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chap6_7

chap6_7 - 材材材材材材 Fundamental of Materials Prof...

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Unformatted text preview: 材材材材材材 Fundamental of Materials Prof: Tian Min Bo Prof: Tian Tel: 62795426 材 62772851 E-mail: [email protected] [email protected] 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 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 parabola law. 3. Phase’s width Ⅱ.Basic features: 1. 2.. 2 3. 4. Diffusion is accompanied by reaction or phase Diffusion transformation. In general, diffusion is rate-determining step while reaction take place instantaneously. For diffusion in binary systems there appear only a For series of single phase, one adjacent to another, while mixed phase zone doesn’t appear. mixed Concentrating changes abruptly at phase boundary. The phase boundaries and the width of each phase The change parabolic ally with time. change Ⅲ.Reaction Diffusion dynamics Reaction dynamics 1. Speed of interface ∂C ∂C (− D ∂x ) βα − (− D ∂x )αβ dt = (Cβα − Cαβ ) ⋅ dx ⋅1 ∂C ∂C (D )αβ − ( D ) βα dx ∂x ∂x ∴ = dt Cβα − Cαβ x t ∂C 1 dC = ∂x t dλ let λ = dC dC (D )αβ − ( D ) βα dx 1 1 dt dt ∴ = ⋅ = K (C ) dt C βα − Cαβ t t ∴ x = t ⋅ K ′(C ) 2. Phase width Wβ = xβα − xγ β dWβ 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 3. Ⅳ.Discussion 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 special cases: 材 (1) is tenable in volume (lattice) diffusion (1) ffactors influencing growth: actors a.. Diffusion path (lattice grain boundaries pore surface). a Diffusion b. Relative rate of diffusion and reaction Relative Examples and Discussions Examples 1. F-N 2. F-C Exercise Exercise Thank you ! Thank you ! 29 ...
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