Review: Binary Phase Diagramsmix mix mixG H T S

ln lnmixA A B BS RX X RX X

0mixH mix

A BH X X N0zєXAXB

є = AB – ½ (AA + BB)

, є > 0 AB is large avoid A-B bonds

clustering, unmixing, phase separation

all solutions:

when entropy is only configurational:

ideal solutions:

regular solutions:

regular, positive enthalpy

Regular solutions, positive enthalpysolid phase is a regular solution, > 0; liquid phase is a an ideal solution

LiquidLiquid

Binary Eutectic

´ ´´

+ L

TMA

TMB

´+´´

liquidussolidus

increasing

´ ´´

´+´´

+ L + L

liquidus

liquidus

solidus

TMA

TMB

solidus

Binary Eutectic Phase DiagramFor >> 0, no longer useful to think of A and B as forming a continuous solution

T1

XB XB

Binary Eutectic Phase DiagramFor >> 0, no longer useful to think of A and B as forming a continuous solution

XB XB

At the eutectic temperature

three phases in equilibrium

Regular solutions, negative enthalpymix

A BH X X N0zєXAXB

є = AB – ½ (AA + BB)

, є < 0 AB is small favor A-B bonds

ordering, compound formation

regular solutions:

regular, negative enthalpy

ln lnmixA B A A B BG X X RTX X RTX X

both terms < 0 and symmetric about XA = 0.5

Regular solutions, negative enthalpysolid phase is a regular solution, < 0; liquid phase is a an ideal solution

Gmix

XB

maximize AB bonds ‘AB’ compound

AB´+ AB ´´+ AB ´´´

at high T, TSmix dominates, at low T, Hmix becomes important

ln lnmixA B A A B BG X X RTX X RTX X

Regular solutions, negative enthalpysolid phase is a regular solution, < 0; liquid phase is a an ideal solution

Gmix

XB

AB´+ AB ´´+ AB

´´´

high T

low T

‘AB’ region narrows at high T

XB

liquid

L + S()

|| is small so liquid region unaffected

|| will impact liquid region

TMA

TMB

Regular solutions, negative enthalpy

liquid

L + S()

TMA

TMB

solid phase is a regular solution, < 0; liquid phase is a an ideal solution

increasing ||

XB XB

T

TMA TM

B

AB

´+ AB ´´+ AB

´´´

L + S(´) L + S(´´)

solid with AB (solid) bonds preferred over random liquid

also moves up

Regular solutions, negative enthalpysolid phase << 0, AB compound forms (), no longer meaningful treat as a solution; liquid phase is a an ideal solution

increasing ||

XB

T

TMA TM

B

AB

´+ AB ´´+ AB

´´´

L + S(´) L + S(´´)

really moves up

XB

TMB

TMA

liquidTM

Regular solutions, negative enthalpysolid phase << 0, AB compound forms (), no longer meaningful treat as a solution; liquid phase is a an ideal solution

XB

TMB

TMA

liquidTM

G

XB

L

T1

consider , , as distinct

Shape of G curves

wide composition range, anti-site defects

narrow composition range, few defects

G

narrow

Now consider non-ideal liquid

XBXB

solid and liquid > 0, Hmix > 0 tendency to cluster (unmix)

increasing

Peritectic

Now consider non-ideal liquid

XBXB

solid and liquid >> 0, A hates B and B hates A, phase separation even in the liquid

or

Monotectic

Now consider structure change in solid

TL +

+

+ +

Liquid = ideal

solid = ideal

/ – not a continuous solution

(or >> 0)

Eutectoid

Invariant Reactions