Solidification microstructure selection and characteristics in the Zn-based ZnAl system

Acta metall, mater. Vol. 40, No. 8, pp. 2003-2009, 1992

0956-7151/92 $5.00 + 0.00 Copyright © 1992 Pergamon Press Ltd

Printed in Great Britain. All rights reserved

SOLIDIFICATION MICROSTRUCTURE SELECTION AND CHARACTERISTICS IN THE Zn-BASED Zn-A1 SYSTEM H. Y. LIU and H. JONES Department of Engineering Materials, University of Sheffield, Sheffield SI 4DU, England (Received 8 November 1991)

Abstract--A solidification microstructure selection diagram has been determined for Zn-A1 alloys containing 2-10wt% A1 by Bridgman and TIG weld traversing over the growth velocity range 0.01-21 mm/s. Secondary dendrite arm spacings 2: of ~ Zn and/~ A1 decreased with increasing V such that J.2V I/3 is constant at fixed alloy concentration. Eutectic cell size A decreased with increasing V such that A V m is constant at 690 + 130 k~m3/2s ~/2.Eutectic interphase spacing 2 decreased with increasing V such that 2V ~,'2 is constant at 7.1 +0.8 #m3/2s -~/2 over the growth velocity range 0.01-21 mm/s in excellent agreement with predictions of the Jackson-Hunt model. Hardness of the eutectic exhibited a Hall-Petch relationship with eutectic interphase spacing 2 and eutectic cell size A. The value of ky from the eutectic interphase spacing is intermediate in value between those for grain size hardening of the pure constituents. R6sum4--On d&ermine le diagramme de s61ection des microstructures au cours de la solidification pour les alliages Zn-A1 contenant 2 10% en poids d'aluminium pr6par6s par la m~thode de Bridgman et par soudure TIG dans une gamme de vitesses de 0,01-21 mm/s. Les espacements 42 entre bras de dendrites secondaires du Zn:t et du A1/~ diminuent lorsque V croit de telle fad;on que 42 V ~/3 soit constant pour une concentration donn6e de l'alliage. La taille A des cellules de l'eutectique diminue lorsque V croit de telle fa~on que A V ~2 soit constant ~. 690 + 130 #m L'2 s -~/z. L'espacement interphase 2 de l'eutectique d6croit lorsque V croit de telle faqon que 2V 3~2 soit constant ~. 7,1 +_ 0,8 # m 3'2 s -~/2 pour la gamme de vitesses allant de 0,01-21 mm/s, en excellent accord avec les pr6visions du mod61e de Jackson et Hunt. La duret6 de l'eutectique r6v6le une relation de Hall et Petch avec l'espacement interphase 2 de l'eutectique et la taille A de la cellule de l'eutectique. La valeur de ky obtenue ~, partir de l'espacement interphase de l'eutectique est interm6diaire entre celles qu'on obtient pour le durcissement par la taille du grain des constituants purs.

Zusammenfassung--Fiir Zn-A1-Legierungen mit 2 bis 10 Gew.% A1 wird mittels der Bridgman- und TIG-SchweiBung ein Diagramm der Erstarrungsmikrostruktur ffir Erstarrungsraten zwischen 0,01-21 mm/s bestimmt. Der Abstand 3.2 sekund~irer Dendritenarme yon :~Zn und/1 A1 sinkt mit steigender Rate so, dab 22 V ~/3 bei fester Legierungszusammensetzung konstant bleibt. Die eutektische Zellengr6Be A nimmt mit ansteigendem V so ab, da/~ A V ~/2 konstant bei 690 + 130 #m 3/2 s -L/2 bleibt. Der Abstand 2 zwischen den eutektischen Phasen sinkt mit steigendem V so, dab 2V t'2 im untersuchten Bereich der Wachstumsrate konstant 7,1 ___0,8/~m 3/2s -~/2 ist, welches ausgezeichnet mit den Voraussagen des Jackson-Hunt-Modelles fibereinstimmt. Die Hiirte des Eutektikums hiingt yon dem Abstand 2 zwischen den Phasen und der eutektischen Zellengr6Be A jeweils im Sinne einer Hall-Petch-Beziehung ab. Der Wert yon k~. in der Hall-Petch-Beziehung ffir 2 liegt zwischen dem ffir die Korngr6BenMrtung bei den beiden reinen Konstituenten.

