Foundations of Materials Science and Engineering Lecture Note 4

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1 Foundations of Materials Science and Engineering Lecture Note 4 April 2, 2013 Kwang Kim Yonsei University kbkim@yonsei.ac.kr Y O N Se I

2 Solidification of Metals

3 Solidification of Metals The solidification of metals and their alloys is an important industrial process. Not only do structural alloys start with the casting of ingots for processing into reinforcing bars or structural shapes, but when a metal is welded a small portion of metal near the weld melts and resolidifies. It also serves as a model to represent first order phase transformations in general.

Solidification of Metals Metals are melted to produce finished and semi-finished parts. Two steps of solidification Nucleation : Formation of stable nuclei.

4 Solidification of Metals Metals are melted to produce finished and semi-finished 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. (a) Formation of stable nuclei (b) Growth of crystals (c) Grain structure

5 Solidification of Metals Phase transformations involve change in structure and composition rearrangement and redistribution of atoms via diffusion is required. - Nucleation : Formation of stable nuclei. - Growth of nuclei : Formation of grain structure. The process of phase transformation involves: - Nucleation of the new phase(s) - formation of stable small particles (nuclei) of the new phase(s). Nuclei are often formed at grain boundaries and other defects. - Growth of the new phase(s) at the expense of the original phase(s).

6 Ideal Gas Law An ideal gas : all collisions between atoms or molecules are perfectly elastic there are no intermolecular attractive forces a collection of perfectly hard spheres which collide but which otherwise do not interact with each other no potential energy (no force field) all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature. An ideal gas : characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T).

7 Non- ideal Gas

8 Non ideal Gas Ideal Gas Intermolecular force? : condensation, liquefaction at high P Liquefaction of a real gas No liquefaction of an ideal gas Requirements for liquefaction of a real gas?

9 Phase Equilibria in water

10 Phase Equilibria in water temperature increase pressure increase

11 Phase Equilibria in water Temp. temperature increase V L + V S + L L S pressure increase time

12 Phase Equilibria in water Pressure temperature increase V V +L L pressure increase time

Non- ideal Gas D D E D Definition: a physically distinctive form of matter, such

A phase of matter is characterized by having relatively uniform chemical and

13 Non- ideal Gas D D E D Definition: a physically distinctive form of matter, such as a solid, liquid, gas or At point C plasma. A phase of matter is characterized by having relatively uniform chemical and physical properties. Phases are different from states of matter. The states of matter (e.g., liquid, solid, gas) are phases, but matter can exist in different phases yet the same state of matter. For example, mixtures can exist in multiple phases, such as an oil phase and an aqueous phase.

14 Pc At Critical Point, Molar volume of liquid = Molar volume of gas Critical Point Critical Temperature Tc Critical Pressure Pc Critical Volume Vc Molar volume of liquid Molar volume of gas Vc

15 Cryophorus : an instrument that illustrates the freezing of water by its own evaporation A cryophorus is a glass container containing liquid water and water vapor. It is used to demonstrate rapid freezing by evaporation. A typical cryophorus has a bulb at one end connected to a tube of the same material. When the liquid water is manipulated into the bulbed end and the other end is connected to a vacuum pump, the gas pressure drops as it is cooled. The liquid water begins to evaporate, producing more water vapor. Evaporation causes the water to cool rapidly to its freezing point and it solidifies suddenly. Finally, a piece of ice disappears as a result of ice sublimation to water vapor/ Vacuum pump Water droplet in a bottle under vacuum

16 Cryophorus 실험 1) 진공상태에위치한 water droplet 의 evaporation 2) 흡열반응인 evaporation 진행 자체의온도가감소 liquid water/vapor 평형상태공존선도달 * 3) 지속적인온도감소에의해 3중점도달 (ice/ liquid water/vapor 평형상태공존점 ) 4) 온도, 압력저하 liquid water/vapor 평형상태공존선에서 solid/vapor 평형공존선으로변화 5) liquid water droplet가 solid ice 로변화 6) solid ice는 sublimation에의해 vapor 상으로승화궁극적으로는 solid ice는모두 sublimation 하여사라짐

17 Nucleation Heterogeneous the new phase appears on the walls of the container, at impurity particles, etc. Homogeneous solid nuclei spontaneously appear within the undercooled phase. solidification of a liquid phase undercooled below the melting temperature as a simple example of a phase transformation.

18 Homogenous Nucleation Homogeneous nucleation occurs when there are no special objects inside a phase which can cause nucleation. For instance when a pure liquid metal is slowly cooled below its equilibrium freezing temperature to a sufficient degree numerous homogeneous nuclei are created by slow-moving atoms bonding together in a crystalline form.

