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The dependence of growth temperature on alloy concentration for primary Al3Fe in steady state solidification of Al-Fe alloys
Scripta METALLURGICA et M A T E R I A L I A
Vol. 28, pp. 7-10, 1993 P r i n t e d in the U.S.A.
P e r g a m o n Press Ltd. All rights r e s e r v e d
THE DEPENDENCE OF GROWTH TEMPERATURE O N ALLOY CONCENTRATION FOR PRIMARY A13Fe IN STEADY STATE SOLIDIFICATION OF AI-Fe ALLOYS Dong Liang and Howard Jones Department of Engineering Materials, University of Sheffield Sheffield, S1 4DU, UK ( R e c e i v e d July 23, 1992) (Revised O c t o b e r 21, 1992)
1. Introduction An earlier communication [1] reported the effect of growth velocity V on growth temperature T G of primary AI3Fe in A1-4.6 to 6.1 wt%Fe in steady state Bridgman solidification at an imposed temperature gradient between 8 and 15 K/mm. The results for 0.01 < V < 1 mm/s showed agood fit to the power relationship: . . . . . (i)
AT - BVn
where AT is growth undercooling T L - T~3, T L is A13Fe liquidus temperature, where, for the conditions applicable, B -- 4.4 _+0.7K ~/~,m)r~with n -- 0.34 _+0.04. The present purpose is to report corresponding measurements for the effect of alloy concentration C o at fixed V for the same situation, and to compare these results with those expected (i) from the obseiwed limiting condition for growth of primary AI3Fe in competition with A1-A16Fe eutectic and (ii) from theoretical models of dendrite growth. 2. Experimental Alloys containing 3.5, 4.7, 5.3, 6.1, 9.5 and 14.0 wt%Fe were prepared from 99.99 wt% pure aluminium and iron by vacuum melting and chill casting into cylindrical ingots 25 mm diameter and 150 mm long for A1-3.5 to 6.1 wt%Fe and into rectangular ingots of dimensions 15 x 50 x 150 mm for AI-9.5 and 14.0 wt%Fe. The ingots of A1-3.5 to 6.1 wt%Fe were rolled and swaged to make rods 3 mm in diameter as described in [1]. Because A1-9.5 and 14.0 wt%Fe were too brittle to roll and swage, rods were hacksawed directly from their rectangular ingots. Lengths of these rods were premelted in 3 mm bore alumina crucibles so as to fill gaps between rod and crucible bore. Incorporation of the thermocouple assembly and monitoring of its output during Bridgman growth were carried out as specified in [1]. As previously, growth temperature was determined metallographically from the position of the A13Fe growth front in longitudinal sections of specimens that had been quenched shortly after the eutectic growth front had passed the thermocouple. As before, the applicable temperature gradient ranged between 8 and 15 K/mm. All the measurements were made for a growth velocity of 100 #m/s. 3. Results and Discussion The resulting measurements of growth temperature T G and associated undercooling T L - T G -- AT are given as a function of alloy concentration C O in Table 1. The results show that T G Tncreases and AT decreases with increasing C o. The double logarithmic plot of AT against C O in Figure 1 shows that the results fit the power law relationship AT - ACo-m
..... (2)
where A is 200 _+50 K(wt%) m with m = 1.3 +_0.1. Together with the results for the effect of growth velocity from [1 ], the measurements can be represented by the combined relationship
7 0 9 5 6 - 7 1 6 X / 9 3 $5.00 + .00 C o p y r i g h t (c) 1992 P e r g a m o n Press
Ltd.
8
SOLIDIFICATION OF A1-Fe
AT - B~Co "m
Vol.
