Chapter 5: Atom and Ion Movements in Materials

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1 Slide 1 Chapter 5: Atom and Ion Movements in Materials 5-1 Slide 2 Learning Objectives 1. Applications of diffusion 2. Stability of atoms and ions 3. Mechanisms for diffusion 4. Activation energy for diffusion 5. Rate of diffusion [Fick s first law] 6. Factors affecting diffusion 7. Permeability of polymers 8. Composition profile [Fick s second law] 9. Diffusion and materials processing 5-2 Slide 3 Applications of Diffusion Diffusion Net flux of any species, such as ions, atoms, electrons, holes, and molecules. Carburization for surface hardening of steels - A source of carbon is diffused into steel components. In nitriding, nitrogen is introduced into the surface of a metallic material. Dopant diffusion for semiconductor devices A p-n junction is a region of the semiconductor, one side of which is doped with n-type dopants and the other side is doped with p-type dopants. 5-3

2 Slide 4 Applications of Diffusion Conductive ceramics Used in products such as oxygen sensors in cars, touchscreen displays, fuel cells, and batteries. Creation of plastic beverage bottles - limit the occurrence of diffusion for certain species For instance, the diffusion of CO 2 must be minimized. Oxidation of aluminum Al 2 O 3 forms a thin oxide coating. The coating does not have a color (making it invisible) and hinders further oxidation of the metal. Coatings and thin films Used to limit the diffusion of water vapor, oxygen, or other chemicals. 5-4 Slide 5 Applications of Diffusion Thermal barrier coatings for turbine blades Ceramic coatings that protect the underlying alloy from high temperatures. Optical fibers and microelectronic components Optical fibers are coated with polymeric materials to prevent diffusion of water molecules. 5-5 Slide 6 Stability of Atoms and Ions Arrhenius equation where c 0 constant R gas constant, cal/(mol*k) T absolute temperature (K) Q activation energy required to cause Avogadro s number of atoms or ions to move 5-6

3 Slide 7 Figure Diffusion 5-7 Slide 8 Figure Slide 9 Figure

4 Slide 10 Rate of Diffusion [Fick s First Law] Fick s first law explains the net flux of atoms: where J D dc dx J = -D dc dx flux diffusivity or diffusion coefficient (cm 2 /s) concentration gradient (atoms/(cm 3 cm)) The negative sign in the equation indicates that the flux of diffusing species is from higher to lower concentrations Slide 11 Figure Slide 12 Figure Illustration of the Concentration Gradient 5-12

5 Slide 13 Factors Affecting Diffusion Temperature and the diffusion coefficient where Q activation energy, in units of (cal/mol) R gas constant, cal/(mol*k) T absolute temperature (K) D 0 pre-exponential term 5-13 Slide 14 Figure Slide 15 Figure

6 Slide 16 Figure Slide 17 Figure Slide 18 Factors Affecting Diffusion Types of diffusion Volume diffusion: Diffusion of atoms through the interior of grains. Grain boundary diffusion: Atoms can also diffuse along boundaries, interfaces, and surfaces in the material. In this type of diffusion, atoms can diffuse easily. Surface diffusion: Diffusion of atoms along surfaces, such as cracks or particle surfaces. Time Times for heat treatments may be reduced by using higher temperatures or by making the diffusion distances (related to Δx) as small as possible. 5-18

7 Slide 19 Factors Affecting Diffusion Dependence on bonding and crystal structure Interstitial diffusion, with a low-activation energy, usually occurs much faster than vacancy, or substitutional, diffusion. Activation energy, which depends on the strength of atomic bonds, is higher for diffusion of atoms in materials with a high melting temperature (Figure 5.17). Dependence on concentration of diffusing species and composition of matrix The diffusion coefficient (D) depends on the concentration of diffusing species and composition of the matrix Slide 20 Figure Slide 21 Permeability of Polymers Permeability is expressed in terms of the volume of gas or vapor that can permeate per unit area per unit time, or per unit thickness, at a specified temperature and relative humidity. Polymers that have a polar group (e.g., ethylene vinyl alcohol) have higher permeability for water vapor than for oxygen gas. Diffusion of some molecules into a polymer can cause swelling problems. 5-21

8 Slide 22 Composition Profile [Fick s Second Law] Fick s second law If D is not a function of location x and the concentration (c) of diffusing species 5-22 Slide 23 Composition Profile [Fick s Second Law] Solution to the Fick s second law equation depends on the boundary condition. where c s c 0 c x concentration of the diffusing atoms at the surface of the material. initial uniform concentration of the diffusing atoms in the material. concentration of the diffusing atom at location x below the surface after time t Slide 24 Figure

9 Slide 25 Figure Slide 26 Composition Profile [Fick s Second Law] The mathematical definition of the error function Fick s second law is the technique behind carburization 5-26 Slide 27 Composition Profile [Fick s Second Law] Limitations to applying the error-function solution It is assumed that D is independent of the concentration of the diffusing species. The surface concentration of the diffusing species (c s ) is always constant. There are situations under which these conditions may not be met and hence the concentration profile evolution will not be predicted by the error-function solution. 5-27

10 Slide 28 Diffusion and Materials Processing Melting and casting Diffusion plays a particularly important role in solidification of metals and alloys. Sintering High temperature treatment that causes particles to join, gradually reducing the volume of pore space between them. Powder metallurgy - a processing route by which metal powders are pressed and sintered into dense, monolithic components Slide 29 Diffusion and Materials Processing Liquid phase sintering: Process in which a small amount of liquid forms and assists densification. Hot pressing unidirectional pressure is applied while the material is being sintered. Hot isostatic pressing the pressure is applied in all directions while the material is being sintered Slide 30 Figure

11 Slide 31 Figure Slide 32 Diffusion and Materials Processing Grain growth: Movement of grain boundaries, permitting larger grains to grow at the expense of smaller grains (Figure 5.23). Driving force for grain growth is the reduction in grain boundary area. In normal grain growth, the average grain size increases steadily and the width of the grain size distribution is not affected severely. In abnormal grain growth, the grain size distribution tends to become bi-modal Slide 33 Figure

12 Slide 34 Key Terms Diffusion Nitriding Conductive ceramics Thermal barrier coatings Activation energy Self-diffusion Interdiffusion Vacancy diffusion Interstitial diffusion Diffusion couple Flux Fick s first law Diffusivity or diffusion coefficient 5-34 Slide 35 Concentration gradient Volume diffusion Grain boundary diffusion Diffusion distances Permeability Fick s second law Sintering Powder metallurgy Key Terms Liquid phase sintering Hot pressing Hot isostatic pressing Grain growth Driving force Normal grain growth Abnormal grain growth Diffusion bonding 5-35