Upload
others
View
9
Download
0
Embed Size (px)
Citation preview
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