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Fundamental of Materials
Prof: Tian Min Bo
Tel: 62795426 材 62772851
Department of Material Science and Engineering
Tsinghua University. Beijing 100084 Lesson twentynine §6.7 Reaction Diffusion (Diffusion in
Multiple Phase Zone)
Multiple Ⅰ. Course of reaction diffusion
phase change 1. There have no two-phases area in diffusion
area, every layer is single-phases.
2. Phase’s interface moves according to
3. Phase’s width Ⅱ.Basic features:
4. Diffusion is accompanied by reaction or phase
transformation. In general, diffusion is rate-determining
step while reaction take place instantaneously.
For diffusion in binary systems there appear only a
series of single phase, one adjacent to another, while
mixed phase zone doesn’t appear.
Concentrating changes abruptly at phase boundary.
The phase boundaries and the width of each phase
change parabolic ally with time.
change Ⅲ.Reaction Diffusion dynamics
1. Speed of interface
∂C (− D ∂x ) βα − (− D ∂x )αβ dt = (Cβα − Cαβ ) ⋅ dx ⋅1 ∂C
)αβ − ( D
Cβα − Cαβ
t dλ let λ = dC
)αβ − ( D
= K (C )
C βα − Cαβ
∴ x = t ⋅ K ′(C ) 2. Phase width
Wβ = xβα − xγ β
dt = dxβα
dt − dxγ β
dt = Aβ
t Wβ = Bβ t
W j = x j , j +1 − x j −1, j = B j t 3. Rule of phase appearing
1. Phases that can appear
2. Growth law: in general
Growth W 2 = K (C )t (1i)n x n = K (C )t n =1 4
(1) is tenable in volume (lattice) diffusion
(1) ffactors influencing growth:
a.. Diffusion path (lattice grain boundaries pore surface).
b. Relative rate of diffusion and reaction
Relative Examples and Discussions
1. F-N 2. F-C Exercise
Exercise Thank you !
Thank you !
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This note was uploaded on 10/15/2011 for the course ENG 242 taught by Professor Mingjiezhao during the Spring '11 term at BYU.
- Spring '11