up to now potential phase diagram & molar phase diagram now moving on to the mixed phase diagram...
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up to now potential phase diagram & molar phase diagramnow moving on to the mixed phase diagram
• why a T-X phase diagram? most common var from suitable exp → direct info on that type of diagram → direct predictions of the result of a new exp
• when computerized phase diagrams become available → thermo info stored in a databank → calculate and plot any type of diagram (custom-oriented, tailor-made types)
• apart from T-X
→ c preferred for an axis in understanding
→ enthalpy preferred for an axis in controlling the
• what happens to conjugate var if another thermo energy being used instead of dU as a starting pt?
ii dN
TdV
TP
dUT
dS1 ) : , :V ,
1: (
TN
TP
TU
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from Chapter 4 of Saunders and Miodownik’s book, “CALPHAD”
exp determination of thermo quantities → thermo measurements after Kubaschewski (1993) at Aachen
① methods - powerful for establishing integral and partial enthalpies - but limited use in partial Gibbs energy & activity or activity coefficient - measuring heat & during heating and cooling or from a
rxn - its reliability governed by heat conduction, heat capacity & heat
transfer efficiency isothermal : Ts(surr) = Tc(calorimeter), const T adiabatic : Ts = Tc, T not const, determining heat capacity heat-flow : Ts - Tc = constant isoperibol : const Ts, measuring Tc
i) measurement of H & heat capacity - H measuring HT - HRT vs T - heating the sample to high T and dropping it into a calor at low T - measuring heat evolved, not directly Cv - problems occur if Cv of calorimeter > Cv of the sample
ii) measurement of enthalpy of transformation - DSC, DTA tech (ΔHtr can also be obtained from the method i)
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② 기상평형법 (gas phase equil tech) - activity, ai = pi/pi° → Gi & μi
- how to measure , pi, correctly
③ ( 기전력 ) measurements - in electrochem cells EMF generated Gi, i
- ∆Gi = -nEF = RTln ai
- ∆S & ∆H readily calculated from the above eq
- providing good accuracy for ai & i(act coeff)
- H & S being associated with much higher errors
dTdE
nFdT
GdS
P
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exp determination of phase diagrams
① non-isothermal tech - where a sample is or through a transf and some
properties of the alloy changes as a consequence - inherently non-equil in nature - dealing with the of transf rather than the
transf itself
i) thermal analysis tech: typical simple cooling curve method by Haycock and Neville (1890, 1897)
the curve of vs time preferred to T vs time more refined DSC or DTA methods be aware of or solid state diffusion in heating be aware of in cooling
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Fig. 4.3 Cooling curve to determine liquidus point.
Fig. 4.4 Liquidus points for Cu-Sn determined by Hycock and Neville (1890,1897).
Fig. 4.5 Experimentally measured liquidus(Ο) and solidus (□) points measured by using DTA by Evans and Prince (1978) for In-Pb. (●) refers to the ‘near-equilibrium’ solidus found after employing re-heating/cycling method.
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Fig. 3.14 SiO2-Al2O3 system with sketches of representative DTA from cooling the specified composition.
Fig. 4 DSC thermogram of solders taken at heating and cooling rates of 5°C/min. TS (solidus temp., set temp.) and TL (liquidus temp.) are recorded in the graph. (a) Sn-4Bi-2In-9Zn in heating. (b) 4Bi-2In-9Zn in cooling. (c) Sn-1Bi-5In-9Zn in heating, and (d) Sn-1Bi-5In-9Zn in cooling.
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Calculated isopleths of (a) Sn-Bi-2In-9Zn and (b) Sn-Bi-5In-9Zn alloys. Symbols of ∆, Ο, □ represent temperatures experimentally
measured through DSC.
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ii) chemical potential tech: activity of one or both of the comp being measured during a cooling or heating cycle and a series of characteristic breaks defining
Fig. 4.6 EMF vs temperature measurements for Al-Sn alloys (Massart et al., 1965)
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ⅲ) magnetic susceptibility measurement: an interesting tech for
determining phase boundaries in systemsⅳ) resistivity method: a simple tech, the resistivity of an alloy during measured as a ft of T
Fig. 4.7 Magnetic susceptibility () vs temperature measurements for a Fe-0.68at%Nb alloy (Ferrier et al. 1964). ●=heating, X=cooling
Fig. 4.8 Plot of resistivity vs temperature for a Al-12.6at%Li alloy (Costas and Marshall, 1962).
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ⅴ) dilatometric method: a sensitive method, in phase transf having different coeff of
Fig. 4.9 Expansion vs temperature plot for a (Ni79.9Al20.1)0.87Fe0.13 alloy showing ’/’+-phase boundary at 1159°C from Cahn et al. (1987).
Fig. 4.10 ’/’+-phase boundary as a function of Fe constent, at a constant Ni/Al ratio=77.5/22.5 (from Cahn et al. 1987).
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② isothermal tech (const T)
inherently closer to → substantial periods to allow equil needed → how long is enough? → no easy ans → (as a first approx) (x : grain size)Dtx
i) metallogrophy: OM, BS-SEM → phase boundary, identification & qualitative delineation of phases (heavy elements appearing
light, light elements dark)
Fig. 4.11 Equilibrium phase diagram for the Mo-Re system after Knapton (1958-59).
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ii) XRD: used to support some other tech, identification of and a more exact determine of phase boundary using
Fig. 4.12 Lattice parameter vs composition measurements for Hf(1-c)C (Rudy 1969).
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iii) quantitative determination of phase : STEM, EDX & AP/FIM
ⅳ) sampling/equilibration method:
- in equil involving liq + sol → removal of some of the liq → defining liquidus comp
- using the different density of liq and sol (gravity then sufficient for separation)
ⅴ) diffusion couple: increased use of EPMA →
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Fig. 4.13 Measured diffusion path between alloys, A and B, in the Ni-Al-Fe system at 1000°C (Cheng and Dayanada 1979).
Fig. 4.14 Concentration profile in a diffusion couple from the Al-Nb-Ti system at 1200°C (Hellwig 1990).