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
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