Chapter 8 Multicomponent Homogeneous Nonreacting Systems: Solutions

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Chapter 8Multicomponent Homogeneous Nonreacting
Systems Solutions
Quasichemical Theory

• Notes on
• Thermodynamics in Materials Science
• by
• Robert T. DeHoff
• (McGraw-Hill, 1993).

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Quasichemical Theory
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Binding Energy Model
Nuclear Repulsion
Electronic Attraction
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Quasichemical Theory Assumptions
Only nearest neighbor bonds are considered.

• Single bond energy for each type of bond.
• eAA, eAB, eBB.

• Solution is random.
• Probability site is occupied by an A XA.
• Probability site is occupied by a B XB.

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Quasichemical Theory Number of Bonds
Where Z number of nearest neighbors.
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Square Array
N20
Z4
P 1/2 x 20 x 4 40
P 311/2 x 18 40
Unit cell
p 1/2 x 1 x 4 2
z4
n 4 x 1/4 1
p 1/2 x 4 2
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Face Centered Cubic
N8 x 1/8 6 x ½ 4
Z12
P 1/2 x 4 x 12 24
P 6 x 4 x 1/2 3 x 4 x 1 24
P 6 x 4 x 1/2
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Body Centered Cubic
N8 x 1/8 1 2
Z8
P 1/2 x 2 x 8 8
P 8 x 1 8
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Quasichemical Theory Number of Bonds
Where Z number of nearest neighbors.
Bonds with A atoms
Bonds with A atoms
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Quasichemical Theory
Express PAA PBB as function of PAB.
Internal energy per mole of solution.
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Quasichemical Theory
Internal energy of pure crystals.
Molar energy of mixing.
For crystals
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Quasichemical Theory Probability of Bond Type
XA
XA
Random
Random
XB
XA
XB
XA
XB
XB
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Quasichemical Theory
Write PAB in terms of XA, XB.
Substitute in enthalpy of mixing.