Difference between steady state and unsteady state diffusion
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sieady state
Consider diffusion of solute atoms (b) in solid state solution (AB) in direction x between two parallel atomic planes (separated by ∆x)• if there is no changes with timein CBat these planes – such diffusion condition is called steady-state diffusionFor a steady-state diffusion, flux (flow),J,of atoms is:dxdCDJ−=J– flux of atoms, atoms/(m2s): the number of particles which pass through a unit area in a unit of time;D– diffusivity or diffusion coefficient, m2/sdC/dx– concentration gradient, atoms/m4
non steady diffussion
2Chapter 5Fick’s first law of diffusionFor steady-state diffusion condition (no change in the system with time), the net flow of atoms is equal to the diffusivity Dtimes the diffusion gradient dC/dxdxdCDJ−=⎟⎠⎞⎜⎝⎛×⎟⎟⎠⎞⎜⎜⎝⎛−=⎟⎠⎞⎜⎝⎛mmatomsdxdCsmDsmatomsJ1322Diffusivity Ddepends on:1. Diffusion mechanism2. Temperature of diffusion3. Type of crystal structure (bcc > fcc)4. Crystal imperfections5. Concentration of diffusing species‘-’ sign: flux direction is from the higher to the lower concentration; i.e. it is the opposite to the concentration gradientChapter 5Non-Steady-State DiffusionIn practice the concentrationof solute atoms at any point in the material changes with time–non-steady-state diffusionFor non-steady-state condition, diffusion coefficient, D- NOT dependent on time:⎟⎠⎞⎜⎝⎛=dxdCDdxddtdCxxSecondFick’s law of diffusion:The rate of compositional change is equal to the diffusivity times the rate of the change of the concentration gradient22xCDdtdCx∂∂=If D ≠D(x), in 1D case:⎟⎟⎠⎞⎜⎜⎝⎛∂∂+∂∂+∂∂=222222zCyCxCDdtdCxIn 3D case:
Consider diffusion of solute atoms (b) in solid state solution (AB) in direction x between two parallel atomic planes (separated by ∆x)• if there is no changes with timein CBat these planes – such diffusion condition is called steady-state diffusionFor a steady-state diffusion, flux (flow),J,of atoms is:dxdCDJ−=J– flux of atoms, atoms/(m2s): the number of particles which pass through a unit area in a unit of time;D– diffusivity or diffusion coefficient, m2/sdC/dx– concentration gradient, atoms/m4
non steady diffussion
2Chapter 5Fick’s first law of diffusionFor steady-state diffusion condition (no change in the system with time), the net flow of atoms is equal to the diffusivity Dtimes the diffusion gradient dC/dxdxdCDJ−=⎟⎠⎞⎜⎝⎛×⎟⎟⎠⎞⎜⎜⎝⎛−=⎟⎠⎞⎜⎝⎛mmatomsdxdCsmDsmatomsJ1322Diffusivity Ddepends on:1. Diffusion mechanism2. Temperature of diffusion3. Type of crystal structure (bcc > fcc)4. Crystal imperfections5. Concentration of diffusing species‘-’ sign: flux direction is from the higher to the lower concentration; i.e. it is the opposite to the concentration gradientChapter 5Non-Steady-State DiffusionIn practice the concentrationof solute atoms at any point in the material changes with time–non-steady-state diffusionFor non-steady-state condition, diffusion coefficient, D- NOT dependent on time:⎟⎠⎞⎜⎝⎛=dxdCDdxddtdCxxSecondFick’s law of diffusion:The rate of compositional change is equal to the diffusivity times the rate of the change of the concentration gradient22xCDdtdCx∂∂=If D ≠D(x), in 1D case:⎟⎟⎠⎞⎜⎜⎝⎛∂∂+∂∂+∂∂=222222zCyCxCDdtdCxIn 3D case:
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