28, No. 1
. . . . . (3)
with B = 34 +_3 K(t~m/s) "n (wt%) m, n = 0.36 + 0.02 and m ffi 1.23 + 0.04. Equation (3) with these values for B, m and n represents a constitutive equation for growth undercooling of AI3Fe over the ranges 10 < V < 1000 ~m/s and 3.5 < Co < 14.0 wt%Fe, and is, to the authors' knowledge, the first of its type to be evaluated for an intermeta]lic phase growing in an alloy melt. Table 2 demonstrates that this relation with these values of B, n and m fits the measurements within +_5K in nearly all cases. Table 2 also shows predicted values of nT for needle morphology on the basis of the Trivedi and Kurz [2] formulation of the model of Kurz, Giovanola and Trivedi [3], with the materials parameters as specified in [1]. These predictions exceed the measurements by a factor of 1.1 to 2.5. This small theoretical overestimate could possibly be a result of the ne~glect by the model of any effect of the convective transport of solute from the dendrite tip which almost certainly occurred in the experiments. Deep etching away of the aA1 matrix from transverse and longitudinal microsections to reveal the morphology of the A13Fe dendrite tips indicated that they were dome-shaped, as for the paraboloid Ivantsov dendrites assumed by the predictive model, and that facet formation was evident only well behind the dendrite tips. As for the previously reported measurements [1], experimental consistency can be checked by comparison with values of nT needed to account for the dependence on C O of V required to suppress growth of primary A13Fe in competition with A1-A16Fe eutectic [4,5]. The appropriate value oftxT is plotted in Figure 1 for V -- 100 ~m/s and shows an excellent fit with the present experimental data. 4. Conclusions 1. Measurements reported herewith in combination with those of [1] indicate that the growth of AlaFe from A1-Fe alloy melts can be represented by the constitutive relations nT = BVnC,~'mwith B = 3~1_+ 3 K (vm/s) "n (wt%) m, n = 0.36 _+0.02 and m = 1.23 _+0.04 for the ranges 3.5 < Co-< 14.0 wt%Fe and 10 < V < 1000 vm/s at temperature gradients of 8 to 15 K/mm. 2. The measurements of aT exceed the predictions of Kurz, Giovanola and Trivedi's formulation for dendrite growth of a needle by a factor between 1.1 and 2.5, possibly attributable to neglect in the predictive model of convective transport of solute from the dendrite tip. 3. The measurements for dependence of AT on C O at V = 100 t,m/s are in excellent accord with the value of AT required to account for observed limiting C O for A13Fe dendrites to grow in competition with AI-A16Fe eutectic at this V. Acknowledgement~ This work forms part of a programme of work funded under UK SERC Research Grant G R / H 32766 (1992 to 1994). The authors are grateful to Professor W Kurz and his collaborators for helpful advice on the application of the Kurz, Giovanola and Trivedi model to these results. References 1. 2. 3. 4. 5.
D Liang and H Jones, Scripta Met Mater, 1991, 25, 2855-2859. R Trivedi and W Kurz, in 'Intelligent Processing of Materials', eds H N G Wadley and W E Eckhart, Jr, MMMS, Warrendale, Pa, 1990, pp 177-193. W Kurz, B Giovanola and R Trivedi, Acta Met, 1986, 34, 823-830. C M Adam and L M Hogan, J Austral Inst Met, 1972, 17, 81-90. I R Hughes and H Jones, J Mater Sci, 1976, 11, 1781-1793.
Vol.
28,
No.
i
SOLIDIFICATION
OF A I - F e
9
TABLE 1
Growth temperature T G (and associated undercooling AT) as a function of alloy concentration CO for primary AI~Fe growing m A1-2.5 to 14.0 wt%Fe at growth velocity 100 ~,m/sand temperature gradient between 8 grid 15 K/mm. Growth Temperature TG, °C
Liquidus Temperature TL, °C
Alloy Concentration Co, wt%Fe
735.2 783.0 803.8 828.8 911.7 970.0
3.5 4.7 5.3 6.1 9.5 14.0
695.2 752.0 774.2 806.2 896.0 965.1
++ + + + +
0.6, 0.6 0.5, 0.7 0.4, 0.8,
Growth Undercooling T L- T G , K
696.5 + 0.8 776.4 + 0.6 899.3 + 0.2 963.0 -+ 0.8
[
40.0, 38.7 31.0 29.6, 27.4 22.6 15.7, 12.4 4.9, 7.0
i
TABLE 2 Combined measurements from [1] and present work showing fit with equation (3) with B = 34 (K, ~,m/s, w t % F e ) , n = 0.36 and m = 1.23, and comparison with predictions for needle dendritic growth. i Undercooling AT - TL-TG,
V, #m/s
Measured
Predicted
Eqn 3 I Predicted
i0 30 30 30 I00 i00 I00 340 340 I000
5.3 4.7 5.3 6.1 4.7 5.3 6.1 4.7 5.3 6.1
*ii. 3 "13.0 "11.3 "15.8 *24.0 "15.0 "18.0 *32.0 *34.8 *48.8
i0.0 17.1 14.8 12.4 26.8 22.8 19.2 41.1 35.4 44.0
I00 i00 i00 I00 I00 I00 I00 I00 I00 I00
3.5 3.5 4.7 5.3 5.3
40.0 38.7 31.0 29.6 27.4 22.6 15.7 12.4 4.9 7.0
38.0 38.0 26.4 22.8 22.8 19.2 ii.I ii.I 6.9 6.9
*From [I].
