chapter11 - Charter 10, Phase Transformations p311-357...

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1 ISSUES TO ADDRESS. .. Transforming one phase into another takes time . How does the rate of transformation depend on time and temperature ? How can we slow down the transformation so that we can engineering non-equilibrium structures ? Are the mechanical properties of non-equilibrium structures better? Fe γ (Austenite) Eutectoid transformation C FCC Fe 3 C (cementite) α (ferrite) + (BCC) Charter 10, Phase Transformations p311-357 Phase Transformations Nucleation nuclei (seeds) act as template to grow crystals for nucleus to form, rate of addition of atoms to nucleus must be faster than rate of loss once nucleated, grow until reach equilibrium Driving force to nucleate increases as we increase T supercooling (eutectic, eutectoid) superheating (peritectic) Small supercooling Æ few nuclei - large crystals Large supercooling Æ rapid nucleation - many nuclei, small crystals
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2 liquid G= G S + G V = 4 π r 2 γ + 4/3π r 3 G ν Homogeneous nucleation G G ν :Volume free energy, <0 G S : Surface Free Energy, >0 r * = critical nucleus : nuclei < r * shrink; nuclei> r * grow (to reduce energy) Homogeneous Nucleation & Energy Effects G T = Total Free Energy = G S + G V Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface) γ π = 2 4 r G S γ = surface tension Volume (Bulk) Free Energy stabilizes the nuclei (releases energy) υ π = G r G V 3 3 4 volume unit energy free volume = υ G
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3 Solidification: Nucleation Processes Homogeneous nucleation nuclei form in the bulk of liquid metal requires supercooling (typically 80-300°C max) Heterogeneous nucleation much easier since stable “nucleus” is already present Could be wall of mold or impurities in the liquid phase allows solidification with only 0.1-10ºC supercooling Solidification T H T r S m γ = 2 * Note: H S = strong function of T γ = weak function of T r * decreases as T increases For typical T r * ca. 100Å H S = latent heat of solidification T m = melting temperature γ = surface free energy T = T m -T = supercooling r* = critical radius For r = r*, d( G)/dr = 0
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4 Rate of Phase Transformations p322 Kinetics – the time dependence of rate The fraction of reaction that has occurred is measured as a function of time Hold temperature constant & measure conversion vs. time sound waves – one sample electrical conductivity – follow one sample X-ray diffraction – have to do many samples How is conversion measured? Rate of Phase Transformation Avrami rate equation => y = 1- exp (- k t n ) k & n fit for specific sample All out of material - done log t Fraction transformed, y Fixed T fraction transformed time 0.5 By convention r = 1 / t 0.5 Adapted from Fig. 10.10, Callister 7e.
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This note was uploaded on 03/08/2010 for the course CHEN 313 taught by Professor Seminario during the Fall '07 term at Texas A&M.

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chapter11 - Charter 10, Phase Transformations p311-357...

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