1 Materials Science and Engineering I Chapter 4 Solidification and Crystalline Imperfections
2 Outline of Chapter 4 Solidification of metals:nuclei, growth of unclei into crystals, Grain growth. Growth of cyrstalline in Liquid Metal and formation of a grain strucutre Grain structure of industrial casting Solidification of single crystals Metallic sold solutions: Substitutional solid solution, Interstitial solid Solution Crystalline Imperfections: Zero-dimensional defects: point defects One-dimensional defects: line defects Two-dimensional defects:external surface, grain boundaries, twins, low-angle and highangle boundaries, Three dimensional defects: pore, cracks, and foreign inclusions. Experimental techniques for identification of microstructure and defects: Optical metallography, Scanning electron microscopy (SEM), Transmission electron microscopy (TEM), High-Resolution Transmission Electrons Microscopy (HRTEM), Scanning probe microscopes (STM, AFM) 2
3 Solidification of Metals Metals are melted to produce finished and semifinished parts. Two steps of solidification Nucleation : Formation of stable nuclei. Growth of nuclei : Formation of grain structure. Thermal gradients define the shape of each grain. Grains Nuclei 3 Liquid Crystals that will Form grains Grain Boundaries Figure 4.2
4 Formation of Stable Nuclei Two main mechanisms: Homogenous and heterogeneous. Homogenous Nucleation : First and simplest case. Metal itself will provide atoms to form nuclei. Metal, when significantly undercooled, has several slow moving atoms which bond each other to form nuclei. Cluster of atoms below critical size is called embryo. If the cluster of atoms reach critical size, they grow into crystals. Else get dissolved. Cluster of atoms that are grater than critical size are called nucleus. 4
5 Energies involved in homogenous nucleation. Volume free energy G v Surface energy Gs Released by liquid to solid transformation. ΔG v is change in free energy per unit volume between liquid and solid. free energy change for a spherical nucleus of radius r is given by r 4 r 3 3 G v Required to form new solid surface ΔG s is energy needed to create a surface. γ is specific surface free energy. Then Gs 4r 2 ΔG s is retarding energy. 5
6 Total Free Energy Total free energy is given by G r G 4r Since when r=r*, d(δg T )/dr = 0 G V ΔG s Nucleus T r* v ΔG T ΔG r* r* r Above critical radius r* Below critical radius r* - Figure 4.4 ΔG v 6 Energy lowered by growing into crystals Energy Lowered by redissolving
7 Critical Radius Versus Undercooling Greater the degree of undercooling, greater the change in volume free energy ΔG v ΔGs does not change significantly. As the amount of undercooling ΔT increases, critical nucleus size decreases. Critical radius is related to undercooling by relation r* 2T H f m T r* = critical radius of nucleus γ = Surface free energy ΔH f = Latent heat of fusion Δ T = Amount of undercooling. 7
9 Heterogenous Nucleation Nucleation occurs in a liquid on the surfaces of structural material. Eg:- Insoluble impurities. These structures, called nucleating agents, lower the free energy required to form stable nucleus. Liquid θ Figure 4.6 Nucleating agents also lower the critical size. Smaller amount of undercooling is required to solidify. Used excessively in industries. Solid Nucleating agent 4-7
10 Growth of Crystals and Formation of Grain Structure Nucleus grow into crystals in different orientations. Crystal boundaries are formed when crystals join together at complete solidification. Crystals in solidified metals are called grains. Grains are separated by grain boundaries. More the number of nucleation sites available, more the number of grains formed. Nuclei growing into grains Forming grain boundaries 4-8
11 Types of Grains Equiaxed Grains: Crystals, smaller in size, grow equally in all directions. Formed at the sites of high concentration of the nuclie. Example:- Cold mold wall Mold Columnar Grains: Long thin and coarse. Grow predominantly in one direction. Formed at the sites of slow cooling and steep temperature gradient. Example:- Grains that are away from the mold wall. Columnar Grains 4-9 Equiaxed Grains Figure 4.7a
12 Casting in Industries In industries, molten metal is cast into either semi finished or finished parts. Figure 4.9b Continuous casting Of steel ingots Figure 4.8 Direct-Chill semicontinuous 4-10 Casting unit for aluminum
13 Grain Structure in Industrial castings To produce cast ingots with fine grain size, grain refiners are added. Example:- For aluminum alloy, small amount of Titanium, Boron or Zirconium is added. Grain structure of Aluminum cast with (a) and without (b) grain refiners (a) (b) Figure 4.10 After Metals Handbook vol. 8, 8 th ed., American Society of Metals, 1973, p.164)
14 Solidification of Single Crystal For some applications (Eg: Gas turbine blades-high temperature environment), single crystals are needed. Single crystals have high temperature creep resistance. Latent head of solidification is conducted through solidifying crystal to grow single crystal. Growth rate is kept slow so that temperature at solidliquid interface is slightly below melting point. Figure 4.12 Growth of single crystal for turbine airfoil (After Pratt and Whitney Co.)
