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Diffusion of Al-27 in an Al-10wt. %Ga alloy by NMR technique
Scripta METALLURGICA
Vol. 12, pp. 649-652, 1978 Printed in the United States
Pergamon Press,
Inc.
DIFFUSION OF AI-27 IN AN Al-lOwt.%Ga ALLOY BY NMR TECHNIQUE
Jan Filipensk9 and Jaroslav Ku~era Institute of Physical Metallurgy ~SAV, ~i~kova 22, 61662 Brno Czechoslovakia (Received April
17, 1978)
Introduction Motional narrowing studies of A1-27 diffusion in aluminium alloys and in pure aluminium have been reported by Spokas and Slichter (1), by Seymour (2), Flynn and Seymour (3) and by Stoebe et al. (4). The diffusion characteristics, the activation enthalpy ~ H and frequency factor Do , obtained by the NMR technique (4) agree quite well with the data estimated from AI-26 tracer measurements (5) and from the chemical diffusivity (6). Since the tracer AI-26 is not readily available, the diffusion characteristics of A1 in Al-Cu, AI-Mg and AI-Zn systems were measured by nuclear magnetic resonance only (4). The results show that the addition of any given solutes (Cu, Mg, Zn) causes an increase in solvent diffusivity accompanied by a decrease in boths the D O and ~ H values. The decrease of ~ H ~ } _ x is inversely proportional to the magnitude of the respective solidus curve slope (7). The most effective in this respect is the Cu solute giving A1 = 6xlO-4cm2/s DOAI_Cu
and
~
l-Cu = (100.87+6 - "28) kJ/mol in the O.15at.%Cu alloy.
In this work the NMR diffusion studies have been extended to the AI-Ga system, which is characterized by a sharp decrease of the solidus within O.0 to 9.5at.% Ga (Ta). The diffusion characteristics were estimated from the measured temperature dependence of the AI-27 NMR line width rm(T). In these estimations on the one hand Stoebe's and col. (4) and on the other Rowland's (8) formula has been used. Experimental The powder samples of pure aluminium and AI-Ga alloys were prepared by filing and rubbing in an agate mortar from the melted ingots (see Tab. 1.). TABLE
1
Nominal Chemical Composition of Indlvidual AI-Ga Samples
Sample number
1
2
3
Ga-content (at.%)
O.O
0.488
0.983
4
2.00
5
4.13
6
6.41
7
8.85
The AI-27 nuclear magnetic resonance signals were observed by using a modified CW spectrometer TESLA BS 487 C eguipped with a temperature probe and with a through-flow preheater. Nitrogen was used as the heat transporting medium. 649
650
DIFFUSION
OF AlGa ALLOY
Results
Vol.
12, No.
7
and discussion
The temperature dependence o f the motional narrowin~ was measured in the sample No.5 within the temperature interval of 22 ° to 387 u C and the experimental values of Fm(T) are given in Fig. i.
.+
+_
==. k-
~e I
FIG. i
~
.. . . . . . . . . . . . . .
Temperature dependence of NMR line width. ooo A1-4.13 at.% Ga +++ pure A1 (4) D O m and ~ are the maximum and m l n i m u ~ computed line widths.
CO m
,~
,.
AI- G¢I~
AI
\'\
1 o \*
,
0300
400
i
~k_;
500
600 --T[K]
700
When Pm(T) is plotted as a function of I03/T it can be easily seen that the values corresponding to the temperatures T ~ 515 K may be considered high enough in the sense of Eisenstadt - Redfield (9) model. On applying the exponential fit to these data we obtain for the AI-27 diffusion coefficient (I)
D A1 AI-Ga = (169.1+7 - " 9)xlO -9 exp(-
44"7~6"0 RT
)
[cm2/s
, kJ/mol]
and for the temperature independent line width ~k = (843+60) Hz (see Fig. i.). In Rowland's interpretation the LSQ fitting (see ~ull line in Fig. i.) procedure results in following values: (2)
DAI_GaA1 = (724+337)xi0 - 9 _ Pk = (947+7)
Hz
exp(-
and
C 0 = (7377+6)
F 0
m
55"4~2"2RT )
m
is the low temperature
[cm2/s
, kJ/mol]
Hz;
-
line width.
