Interdiffusion and Phase Growth Kinetics in theMagnesium-Aluminum Binary System

Kaustubh N. KulkarniGeneral Motors Global R&D, Bangalore, India

(Currently Indian Institute of Technology, Kanpur, India)

Alan A. LuoGeneral Motors Global R&D, Warren, MI, USA

Kaustubh N. Kulkarni and Alan A. Luo; J. Phase Equilib. Diff.; 34; 2013; p. 104

OutlineUse of CALPHAD in Mg alloy development

Why interdiffusion data needed in Mg-Al alloys

Experimental methodology

Analysis of interdiffusion coefficients as functions of composition

Analysis of impurity diffusion coefficients

Growth kinetics of Mg17Al12 ( ) and Al3Mg2 ( ) phases

Conclusions

2

Mg-Al Binary SystemMg17Al12 ( phase) - low eutectic temperature 436°C

Limited strengthening - no metastable phases and large precipitates

w%(AL)

0.0

8.7

17.3

26.0

34.6

0 10 20 30 400 10 20 30 400

10

20

30

40

w%(AL)

w%(C

A)

MG

-Mg

C14 - Mg2Ca

C36 - (Mg,Al)2Ca

Mg17Al12

AX51 (Mg-5Al-1Ca)AX52 (Mg-5Al-2Ca)AX53 (Mg-5Al-3Ca)

AX51AX52

AX53

850K

800K

900K750K

950K

900K

850K

800K790K

922K 711K

4

3.0

4.0

5.0

6.0

7.0

8.0

9.0

1.0 2.0 3.0 4.0 5.0 6.0 7.0

AlCo

nten

t,%

Ca Content, %

No Mg17Al12

Mg17Al12

No Mg17Al12

Mg17Al12

Mg-Al-Ca System: Creep-Resistant Alloys

00.10.20.30.40.50.60.70.80.9

1

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

Frac

tion

ofM

g 17A

l 12Ph

ase,

%

Ca Content, %

Al content: 5%

No Mg17Al12when Ca > 2.8%

@ 5% Al

Calculated liquidus projection & alloy solidification paths

A.A. Luo, B.R. Powell, A.K. Sachdev, Intermetallics, 2012, 24, 22-29

5

Solidification Microstructure:Scheil Simulation vs. Experimental Results

Alloy Scheil Simulation, vol.% Measurement, vol.%(Mg,Al)2Ca Mg2Ca Mg17Al12 Total Fraction Total Fraction

AM50 - - 4.3 4.3 4.8AX51 2.0 0 2.7 4.7 5.5AX52 4.1 0 0.9 5.0 5.8AX53 5.8 0.1 0 5.9 6.2

Gap: back diffusion of alloying elements is related to solidification rates

A.A. Luo, B.R. Powell, A.K. Sachdev, Intermetallics, 2012, 24, 22-29

X. Zheng, A.A. Luo, C. Zhang, J. Dong, R.A. Waldo, Metallurgical and Materials Transactions A, 2012, 43A, 3239-3248.

Dual phase strengthening: Mg17Al12 and Mg2SnMg2Sn: decreasing solubility with T -potentialprecipitation hardening

6

T[C

]

w%(SN)

0

100

200

300

400

500

600

700

800

0 10 20 30 40 50 60 70 80 90 100w%(SN)

T[C

]

MG SN

0 10 20 30 40 50 60 70 80 90 1000

100

200

300

400

500

600

700

800

(Mg)+Mg2Sn

13%562°C

Mg-Al-Sn System: Precipitation Hardening

A.A. Luo, P. Fu, X. Zeng, L. Peng, B. Hu, A.K. Sachdev, in Magnesium Technology 2013, TMS, 341-345.

Modeling Precipitation KineticsImportance of diffusion coefficients

Precipitation kinetics depends strongly on the diffusivities of alloyingelements in the matrixLack of experimental data on diffusivities as functions of compositions in Aland Mg alloys

Ref: J. D. Robson, “Modeling the evolution of particle size distribution during nucleation, growth and coarsening”; Materials Science and Technology; Vo. 20; pp 441-448

Nucleation Growth

tkT

RZNJ v exp3

*4exp*2

42

216*aGcD

V4

22

8 akTDcGV V

r

ri

cccc

RD

dtdR

Coarsening

)()(9

81

30

3 ttccTR

cDVRRg

m

7

Interdiffusion in Multicomponent Systems

n-component system = (n-1)2 interdiffusion coefficients

More complications: Dependence on composition

Experimental data on interdiffusion, tracer diffusion and selfdiffusion coefficients used to evaluate Atomic Mobilities, which aremore fundamentally related to individual elements

