in-situ observations of moving interfaces during dp reaction · matrix pfz α lamella b....

1.1. SteadySteady state growthstate growth-- regularregular morphologymorphology

1.1. 1.1. OverallOverall viewview

1.2. 1.2. SoluteSolute concentrationconcentration profilesprofiles

1.2.1. 1.2.1. AcrossAcross thethe reactionreaction frontfront

1.2.2. 1.2.2. AcrossAcross thethe αααααααα lamellalamella

Paweł Zięba – Chemical and kinetic characterization of diffusional…

In-situ observations of moving interfaces during DP reaction

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2. 2. SteadySteady state growthstate growth-- irregularirregular morphologymorphology

2.1. 2.1. ChangesChanges of of thethe reactionreaction front front shapeshape

2.2. 2.2. ReRe--nucleationnucleation and and branchingbranching of of thethe ββββββββ lamellalamella

2.3. Stop2.3. Stop-- and go and go motionmotion ((oscillatoryoscillatory movementmovement))

3. Growth 3. Growth terminationtermination

3.1. 3.1. ImpingementImpingement of of coloniescolonies

3. 2. 3. 2. PrecipitatePrecipitate freefree zonezone

4. 4. SummarySummary, , unsolvedunsolved problemsproblems

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LT

αo

α β

vRF δ

λα


TheThe solutesolute redistributionredistribution occursoccurs atat thethe movingmoving RFRF

α+β

βα

xoA BxBxavxe

GB αo�α+β

ThereThere existsexists anan excessexcess ofof solutesolute atomsatoms withinwithin thethe αααααααα

lamellalamella comparedcompared toto thethe equilibriumequilibrium statestate

Nucleation


430 oC/0

460 oC/32 min

Fe-15 at.%Zn-C

E.P. Butler, V. Ramaswamy,

P.R. Swann, Acta Metall. 21

(1973-517-524.

470 oC/41 min

470 oC/45 min (DF)

470 oC/48 min

G.R. Purdy, N. Lange, in

Decomposition of Alloys:

the early stage, Proc. 2nd

Acta-Scripta Metallurgica

(P. Haasen, V. Gerold., R.

Wagner, M.F. Ashby- eds.),

Pergamon Press 1984, pp.

214-220

Al-28 at. % Zn: 105 oC±15 oC

STEADY STATE GROWTH – REGULAR MORPHOLOGY


Solute Distribution Across Reaction Front

20

30

at.

%]

RF


-200 -100 0 100 200

Distance [nm]

0

10

20

Zn c

on

ten

t [a

Matrix α lamella

Solute concentration profile across the α lamella

( )[ ]ooe x

Cyxxyx +

−−=

5.0cosh)()(

ins

Ds

vC

δ

λα2

=o

b

x

xs =


x(y)

λλλλαααα

y0 1

ooe xC

xxyx +−=)2/cosh(

)()(bDsδ ox

λλλλαααα

vinsRF

Shape changing

10

15

20

n c

on

tent

[at.

%]

0 s

50 s

90 s


0 s

50 nm

50 s 90 s

0.0 0.5 1.0

Spacing [arbitrary units]

5

Zn

α ββ

52o

41o

28o

73o

63o

48o

0.1 µm

Al-22 at.% Zn aged at 403 K.

K. Tashiro and G.R. Purdy:

Metall. Transactions A20 (1989) 1593.

RF RF shapeshape modellingmodelling (for (for knownknown solutesoluteconcentrationconcentration profile profile inin thethe αα phasephase lamellalamella


αβ β

49o

34o

34o

33o

23o

23o

0.1 µm

α

αα

αα

ρ

γc

m GM

vVo

o

∆−=

2

2

5.12

1

dy

zd

dy

dz

+

=ρ

( )( )

cosh,

)(C

ys

lxxxxy

−−= αλ

RF RF shapeshape modellingmodelling (for (for knownknown solutesoluteconcentrationconcentration profile profile inin thethe αα phasephase lamellalamella


( ) ( )2/cosh

,

)(Ceoo

lxxxxy

−−= αλ

∆G – local change of free energy at RF, M –RF mobility, Vm – molar volume of cellular

aggregate, γα/αο – α/αοinterfacial energy, r – local curvature of RF, v – growth rate