It is expedient to compare the diffusion characteristics obtained in the present work with those for pure A1 and Ga given in Tab. 2. The values of Do and d H for pure Ga were evaluated from Carter - Wilson's data (IO); the solitary ~ H values have been calculated from the equation (3)
~ H = (2.1Z20.I)
where T m ks the melting state (ii).
+(0.146±0.O12)
point.
Eq.
Tm
(3) may be applied
[kJ/mol]
,
to the elements
in solid
It is obvious that the activation enthalpy of A1 homodlffusion in Ai-4.13 at.% Ga is very close to that of Ga homodiffusion and much lower than H~} . Such an extremely high effect of the comparatively low solute content is in good agreement with the empirical statement according to which the reduced activation enthalpy ~ H / T c of A1 homodiffusion in aluminium primary solid s o lutions is inversely proportional to the slope of the solidus curve. This is demonstrated in Fig.2.
Vol.
12, No.
7
D I F F U S I O N OF AlGa A L L O Y
651
TABLE 2 D i f f u s i o n C h a r a c t e r i s t i c s of Pure A1 and Ga Element
Method
Do [ cm2/s ]
~ H [ kJ/mol ]
A1
NMR, E-R m o d e l
O.iO
127.7+4.2
A1
NMR, R m o d e l
O.18
122.3~5.8
A1 Ga
eq.
(3)
-
RI, LSQ fit
Ga
eq.
(4) present work w i t h (4) data
138~18
2.27xlO -3
(3)
References
(Ii)
53+32 -
-
present work w i t h dO) data
46+24
(ii)
TABLE 3 C o n c e n t r a t i o n D e p e n d e n c e of NMR Line W i d t h in A I - G a Solid S o l u t i o n s at Room T e m p e r a t u r e Sample number T_(c) [mHzJ
i 9739 ~55
2
3
9584 89
4
9185 89
5
8508 67
7377 55
~140'
~0
FIG~ 2 Plot of r e d u c e d a c t i v a t i o n e n t h a l p y H/T s (T s is solidus temperature) versus inverse c o n c e n t r a t i o n gradient. o [] •
pure A1 (4) AI-Zn, ~ AI-Mg, ~ A l - C u A 1 - G a ( p r e s e n t work)
(4)
6
7
8209 iOO
,
9052 iii
i
,
~)0
r~ 0
'
'
4'o
'
-- IAT,/Acl ['C/ot.~]
M o t i o n a l n a r r o w i n g m e a s u r e m e n t s of A1 d i f f u s i o n in the sample No. 5 were s u p p l e m e n t e d by studies o f / t h e Ga c o n t e n t i n f l u e n c e on the NMR line w i d t h at room temperature. T h e s e r e s u l t s are g i v e n in Tab. 3. It can be seen that the c o n c e n t r a t i o n d e p e n d e n c e of F m has a p a r a b o l i c shape w i t h a m i n i m u m close to
652
D~FFUSION OF AlGa ALLOY
Vol.
12, No. 7
4.13 at.% Ga. We may interpret this as a superposition of two components : one decreasing and the other increasing with Ga content. The former is controlled by motional narrowing, the latter by quadrupole broadening (12). Conclusion From the data given in (4)and in the present paper it may be concluded that the addition of Cu, Mg, Zn and Ga to aluminium increases the solvent diffusivity accompanied by a high decrease in both, frequency factor D O and activation enthalpy ~ H . It can be seen in Fig. 2 that G a is the most effective in this respect. Furthermore it is visible in this Fig. 2 that the reduced activation enthalpy A H / T s of A1 in some primary A1 solid solutions is inversely proportional to the slope of the solidus in the respective solution. Taking into account that the valency of Ga may be equal to 1 (13) we can conclude that ~ H / T s is roughly proportional to the square of the valency of the solute in the above systems and falls as the absolute value of the valency is increase~ This indicates that the Hume-Rothery rules concerning the form of solidus curves (14) in Cu and Ag solid solutions may be related to the primary A1 solid solutions as well. The concentration dependence of NMR line width in AI-Ga solid solutlons 2 may be approximately described by the parabola Fm(C) = 9.884 - 0 . 9 0 3 1 c + 0 . 0 9 2 5 8 c at room temperature and within the concentration range O.0 to 9.5 at.% Ga. Acknowledgement The authors wish to thank Ing. K. ~v4da from ~PT ~SAV Brno who made it possible them to carry out the NMR experiments in his laboratory, and Dr. T. Zem~ik from ~FM ~SAV Brno for some consultations concerning the experimental part of this work. They are also obliged to Dr. J. Kope~ek for his help in the computer evaluation of experimental data. References 1.