15 Czochralski Process This method is used to produce single crystal of silicon for electronic wafers. A seed crystal is dipped in molten silicon and rotated. The seed crystal is withdrawn slowly while silicon adheres to seed crystal and grows as a single crystal. Figure
16 Metallic Solid Solutions Alloys are used in most engineering applications. Alloy is an mixture of two or more metals and nonmetals. Example: Cartridge brass is binary alloy of 70% Cu and 30% Zinc. Iconel is a nickel based superalloy with about 10 elements. Solid solution is a simple type of alloy in which elements are dispersed in a single phase. 4-14
17 Substitutional Solid Solution Solute atoms substitute for solvent atom in a crystal lattice. The structure remains unchanged. Lattice might get slightly distorted due to change in diameter of the atoms. Solute percentage in solvent can vary from fraction of a percentage to 100% Solvent atoms Figure 4.14 Solute atoms 4-15
18 Substitutional Solid Solution (Cont..) The solubility of solids is greater if (Hume Rothery rules) The diameter of atoms not differ by more than 15% Crystal structures are similar. No much difference in electronegativity (else compounds will be formed). Have some valence. System Atomic radius Difference Examples: Electronegativity difference Solid Solibility Cu-Zn 3.9% % Cu-Pb 36.7% % Cu-Ni 2.3% 0 100% 4-16
20 Interstitial Solid Solution Solute atoms fit in between the voids (interstices) of solvent atoms. Solvent atoms in this case should be much larger than solute atoms. Example:- between 912 and C, interstitial solid solution of carbon in γ iron (FCC) is formed. A maximum of 2.8% of carbon can dissolve interstitially in iron. Iron atoms r=0.129nm 4-17 Carbon atoms r=0.075nm Figure 4.15a
22 Crystalline Imperfections No crystal is perfect. Imperfections affect mechanical properties, chemical properties and electrical properties. Imperfections can be classified as Zero dimension point deffects. One dimension / line deffects (dislocations). Two dimension deffects. Three dimension deffects (cracks). 4-18
23 Point Defects Vacancy Vacancy is formed due to a missing atom. Vacancy is formed (one in atoms) during crystallization or mobility of atoms. Energy of formation is 1 ev. Mobility of vacancy results in cluster of vacancies. Also caused due to plastic defor- -mation, rapid cooling or particle bombardment Figure: Vacancies moving to form vacancy cluster
24 Point Defects - Interstitially Atom in a crystal, sometimes, occupies interstitial site. This does not occur naturally. Can be induced by irradiation. This defects caused structural distortion. Figure 4.16b 4-20
25 Point Defects Vacancies: -vacant atomic sites in a structure. distortion of planes Vacancy Self-Interstitials: -"extra" atoms positioned between atomic sites. distortion of planes selfinterstitial 25
26 Point Defects in Ionic Crystals Complex as electric neutrality has to be maintained. If two appositely charged particles are missing, cationanion divacancy is created. This is scohttky imperfection. Frenkel imperfection is created when cation moves to interstitial site. Impurity atoms are also considered as point defects. Figure 4.17
27 Line Defects (Dislocations) Lattice distortions are centered around a line. Formed during Solidification Permanent Deformation Vacancy condensation Different types of line defects are Edge dislocation ( 刃差排 ) Screw dislocation ( 螺絲差排 ) Mixed dislocation
28 Edge Dislocation Created by insertion of extra half planes of atoms. Positive edge dislocation Negative edge dislocation Burgers vector Shows displacement of atoms (slip). Burger s cricuit Burgers vector Figure 4.18
29 Screw Dislocation Created due to shear stresses applied to regions of a perfect crystal separated by cutting plane. Distortion of lattice in form of a spiral ramp. Burgers vector is parallel to dislocation line.
