Fundamentals of Solidification

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Fundamentals of Solidification

• Lecture 3 Thermodynamics

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Why does liquid solidify at this condition?
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Why does melting point change with composition?
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Why does microstructure change with temperature?
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Why?
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Why?
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Outline

• Thermodynamic function of state
• Thermodynamic law
• Computational phase diagram

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Thermodynamic function of state

• Internal energy

Kinetic energy Potential energy
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Thermodynamic function of state

• Internal energy, U
• The internal energy of a thermodynamic system is
  the total of the kinetic energy due to the motion
  of molecules (translational, rotational,
  vibrational) and the potential energy associated
  with the vibrational and electric energy of atoms
  within molecules or crystals. It includes the
  energy in all the chemical bonds, and the energy
  of the free, conduction electrons in metals.
• From Wikipedia

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Thermodynamic function of state

• Work, W

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Thermodynamic function of state

• Enthalpy, H

Constant pressure
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Thermodynamic function of state

• Entropy, S

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Thermodynamic function of state

• Entropy, S

k1.3806502 ? 10-23 Joule/Kelvin W is the
possibility of arrangement
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Thermodynamic function of state

• Heat dissipation, Q

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Thermodynamic function of state

• General free energy

• Gibbs energy constant pressure

• Holmholtz energy constant volume

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Thermodynamic law

• 2nd law of thermodynamics
• Evolution of system follows a routine of free
  energy dropping.

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Thermodynamic law
solid
Free energy
liquid
melting point
Temperature
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Thermodynamic law
solid b
solid
Free energy
liquid
melting point
Temperature
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Thermodynamic law
solid c
solid
Free energy
liquid
melting point
Temperature
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Thermodynamic law
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Thermodynamic law
Free energy
Solute composition
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Computational phase diagram

• Calculation of free energy
• Consider the simple case where everything else
  are the same except the atom configurations

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Computational phase diagram

• Ideal solution
• No repulsive and attractive interactions between
  various atoms.
• Atoms 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 free energy of ideal solution

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Computational phase diagram
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Free energy of non-ideal solution

• 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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Free energy of non-ideal solution
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Free energy of non-ideal solution
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Free energy of non-ideal solution
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References

• M.C. Flemings, Solidification processing, 1974.
• A.T. Dinsdale, CALPHAD 15 (1991) 317.
• H.L. Lukas, S.G. Fries and B. Sundman,
  Computational Thermodynamics The Calphad Method,
  Cambridge University Press, (2007)