19 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.

20 Solidification of Metals Typical data relevant to the solidification of metals

21 Energies Involved in Homogeneous Nucleation Gibbs Free Energy G = H - TS where H = Enthalpy, T = Absolute Temperature, and S = Entropy Materials Scientists refer to the difference in G between the old and new phases as the driving force for the phase transformation. The release of heat when a metal solidifies indicates that the crystalline phase has a lower Gibbs Free Energy, G, than the liquid. At the equilibrium freezing temperature the Gibbs Free Energy of the liquid and the crystalline phase are equal.

22 Energies Involved in Homogeneous Nucleation Phase transformation of liquid to solid G = G solid -G liquid G liquid G solid G solid G liquid

23 Energies Involved in Homogeneous Nucleation Is the transition from undercooled liquid to a solid spherical particle in the liquid a spontaneous one? That is, is the Gibbs free energy decreases? The formation of a solid nucleus leads to a Gibbs free energy change of ΔG

24 Energies Involved in Homogeneous Nucleation The formation of a solid nucleus leads to a Gibbs free energy change of ΔG

25 Energies Involved in Homogeneous Nucleation (1)Volume free energy (2) Surface energy

26 Energies involved in homogenous nucleation Volume free energy G v (Gibbs Free Energy G = H-TS) 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 Surface energy Gs Required to form new solid surface ΔG s is energy needed to create a surface. γ is specific surface free energy. Then Gs 4 r 2 ΔG s is retarding energy.

27 Energies involved in homogenous nucleation

28 Total Free Energy Total free energy is given by + Since when r=r*, d(δg T )/dr = 0 ΔG s r* 2 G V Nucleus ΔG r* r* ΔG T r Above critical radius r* Below critical radius r* - ΔG v Energy lowered by growing into crystals Energy Lowered by redissolving

29 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* 2 T H f m T r* = critical radius of nucleus γ = Surface free energy ΔH f = Latent heat of fusion Δ T = Amount of undercooling. Both r* and G* decrease with increasing undercooling.

30 Critical Radius Versus Undercooling

gas/vapor, solidification from liquid, bubble formation from liquid, etc.

31 Heterogeneous Nucleation Heterogeneous nucleation occurs much more often than homogeneous nucleation. Heterogeneous nucleation applies to the phase transformation between any two phases of gas, liquid, or solid, typically for example, condensation of gas/vapor, solidification from liquid, bubble formation from liquid, etc. Heterogeneous nucleation forms at preferential sites such as phase boundaries, surfaces (of container, bottles, etc.) or impurities like dust. At such preferential sites, the effective surface energy is lower, thus diminishes the free energy barrier and facilitating nucleation.

32 Heterogeneous Nucleation Heterogeneous nucleation can be considered as a surface catalyzed or assisted nucleation process. The extent of how a surface can catalyze or facilitate the nucleation depends on the contact angle of the nucleus with respect to the substrate. The smaller the angle (or the stronger the wetting of the surface), the lower the free energy change, and the lower the nucleation barrier will be.

Heterogeneous Nucleation Critical radius of the nucleus (r*) for a heterogeneous nucleation is the same as that for a homogeneous nucleation, whereas the critical volume of the

33 Heterogeneous Nucleation Critical radius of the nucleus (r*) for a heterogeneous nucleation is the same as that for a homogeneous nucleation, whereas the critical volume of the nucleus (like the droplet for liquid nucleated from gas/vapor phase) is usually smaller for heterogeneous nucleation than for homogeneous nucleation, due to the surface wetting (spreading).

34 Homogeneous nucleation : Total Free Energy Total free energy is given by + Since when r=r*, d(δg T )/dr = 0 ΔG s r* 2 G V Nucleus ΔG r* r* ΔG T r Above critical radius r* Below critical radius r* - ΔG v Energy lowered by growing into crystals Energy Lowered by redissolving

35 Heterogeneous Nucleation

36 Heterogeneous Nucleation γαβ= (gas - liquid), γαδ= (gas - solid), γβδ= (liquid - solid) Consider a droplet of liquid on a flat surface with fixed volume. The total surface energy of the system is a function of the shape of the droplet. The diagram above shows two different shapes of the same volume, but of different surface area leading to different Surface energy: Gs= γαβaαβ+ γαδaαδ+ γβδaβδ where Aαβ,Aαδand Aβδare areas of αβ, αδ and βδ interfaces, respectively

37 Heterogeneous Nucleation Gs= γαβaαβ+ γαδaαδ+ γβδaβδ where Aαβ,Aαδand Aβδare areas of αβ, αδ and βδ interfaces, respectively Assume r be the radius of curvature of the droplet, then: Aβδ= π r2sin2θ Aαδ=A0- π r2sin2θ;a0is the area of αδ interface without β Thus,