30 Dislocations in Solids Linear Defects (Dislocations) Are one-dimensional defects around which atoms are misaligned Edge dislocation: extra half-plane of atoms inserted in a crystal structure b to dislocation line Screw dislocation: resulting from shear deformation b to dislocation line Burger s vector, b: measure of lattice distortion 30
31 Mixed Dislocation Most crystal have components of both edge and screw dislocation Dislocation, since have irregular atomic arrangement will appear as dark lines when observed in electron microscope. Figure 4.22 Figure 4.21 Dislocation structure of iron deformed 14% at C
32 Planar Defects Grain boundaries, twins, low/high angle boundaries, twists and stacking faults Free surface is also a defect : Bonded to atoms on only one side and hence has higher state of energy Highly reactive Nanomaterials have small clusters of atoms and hence are highly reactive.
33 Grain Boundaries Grain boundaries separate grains. Formed due to simultaneously growing crystals meeting each other. Width = 2 5 atomic diameters. Some atoms in grain boundaries have higher energy. Restrict plastic flow and prevent dislocation movement. Figure D view of grains Grain Boundaries In 1018 steel 4-27 (After A.G. Guy, Essentials of materials Science, McGraw-Hill, 1976.)
34 Twin Boundaries Twin: A region in which mirror image of structure exists across a boundary. Formed during plastic deformation and recrystallization. Strengthens the metal. Twin Plane Twin
35 Free Surfaces Atoms at the crystal surface possess incomplete bonding Extra energy due to unsatisfied bonds enhanced chemical reactivity at surfaces (catalysis) Example: Three-Way Cataytic Converter (TWC) in cars (Ce 0.5 Zr 0.5 )O 2 35
36 Other Planar Defects Small angle tilt boundary: Array of edge dislocations tilts two regions of a crystal by < 10 0 Stacking faults: Piling up faults during recrystallization due to collapsing. Example: ABCABAACBABC FCC fault
37 Observing Grain Boundaries - Metallography To observe grain boundaries, the metal sample must be first mounted for easy handling Then the sample should be ground and polished with different grades of abrasive paper and abrasive solution. The surface is then etched chemically. Tiny groves are produced at grain boundaries. Groves do not intensely reflect light. Hence observed by optical Figure 4.27 microscope.
38 Effect of Etching Figure 4.28 Unetched Steel 200 X Etched Steel 200 X Unetched Brass 200 X Etched Brass 200 X
39 Grain Size Affects the mechanical properties of the material The smaller the grain size, more are the grain boundaries. More grain boundaries means higher resistance to slip (plastic deformation occurs due to slip). More grains means more uniform the mechanical properties are.
40 Measuring Grain Size ASTM grain size number n is a measure of grain size. N < 3 Coarse grained 4 < n < 6 Medium grained 7 < n < 9 Fine grained N > 10 ultrafine grained N = 2 n 1 N = Number of grains per square inch of a polished and etched specimen at 100 x. n = ASTM grain size number per m X 100 X 1018 cold rolled steel, n= cold rolled steel, n=8
41 Average Grain Diameter Average grain diameter more directly represents grain size. Random line of known length is drawn on photomicrograph. Number of grains intersected is counted. Ratio of number of grains intersected to length of line, n L is determined. 3 inches 5 grains.
