ThePhaseRuleF=C-p+2F=#degrees of freedomThe number of intensive parameters that must be specifiedinordertocompletelydeterminethesystemp=#ofphasesphases aremechanically separableconstituentsC= minimum # of components (chemical constituents that mustbespecifiedinordertodefineallphases)2=2intensiveparametersUsually=temperature and pressure
The Phase Rule
EutecticsZTTLiquidusLiquidcurveXB + liquidA+liquiddCySoliduseA+BcurveABCompositionGibbs'phase rule:F=C-P+2orthecondensed rule ifthevaporpressureisnegligibleF=C-P+1.F: # degrees of freedom (independent variables) among T, p, compositionC: # constituents needed to completely describe the composition;P: # phases present at equilibrium.Examples: x, z: F = 1 - 2 + 1 = 0 (invariant points); y: F = 2 - 3 + 1 = 0:e: F = 1 - 1 + 1 = 1 (univariant); liquid: F = 2 - 1 + 1 = 2 (bivariant)
Compositionsof PhasesinCu-NiPhaseDiagramDeterminethecompositionof each phase ina Cu-40%Nialloyat1300C,1270C,1250C.and120015001453T<1085oC:Cu&Niaremutuallysolubleinsolidstate-complete1400solubilityL→bothhavethesameFCCα+401300structures;atomicradii and1270°3750electronegativities are nearly3245identical;similarvalences化合价1250°120040→isomorphousa1100Tielinesandphasecompositions1085foraCu-40%Nialloyatseveraltemperatures1000Ni20406080CuWeightpercent nickel
Compositions of Phases in Cu-Ni Phase Diagram Determine the composition of each phase in a Cu-40% Ni alloy at 1300℃, 1270 ℃, 1250 ℃, and 1200 ℃
Determinationof PhaseCompositionsCu-Ni:Tie-lines for Two-phase Regions1.Atie lineis constructedacrossthe two-phase region at thetemperatureofthealloy1300Lquid2.The intersections of the tie lineDsanedTielinea-Liquidand the phase boundaries oneithersidearenoted.ua3.PerpendicularsaredroppedLiquid1200fromtheseintersections to thehorizontalcompositionaxis,fromwhichthecompositionofeachofthe respective phases is read.20305040CCo31.5wt%Niompeition(w%Ni)42.5wt%Ni68.5%Cu57.5wt%Cu
Determination of Phase Compositions Cu-Ni: Tie-lines for Two-phase Regions