Introduction to Solidification 2' Thermodynamics

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Introduction to Solidification2. Thermodynamics

• Rongshan QIN
• http//cml.postech.ac.kr/rqin

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In this lecture

• Thermodynamic properties
• Internal energy
• Enthalpy
• Entropy
• Free energy
• Phase transition - possibility

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Why?
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Thermodynamics

• Thermodynamics concerns energy and the way that
  energy is transferred.
• Energy conservation
• Free energy minimization
• Lowest temperature

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The first law of thermodynamics

• Energy can neither be created nor destroyed in a
  system of constant mass, although it may be
  converted from one form to another.

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The first law of thermodynamics

• U the change of internal energy
• w the work done by the system
• Q energy exchanged between the system and
  environment

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Constant pressure Enthalpy
H Enthalpy
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Entropy thermodynamic definition
Entropy
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Free energy

• General free energy

• Gibbs energy constant pressure

• Holmholtz energy constant volume

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The second law of thermodynamics

• Evolution of system follows a routine that free
  energy dropping.

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Schematic diagram of free energy changes vs
temperature
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Free energy minimization during solidification
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Entropy Statistical definition

• Non-equilibrium definition

k1.3806502 ? 10-23 Joule/Kelvin W is the
possibility (a measure of disorder)
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Entropy of solution at ideal-mixing

• Ideal solution
• No repulsive and attractive interactions between
  various components.
• Components can mix up ideally

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Entropy of solution at ideal-mixing

• n atom of A N-n atom B

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Entropy of solution at ideal-mixing

• Stirling approximation

• Entropy

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Entropy of solution at ideal-mixing

• Molar entropy of ideal binary solution

• Molar Gibbs energy of ideal solution

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Entropy of solution at non-ideal mixing

• Interactions between different atoms or molecules
  of various components

• Excess mixing energy

?gt0 corresponds to repulsive interaction, such as
Cu-Ag. ?lt0 corresponds to the attractive
interaction, such as Fe-Ni.
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Gibbs mixing energy

• Total Gibbs mixing energy

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Gibbs mixing energy

• In general, the excess energy format

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Gibbs energy of solution

• Reference point

• Gibbs energy in general

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System free energy
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In summary

• Basic definitions of internal energy, enthalpy,
  entropy, Helmholtz and Gibbs free energies.
• Three laws of thermodynamics
• Phase transition direction

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References

• M.C. Flemings, Solidification processing, 1974.
• N. Saunders and A.P. Miodownik, CALPHAD, 1998.
• A.T. Dinsdale, CALPHAD 15 (1991) 317.