffraction angle (2θ) → → Intensity 0 9 18 0 0 → Diffraction angle (2θ) → 0 School 9 of Physics & Materials Science, THAPAR UNIVERSITY C Scattering by the Unit cell (uc) ▪ Coherent Scattering ▪ Unit Cell (uc) representative of the crystal structure ▪ Scattered waves from various atoms in the uc interfere to create the diffraction pattern The wave scattered from the middle plane is out of phase with the ones scattered from top and bottom planes School of Physics & Materials Science, THAPAR UNIVERSITY Determination of Crystal Structure from 2θ versus Intensity Data peak 2θ θ Sinθ Sin2 θ ratio Index no 1 38.52 19.26 0.33 0.11 3 111 2 44.76 22.38 0.38 0.14 4 200 3 65.14 32.57 0.54 0.29 8 220 4 78.26 39.13 0.63 0.40 11 311 5 82.47 41.235 0.66 0.43 12 222 6 99.11 49.555 0.76 0.58 16 400 7 112.03 56.015 0.83 0.69 19 331 8 116.60 58.3 0.85 0.72 20 420 9 137.47 68.735 0.93 0.87 24 422 School of Physics & Materials Science, THAPAR UNIVERSITY  Extinction Rules Reflections which Reflections Bravais Lattice may be present necessarily absent Simple all None Body centred (h + k + l) even (h + k + l) odd h, k and l all odd / all h, k and l not all even Face centred even / odd Bravais Lattice Allowed Reflections SC All BCC (h + k + l) even FCC h, k and l all odd / even h, k and l are all odd DC Or all are even (h + k + l) divisible by 4 School of Physics & Materials Science, THAPAR UNIVERSITY The ratio of (h2 + K2 + l2) derived from extinction rules SC 1 2 3 4 5 6 8 BCC 2 4 6 FCC 3 4 8 11 12 … DC 3 8 11 16 … School of Physics & Materials Science, THAPAR UNIVERSITY  2θ→ θ Intensity Sinθ Sin2 θ ratio 1 21.5 0.366 0.134 3 2 25 0.422 0.178 4 3 37 0.60 0.362 8 4 45 0.707 0.500 11 5 47 0.731 0.535 12 6 58 0.848 0.719 16 7 68 0.927 0.859 19 FC C School of Physics & Materials Science, THAPAR UNIVERSITY h2 + k2 + l2 SC FCC BCC DC 1 100 2 110 110 3 111 111 111 4 200 200 200 5 210 6 211 211 7 8 220 220 220 220 9 300, 221 10 310 310 11 311 311 311 12 222 222 222 13 320 14 321 321 15 16 400 400 400 400 17 410, 322 18 411, 330 411, 330 19 331of Physics &331 School 331 Materials Science, THAPAR UNIVERSITY  Solved example Determination of Crystal Structure (lattice type) from 2θ versus Intensity Data 1 Let us assume that we have the 2θ versus intensity plot from a diffractometer ⮚ To know the lattice type we need only the position of the peaks (as tabulated below) # 2θ θ Sinθ Sin2 θ ratio Index d 1 38.52 19.26 0.33 0.11 3 111 2.34 2 44.76 22.38 0.38 0.14 4 200 2.03 3 65.14 32.57 0.54 0.29 8 220 1.43 4 78.26 39.13 0.63 0.40 11 311 1.22 5 82.47 41.235 0.66 0.43 12 222 1.17 6 99.11 49.555 0.76 0.58 16 400 1.01 7 112.03 56.015 0.83 0.69 19 331 0.93 8 116.60 58.3 0.85 0.72 20 420 0.91 9 137.47 68.735 0.93 0.87 24 422 0.83 10 163.78 81.89 0.99 0.98 27 333 0.78 Note that Sinθ cannot be > 1 From the ratios in column 6 we conclude FC Not that C e Usin g We can get the lattice parameter → which correspond to that for Al Note: Error in d spacing decreases with θ → so we should use high angle lines for lattice parameter calculation XRD_lattice_parameter_calculation. School of Physics & Materials Science, THAPAR UNIVERSITY ppt Tetrahedral voids ¼ way along body diagonal {¼, ¼, ¼}, {¾, ¾, ¾} + face centering translations 1 Vtetrahedron  Vcell rvoid / ratom = 0.225 24 Note: Atoms are coloured differently but are the same Octahedral voids At body Centre {½, ½, ½} + face centering translations 1 Voctahedron  Vcell rVoid / ratom = 0.414 6 Size of the largest atom which can fit into the tetrahedral void of FCC Length of the body diagonal = 3a  2 R Distance between lattice atom to void atom =r+R 3a = 4 In FCC lattice closest distance of paking is 2a  4 R 4R a 2 3 6R r+R= 2 2R  4 2 r  6     1  0.225 R  2  Size of the largest atom which can fit into the Octahedral void of FCC Thus, the octahedral void is the bigger one and interstitial atoms (which are usually bigger than the voids) would prefer to sit here 2r + 2x = a 2a  4r x r    2  1 ~ 0.414 FCC voids Position Voids / cell Voids / atom ¼ way from each vertex of the cube Tetrahedral along body diagonal 8 2 ((¼, ¼, ¼)) Body centre: 1 (½, ½, ½) Octahedral 4 1 Edge centre: (12/4 = 3) (½, 0, 0) NaCl structure Zinc blend  Diamond cubic Perovskite (CaTiO3)  Rutile (TiO2) Fluorite (CaF2) Wurtzite (ZnO)  Fullerene 20 Hexagons, 12 pentagons Spinel (AB2O4)  1 Ionic Solids Ionic Solids 2 In ionic solids, cation being smaller is situated at the void position Rules for stable configuration The cation should not be smaller than the void No Rattling formed by the anions Cation size larger than the The cation (+ve) should be larger than the void so void that the anions (-ve) do not touch each other Choose the largest Largest coordination gives the best possible packing coordination possible Ionic Solids 3 Ligacy rc /ra Configuration E.g. rc /ra 2 0 – 0.155 Linear 3 0.155 – 0.225 Triangular 4 0.225 – 0.414 Tetrahedral 6 0.414 – 0.732 Octahedral NaCl 0.54 8 0.732 – 1.0 Cubic CsCl 0.91 12 1.0 FCC or HCP The ratio rc /ra (radius of cation : radius of anion) determines the coordination number / Ligacy for the cation → the local packing Types of Ionic Crystal 4 1. AB type (same no. of anions and cations) A - cation, B - anion 2. ABO3 type - Perovskite structure 3. AB2O4 type - Spinel structure A/B – cation, O-oxygen ion (anion) AX or AB type Ionic crystals 5 CsCl crystal structure Lattice type: Primitive cubic lattice. Void type: Cubic type No. of anion and cations: 1 Relation a and R: a√3 = 2 Ra + 2 Rc Motif: Anions (A): 0 0 0, Cations (B): ½ ½ ½ 100% occupancy of sites according to the stoichiometry. Examples: Halides such as CSCl, AgI, AgBr, CsI, LiMg etc. AX or AB type Ionic crystals 6 NaCl crystal structure Lattice type: FCC lattice. Void type: Octahedral. No. of anion and cations: 4 Relation a and R: a = 2 Ra + 2 Rc Motif: Anions (A): 0 0 0, Cations (B): ½ 0 0 Anions (A) form the cation sub lattice with FCC structure. Cations (B) fill the octahedral sites. 100% occupancy of sites according to the stoichiometry since there will be one octahedral site per anion. Examples NaCl, MgO, NiO, LiF, TiN, FeO etc. AX or AB type Ionic crystals 7 ZnS crystal structure Lattice type: FCC lattice. Void type: Tetrahedral. No. of anion and cations: 4 Relation a and R: ¼ x a √3 = Ra + Rc Motif: Anions (A): 0 0 0, Cations (B): ¼ ¼ ¼ 50% occupancy of sites according to the stoichiometry. Examples ZnO, ZnS, BeO, Sic, ZnTe etc. ABO3 type ionic crystal 8 Lattice type: Primitive Cubic (NOT FCC!) Motif: A ion - 0 0 0, B ion – ½ ½ ½, O ion - ½ ½ 0, 0 ½ ½, ½ 0 ½ Oxygen atoms form an FCC-like (not FCC) cell with atoms missing from the corners which are occupied by A atoms. Coordination B cation is surrounded by oxygen octahedra which share corners. e.g. A2+B4+O3 , BaTiO3, PbTiO3, CaTiO3, SrTiO3 etc. e.g. A3+B3+O3 , LaAlO3, LaGaO3, BiFeO3 etc. AB2O4 type ionic crystal 9 A spinel unit-cell is made up of 8 FCC cells made by oxygen consisting of 32 oxygen atoms, 8 A atoms and 16 B atoms. Crystallize with FCC structure. Two cations occupy tetrahedral and octahedral sites in an FCC lattice made by O atoms. One unit-cell consists of eight formula units of AB2O4 1/8 of 64 TV occupied → A 1/2 of 32 OV occupied → B AB2O4 type ionic crystal 10 Normal Spinel Chemical formula: (A2+)(B3+)O4 MgAl2O4, FeAl2O4, CoAl2O4 and a few ferrites such as ZnFe2O4 and CdFe2O4. In this structure, all the A2+ ions occupy the tetrahedral sites and all the B3+ ions occupy the octahedral sites. Inverse Spinel Chemical formula: (A2+)(B3+)2O4 but can be more conveniently written as B(AB)O4. Fe3O4 (or FeO.Fe2O3), NiFe2O4, CoFe2O4 etc. In this structure, ½ of the B3+ ions occupy the tetrahedral sites and remaining ½ B3+ and all A2+ions occupy the octahedral sites.  11 Covalent Solids Covalent solids 12 1. Made up of covalent bonded materials. 2. Covalent bond is directional and strong bond. Covalent solids 13 Diamond cubic structure Orbital hybridization of C atoms (sp3) requires that the atoms are tetrahedrally coordinated and thus the structure has high degree of directionality. One unit-cell: FCC lattice Motif: Two atoms: one at (0 0 0) and another at (¼ ¼ ¼). Only 50% of the tetrahedral voids are occupied. In case of compounds, FCC lattice can be formed by one type of atom and remaining atoms, usually from the same group, occupy half of the tetrahedral sites. Examples: Si, Ge, GaAs Packing fraction of Diamond cubic structure 14 No of atoms in a unit cell × Volume of one atom APF = Volume of the unit cell The relation between a and r is : a√3/4 = 2r No. of atoms in a diamond cubic unit cell: 8 3  4 3  32  3a  8   r   3  3  8  3 APF = 3 = 3 = = 0.34 a a 16 Therefore, APF = 34% Covalent solids 15 Graphite structure Graphite has a layered structure where in each layer, carbon atoms are sp2 hybridized and they make a hexagonal pattern. However, the bonding between individual layers is Van der Walls type of bonding. That is why Graphite is a soft material and is used as a lubricant.  