Variation of vapor pressure with particle size S.J.T.U. Phase Transformation and Applications The pressure on a small droplet is the sum of the imposed gas pressure and the internal pressure generated by the surface tension of the material 2mrY=2△p 2Y A= ViPr RTIn Figure 4.7 The force holding two hemispheres together is 2mry:the force pushing them apart is mAP. where△P=2ylr. r) The vapor pressure above the small particles is greater than the vapor pressure In- above the large particles.Material would RT then move through the gas phase from small particles to larger ones,Coarsening SJTU Thermodynamics of Materials Spring 2006 ©X.J.Jin ecture 8 Chemical equilibrium
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 8 Chemical equilibrium Variation of vapor pressure with particle size The pressure on a small droplet is the sum of the imposed gas pressure and the internal pressure generated by the surface tension of the material Δ= prr 2 2 πγπ r p 2γ =Δ e Tl RTpV π π = ln e l RT r V π γ π ln 2 ⎟ =⎠⎞ ⎜⎝⎛ ⎟⎠⎞ ⎜⎝⎛ = rRTV l e γ ππ 2 ln The vapor pressure above the small particles is greater than the vapor pressure above the large particles. Material would then move through the gas phase from small particles to larger ones. Coarsening
Second-order transition S.J.T.U. Phase Transformation and Applications First derivatives of G with respect to T and p are continuous and the second derivatives of G with respect to T and P are discontinuous S4=SB S=S(T,p) dS dT dp T dS = dp SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 8 Chemical equilibrium
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 8 Chemical equilibrium Second-order transition First derivatives of G with respect to T and p are continuous and the second derivatives of G with respect to T and P are discontinuous BA = SS = ( , pTSS ) dp p S dT T S Sd p T ⎟⎟⎠⎞ ⎜⎜⎝⎛ ∂∂ ⎟ + ⎠⎞ ⎜⎝⎛ ∂∂ = dp TV dT TC Sd p p ⎟⎠⎞ ⎜⎝⎛ ∂∂ −= p p TS TC ⎟⎠⎞ ⎜⎝⎛ ∂∂ =
Second-order transition(2) S.J.T.U. Phase Transformation and Applications ds-dro) ds=dSB dS-dS-0-CCd-Wus-L.cdp" VA=VREV dp △Cp The thermal expansion dTeg VTe9△a coefficient does change! △O dTeg △B SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 8 Chemical equilibrium
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 8 Chemical equilibrium Second-order transition (2) dp TV dT TC Sd p p ⎟⎠⎞ ⎜⎝⎛ ∂∂ −= A B = SdSd ( ) eq AABB eq eq ApBp A B dpVVdT T CC SdSd −− αα − ==− ,, 0 = BA =VVV Δα Δ = eq p eq eq TV C dT dp The thermal expansion coefficient does change! β α Δ Δ = eq eq dT dp
Superconductivity:an example S.J.T.U. Phase Transformation and Applications 2 C。-C,=-T.4 ≠0 atT-To Normal state Super conducting state Tc→ Figure 4.8 Critical temperature as a function of magnetic field for a superconducting material. SJTU Thermodynamics of Materials Spring2006©X.J.Jin Lecture 8 Chemical equilibrium
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2006 © X. J. Jin Lecture 8 Chemical equilibrium Superconductivity: an example 0 2 0 ⎟ ≠ ⎠⎞ ⎜⎝⎛ Η∂ −=− dT =TatT c sn VTCC cμ