in K
Co, wt%Fe
6.1 9.5 9.5 14.0 14.0
I
12.9 22.1 21.1 19.5 38.0 36.3 33.1 66.0 68.0 91.2
45.7 45.7 38.0 36.3 36.3 33.1 21.9 21.9 12.0 12.0
Measured
i i
I.i 1.7 1.8 1.2 1.6 2.4 1.8 2.1 1.8 i. 9
i.i 1.2 1.2 1.2 1.3 1.5 1.4 1.8 2.5 1.7
10
SOLIDIFICATION OF A1-Fe
Vol.
28, No. 1
1 O0
50
30
AT (K) 20
10
5
3 2
I
1
I
3
5
10
20
Co (wt%Fe)
Figure 1: Growth undercooling zxT for primary A13Fe as a function of alloy concentration CO at growth velocity V of 100 ~m/s and temperature gradient between 8 and 15 K/mm. Direct measurements: I"1 Present work, • Reported earlier [1]. From observed limiting condition for growth of primary A13Fe in competition with A1-A16Fe eutectic" (D Ref [4], • Ref [5].
Vol. 28, pp. 7-10, 1993 P r i n t e d in the U.S.A.
P e r g a m o n Press Ltd. All rights r e s e r v e d
THE DEPENDENCE OF GROWTH TEMPERATURE O N ALLOY CONCENTRATION FOR PRIMARY A13Fe IN STEADY STATE SOLIDIFICATION OF AI-Fe ALLOYS Dong Liang and Howard Jones Department of Engineering Materials, University of Sheffield Sheffield, S1 4DU, UK ( R e c e i v e d July 23, 1992) (Revised O c t o b e r 21, 1992)
1. Introduction An earlier communication [1] reported the effect of growth velocity V on growth temperature T G of primary AI3Fe in A1-4.6 to 6.1 wt%Fe in steady state Bridgman solidification at an imposed temperature gradient between 8 and 15 K/mm. The results for 0.01 < V < 1 mm/s showed agood fit to the power relationship: . . . . . (i)
AT - BVn
where AT is growth undercooling T L - T~3, T L is A13Fe liquidus temperature, where, for the conditions applicable, B -- 4.4 _+0.7K ~/~,m)r~with n -- 0.34 _+0.04. The present purpose is to report corresponding measurements for the effect of alloy concentration C o at fixed V for the same situation, and to compare these results with those expected (i) from the obseiwed limiting condition for growth of primary AI3Fe in competition with A1-A16Fe eutectic and (ii) from theoretical models of dendrite growth. 2. Experimental Alloys containing 3.5, 4.7, 5.3, 6.1, 9.5 and 14.0 wt%Fe were prepared from 99.99 wt% pure aluminium and iron by vacuum melting and chill casting into cylindrical ingots 25 mm diameter and 150 mm long for A1-3.5 to 6.1 wt%Fe and into rectangular ingots of dimensions 15 x 50 x 150 mm for AI-9.5 and 14.0 wt%Fe. The ingots of A1-3.5 to 6.1 wt%Fe were rolled and swaged to make rods 3 mm in diameter as described in [1]. Because A1-9.5 and 14.0 wt%Fe were too brittle to roll and swage, rods were hacksawed directly from their rectangular ingots. Lengths of these rods were premelted in 3 mm bore alumina crucibles so as to fill gaps between rod and crucible bore. Incorporation of the thermocouple assembly and monitoring of its output during Bridgman growth were carried out as specified in [1]. As previously, growth temperature was determined metallographically from the position of the A13Fe growth front in longitudinal sections of specimens that had been quenched shortly after the eutectic growth front had passed the thermocouple. As before, the applicable temperature gradient ranged between 8 and 15 K/mm. All the measurements were made for a growth velocity of 100 #m/s. 3. Results and Discussion The resulting measurements of growth temperature T G and associated undercooling T L - T G -- AT are given as a function of alloy concentration C O in Table 1. The results show that T G Tncreases and AT decreases with increasing C o. The double logarithmic plot of AT against C O in Figure 1 shows that the results fit the power law relationship AT - ACo-m
