PHASE DIAGRAMS THEORY AND APPLICATIONS

Some basic concepts u Phase A homogeneous region with distinct structure and physical properties In principle, can be isolated Can be solid, liquid or gas u Phase Diagram Representation of phases present under a set of conditions (P, T, Composition etc.)

Concepts…... u Phase transformation Change from one phase to another E.g. L S, S S etc. Occurs because energy change is negative/goes from high to low energy state u Phase boundary Boundary between phases in a phase diagram

A simple phase diagram Triple point (Invariant point) Solid Liquid Vapor Pressure Temperature Phase boundary System: H 2 O

Gibb’s Phase Rule P + F = C + 2 P=number of phases C=number of components F=number of degrees of freedom (number of independent variables) Modified Gibbs Phase Rule (for incompressible systems) P + F = C + 1 Pressure is a constant variable F = C - P + 2 F = C - P + 1

Application of the phase rule At triple point, P=3, C=1, F=0 i.e. this is an invariant point At phase boundary, P=2, C=1, F=1 In each phase, P=1, C=1, F=2

Solidification(cooling) curves L S L S Pure metalAlloy TmTm LS L + S Solidification complete Soldification begins TLTL TSTS

Construction of a simple phase diagram u Conduct an experiment u Take 10 metal samples(pure Cu, Cu-10%Ni, Cu-20%Ni, Cu-30%Ni………, pure Ni) u Melt each sample and then let it solidify u Record the cooling curves u Note temperatures at which phase transformations occur

Results L S LS t T L L + S TLTL TSTS S L TLTL TSTS Pure Cu Cu-10%Ni Cu-20%Ni L LS Pure Ni S T Ni T Cu

Binary isomorphous phase diagram x x x x x x x x x x x x x x x x x xx x L+S L S Composition Temp T Cu T Ni CuNi%Ni Cu Ni

Microstructural changes during solidification L S LS T t TmTm L S Pure metal S

Microstructural changes during solidification L S Alloy L + S TLTL TSTS L S T t

L Binary isomorphous phase diagram L+S L S Composition T AB%B L L S T1T1 T2T2 T3T3 T4T4 CLCL C0C0 CSCS

Notes u This is an equilibrium phase diagram (slow cooling) u The phase boundary which separates the L from the L+S region is called LIQUIDUS u The phase boundary which separates the S from the L+S region is called SOLIDUS u The horizontal (isothermal) line drawn at a specific temperature is called the TIE LINE u The tie line can be meaningfully drawn only in a two-phase region u The average composition of the alloy is C O

Notes….. u The intersection of the tie line with the liquidus gives the composition of the liquid, C L u The intersection of the tie line with the solidus gives the composition of the solid, C S u By simple mass balance, C O = f S C S + f L C L and f S + f L = 1 C O = f S C S + (1- f S ) C L Lever Rule

Some calculations u In our diagram at T 3, C O = A-40%B, C S =A-90%B and C L =A-11%B u Therefore, f S =29/79 or 37% and f L =50/79 or 63% u If we take an initial amount of alloy =100 g, amt. of solid=37 g (3.7 g of A and 33.4 g of B) and amt. of liquid=63 g (56.07 g of A and 6.93 g of B)

The Eutectic Phase Diagram T ABWt%B L  +L  +L ++ E TETE CECE   Liquidus Solidus Solvus L  +  T E, C L =C E 

T AB Wt%B L  +L  +L ++ E TETE CECE   Pure A or B Other alloys between A and B CECE L S L ++ L ++ L L L+  L ++ ++

T AB Wt%B L  +L  +L ++ E TETE CECE   Solidification for alloy of eutectic composition L S ++ ++

Eutectic microstructure Lamellar structure

T AB Wt%B L  +L  +L ++ TETE CECE   L Proeutectic  ++ ++

L T AB Wt%B L  +L  +L ++ TETE CECE   L   particles

The Eutectoid Phase Diagram T ABWt%B   +   +  ++ E TETE CECE     +  T E, C  =C E 

 T AB Wt%B   +   +  ++ E TETE CECE   Cooling of an alloy of eutectoid composition S ++ ++ 

 T AB Wt%B   +   +  ++ E TETE   Cooling of an alloy of hypoeutectoid composition S ++ ++   Pro-eutectiod 

The Peritectic Phase Diagram T ABWt%B L  + L  + L ++ P TPTP CPCP    L  at T P  N M Note:  and L will react only in a certain proportion= NP:PM L L  

T ABWt%B L  + L  + L ++ P TPTP CPCP    L  at T P  N M Note:  and L will react only in a certain proportion= NP:PM NP:PM=1:2 60 L L  L  

T ABWt%B L  + L  + L ++ P TPTP CPCP    L  at T P  N M Note:  and L will react only in a certain proportion= NP:PM L L  L  