1. INTRODUCTION Since Kofler [1] first represented zones of occurrence of fully eutectic structure in organic systems o n plots of g r o w t h t e m p e r a t u r e against c o n c e n t r a t i o n , m a n y systems [2, 3] have been s h o w n to exhibit such solidification m i c r o s t r u c t u r e selection diagrams. Alloy systems such as AI-Si a n d A g - C u exhibited relatively simple m i c r o s t r u c t u r e maps which do not involve f o r m a t i o n o f new n o n e q u i l i b r i u m phases while systems such as A I - F e a n d Z n - M g [4] involve n u m e r ous equilibrium a n d n o n e q u i l i b r i u m intermetallic phases which can form as p r i m a r y a n d / o r eutectic phases in different regimes of growth velocity V a n d alloy c o n c e n t r a t i o n Co. U n d e r s t a n d i n g a n d prediction of the characteristics of dendritic a n d eutectic

growth of the competing phases a n d constituents can lead to prediction of such maps o n the basis of competitive growth for c o m p a r i s o n with experimental results, As for A1-Si or A g - C u , solidification of Zn-rich alloys of the Zn-A1 system does n o t involve f o r m a t i o n of new n o n e q u i l i b r i u m phases. Previous studies [5-9] featured lamellar eutectic growth of ~ Z n - / 3 A I (eutectic c o m p o s i t i o n Cru = 5 w t % A1 a n d eutectic t e m p e r a t u r e TEu = 381°C) a n d established t h a t eutectic spacing 2 was related to g r o w t h velocity V by 2V ~'2= 7.3 ___!.8 pm3/Z s -~/2. The present purpose was to employ B r i d g m a n a n d T I G weld traversing to provide a solidification microstructure selection d i a g r a m for Zn-rich Z n - A I alloys over the growth velocity range 0 . 0 1 - 2 1 m m / s a n d to investigate

2003

2004

LIU and JONES: SOLIDIFICATION MICROSTRUCTURE IN THE Zn-AI SYSTEM

systematically the effect of solidification front velocity V, temperature gradient G and alloy concentration Co on secondary dendrite arm spacing 22 of a Z n and flA1, eutectic cell size A, eutectic interphase spacing 2 and micro and macro hardness Hv. 2. EXPERIMENTAL Pure 99.995% zinc and pure 99.999% aluminium were melted in air in a high purity graphite crucible and cast into a rectangular cast iron mould to form ingots of dimensions 15 x 50 x 150 mm. Bridgman solidification was at withdrawal velocities between 0.01 and 3.4mm/s with operative temperature gradient 15 K/mm [4]. A 50 x 150 mm face of such ingots Was ground flat for TIG weld traversing at speeds between 10 and 40mm/s with estimated G = 95 K/mm. Measurements of secondary arm spacing and eutectic cell size were made by the mean linear intercept method taking at least 8 readings per samples. Lamellar eutectic spacing was measured from enlarged SEM and TEM prints of representative areas of transverse sections. Hardness (5 kg load) and microhardness (100 g load) measurements were made on longitudinal and transverse sections respectively. Samples for TEM were electrothinned using an electrolyte of 10% perchloric acid in methanol at a temperature of about - 3 0 ° C under an applied potential of 10 V. 100

i 10

A

V mm/s

A

-A

• •

E~ •

I

•

A

AI

Zn A

0.1

A

_A

0.01

0.001

, 0

f 2

•

A

•

A

•

I 4

•

i f 6

I 8

,

1 10

12

Alloy concentration wt%AI Fig. 1. Dominant growth morphology as a function of alloy concentration COand front velocity V in Bridgman (0.01~
Fig. 2. Types of solidification microstructure in the Zn-A1 samples. (a) Dendritic ~tZn plus lamellar eutectic, 4wt% A1, grown at 0.05mm/s. (b) Dendritic flA1 plus eutectic, 7 wt% A1, grown at 0.01 mm/s. (c) Colony eutectic, 5wt% A1, grown at 0.5mm/s. (d) TEM micrograph of lamellar eutectic, 5 wt% A1, solidified at 13.6 mm/s.