..... (2)
where A is 200 _+50 K(wt%) m with m = 1.3 +_0.1. Together with the results for the effect of growth velocity from [1 ], the measurements can be represented by the combined relationship
7 0 9 5 6 - 7 1 6 X / 9 3 $5.00 + .00 C o p y r i g h t (c) 1992 P e r g a m o n Press
Ltd.
8
SOLIDIFICATION OF A1-Fe
AT - B~Co "m
Vol.
28, No. 1
. . . . . (3)
with B = 34 +_3 K(t~m/s) "n (wt%) m, n = 0.36 + 0.02 and m ffi 1.23 + 0.04. Equation (3) with these values for B, m and n represents a constitutive equation for growth undercooling of AI3Fe over the ranges 10 < V < 1000 ~m/s and 3.5 < Co < 14.0 wt%Fe, and is, to the authors' knowledge, the first of its type to be evaluated for an intermeta]lic phase growing in an alloy melt. Table 2 demonstrates that this relation with these values of B, n and m fits the measurements within +_5K in nearly all cases. Table 2 also shows predicted values of nT for needle morphology on the basis of the Trivedi and Kurz [2] formulation of the model of Kurz, Giovanola and Trivedi [3], with the materials parameters as specified in [1]. These predictions exceed the measurements by a factor of 1.1 to 2.5. This small theoretical overestimate could possibly be a result of the ne~glect by the model of any effect of the convective transport of solute from the dendrite tip which almost certainly occurred in the experiments. Deep etching away of the aA1 matrix from transverse and longitudinal microsections to reveal the morphology of the A13Fe dendrite tips indicated that they were dome-shaped, as for the paraboloid Ivantsov dendrites assumed by the predictive model, and that facet formation was evident only well behind the dendrite tips. As for the previously reported measurements [1], experimental consistency can be checked by comparison with values of nT needed to account for the dependence on C O of V required to suppress growth of primary A13Fe in competition with A1-A16Fe eutectic [4,5]. The appropriate value oftxT is plotted in Figure 1 for V -- 100 ~m/s and shows an excellent fit with the present experimental data. 4. Conclusions 1. Measurements reported herewith in combination with those of [1] indicate that the growth of AlaFe from A1-Fe alloy melts can be represented by the constitutive relations nT = BVnC,~'mwith B = 3~1_+ 3 K (vm/s) "n (wt%) m, n = 0.36 _+0.02 and m = 1.23 _+0.04 for the ranges 3.5 < Co-< 14.0 wt%Fe and 10 < V < 1000 vm/s at temperature gradients of 8 to 15 K/mm. 2. The measurements of aT exceed the predictions of Kurz, Giovanola and Trivedi's formulation for dendrite growth of a needle by a factor between 1.1 and 2.5, possibly attributable to neglect in the predictive model of convective transport of solute from the dendrite tip. 3. The measurements for dependence of AT on C O at V = 100 t,m/s are in excellent accord with the value of AT required to account for observed limiting C O for A13Fe dendrites to grow in competition with AI-A16Fe eutectic at this V. Acknowledgement~ This work forms part of a programme of work funded under UK SERC Research Grant G R / H 32766 (1992 to 1994). The authors are grateful to Professor W Kurz and his collaborators for helpful advice on the application of the Kurz, Giovanola and Trivedi model to these results. References 1. 2. 3. 4. 5.
