1. 1 Diffusion Diffusion: Atom and Ion Movements in Materials Applications of Diffusion  Nitriding - Carburization for Surface Hardening of Steels  p-n junction - Dopant Diffusion for Semiconductor Devices  Manufacturing of Plastic Beverage Bottles/Mylar TM Balloons  Sputtering, Annealing - Magnetic Materials for Hard Drives  Hot dip galvanizing - Coatings and Thin Films  Thermal Barrier Coatings for Turbine Blades

2. 2 Mechanisms for Diffusion  Self-diffusion - The random movement of atoms within an essentially pure material.  Vacancy diffusion - Diffusion of atoms when an atom leaves a regular lattice position to fill a vacancy in the crystal.  Interstitial diffusion - Diffusion of small atoms from one interstitial position to another in the crystal structure. ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license.

3. 3 Activation Energy for Diffusion  Diffusion couple - A combination of elements involved in diffusion studies ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 5.12 A high energy is required to squeeze atoms past one another during diffusion. This energy is the activation energy Q. Generally more energy is required for a substitutional atom than for an interstitial atom

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5. 5 Rate of Diffusion (Fick’s First Law)  Fick’s first law - The equation relating the flux of atoms by diffusion to the diffusion coefficient and the concentration gradient.  Diffusion coefficient (D) - A temperature-dependent coefficient related to the rate at which atoms, ions, or other species diffuse.  Concentration gradient - The rate of change of composition with distance in a nonuniform material, typically expressed as atoms/cm 3. cm or at%/cm. ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 5.14 The flux during diffusion is defined as the number of atoms passing through a plane of unit area per unit time

6. 6 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 5.15 Illustration of the concentration gradient

7. 7 Factors Affecting Diffusion  Temperature and the Diffusion Coefficient (D)  Types of Diffusion - volume diffusion, grain boundary diffusion, Surface diffusion  Time  Dependence on Bonding and Crystal Structure  Dependence on Concentration of Diffusing Species and Composition of Matrix

8. 8 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 5.18 The diffusion coefficient D as a function of reciprocal temperature for some metals and ceramics. In the Arrhenius plot, D represents the rate of the diffusion process. A steep slope denotes a high activation energy

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10. 10 ©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning ™ is a trademark used herein under license. Figure 5.24 The dependence of diffusion coefficient of Au on concentration. (Source: Adapted from Physical Metallurgy Principles, Third Edition, by R.E. Reed-Hill and R. Abbaschian, p. 363, Fig. 12-3. Copyright © 1991 Brooks/Cole Thomson Learning. Adapted with permission.)

11. 11 (Fick’s Second Law)  Fick’s second law - The partial differential equation that describes the rate at which atoms are redistributed in a material by diffusion.

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13. 13 Example 1: Design of a Carburizing Treatment The surface of a 0.1% C steel gears is to be hardened by carburizing. In gas carburizing, the steel gears are placed in an atmosphere that provides 1.2% C at the surface of the steel at a high temperature (Figure 5.1). Carbon then diffuses from the surface into the steel. For optimum properties, the steel must contain 0.45% C at a depth of 0.2 cm below the surface. Design a carburizing heat treatment that will produce these optimum properties. Assume that the temperature is high enough (at least 900 o C) so that the iron has the FCC structure.

14. 14 Example 1 SOLUTION

15. 15 Example 1 SOLUTION(Continued)

16. 16 Diffusion and Materials Processing  Sintering - A high-temperature treatment used to join small particles.  Powder metallurgy - A method for producing monolithic metallic parts.  Dielectric resonators -Hockey puck-like pieces of ceramics such as barium magnesium tantalate (BMT) or barium zinc tantalate (BZN).  Grain growth - Movement of grain boundaries by diffusion in order to reduce the amount of grain boundary area.  Diffusion bonding - A joining technique in which two surfaces are pressed together at high pressures and temperatures.