38 Heterogeneous Nucleation dgs= {4 π r γαβ (1-cosθ) + 2 π r (γβδ - γαδ) sin2θ} d r + {2 π r2γαβ sinθ + 2 π r2 (γβδ - γαδ) sinθ cosθ}dθ = 0

39 Heterogeneous Nucleation

40 Heterogeneous Nucleation

41 Heterogeneous Nucleation

42 Heterogeneous Nucleation

43 Heterogeneous Nucleation

44 Heterogeneous Nucleation The cloud : Lots of small spherical water droplets too light to fall under gravity The droplets need to freeze to ice which becomes a nucleus capable of attracting water vapor. In cold days it snows and In hot days it rains. The ice : The homogeneous nucleation temperature is 40 C (way too cold) The solution : Heterogeneous nucleation Air Pollution will provide the seeds (OK, not the best solution) Use silver iodide crystals decreases the nucleation T from -40 C to 4 C.

45 Heterogeneous Nucleation Carbonate drinks have carbon dioxide which is dissolved under pressure. When the can is opened the pressure drops and the gas comes out of solution in the form of bubbles. Aluminum and glass are poor catalysts for heterogeneous nucleation.

46 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.

Types of Grains Equiaxed Grains: Crystals, smaller in size, grow equally in all directions. Formed at the sites of high concentration of the nuclie.

47 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 Equiaxed Grains

48 Types of Grains

49 Casting in Industries In industries, molten metal is cast into either semi finished or finished parts. Continuous casting of steel ingots Direct-Chill semicontinuous Casting unit for aluminum

50 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)

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.

51 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. Growth of single crystal for turbine airfoil.

52 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.

53 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.

54 Substitutional Solid Solution Solute atoms substitute for parent 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 Solute atoms

55 Substitutional Solid Solution The solubility of solids is greater if 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%

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.

56 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 r00.129nm Carbon atoms r=0.075nm

57 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).

Point Defects Vacancy Vacancy is formed due to a missing atom. Vacancy is formed (one in 10000 atoms) during crystallization or mobility of atoms. Energy of formation is 1 ev.

58 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. Vacancies moving to form vacancy cluster

59 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.

60 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.

61 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 Screw dislocation Mixed dislocation

62 Edge Dislocation Created by insertion of extra half planes of atoms. Positive edge dislocation Negative edge dislocation Burgers vector Shows displacement of atoms (slip). Burgers vector

63 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.

64 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. Dislocation structure of iron deformed 14% at C

65 Grain Boundaries 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. 65

66 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. 3D view of grains 66 Grain Boundaries In 1018 steel

67 Twin Boundaries Twin: A region in which mirror image pf structure exists across a boundary. Formed during plastic deformation and recrystallization. Strengthens the metal. Twin Plane Twin

68 Other Planar Defects Small angle tilt boundary: Array of edge dislocations tilts two regions of a crystal by < 10 o Stacking faults: Piling up faults during recrystallization due to collapsing. Example: ABCABAACBABC FCC fault Volume defects: Cluster of point defects join to form 3-D void.

69 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 microscope.

70 Effect of Etching Unetched Steel 200 X Etched Steel 200 X Unetched Brass 200 X Etched Brass 200 X

71 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.

< 6 Medium grained and etched specimen at 100 x. n = ASTM grain size number.

72 Measuring Grain Size ASTM grain size number n is a measure of grain size. N = 2 n-1 N = Number of grains per N < 3 Coarse grained square inch of a polished 4 < n < 6 Medium grained and etched specimen at 100 x. n = ASTM grain size number. 7 < n < 9 Fine grained N > 10 ultrafine grained 200 X 200 X 1018 cold rolled steel, n= cold rolled steel, n=8

73 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. d = C/n L M C=1.5, and M is magnification 3 inches 5 grains.

specimen. Difference in atomic arrangement change directions of electrons.

74 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

Transmission Electron Microscope TEM needs complex sample preparation Very thin specimen needed ( several hundred nanometers) High resolution

75 Transmission Electron Microscope 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

The secondary electrons are collected to

76 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. TEM of fractured metal end

CHAPTER 4. Solidification and Crystalline Imperfections in Solids 4-1

CHAPTER 4. Solidification and Crystalline Imperfections in Solids 4-1 CHAPTER 4 Solidification and Crystalline Imperfections in Solids 4-1 Solidification of Metals Metals are melted to produce finished and semifinished parts. Two steps of solidification Nucleation : Formation