D Liang and H Jones, Scripta Met Mater, 1991, 25, 2855-2859. R Trivedi and W Kurz, in 'Intelligent Processing of Materials', eds H N G Wadley and W E Eckhart, Jr, MMMS, Warrendale, Pa, 1990, pp 177-193. W Kurz, B Giovanola and R Trivedi, Acta Met, 1986, 34, 823-830. C M Adam and L M Hogan, J Austral Inst Met, 1972, 17, 81-90. I R Hughes and H Jones, J Mater Sci, 1976, 11, 1781-1793.
Vol.
28,
No.
i
SOLIDIFICATION
OF A I - F e
9
TABLE 1
Growth temperature T G (and associated undercooling AT) as a function of alloy concentration CO for primary AI~Fe growing m A1-2.5 to 14.0 wt%Fe at growth velocity 100 ~,m/sand temperature gradient between 8 grid 15 K/mm. Growth Temperature TG, °C
Liquidus Temperature TL, °C
Alloy Concentration Co, wt%Fe
735.2 783.0 803.8 828.8 911.7 970.0
3.5 4.7 5.3 6.1 9.5 14.0
695.2 752.0 774.2 806.2 896.0 965.1
++ + + + +
0.6, 0.6 0.5, 0.7 0.4, 0.8,
Growth Undercooling T L- T G , K
696.5 + 0.8 776.4 + 0.6 899.3 + 0.2 963.0 -+ 0.8
[
40.0, 38.7 31.0 29.6, 27.4 22.6 15.7, 12.4 4.9, 7.0
i
TABLE 2 Combined measurements from [1] and present work showing fit with equation (3) with B = 34 (K, ~,m/s, w t % F e ) , n = 0.36 and m = 1.23, and comparison with predictions for needle dendritic growth. i Undercooling AT - TL-TG,
V, #m/s
Measured
Predicted
Eqn 3 I Predicted
i0 30 30 30 I00 i00 I00 340 340 I000
5.3 4.7 5.3 6.1 4.7 5.3 6.1 4.7 5.3 6.1
*ii. 3 "13.0 "11.3 "15.8 *24.0 "15.0 "18.0 *32.0 *34.8 *48.8
i0.0 17.1 14.8 12.4 26.8 22.8 19.2 41.1 35.4 44.0
I00 i00 i00 I00 I00 I00 I00 I00 I00 I00
3.5 3.5 4.7 5.3 5.3
40.0 38.7 31.0 29.6 27.4 22.6 15.7 12.4 4.9 7.0
38.0 38.0 26.4 22.8 22.8 19.2 ii.I ii.I 6.9 6.9
*From [I].
in K
Co, wt%Fe
6.1 9.5 9.5 14.0 14.0
I
12.9 22.1 21.1 19.5 38.0 36.3 33.1 66.0 68.0 91.2
45.7 45.7 38.0 36.3 36.3 33.1 21.9 21.9 12.0 12.0
Measured
i i
I.i 1.7 1.8 1.2 1.6 2.4 1.8 2.1 1.8 i. 9
i.i 1.2 1.2 1.2 1.3 1.5 1.4 1.8 2.5 1.7
10
SOLIDIFICATION OF A1-Fe
Vol.
28, No. 1
1 O0
50
30
AT (K) 20
10
5
3 2
I
1
I
3
5
10
20
Co (wt%Fe)
Figure 1: Growth undercooling zxT for primary A13Fe as a function of alloy concentration CO at growth velocity V of 100 ~m/s and temperature gradient between 8 and 15 K/mm. Direct measurements: I"1 Present work, • Reported earlier [1]. From observed limiting condition for growth of primary A13Fe in competition with A1-A16Fe eutectic" (D Ref [4], • Ref [5].