45 Scanning Electron Microscope Electron source generates electrons. Electrons hit the surface and secondary electrons are produced. The secondary electrons are collected to produce the signal. The signal is used to produce the image. Figure TEM of fractured metal end After V.A. Phillips, Modern Photographic techniques and Their Applications, Wiley, 1971, p.425
49 Lenses Rotational force F = -e v z x B r Radial force F r = - e v x B z
50 Transmission Electron Microscope Electron produced by heated tungsten filament. Accelerated by high voltage ( KV) Electron beam passes through very thin specimen. Difference in atomic arrangement change directions of electrons. Beam is enlarged and focused on fluorescent screen. Collagen Fibrils of ligament as seen in TEM Figure (After L.E. Murr, Electron and Ion Microscopy and Microanalysis, Marcel Decker, 1982, p.105)
53 Field-Emission Guns V 1 extractiion voltage ~ a few kv V 0 accelerating voltage 1-30 kv R tip ~ 0.1 μm
54 Amplitude Contrast BF and DF images. using objective aperture BF DF
55 ROCK/ROTATE CONTROL ROCK ANGLE ROCK /SEC ROTATE rpm FIXED LEFT GUN ETCHING GUN RIGHT GUN 420uA 0uA 400uA BEAM KeV 10.0 FORELINE 3.0 TORR MDP RPM 100% ROCK OFF ON LEFT GUN VAC ETCHING GUN ION GUN GAS FLOW CONTROL AIRLOCK CONTROL IN OUT HIGH VOLTAGE TIMER START STOP RIGHT GUN VENT Torr BEAM ENERGY kev OFF 10 Penning Gauge 5 5 POWER TEM sample preparation Grid, typically 3 mm in diameter. Membrance (thickness usually below 10 nm) often suspended over grid. Fabricate thin section by ion milling Diamond Saw Bulk, surface and small pieces : plan-view and cross-section samples cutting prethinning Target Assembly Etching Gun Coating Guns final thinning Specimen Holder Dimpling Grinding and polishing Ion milling 59: kv Ar ions 55 Model 682 Precision Etching Coating System 3-10 º Vacuum
56 TEM TEM needs complex sample preparation Very thin specimen needed ( several hundred nanometers) High resolution TEM (HRTEM) allows resolution of 0.1 nm. 2 D projections of a crystal with accompanying defects can be observed. Low angle boundary As seen In HTREM Dislocaion-edge
57 Oxygen vacancies inside the nanowires The corresponding diffraction pattern is shown in the inset of Fig. (a), obviously revealing that the phase of NWs is of α-fe 2 O 3 Extra spots can be found in the diffraction pattern, which has five times the distance of plane, as shown by arrow heads after a detailed examination of the diffraction pattern,as presented schematically in Fig (d). This superstructure is suggested to be caused by oxygen vacancies inside the α-fe 2 O 3 NWs during the growth. The five period distance of the Fe-O lattice plane, fits coherently with the individual sites of the corresponding high resolution TEM image Y. L. Chueh et. al. Adv. Funct. Mater. 16, (2006).
58 In-Situ HRTEM Evaporator Ultra High Vacuum Transmission Electron Microscope Specimen Chamber Vacuum < Pa Pretreatment Chamber Vacuum < Pa Point Resolution : 0.21 nm Lattice Resolution : 0.14 nm Accelerating Voltage : 200 KV Double Title Direct Heating Holder (T max = 1200 C) CCD Camera EELS Ultra High Vacuum Transmission Electron Microscope in NTHU Observation of Atomic Diffusion at Twin-modified Grain Boundaries in Copper Wen-Wei Wu et al., Science 321, 1066 (2008)
59 Scanning Probe Microscopy Scanning Tunneling Microscope (STM) and Atomic Force Microscope (AFM). Sub-nanometer magnification. Atomic scale topographic map of surface. STM uses extremely sharp tip. Tungsten, nickel, platinum - iridium or carbon nanotubes are used for tips.
60 Scanning Tunneling Microscope Tip placed one atom diameter from surface. Voltage applied across tip and surface. Electrons tunnel the gap and produce current. Current produced is proportional to change in gap. Can be used only for conductive materials. Surface of platinum with defects Constant high: much sensitive to modulation of atomic level. Constant current: can measure rough surface with topographical accuracy, but data acquisition is slow.
61 目前無法顯示此圖像 Atomic Force Microscope Similar to STM but tip attached to cantilever beam. When tip interacts with surface, van der waals forces deflect the beam. Deflection detected by laser and photo-detector. Non-conductive materials can be scanned. Used in DNA research and polymer coating technique.