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up to now potential phase diagram & molar phase diagram now 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? i i dN T dV T P dU T dS 1 ) : , : V , 1 : ( T N T P T U

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 diagram now 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 - PowerPoint PPT Presentation

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Page 1: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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

Page 2: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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)

Page 3: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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

Page 4: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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

Page 5: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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.

Page 6: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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.

Page 7: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

Calculated isopleths of (a) Sn-Bi-2In-9Zn and (b) Sn-Bi-5In-9Zn alloys. Symbols of ∆, Ο, □ represent temperatures experimentally

measured through DSC.

Page 8: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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)

Page 9: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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).

Page 10: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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).

Page 11: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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).

Page 12: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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).

Page 13: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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 →

Page 14: up to now potential phase diagram & molar phase diagram now moving on to the  mixed  phase diagram

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).