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Chapter5

# Chapter5 - Chapter Outline Diffusion how do atoms move...

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1 MSE 2090: Introduction to Materials Science Chapter 5, Diffusion Diffusion - how do atoms move through solids? Diffusion mechanisms ¾ Vacancy diffusion ¾ Interstitial diffusion ¾ Impurities The mathematics of diffusion ¾ Steady-state diffusion (Fick’s first law) ¾ Nonsteady-State Diffusion (Fick’s second law) Factors that influence diffusion ¾ Diffusing species ¾ Host solid ¾ Temperature ¾ Microstructure Chapter Outline

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2 MSE 2090: Introduction to Materials Science Chapter 5, Diffusion Diffusion is material transport by atomic motion . Inhomogeneous materials can become homogeneous by diffusion. For an active diffusion to occur, the temperature should be high enough to overcome energy barriers to atomic motion. What is diffusion? results of an atomistic simulation of atomic mixing homework project in MSE 4592/6270
3 MSE 2090: Introduction to Materials Science Chapter 5, Diffusion Interdiffusion (or impurity diffusion) occurs in response to a concentration gradient . Self-diffusion is diffusion in one-component material, when all atoms that exchange positions are of the same type. Interdiffusion and Self-diffusion Before After (Heat)

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4 MSE 2090: Introduction to Materials Science Chapter 5, Diffusion Vacancy diffusion mechanism To jump from lattice site to lattice site, atoms need energy to break bonds with neighbors, and to cause the necessary lattice distortions during jump. This energy comes from the thermal energy of atomic vibrations (E av ~ k B T) The direction of flow of atoms is opposite the vacancy flow direction. Diffusion Mechanisms (I) Atom migration Vacancy migration After Before
5 MSE 2090: Introduction to Materials Science Chapter 5, Diffusion Interstitial diffusion mechanism Diffusion Mechanisms (II) Interstitial atom before jump Interstitial atom after jump Interstitial diffusion is generally faster than vacancy diffusion because bonding of interstitials to the surrounding atoms is normally weaker and there are many more interstitial sites than vacancy sites to jump to. Requires small impurity atoms (e.g. C, H, O) to fit into interstices in host.

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6 MSE 2090: Introduction to Materials Science Chapter 5, Diffusion The flux of diffusing atoms, J, is used to quantify how fast diffusion occurs. The flux is defined as either the number of atoms diffusing through unit area per unit time (atoms/m 2 -second) or the mass of atoms diffusing through unit area per unit time, (kg/m 2 - second). For example, for the mass flux we can write Diffusion Flux J = M / At # (1/A) (dM/dt) (Kg m -2 s -1 ) where M is the mass of atoms diffusing through the area A during time t. A J
7 MSE 2090: Introduction to Materials Science Chapter 5, Diffusion Steady state diffusion: the diffusion flux does not change with time. Concentration profile: concentration of atoms/molecules of interest as function of position in the sample.

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Chapter5 - Chapter Outline Diffusion how do atoms move...

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