J i =- Dijn

j=1

n-1 C j

xi=1,2,...,n-1

Interdiffusionflux of

component i

8

Experimental Work

Mg AlPure Mg and Al discs polished to 0.05 m finish; placed incontact with each other and clamped in a stainless steel jig

9

Diffusion annealing carried out in tube furnacewith couple sealed in evacuated quartz capsule

Representative Photo

Conc

.Co

nc.

x-coordinatex-coordinate

x0x0 xIxI

C1+C1+

C1-C1-C2

+C2+

C2-C2-

C1C1

C2C2

C1C1

C2C2

Matano PlaneMatano Plane interfaceinterface

Typical concentration profiles for binary multiphase diffusion coupleTypical concentration profiles for binary multiphase diffusion couple

-Phase-Phase -Phase-Phase

0

1

Conc

.

x-coordinate

x0 xI

C1+

C1-C2

+

C2-

C1

C2

C1

C2

Matano Plane interface

Typical concentration profiles for binary multiphase diffusion couple

-Phase -Phase

SEM and Optical for Diffusion Structures

EPMA point-by-point for concentration profilesAl-intensity measuredBalance Mg

Experimental Work

10

Diffusion annealing done at three different temperatures each forthree different timesAll couples used for studying phase growth kineticsThree couples (indicated by Squares) selected for EPMA analysis

Temperature (°C)

TIM

E(H

ours

)

380 400 420

24 24 24

50 50 50

91 94 94

Determination of Binary Interdiffusion Coefficients

11

Fick’s Law:

Ji D Ci

x

= Interdiffusion FluxJi

= Interdiffusion CoefficientD= Concentration gradientCi

x

is a function of compositionNeed to determine interdiffusion fluxes and concentration gradientsfrom experimental profiles

D

Determination of Interdiffusion Fluxes [1]

12

= Molar Volume (Assumed constant for this work)

Fluxes determined directly from concentration profilesAvoids errors related to positioning of Matano planeMultiDiflux program:

Fitting of concentration profilesDetermination of gradients and fluxes

1. M. A. Dayananda, Metall. Trans. A, 1983, 14A (9), pp. 1851-1858

Ji x Ci Ci

2tYi

1 Yi

Vm

dxxi

1 YiYi

Vm

dxxi

Vm

YiCi Ci

Ci Ci

Diffusion Structures Developed in Mg/Al Couples[1]

13

Two intermediate phases developed inaccordance with Phase Diagram by Muray [2]

Planar Interfaces Developed1. Kaustubh N. Kulkarni and Alan A. Luo; J. Phase Equilib. Diff.; 34; 2013; p. 1042. T. B. Massalski ed.; Binary Alloy Phase Diagram; ASM International

380°C24hr

400°C24hr

420°C50hr

Concentration and Flux Profiles [1]

1. Kaustubh N. Kulkarni and Alan A. Luo; J. Phase Equilib. Diff.; 34; 2013; p. 1042. M. A. Dayananda and L. R. Ram-Mohan; MultiDiflux; Purdue University

380°C 24 hr

MultiDiflux[2] program used forinterdiffusion analysisConcentration profiles fitted withcubic hermite polynomials in eachphaseConcentration profiles in phaseassumed linear due to smallgradientInterdiffusion fluxes evaluateddirectly from fitted concentrationprofilesInterdiffusion coefficients were thenevaluated as functions ofcomposition

Interdiffusion Coefficients in Al and Mg [1]

151. Kaustubh N. Kulkarni and Alan A. Luo; J. Phase Equilib. Diff.; 34; 2013; p. 104

The activation energy for interdiffusion in Mg does notchange much with composition but that in Alincreases with increasing Mg

Atomic radius of Mg (0.16nm) is 12% larger than thatof Al (0.143nm)

Al matrix maybe strained with increasing Mg-contentincreasing the activation energy for migration

in HCP MgD in FCC AlD

at% Al or Mg

Q(k

J/m

ol)

80

120

160

200

240

0 5 10

Interdiffusion Activation Energies

HCP Mg

FCC Al

Interdiffusion Coefficients in Intermetallics[1]

161. Kaustubh N. Kulkarni and Alan A. Luo; J. Phase Equilib. Diff.; 34; 2013; p. 104

Activation energy for interdiffusion in Mg17Al12 does not vary muchwith composition

