# Atomic Transport Phase Transformations - uni .Atomic Transport & Phase Transformations Lecture 8

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Atomic Transport

&

Phase Transformations

Lecture 8

PD Dr. Nikolay Zotov

zotov@imw.uni-stuttgart.de

Lecture I-8 Outline

Binary phase diagrams with limited solubility in the liquid state

Classification of (intermediate) intermetallic compounds

Formation of intermetallic compounds

Gibbs energy of intermediate phases

Examples of phase diagrams with intermediate phases

Calculation of phase diagrams with intermediate phases

Binary Phase DiagramsClassification

WL = 0

WS = 0

Unlimited Solubilityin Liquid and Solid

Limited Solubilty

in Solid in Liquid in Liquidand in Solid

WS > 0 WL > 0

WL > 0

WS > 0with intermetallicphases WS < 0

Binary Phase Diagrams

Limited solubility in the Liquid State (WL > 0)

Regular solution

ln(gAL) = WL(1 XA

L)2 > 0 gAL > 1

ln(gBL) = WL(1 XB

L)2 > 0 gBL > 1 Tendency for phase separation in the liquid state

If WL> 0 a miscibility gap will form in the liquid state!

Binary Phase Diagrams

Limited solubility in the Liquid State (WL > 0)

DeHoff (2006)

WL = 0 WL = 10000 J/mol WL = 20000 J/mol

Binary Phase Diagrams

Limited solubility in the Liquid State (WL > 0)

# very different melting points

# inflection point in the liquidus curve

# retrograde solubility of Tl in Ag above 300 oC;

# very low solubility of Ag in Tl;

# Allotropic phase transition in Tl at 234 oC;

a(Tl) hexagonal P 63/mmc

(Tl) cubic Im-3m

Binary Phase Diagrams

Limited solubility in the Liquid State (WL > 0)

# Maximum of the liquid missibility gap at 1071 K

# WL = 2R TgmL ~ 17800 J/mol

# Eutectic point TE ~ 591 K

# below 591 K two phase mixture Pb + Zn

Zn hexagonal; Pb cubic

L1 + L2

L

L1 + Zn

Pb + Zn

TgmL

E

Binary Phase Diagrams

Limited solubility in the Liquid State (WL > 0)

A

B

C

D

F

G

A T > 1071 K homogeneous liquid L with XZn = 0.4

B L starts to segregate

XZn(L1) ~ 0.4, XZn(L2) ~ 0.92

fraction(L1) ~ 100%

C Two liquids mixture

XZn(L1) ~ 0.11, XZn(L2) ~ 0.98 (almost pure Zn melt)

fraction (L1) ~ 56 %

D The Zn-rich liquid disappears (Zn crystallizes)

Mixture of Pb-rich liquid (L1) + Zn

XZn(L1) ~ 0.06, XZn(Zn) ~ 0.999

fraction(Zn) = 38%

F Eutectic Tie-line; L1 + Pb + Zn in equilibrium

XZn(Pb) ~ 0.024, XZn(Zn) ~ 0.99

G Two phase mixture of solid Pb and solid Zn

Binary Phase Diagrams

Limited solubility in the Liquid State (WL > 0)

# Temperature of the maximum of theSolubility gap Tgm

L ~ 879 K at XPb ~0.38

# WL = 2RTgmL ~ 14600 J/mol

# B Two liquid mixture

XPb(L1) ~ 0.13, XPb(L2) ~ 0.76

# Monotectic point M

(MM monotectic tie-line)

XPb(L1) ~ 0.016, XPb(L2) ~ 0.97 XPb(fcc) ~ 0.998

# Monotectic reaction

L2 L1 + Pb

# Below 302 K two phase mixture of Ga and Pb

Ga orthorhombic oC8 Cmca

Pb cubic cF4 F m-3m

TgmL

L1L1 + L2

L2

L

L1 + Pb

Ga + Pb

MM

B

Binary Phase Diagrams

Limited solubility in the Liquid State (WL > 0)

M

# TgmL ~ 3162 K

WL ~ 52490 J/mol

# Monotectic point M

Monotectic T = 2124 K;

# Solubility of Ag in bcc V

increases with increasing T

# Solubility of V in Ag

negligible:

V bcc structure I m-3 m

(5+, 4+, 3+, 2+)

Ag fcc structure F m -3 m

TgmL

Binary Phase Diagrams

Limited solubility in the Liquid State (WL > 0)

# Maximum of the liquid immisibility

gap unknown

WL probably very high

# Very high Monotectic point 3240 oC

# practically no mutual solubility

below 2000 oC

Binary Phase Diagrams

Monotetctic Reaction - DG curves

Binary Phase Diagrams

Monotectic Reactions

# temperature of the maximum of

the liquid miscibility gap 849 K

at XTl = 0.32;

# WL ~ 14100 J/mol;

# Monotectic Temperature 559 K;

# Allotropic phase transition

L1 + L1 + a Tl at 234 oC;

# 2 phase mixture Ga + aTl below 30 oC.

Binary Phase Diagrams

Invariant reactions - Summary

Limited Reaction Description

Solubility

Solid Eutectic l a +

Eutectoid g a +

Peritectic l + a

Metatectic l + a

Liquid Monotectic l1 l2 + a

Binary Phase Diagrams

Impossible eutectic phase diagrams

Gibbs phase rule:

The invariant tie -line means that the there isno degree of freedom: the composiiton and thetemperature are fixed

Inclined tie-line in an eutectic phase diagram means thatT can be varied as a function of composition, which is notpossible.