D. Duly, M.G. Cheynet, Y. Brechet:

Acta Metall. & Mater. 42 (1994) 3855.

cosθαα =0.1

γαβ=270 mJ/m2

cosθαα =0.4

γαβ=270 mJ/m2

cosθαα =0.707

γαβ=270 mJ/m2

cosθαα =0.707

γαβ=150 mJ/m2

y

yy

y

z

0.3

-0.3

-0.5 0.5

-0.5-0.5

-0.5

0.5

z

0.3

-0.3

zz

0.5

0.3 0.3


cosθαα =0.707

γαβ=400 mJ/m2

cosθαα =0.4

γαβ=400 mJ/m2

yy

-0.3 -0.3

-0.5 0.5-0.50.5

zz

-0.3-0.3

0.3 0.3

Mg-10 at.% Al aged at 493 K

D. Duly, M.G. Cheynet, Y. Brechet: Acta Metall. & Mater. 42 (1994) 3855.

ReconstructionReconstruction of of solutesolute concentrationconcentration profile profile inin thethe α α phasephase lamellalamella((fromfrom knownknown RF RF shapeshape))

α

αα

αα

ρ

γc

m GM

vVo

∆−=2

5.12

1

zd

dy

dz

+

=ρ [ ]oxxyRTG

)(2

−=∆ α

0 s

50 nm

50 s 90 s

For small solute content and small saturation (parabolic curve)

ααρcG

M o∆−=

2

2

dy

zdo

oc

xG

2=∆

[ ]2

22

)(5.0dx

GdxyxG c

oc

αα −=∆

)(yGc

α∆

x(y) xo

For small solute content (constant curvature)

Giibs free energy change

(thermodynamic data)

STEADY STATE GROWTH – IRREGULAR MORPHOLOGY

0 s

1

3

2�

1

2

3

12 sRe-nucleation


1

3B

2

3A

19 s

3A

3B

23 s

0.3 µm

30 s

45 s 90 s

33 s 0 s

Re-nucleation and branching


185 s � 200 s

240 s

0.4 µm

0 s

0.2 µm

15 s

20 s 35 s

Shape changing


400 s 310 s

65 s 105 s

160 s 265 s

6

8

10

en

t [a

t.%

]

b

Shape changing


0 100 200 300 400 500 600

Distance [µm]

4

6

Zn

con

te

Zmiana kształtu frontu reakcji

WZROST USTABILIZOWANY-MORFOLOGIA NIEREGULARNA

Oscillatory movement?


Stop- and go motion

oscillatory movement?

STEADY STATE GROWTH – IRREGULAR MORPHOLOGY


S. Abdou, G.I. Solorzano, M. El-Boragy,

W. Gust, B. Predel,

Scripta Mater. 34 (1995) 1431

Al-15 at.% Zn alloy: DP: 433 K

Impingement of colonies

0 s

C

A

B

0.4 µm

20 s


0 s 20 s

35 s 40 s

50 s 65 s

Precipitate free zone

a

A

A

0.1 µm


-80 -60 -40 -20 0 20 40

Distance [nm]

0

10

20

30

Zn c

onte

nt [a

t.%

]

Matrix α lamellaPFZ

b

A0.1 µm

Steady-state period of growth of DP reaction is influenced by variousinstabilities.

The system possesses some intrinsic capability to correct local RF shape tobalance the forces acting on it if the perturbation is not larger than a certaincritical value.


critical value.

This sensitivity of the system may result in some asymmetry of the soluteconcentration profile.

If the critical value is exceeded or simply perturbation imposed is too large,re-nucleation and branching phenomena occur.

In some cases system becomes to be unstable: non-steady state growth.

Termination of the DP reaction is due to impingement of colonies or PFZformation (backward migration of the RF).

There is no HREM in-situ observation: How the atomic transport at the RFreally looks like?

How to determine the solute profile across the αααα lamellae without a need forEDX/EELS analysis but based only on in situ recording of the RF shape?

What is the solute concentration profile within the RF from one to another


What is the solute concentration profile within the RF from one to anotherneighbouring ββββ lamella?

in-situ observations of moving interfaces during dp reaction · matrix pfz α lamella b....

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