Materials Science & Engineering (UES012) Corrosion in metals For metallic materials, the corrosion process is normally electrochemical. Electrochemical reaction - a chemical reaction in which there is transfer of electrons from one chemical species to another. Metal atoms characteristically lose or give up electrons in what is called an oxidation reaction. M →Mn++ ne- School of Physics & Materials Science, THAPAR UNIVERSITY 1  The electrons generated from each metal atom that is oxidized are transferred to and become a part of another chemical species. This is a reduction reaction. Reduction of hydrogen ions in an acid solution Reduction reaction in an acid solution containing dissolved oxygen Reduction reaction in a neutral or basic solution containing dissolved oxygen School of Physics & Materials Science, THAPAR UNIVERSITY Electrode potential Not all metallic materials oxidize to form ions with same degree of ease. If the iron and copper electrodes are connected electrically, reduction will occur for copper at the expense of the oxidation of iron. Cu2+ + Fe → Cu + Fe2+ In terms of half-cell reactions: Fe → Fe2++ 2e- Cu2+ + 2e- → Cu Cu2+will Cu2+ ions + Fe → Cu(electrodeposit) deposit + Fe2+ as metallic copper on the copper electrode, while iron dissolves (corrodes) on the other side of the cell and goes into solution as Fe2+ ions. Standard half-cell School of Physics & Materials Science, THAPAR UNIVERSITY Galvanic cell When externally connected, electrons generated from the oxidation of iron flow to the copper cell in order that Cu2+ be reduced. In addition, there will be some net ion motion from each cell to the other across the membrane. This is called a galvanic couple - two metals electrically connected in a liquid electrolyte wherein one metal becomes an anode and corrodes, while the other acts as a cathode. An electric potential or voltage will exist between the two cell halves. For example: Cu2+ + Fe → Cu + Fe2+ Potential: 0.780 V Fe2+ + Zn → Fe + Zn2+ Potential: 0.323 V Various electrode pairs have different voltages ! School of Physics & Materials Science, THAPAR UNIVERSITY Standard EMF series This table is for reduction reactions. For oxidation reactions, the corresponding voltage will change sign. School of Physics & Materials Science, THAPAR UNIVERSITY  As a consequence of oxidation, the metal ions may either go into the corroding solution as ions or they may form an insoluble compound with nonmetallic elements. School of Physics & Materials Science, THAPAR UNIVERSITY School of Physics & Materials Science, THAPAR UNIVERSITY galvanic series: This represents the relative reactivities of a number of metals and commercial alloys in seawater. School of Physics & Materials Science, THAPAR UNIVERSITY Corrosion rate The corrosion rate, or the rate of material removal as a consequence of the chemical action, is an important corrosion parameter. Corrosion penetration rate (CPR), or the thickness loss of material per unit of time. where W = weight loss after exposure time t ; ρ = density, and A = exposed specimen area, K is a constant. There is an electric current associated with electrochemical corrosion reactions. Corrosion rate r can be written as r = i/nF i = current density (the current per unit surface area of material corroding) n = number of electrons associated with the ionization of each metal atom F = 96,500 C/mol. School of Physics & Materials Science, THAPAR UNIVERSITY Passivity: Some normally active metals and alloys, under particular environmental conditions, lose their chemical reactivity and become extremely inert. E.g., chromium, iron, nickel, titanium, and many of their alloys. This passive behaviour results from the formation of a highly adherent and very thin oxide film on the metal surface, which serves as a protective barrier to further corrosion. School of Physics & Materials Science, THAPAR UNIVERSITY Types of Corrosion: 1. Uniform/general attack Corrosion 2. Galvanic