LIU and JONES: SOLIDIFICATION MICROSTRUCTURE IN THE Zn-A1 SYSTEM

2005

Table 1. Resultsfor pool width w, depth d, angle0mas a functionof the conditionsof TIG weld traversing of Zn-5wt% AI alloy

V

A

W

Traverse speed, Vb (mm/s)

14 14 14 14

160 160 160 160

2240 2240 2240 2240

10 20 30 40

Pool depth, d (ram)

Pool width, w (mm)

w 2d

Observed (degrees)

Growth rate, V~ (mm/s)

1.4 1.0 1.1 0.9

5.0 4.5 4.2 4

1.8 2.3 1.9 1.8

27 47 53 60

8.9 13.6 18.1 21.8

0m

V, A and W are applied voltage, current and power in volts, amps and watts respectively.

3. RESULTS Figure 1 shows zones of dominant growth structure as a function of growth velocity V and alloy concentration Co processed by Bridgman growth and TIG weld traversing. Three main growth constituents, namely eutectic ~Zn-flA1 alone or together with primary ~Zn or flA1, were observed within the range of conditions studied. Representative microstructures are shown in Fig. 2(a~i). The results for traverse width w, depth d and inclination 0m of growth direction to the traverse direction as a function of TIG weld traversing conditions are given in Table 1. A typical longitudinal section illustrating the determination of 0m is shown in Fig. 3. The measured secondary dendrite arm spacings 22 of primary a Z n and primary flAl are shown as a function of V and Coin Table 2 and Fig. 4. Results conform to 22VL'~ constant for each Co, with a decrease in ~,2VI/3 for ~Zn from 90 _+ 6//m 4/3 S -1/3 at 2 w t % A l to 36_+3/~m4/3s ~/3 at 4wt%A1 and an increase in 22 V~/3 for flA1 from 37 + 2/~m 4/3 s -1/3 at 7 wt% Al to 57 + 5/~m 4'3 S -1/3 at i0 wt% Al. Eutectic cell spacing A is given as a function of Co and V in Table 3 and Fig. 5. Results conform to A V 1/2 constant for each Co and for both Bridgman and TIG weld traversing with the average A V 1/2 as 690 + 130 #m 3/2s -1/2 for both Zn-5 and 6 wt% Al. Eutectic interphase spacing 2 as a function of V is shown in Table 3 and Figure 6 for comparison with previous work [5-9]. Agreement is excellent. The results give 2 V 1/2 a s 7.1 + 0.8 # m 3/2 s-1/2 over the range 2.4 x 10-4 ~ V ~<21 mm/s. Hardness as a function of V and Co is shown in Table 4 and Figs 7 and 8. The macro and micro hardness of the eutectic exhibits a Hall-Petch relationship with eutectic interphase spacing 2 and eutectic cell size A : Hv = Ho + ky)L 1/2 (or 11o + kyA i/2) with H 0 = 58.7 + 3.2 (or 57.7 + 2.7) kg/mm 2 and ky = 0.34 + 0.03 (or 3.4 __.0.5) kg/mm 3/2 as shown in Figs 7 and 8 respectively.

Fig. 3. Showing determination of 0 m from an etched longitudinal section of TIG weld traversed Zn-5 wt% AI alloy (Vb = 10 mm/s).

