Diffusion mechanisms Activation Energy for Diffusion Diffusion of unlike atoms Vacancy Diffusion Interstitial 舒游 88。 000 3 000000 Figure: Diffusion mechanisms in :33 substitutional atom diffusion and b) interstitial diffusion 8888888 Aspects of Solid-Solid Reactions Rate of Diffusion( Fick's First Law COnventional solid state synthesis techniques involve Ficks first law ting mixtures of two or more solids to form a solid phase roduct. Unlike gas phase and solution reactions. the here D=Doexpeey Ficks la J: the flux (atoms/ems) dFlux =-d deldx D: diffusion coefficient (emy/s) a per unit ti Ac Ax: the concentration gradient (atoms/em .cm) OD is the diffusion coefficient (em/sec). this is the average istance the molecule would travel in the direetion of flow hrough unit thickness in unit time .D is independent of concentration only at low The flux during diffusion is centration de/dx is the concentration gradient across the boundary of through a plane of unit tme Table: Diffusion data Fick's First Law selected materiala for Types of Diffusion Volume diffusion 2. Grain Boundary Diffusion where D=Do exp(R 3. Surface Diffusion Table: The effect of the type of diffusion for thorium in ngsten and for self-diffusion in silver 3:8 0格p(-890k7 00ep-12007 099 npt-4s30eRn3 Diffusion Mechanisms Diffusion of unlike atoms Vacancy Diffusion & Interstitial Diffusion Figure: Diffusion mechanisms in materials: (a)vacancy or substitutional atom diffusion and (b) interstitial diffusion Activation Energy for Diffusion Aspects of Solid-Solid Reactions Conventional solid state synthesis techniques involve heating mixtures of two or more solids to form a solid phase product. Unlike gas phase and solution reactions, the limiting factor in solid-solid reactions is usually diffusion. Fick’s law : Flux = -D dc/dx Flux is mass moving through unit area per unit time D is the diffusion coefficient (cm2 /sec), this is the average distance the molecule would travel in the direction of flow through unit thickness in unit time D is independent of concentration only at low concentrations dc/dx is the concentration gradient across the boundary of interest Rate of Diffusion ( Fick’s First Law ) Fick’s First Law ) RT Q where D D exp( x c J D 0 - = D D = - J : the flux (atoms/cm2 ·s) D : diffusion coefficient (cm2 /s) Dc/Dx: the concentration gradient (atoms/cm3 · cm) The flux during diffusion is defined as the number of atoms passing through a plane of unit area per unit time Fick’s First Law Table: Diffusion data for selected materials ) RT Q where D D exp( x c J D 0 - = D D = - Types of Diffusion 1. Volume Diffusion 2. Grain Boundary Diffusion 3. Surface Diffusion Table: The effect of the type of diffusion for thorium in tungsten and for self-diffusion in silver