or two-metal Corrosion 3. Pitting Corrosion 4. Crevice Corrosion 5. Intergranular Corrosion 6. Stress Corrosion 7. Erosion Corrosion 8. Cavitation Damage 9. Fretting Corrosion 10. Selective Leaching 11. Hydrogen Damage School of Physics & Materials Science, THAPAR UNIVERSITY 1. Uniform / general attack Corrosion: The chemical reaction proceeds uniformly on the entire metal surface exposed to the corrosive environment. It often leaves behind a scale or deposit. E.g., general rusting of steel and iron and the tarnishing of silverware Represent greatest destruction of metals! The most common form of corrosion. It is also the least objectionable because it can be predicted and designed for with relative ease. Prevention: 1. Protective Coating 2. Inhibitors 3. Cathodic Protection School of Physics & Materials Science, THAPAR UNIVERSITY  2. Galvanic or two-metal Corrosion: Galvanic corrosion occurs when two metals or alloys having different compositions are electrically coupled while exposed to an electrolyte. Galvanized Steel Tin-Plate The less noble or more reactive metal in the particular environment will experience corrosion; the more inert metal, the cathode, will be protected from corrosion. For example, a) steel screws corrode when in contact with brass in a marine environment b) copper and steel tubing are joined in a domestic water heater, the steel will corrode in the vicinity of the junction. School of Physics & Materials Science, THAPAR UNIVERSITY School of Physics & Materials Science, THAPAR UNIVERSITY Area Effect: The rate of galvanic attack depends on the cathode–anode area ratio; that is, for a given cathode area, a smaller anode will corrode more rapidly than a larger one. Reason: corrosion rate depends on current density, the current per unit area of corroding surface, and not simply the current. Thus, a high current density results for the anode when its area is small relative to that of the cathode. A number of measures may be taken to significantly reduce the effects of galvanic corrosion. These include the following: 1. If coupling of dissimilar metals is necessary, choose two that are close together in the galvanic series. 2. Avoid an unfavorable anode-to-cathode surface area ratio; use an anode area as large as possible. 3. Electrically insulate dissimilar metals from each other. 4. Electrically connect a third, anodic metal to the other two; this is a form of cathodic protection, discussed presently. School of Physics & Materials Science, THAPAR UNIVERSITY School of Physics & Materials Science, THAPAR UNIVERSITY 3. Pitting Corrosion: Localized corrosive attack which produces holes or pits in a metal. Very destructive! leads to perforation of the metal. Difficult to detect: May be covered by corrosion products Depth and no of pits vary Until Failure!! Generally requires an initiation period. Once started the pits grow at an ever increasing rate. Grow in the direction of gravity and on lower surfaces of the equipment. Pits are initiated at places where local increase in corrosion rates occurs. Local structural and/or compositional heterogeneities School of Physics & Materials Science, THAPAR UNIVERSITY O2 + 2H2O + 4e- 4OH- M+Cl- + H2O MOH + H+Cl- Reaction is autocatalytic! Use materials with non-pitting tendency. Best resistance (2% molybdenum Steels) Always do corrosion test before final selection. School of Physics & Materials Science, THAPAR UNIVERSITY 4. Crevice Corrosion: localized Concentration cell corrosion occurs in crevices and recesses or under deposits of dirt or corrosion products where the solution becomes stagnant and there is localized depletion of dissolved oxygen. Corrosion preferentially occurring at these positions is called crevice corrosion. The crevice must be wide enough for the solution to penetrate, yet narrow enough for stagnancy; usually the width is several thousandths of an inch. School of Physics & Materials Science, THAPAR UNIVERSITY In many aqueous environments, the solution within the crevice has been found to develop high concentrations of H+ and Cl- ions, which are especially corrosive. (Stainless steel, Ti, Al and Cu alloys) Many alloys that passivate are susceptible to crevice corrosion because protective films are often destroyed by the H+ and Cl- ions. Crevice corrosion may be