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Sept. 25, 2008
Phase Transformation of Materials
Nong-Moon Hwang
1.9 The Kinetics of Phase Transformations
The thermodynamic functions apply to systems that are in stable or metastable equilibrium.
Thermodynamics can therefore be used to
calculate the driving force for a transformation,
but it cannot say how fast a transformation will
proceed. The study of how fast
processesoccur belongs to the science of kinetics.
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Mechanism of Solid-State Diffusion
R.E. Reed-Hill, Physical Metallurgy Principles
Mechanism of Solid-State Diffusion
R.E. Reed-Hill, Physical Metallurgy Principles
Zener, C., Acta Cryst., 3 346-354 (1950)
R.E. Reed-Hill, Physical Metallurgy Principles
Mechanism of Solid-State Diffusion
R.E. Reed-Hill, Physical Metallurgy Principles
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Mechanism of Solid-State Diffusion
XeVreaches a value of about 10-4~10-3 at the melting point of the solid. →How to determine experimentally?
Diffusion
Diffusion : Mechanism by which matter transported through matter What is the driving force for diffusion?
⇒ a concentration gradient (x)
⇒ a chemical potential (o)
But this chapter will explain with concentration gradients for a convenience.
The mean vibrational energy is 3kT, therefore increase in proportion to the absolute temperature.
If an adjacent site is vacant it can happen that a particularly violent oscillation results in the atom jumping over on to the vacancy. (Fig. 2.2)
2.1 Atomic mechanisms of diffusion
Substitutional Diffusion
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Sept. 25, 2008
Problems that will be asked in the next class
2.2 Interstitial diffusion
• Random jump of solute B atoms in a dilute solid solution of a simple cubic lattice
Assume that there is no lattice distortion and also that there are always six vacant sites around the diffusing atom.
Derive the expression of JB (Fick’s first law)?
( )
α
− = − ∂ ∂
B B B
C (1) C (2) C x
B
The flux will depend
on D and∂CB ∂x. ∂C∂Bt = ∂∂x⎛⎜⎝DB ∂∂CxB ⎞⎟⎠