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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/MylarTM Balloons Sputtering, Annealing - Magnetic Materials for Hard Drives Hot dip galvanizing - Coatings and Thin Films Thermal Barrier Coatings for Turbine Blades

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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.

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Activation Energy for Diffusion

Diffusion couple - A combination of elements involved in diffusion studies

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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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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/cm3.cm or at%/cm.

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Figure 5.14 The flux during diffusion is defined as the number of atoms passing through a plane of unit area per unit time

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Figure 5.15 Illustration of the concentration gradient

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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

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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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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.)

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(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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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 900oC) so that the iron has the FCC structure.

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Example 1 SOLUTION

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Example 1 SOLUTION(Continued)

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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.