J.J. Spokas and C.P. Slichter, Seymour,
Phys.Rev.
113, 1462 (1959), acc. to (4).
2.
E.F.W.
3.
C.P. Flynn and E.F.W.
Proc.Phys. Soc.Lond. A66, 85 (1957), acc. to (4).
4.
T.G. Stoebe et al., Acta Met.
5.
J.T. Lundy and J.F. Murdock,
6.
A.S. Nowick, J.Appl,Phys.
22, 1182 (1952), acc. to (4).
7.
M. Hansen and K. Anderko, New York (1958).
Constitution of Binary Alloys, McGraw-Hill
7a.
R.P. Elliot, Constitution of Binary Alloys, B.C., New York (1965).
8.
T.J. Rowland, Nuclear Magnetic Resonance in Metals; Vol.9, p.47, Pergamon Press, New York --(1961).
Seymour,
Proc.Phys.Soc.Lond.
77, 922(1964),acc.to(4).
13, 701 (1965). J.Appl.Phys.
33, 1671 (1962).
Phys. Rev.
B.C.,
First Supplement, McGraw-Hill Progress Mat.Sci.
9.
M. Eisenstadt and A.G. Redfield,
iO.
A.C. Carter and C.G. Wilson,
132, 635 (1963).
ii.
J. Ku~era, II. Sem. on Diffusion and Thermodynamics of Metals and Alloys, p. ii, ~FM ~SAV Brno (1976).
Brit.J.Appl.Phys.
Sol.St.Comm.
Ser.2,
i, 515 (1968).
12.
C. Berthier and M. Minier,
13.
V.K. Grigorovi~, Elektronnoje strojenije i termodinamika p. 31, Izd. Nauka, Moskva (1970).
i0, 257 (1972).
14.
W. Hume-Rothery,
splavov ~eleza,
The Structure of Metals and Alloys, p.121,Inst.Met.(1956).
Vol. 12, pp. 649-652, 1978 Printed in the United States
Pergamon Press,
Inc.
DIFFUSION OF AI-27 IN AN Al-lOwt.%Ga ALLOY BY NMR TECHNIQUE
Jan Filipensk9 and Jaroslav Ku~era Institute of Physical Metallurgy ~SAV, ~i~kova 22, 61662 Brno Czechoslovakia (Received April
17, 1978)
Introduction Motional narrowing studies of A1-27 diffusion in aluminium alloys and in pure aluminium have been reported by Spokas and Slichter (1), by Seymour (2), Flynn and Seymour (3) and by Stoebe et al. (4). The diffusion characteristics, the activation enthalpy ~ H and frequency factor Do , obtained by the NMR technique (4) agree quite well with the data estimated from AI-26 tracer measurements (5) and from the chemical diffusivity (6). Since the tracer AI-26 is not readily available, the diffusion characteristics of A1 in Al-Cu, AI-Mg and AI-Zn systems were measured by nuclear magnetic resonance only (4). The results show that the addition of any given solutes (Cu, Mg, Zn) causes an increase in solvent diffusivity accompanied by a decrease in boths the D O and ~ H values. The decrease of ~ H ~ } _ x is inversely proportional to the magnitude of the respective solidus curve slope (7). The most effective in this respect is the Cu solute giving A1 = 6xlO-4cm2/s DOAI_Cu
and
~
l-Cu = (100.87+6 - "28) kJ/mol in the O.15at.%Cu alloy.
In this work the NMR diffusion studies have been extended to the AI-Ga system, which is characterized by a sharp decrease of the solidus within O.0 to 9.5at.% Ga (Ta). The diffusion characteristics were estimated from the measured temperature dependence of the AI-27 NMR line width rm(T). In these estimations on the one hand Stoebe's and col. (4) and on the other Rowland's (8) formula has been used. Experimental The powder samples of pure aluminium and AI-Ga alloys were prepared by filing and rubbing in an agate mortar from the melted ingots (see Tab. 1.). TABLE
1
Nominal Chemical Composition of Indlvidual AI-Ga Samples
Sample number
1
2
3
Ga-content (at.%)
O.O
0.488
0.983
4
2.00
5
4.13
6
6.41
7
8.85
The AI-27 nuclear magnetic resonance signals were observed by using a modified CW spectrometer TESLA BS 487 C eguipped with a temperature probe and with a through-flow preheater. Nitrogen was used as the heat transporting medium. 649
650
DIFFUSION
OF AlGa ALLOY
Results
Vol.