Binary Phase Diagrams

Impossible eutectic phase diagrams

Prince (1966)

Complete misciblity is not possible

Addition of B into A (or B in A) will increase the Entropy of mixing and reduce the Gibbs eneryg of the solution

Binary Phase DiagramsClassification

WL = 0

WS = 0

Unlimited Solubilityin Liquid and Solid

Limited Solubilty

in Solid in Liquid in Liquidand in Solid

WS > 0 WL > 0

WL > 0

WS > 0with intermetallicphases WS < 0

Intermetallic Compounds

Classification

Entropy

ordered disordered

Variations in chemical composition

Stoichiometric Non-stoichiometricDefect compounds

Electronic configuration

Normal ValenceCompounds

Hume-Rotheryphases

Binary Phase DiagramsIntermediate phases - Formation

# Enthalpy stabilisation with respect to the termianl solid solutions

Strong preference for the formation of bonds between unlike atoms in the solid

De = eAB (eAA + eBB ) < 0 WS < 0

# usually (very) different structures from the terminal solid solutions

Binary Phase DiagramsFormation of intermediate phases

WS < 0

WL = 0

# WS < 0 and WL = 0 Increase of the melting temperatures

of the solid solutions with respect to the pure components

is observed;

# congruent melting at XBCM

# Congruent melting (freezing) the melt freezes in a solid phase

with the same composition

# Incongruent melting (freezing) the solid and the melt do not have

the same composition

XBCM

Binary Phase DiagramsFormation of intermediate phases

Extention of the Regular solution model:

DH mix = XB(1 XB)

WS(XB) = - a[b(1-2XB)4 + c/(d XB)

2]

The second term describes a strong tendency for

unlike bond formation

-ac/(d XB)2 ; XB d deep minimum

0,0 0,2 0,4 0,6 0,8 1,0

-4000

-2000

0

DH

mix

(J/m

ol)

XB

a

a+ a+ a

Appearance of an

intermediate phase

Relatively wide

compositional range

Prince (1966)

WS(XB); WS(XB) < 0

Binary Phase DiagramsFormation of intermediate phases

Stoichiometric (line) compounds compounds with

Infinitely large curvature!!!

Binary Phase DiagramsFormation of intermediate phases

The curvature of the DG curve the phase determines the stability range

Prince (1966)

Binary Phase DiagramsPhase diagrams with Intermediate Phases

FeCr

s FeCr phase

Tetragonal, P 42/mnm; 30 atoms in the unit cell

Compositional range 45 49 wt% Cr

Fe DHM = 13.8 kJ/mol

Cr DHM = 21.0 kJ/mol

Binary Phase DiagramsPhase diagrams with Intermediate Phases

Very large compositional range

35 65 wt% V!!!

Fe V

WS

Binary Phase DiagramsPhase diagrams with Intermediate Phases

# Intermediate phase with relatively wide compositional range

# congruent melting of the phase for the composition X*.

# The phase diagram could be regarded as two eutectic phase

diagrams: A X and X B;

XBb/T ~ DHsol

ab/ T(XB XB

a) 2Gmb/(XB

b)2;

T/ XBb ~ T 2Gm

b/(XBb)2 (X* XB

a) / DHsolab ;

# very large curvature of the Gibbs free energy of the

phase vertical phase boundary

# very small solubility of the a phase in

vertical phase boundary

X*

Binary Phase DiagramsPhase diagrams with Intermediate Phases

# Congruent melting at 1065 oC;

# extremely narrow stability range of Mg2Sn(Stoichiometric compound);

# Mg2Sn cubic, antifluoride structure, F m -3 m

# Extremely low solubility of Mg in Sn and Sn in Mg

Different structure

Compared to termianl phases

Mg hexagonal

P 63/mmc

Sn tetragonal

I 41/

Binary Phase DiagramsPhase diagrams with Intermediate Phases

# Congruent melting at 1065 oC

# extremely narrow stability range

(Stoichiometric compound);

# Mg2Si cubic, antifluoride structure, F m -3 m

# Extremely low solubility of Mg in Si and

Si in Mg

Mg hexagonal

P 63/mmc

Si cubic

F d -3 m

Binary Phase DiagramsPhase diagrams with Intermediate Phases

A

B

A Liquid with composition XSi(L) = 0.4

B L + Mg2Si

XSi(Mg2Si) = 0.333, XSi(L) = 0.45

fraction (Mg2Si) ~ 50%

C Mg

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