prevented by: using welded instead of riveted or bolted joints, using nonabsorbing gaskets (like teflon) when possible, removing accumulated deposits frequently, and designing containment vessels to avoid stagnant areas and ensure complete drainage. School of Physics & Materials Science, THAPAR UNIVERSITY 5. Intergranular Corrosion: occurs preferentially along grain boundaries for some alloys and in specific environments. The net result is that a macroscopic specimen disintegrates along its grain boundaries. This type of corrosion is especially prevalent in some stainless steels. When heated to temperatures between 500 0Cand 800 0C for sufficiently long time periods, these alloys become sensitized to intergranular attack. Temp range is called as sensitizing temp range. This heat treatment permits the formation of small precipitate particles of chromium carbide (Cr23C6) by reaction between the chromium and carbon in the stainless steel. These particles form along the grain boundaries Both the chromium and the carbon must diffuse to the grain boundaries to form the precipitates, which leaves a chromium-depleted zone adjacent to the grain boundary. Consequently, this grain boundary region is now highly susceptible to corrosion. School of Physics & Materials Science, THAPAR UNIVERSITY Intergranular corrosion is an especially severe problem in the welding of stainless steels, when it is often termed weld decay. Stainless steels may be protected from intergranular corrosion by the following measures: subjecting the sensitized material to a high-temperature heat treatment (heating follwoed by water quenching) in which all the chromium carbide particles are redissolved, lowering the carbon content below 0.03 wt% C so that carbide formation is minimal, Alloying the stainless steel with another metal such as niobium or titanium, which has a greater tendency to form carbides than does chromium so that the Cr remains in solid solution. School of Physics & Materials Science, THAPAR UNIVERSITY 6. Stress Corrosion: Also known as stress corrosion cracking (SCC). results from the combined action of an applied tensile stress and a corrosive environment. some materials that are virtually inert in a particular corrosive medium become susceptible to this form of corrosion when a stress is applied. School of Physics & Materials Science, THAPAR UNIVERSITY Small cracks form and then propagate in a direction perpendicular to the stress resulting in failure. Failure behavior is characteristic of that for a brittle material, even though the metal alloy is intrinsically ductile. The cracks may form at relatively low stress levels, significantly below the tensile strength. Most alloys are susceptible to stress corrosion in specific environments, especially at moderate stress levels. For example, most stainless steels stress corrode in solutions containing chloride ions, whereas brasses are especially vulnerable when exposed to ammonia. The stress that produces stress corrosion cracking need not be externally applied; it may be: a residual one that results from rapid temperature changes and uneven contraction, for two-phase alloys in which each phase has a different coefficient of expansion. gaseous and solid corrosion products that are entrapped internally can give rise to internal stresses. School of Physics & Materials Science, THAPAR UNIVERSITY Probably the best measure to take in reducing or totally eliminating stress corrosion is to lower the magnitude of the stress: This may be accomplished by reducing the external load increasing the cross-sectional area perpendicular to the applied stress. Furthermore, an appropriate heat treatment may be used to anneal out any residual thermal stresses. Eliminate the corrosive environment. Change the alloy. School of Physics & Materials Science, THAPAR UNIVERSITY 7. Erosion Corrosion: arises from the combined action of chemical attack and mechanical abrasion or wear as a consequence of fluid motion. All metal alloys are susceptible to erosion–corrosion. It is especially harmful to alloys that passivate by forming a protective surface film; the abrasive action may erode away the film, leaving exposed a bare metal surface. If the coating is not capable of continuously and rapidly reforming as a protective barrier, corrosion