12, No.
7
and discussion
The temperature dependence o f the motional narrowin~ was measured in the sample No.5 within the temperature interval of 22 ° to 387 u C and the experimental values of Fm(T) are given in Fig. i.
.+
+_
==. k-
~e I
FIG. i
~
.. . . . . . . . . . . . . .
Temperature dependence of NMR line width. ooo A1-4.13 at.% Ga +++ pure A1 (4) D O m and ~ are the maximum and m l n i m u ~ computed line widths.
CO m
,~
,.
AI- G¢I~
AI
\'\
1 o \*
,
0300
400
i
~k_;
500
600 --T[K]
700
When Pm(T) is plotted as a function of I03/T it can be easily seen that the values corresponding to the temperatures T ~ 515 K may be considered high enough in the sense of Eisenstadt - Redfield (9) model. On applying the exponential fit to these data we obtain for the AI-27 diffusion coefficient (I)
D A1 AI-Ga = (169.1+7 - " 9)xlO -9 exp(-
44"7~6"0 RT
)
[cm2/s
, kJ/mol]
and for the temperature independent line width ~k = (843+60) Hz (see Fig. i.). In Rowland's interpretation the LSQ fitting (see ~ull line in Fig. i.) procedure results in following values: (2)
DAI_GaA1 = (724+337)xi0 - 9 _ Pk = (947+7)
Hz
exp(-
and
C 0 = (7377+6)
F 0
m
55"4~2"2RT )
m
is the low temperature
[cm2/s
, kJ/mol]
Hz;
-
line width.
It is expedient to compare the diffusion characteristics obtained in the present work with those for pure A1 and Ga given in Tab. 2. The values of Do and d H for pure Ga were evaluated from Carter - Wilson's data (IO); the solitary ~ H values have been calculated from the equation (3)
~ H = (2.1Z20.I)
where T m ks the melting state (ii).
+(0.146±0.O12)
point.
Eq.
Tm
(3) may be applied
[kJ/mol]
,
to the elements
in solid
It is obvious that the activation enthalpy of A1 homodlffusion in Ai-4.13 at.% Ga is very close to that of Ga homodiffusion and much lower than H~} . Such an extremely high effect of the comparatively low solute content is in good agreement with the empirical statement according to which the reduced activation enthalpy ~ H / T c of A1 homodiffusion in aluminium primary solid s o lutions is inversely proportional to the slope of the solidus curve. This is demonstrated in Fig.2.
Vol.
12, No.
7
D I F F U S I O N OF AlGa A L L O Y
651
TABLE 2 D i f f u s i o n C h a r a c t e r i s t i c s of Pure A1 and Ga Element
Method
Do [ cm2/s ]
~ H [ kJ/mol ]
A1
NMR, E-R m o d e l
O.iO
127.7+4.2
A1
NMR, R m o d e l
O.18
122.3~5.8
A1 Ga
eq.
(3)
-
RI, LSQ fit
Ga
eq.
(4) present work w i t h (4) data
138~18
2.27xlO -3
(3)
References
(Ii)
53+32 -
-
present work w i t h dO) data
46+24
(ii)
TABLE 3 C o n c e n t r a t i o n D e p e n d e n c e of NMR Line W i d t h in A I - G a Solid S o l u t i o n s at Room T e m p e r a t u r e Sample number T_(c) [mHzJ
i 9739 ~55
2
3
9584 89
4
9185 89
5
8508 67
7377 55
~140'
~0
FIG~ 2 Plot of r e d u c e d a c t i v a t i o n e n t h a l p y H/T s (T s is solidus temperature) versus inverse c o n c e n t r a t i o n gradient. o [] •
pure A1 (4) AI-Zn, ~ AI-Mg, ~ A l - C u A 1 - G a ( p r e s e n t work)
(4)
6
7
8209 iOO
,
9052 iii
i
,
~)0
r~ 0
'
'
4'o
'
-- IAT,/Acl ['C/ot.~]
M o t i o n a l n a r r o w i n g m e a s u r e m e n t s of A1 d i f f u s i o n in the sample No. 5 were s u p p l e m e n t e d by studies o f / t h e Ga c o n t e n t i n f l u e n c e on the NMR line w i d t h at room temperature. T h e s e r e s u l t s are g i v e n in Tab. 3. It can be seen that the c o n c e n t r a t i o n d e p e n d e n c e of F m has a p a r a b o l i c shape w i t h a m i n i m u m close to
652
D~FFUSION OF AlGa ALLOY
Vol.