Average value of activation energy for interdiffusion in Al3Mg2 phaseis 44±1.8 kJ/mol

in Mg17Al12D

Q(k

J/m

ol)

at% Al

Q for Interdiffusion in Mg17Al12

100

150

200

40 42 44 46 48 50

Interdiffusion Coefficients: Comparison with Literature

171. Th. Heumann and A. Kottmann; Z. Metallk.; Vol. 44; 1953; p. 1392. Y. Funamizu and K. Watanabe; Trans. Jap. Inst. Met.; Vol. 13; 1972; p. 278

This is the FIRST report on Interdiffusion Coefficients and Activation Energies as functionsof compositions in Mg-Al Binary System

The interdiffusion coefficients evaluated assuming constant values over given phaseregions as reported in literature match closely with the ones evaluated at averagecomposition in the present study

DiWi

2t Ci

x dci0

Ci1/2

Ji

CiWi

Impurity Diffusion Coefficients in AlHall’s Method[1]

181. L. D. Hall; J. Chem. Phys.; 1953; VO. 21 (1); p. 87

This method is suitable for estimating impurity diffusion coefficient inthe terminal alloys where the concentration profile shows a long tail

Ci Ci

Ci Ci

C ' 12

(1 erf (u))

u hVariable u is assumed to be a linearfunction of Boltzmann Parameter x t

u is evaluated from relativeconcentration variable C’

D 14h2 2h2 exp u2 C 'Values of h and are evaluated from plot of u

versus ; which are then used for evaluatinginterdiffusion coefficients

Di

* limCi 0 D 14h2

Impurity Diffusion Coefficient

Impurity Diffusion Coefficients in Al

191. S. J. Rothman et al.; Phys. Stat. Solidi B; Vol. 63; 1974; p. K292. K. Hirano and S. Fujikawa; J. Nucl. Mater.; Vol. 69/70; 1978; p. 564

Activation energy for impurity diffusion of Mg in Al agrees well withthat estimated by Hirano and Fujikawa by Tracer technique

-34

-33

-32

-31

-300.0014 0.00148 0.00156

1/T

ln(D

*)

Al Single Crystal394-655°C

Al Poly- Crystal325-650°C

Al Poly- Crystal380-420°C

Phase Growth Kinetics

20

AlMg

h h 420°C 400°C

380°C

420°C

400°C380°C

h2 kt c

380°C 400°C 420°C

-Al3Mg2 241 95 1

-Mg17Al12 71 51 6

Incubation time in minutesParabolic growth indicates diffusioncontrolled growth of both intermetallic phases

Growth of phase is faster than . However,incubation times for are also higher at alltemperatures

1. Kaustubh N. Kulkarni and Alan A. Luo; J. Phase Equilib. Diff.; 34; 2013; p. 104

Activation Energies for Growth

21

h2 kt c

The differences on account ofPre-weld treatment in case of Funamizu et al. (phase may have nucleated)not accounting for incubation time by Brubaker et al.

Agreement with Brubaker et al. for -phase having lowerIncubation time

Phase Activation Energy for Growth (kJ/mol)

Funamizu et al. [1] Brubaker et al. [2] Present Work

-Al3Mg2 62.8 ± 2.1 83.2 ± 10.8 37.3 ± 4.1

-Mg17Al12 143.7 ± 1.7 185.9 ± 7.4 187.7 ± 1.9

& No weld treatment athigher temperature

h2 kti.e. Incubation time

not considered

Weld treatment for 15min at 400°C and mostexperiments then done

below 400°C

1. Y. Funamizu and K. Watanabe; Trans. Jap. Inst. Met.; Vol. 13; 1972; p. 2782. C. Brubaker and Z. K. Liu; Magnesium Technology 2004; ed. Alan Luo; TMS, 2004; p. 229

Conclusions

22

Multiphase diffusion couples assembled at 380, 400 and 420°C showed presenceof two intermediate layers viz. Al3Mg2 ) and Mg17Al12 )

FIRST report on interdiffusion coefficients and activation energies as functionsof compositions in binary Mg-Al system

Activation energy for interdiffusion increased with Mg-content in FCC Al possibly due to largeratomic size of MgActivation energy does not change with composition in HCP Mg and inMg17Al12 intermetallic

Activation energy for impurity diffusion of Mg in Al measured by Hall’s methodwas found to be 105.4±4.2 kJ/mol

Parabolic growth of both and phases suggest diffusion controlled growth

Activation energy for the growth of Al3Mg2 ) was found to be much lower thanthat of Mg17Al12 ) however, the incubation time for the former was higher