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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

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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

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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

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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.

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43 200/100=2.54^10-2/X 43

44 Scanning electron microscope 電子顯微鏡與光學顯微鏡比較 光學顯微鏡 掃瞄式電鏡 穿透式電鏡 光源 可見光 電子槍 電子槍 透鏡 玻璃透鏡 電磁透鏡 電磁透鏡 放大倍率 1000~2000 倍 10 萬倍 100 萬倍 解析度 0.2μm 1~10nm 0.1nm~ 真空環境 不需要 需要 需要 景深 0.1~5 μm 0.1mm 500 μm 影像色彩 真實色彩 黑白 黑白 成分分析無可可 樣品大大薄, 小 金屬鍍膜不需需不需 影像 表面或穿透影像 表面影像 穿透影像 44 果蠅的複眼是由許多小眼所組成

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

46 電子槍 操作的時候, 燈絲會進行加熱, 並通入負電壓, 一般為 1~50kV 另外有一柵極在燈絲的周圍, 加入一個負偏壓 (0~2500V), 其功能主要可以聚焦成一個如下圖所示 d 0 大小的交叉點, 由此交叉點開始再進入接下來的各種聚焦透鏡, 來對電子束進行壓縮 一般的鎢燈絲設計為一個彎成 V 形的細線, 其操作溫度大約在 2700K, 電流密度為 1.75A/cm 2, 其使用壽命高達 200 小時 除了一般的鎢燈絲, 還有另一種稱為場發射的電子束來源, 它的陰極採用棒狀的形式, 尖端的直徑小於 100 奈米, 加入負電壓的時候, 其尖端電場可達到 10 7 V/cm 2, 因此電子可經隧道效應, 在不加熱的情況下直接離開陰極, 其電流密度可達 1000~10 6 A/cm 2 在同樣的電壓比較之下, 其造成的亮度是一般熱電子槍的數百倍, 不過其價格也極為昂貴 46 熱游離式 : 包含鎢燈絲 六硼化鑭燈絲 作用方式 : 將燈絲加熱到高溫, 讓電子的能量能克服燈絲表面的位能, 從表面被游離出來 優點 : 較為便宜 不需高真空環境 場發射式 : 鎢燈絲 ( 針尖狀 ) 作用方式 : 加上一個強電場, 讓在燈絲針尖的電子受電場吸引而射出 優點 : 電子能量發散小 光源亮度高, 場發射式電子槍顯微鏡的解析力通常要比熱游離式的還要好

47 電子束與試片的作用原理 電子束和試片的作用分為兩類, 一種是彈性碰撞, 幾乎沒有能量損失 另一種為非彈性碰撞, 入射的電子束會將部分的能量傳遞給試片, 即產生二次電子 背向散射電子 歐傑電子 與 X 光等等 其作用如下圖所示 二次電子指的是, 電子束將試片表面 (10 奈米以內 ) 原子堆中的最外層電子打出所產生, 一般利用二次電子可以看出試片表面的高低形貌 背向散射電子則是, 入射電子撞擊到材料的原子核之後反彈回去, 其原子量越大反彈的愈多, 經過處理之後的成像就愈亮, 因此可以利用它來鑑別出材料成分的差異性 X 光的原理為, 當入射電子將原子核的內層電子敲出, 此時外層電子會躍遷跳入內層軌道, 當一個電子由能量不安定的外層跳入能量安定的內層, 勢必產生能量差, 而此能量差即以 X 光的形式放出 而歐傑電子則是,X 光再將外層電子敲出所形成, 也可用來判斷材料的成分差異及特性 47

48 偵測器 偵測器有各種型式, 收集不同的訊號有時需要不同的偵測器, 例如閃爍計數器是由 CaF 2 +Eu(doped) 閃爍物質構成, 當電子撞擊此材料會產生光子, 此光子再經光導管進入光電倍增器, 產生電子而輸出脈波, 此計數器會再覆上一層 Al 膜, 厚度約 10~50 奈米, 加一個 +10kV 的偏壓來加速電子, 為了避免此偏壓造成散光像差, 閃若計數器會以具有柵孔的籃子包住, 稱為法拉第籠, 可以在上面加上 +300V 的偏壓來促進二次電子的收集, 或是加上 -50V 的偏壓排斥二次電子, 讓能量高的背向電子進入 另一固態偵測器, 則是利用電子束撞擊半導體會產生電子電洞對, 外加電壓時便產生電流, 此電流經過放大即產生信號, 此種偵測器可以以多種形式製作, 其對背向電子較為敏感, 如果要偵測二次電子必須設法加速電子置足夠的能量 48

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)

51 Pictures of emission gun LaB 6 51

52 價錢最便宜使用最普遍的是鎢 (W) 燈絲, 以熱游離式來發射電子, 電子能量散佈為 2 ev, 鎢的功函數約為 4.5 ev 鎢燈絲係一直徑約 100 μm, 彎曲成 V 字形的細線, 操作溫度約 2700 K, 使用壽命約為 100 小時 六硼化鑭 (LaB 6 ) 燈絲的功函數為 2.4 e V, 較鎢絲為低, 因此同樣的電流密度, 使用 LaB 6 只要在 1500 K 即可達到, 而且亮度更高, 因此使用壽命便比鎢絲高出許多, 電子能量散佈為 1 ev, 比鎢絲要好 但因 LaB 6 在加熱時活性很強, 所以必須在較好的真空環境下操作, 因此儀器的購置費用較高 場發射式電子槍則比鎢燈絲和六硼化鑭燈絲的亮度又分別高出 10~100 倍, 同時電子能量散佈僅為 0.2~0.3 ev, 所以目前市售的高解析度掃描式電子顯微鏡都採用場發射式電子槍, 其解析度可高達 1 nm 以下 52

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.