may be severe. Usually it can be identified by surface grooves and waves having contours that are characteristic of the flow of the fluid. School of Physics & Materials Science, THAPAR UNIVERSITY  The nature of the fluid can have a dramatic influence on the corrosion behavior. Increasing fluid velocity normally enhances the rate of corrosion. A solution is more erosive when bubbles and suspended particulate solids are present. Erosion–corrosion is commonly found in piping, especially at bends, elbows, and abrupt changes in pipe diameter—positions where the fluid changes direction or flow suddenly becomes turbulent. Propellers, turbine blades, valves, and pumps are also susceptible to this form of corrosion. One of the best ways to reduce erosion–corrosion is to change the design to eliminate fluid turbulence and impingement effects. Use materials that inherently resist erosion. Removal of particulates and bubbles from the solution will lessen its ability to erode. School of Physics & Materials Science, THAPAR UNIVERSITY 8. Cavitation Damage: type of erosion corrosion caused by the formation and collapse of air bubbles / vapor filled cavities in a liquid near a metal surface. Reason: The rapidly collapsing vapor bubbles can produce locallized pressures as high as 60,000 psi. It is sufficient to remove surface films, tear metal particles from the surface resulting in increased corrosion rates and surface wear. Occurs where high velocity liquid flow and pressure changes exist. Pump impellers and ship propellers. School of Physics & Materials Science, THAPAR UNIVERSITY 9. Fretting Corrosion: caused at the interface of materials under load subjected to vibration and slip. The metal between the rubbing surfaces is oxidized. The oxidized film is torn. And the oxide particles so formed act as abrasive. Appears as grooves / pits surrounded by corrosion product. Tight-fitting surfaces: between shafts and bearings or sleeves. School of Physics & Materials Science, THAPAR UNIVERSITY 10. Selective Leaching: preferential removal of one element of the solid alloy by the corrosion process. Eg: Dezincifiaction of Brass leaving spongy weak matrix of Cu. Method: dissolution followed by replating of Cu while Zn remains in the solution Protection: 1. Lower zinc content. 2. Change the alloy 3. Change the environment 4. Cathodic protection. School of Physics & Materials Science, THAPAR UNIVERSITY 11. Hydrogen Damage: Load carrying capability of metallic component is reduced due to interaction with atomic or molecular hydrogen usually in conjunction with residual or externally applied tensile stresses. Hydrogen Embrittlement: Hydrogen damages directly related to loss of ductility 1) Hydrogen environment embrittlement: occurs during plastic deformation of metals such as steels, stainless steels and titanium alloys. 2) Hydrogen stress cracking: brittle fracture in a ductile material such as carbon and low alloy steels. 3) Loss in tensile ductility: significant reduction in elongation capability and reduction area in steel and aluminium alloys. Hydrogen attack: High temperature mode of attack in which hydrogen enters metals such as steels and reacts with carbon to produce methane gas resulting in formation of cracks or decarburization. Blistering: atomic hydrogen diffuses into internal defects and precipitates as molecular hydrogen which produces high internal pressure resulting in local plastic deformation and blistering. 1. Change the material susceptible 2. Reverse hydrogen Schoolcontamination: Bakeout. of Physics & Materials Science, THAPAR UNIVERSITY Cathodic Protection: Cathodic protection simply involves supplying, from an external source, electrons to the metal to be protected, making it a cathode. The process of galvanizing is simply one in which a layer of zinc is applied to the surface of steel by hot dipping: type of sacrificial protection. high-conductivity backfill material provides good electrical contact between the anode and surrounding soil. A current path exists between the cathode and anode through the intervening soil, completing the electrical circuit. Cathodic protection is especially useful in preventing corrosion of water heaters, underground tanks and pipes, and marine equipment. School of Physics & Materials Science, THAPAR UNIVERSITY