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Test 2-Formula Sheet

Test 2-Formula Sheet - DIFFUSION(material transport by...

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DIFFUSION (material transport by atoms motion, movement of atoms from site to site, requires sufficient vibration energy, can change structure in solids) interfusion -atoms of one molecule diffuse into another, concentration changes w/ time . Self-diffusion – all atoms exchanging positions are the same type, no change in concentration, ex. metals. Steady-state diffusion – diffusion flux does not change with time. Fick’s 1 st Law – J=- D(ΔC/Δx), D-const of proportionality [m 2 /s}, C- concentration gradient [kg/m 3 ], x-distance [m], J-diffusion flux [kg/m 2 -s]. Fick’s 2 nd Law – (dC/dt)=D(d 2 C/dx 2 )-> (C x - C o )/(C s -C o )=1-erf(x/2√(Dt)), C o =initial concentration, C s =surface concentration, C x =concentration at depth ‘x’, erf()=Gaussian error function. Erf(0.5)=0.52, x=sqrt(Dt), C~50%. Erf(1)=0.85, x=2sqrt(Dt), C~15%. Factors Affecting Diffusion – species & temperature. Diffusion coef increases when T rises, atomic size, structure (activation energy), phase change, cold work. D(t)=D o e^(Q d /(RT)), D o =temp-independent preexponential [m 2 /s], Q d =activation energy [J/mol], R=gas const., T=abs temp. metals movement of atoms; ceramics – ion pairs move to preserve electroneutality (long-term), single point defects may not exist, cations diffuse quicker than anions; polymers
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