12, No. 7
4.13 at.% Ga. We may interpret this as a superposition of two components : one decreasing and the other increasing with Ga content. The former is controlled by motional narrowing, the latter by quadrupole broadening (12). Conclusion From the data given in (4)and in the present paper it may be concluded that the addition of Cu, Mg, Zn and Ga to aluminium increases the solvent diffusivity accompanied by a high decrease in both, frequency factor D O and activation enthalpy ~ H . It can be seen in Fig. 2 that G a is the most effective in this respect. Furthermore it is visible in this Fig. 2 that the reduced activation enthalpy A H / T s of A1 in some primary A1 solid solutions is inversely proportional to the slope of the solidus in the respective solution. Taking into account that the valency of Ga may be equal to 1 (13) we can conclude that ~ H / T s is roughly proportional to the square of the valency of the solute in the above systems and falls as the absolute value of the valency is increase~ This indicates that the Hume-Rothery rules concerning the form of solidus curves (14) in Cu and Ag solid solutions may be related to the primary A1 solid solutions as well. The concentration dependence of NMR line width in AI-Ga solid solutlons 2 may be approximately described by the parabola Fm(C) = 9.884 - 0 . 9 0 3 1 c + 0 . 0 9 2 5 8 c at room temperature and within the concentration range O.0 to 9.5 at.% Ga. Acknowledgement The authors wish to thank Ing. K. ~v4da from ~PT ~SAV Brno who made it possible them to carry out the NMR experiments in his laboratory, and Dr. T. Zem~ik from ~FM ~SAV Brno for some consultations concerning the experimental part of this work. They are also obliged to Dr. J. Kope~ek for his help in the computer evaluation of experimental data. References 1.
J.J. Spokas and C.P. Slichter, Seymour,
Phys.Rev.
113, 1462 (1959), acc. to (4).
2.
E.F.W.
3.
C.P. Flynn and E.F.W.
Proc.Phys. Soc.Lond. A66, 85 (1957), acc. to (4).
4.
T.G. Stoebe et al., Acta Met.
5.
J.T. Lundy and J.F. Murdock,
6.
A.S. Nowick, J.Appl,Phys.
22, 1182 (1952), acc. to (4).
7.
M. Hansen and K. Anderko, New York (1958).
Constitution of Binary Alloys, McGraw-Hill
7a.
R.P. Elliot, Constitution of Binary Alloys, B.C., New York (1965).
8.
T.J. Rowland, Nuclear Magnetic Resonance in Metals; Vol.9, p.47, Pergamon Press, New York --(1961).
Seymour,
Proc.Phys.Soc.Lond.
77, 922(1964),acc.to(4).
13, 701 (1965). J.Appl.Phys.
33, 1671 (1962).
Phys. Rev.
B.C.,
First Supplement, McGraw-Hill Progress Mat.Sci.
9.
M. Eisenstadt and A.G. Redfield,
iO.
A.C. Carter and C.G. Wilson,
132, 635 (1963).
ii.
J. Ku~era, II. Sem. on Diffusion and Thermodynamics of Metals and Alloys, p. ii, ~FM ~SAV Brno (1976).
Brit.J.Appl.Phys.
Sol.St.Comm.
Ser.2,
i, 515 (1968).
12.
C. Berthier and M. Minier,
13.
V.K. Grigorovi~, Elektronnoje strojenije i termodinamika p. 31, Izd. Nauka, Moskva (1970).
i0, 257 (1972).
14.
W. Hume-Rothery,
splavov ~eleza,
The Structure of Metals and Alloys, p.121,Inst.Met.(1956).