4. DISCUSSION

4.1. Observed dependencies of 22 of primary etZn and flAl on V and C o The product 22 V~/3 for primary ~Zn decreased from 9 0 + 6 to 36+3/zm4/3s -~/3 with increase in alloy concentration from 2 to 4 wt% A1. This result compares with a decrease in 22 V~/3 from 83 to 25/.tin4/3 8-1/3 with increase in solute content from 0.5 to 2.84 wt% Mg found by us [10] for corresponding Zn-based Z n - M g alloys. Predictions (see Appendix A) using Feurer and Wunderlin's equation [11] give 22 VII3 of primary ~Zn decreasing from 144 to 90 ].tm 4/3 s -1/3 with increase of Co from 2 to 4 wt% AI, which is about two times the experimental values. The value of 22V 1/3 of primary flAl increased from 37 + 5 to 57 + 2/~m4/3 S 1/3 with increase in alloy concentration from 7 to 10 wt% A1. The corresponding values of 2(GV) ~/3 (where GV is identical with cooling rate 7") are 9 + 1 and 14 + 1/lm (K/s) 1/3 for Zn-7 and 10wt% A1 with G = 15 K/mm which are smaller than the values 17 + 2 and 21 + 2/tm (K/s) 1/3

Table 2. Measured secondary arm spacings 22 of primary ~ Zn and flAl as a function of V and C o in the Bridgman samples V (ram/s) 3.4 1 0.34 0.1 0.034 0.01 Mean

Zn-2 wt% AI )~2 22 V i/3 (;~m) (/zm4/3 s ,,,3) 5.6+0.4 8.2+_0.8 12.6+_0.4 20.6+_3.2 28.8+_3.2 46.0 4-_4

84.4 82.0 87.9 92.0 93.3 98.8 90 _+ 6

Zn~4 wt% AI 22 22V i/3 (,urn) (/zm4/3s -U3) 2.2+_0.3 3.4+_0.5 4.9+_0.3 8.4+_0.4 11.8+_0.5

33.1 34.4 34.4 38.8 38.2 36 +_ 3

Zn-7 wt% AI 22 22 V i/3 (gm) (#m4/3s 1/3) 2.5+_0.5 3.7+_0.3 4.9+_0.4 7.8+_0.9 11.8+_0.7 19.2 + 0.9

37.6 36.9 34.2 36.2 38.2 41.4 37 + 2

Zn-10 wt% A1 22 22 V L/3 (,um) (/zm4/3s 1~3) 3.4+_0.4 5.1 +_0.6 8.1 + 0 . 5 13.3+_0.8 18.9+_0.5 27A +_ 1.2

51.1 51.1 56.5 61.7 61.6 59 57 _+ 5

2006

LIU and JONES: SOLIDIFICATION MICROSTRUCTURE IN THE Zn-A1 SYSTEM so

200

k 30

100

2O

5O

X=

m,Zn-5AI k

• Zn.6A

\

A /Jm

gm

2O

10

10

5

2 2

0.01 0.03

0.1

0.3

1

3

V mm/s Fig. 4. Dendrite secondary arm spacing 22 of ~Zn (open points) and of flAl (solid points) as a function of V and CO for Bridgman solidified Zn-2 to 10 wt% A1 alloy. Key: O 2, [] 4, • 7, • 10wt%Al. reported [12] for Z n - 6 . 5 a n d 11 w t % A1 at G between 7.5 to 12 K / m m . These values are typically o n e - h a l f those o f 22T" for p r i m a r y ~AI in Al-based alloys which are between 18 a n d 4 7 p m (K/s)" with n between 0.25 a n d 0.39 [13]. Predictions o f F e u r e r a n d W u n d e r l i n (see A p p e n d i x A) give ~.2V1/3 for p r i m a r y flA1 in Z n - A 1 increasing from 80 to 1 0 9 p m 4/3 s -1/3 with increase o f Co f r o m 7 to 1 0 w t % A l at G = 15 K / m m which are twice the experimental values.

.

10

i

. . . . . .

l

100

.

I

.....

I

,

I

.....

1000

I

.

10000

~

,

.

100000

Vgm/s Fig. 5. Eutectic colony size A as a function of V and Co for Bridgman and TIG weld traversing. Key: • 5 wt% A1, • 6 wt% A1.

Results for eutectic interphase spacing 2 are consistent with 2 V ~a = 7.1 _ 0.8 t t m 3/2 s -~/2 for B r i d g m a n growth a n d T I G weld traversing over the same range o f solidification f r o n t velocity, confirming the results o f previous studies [5-9] (Fig. 6). These c o m p a r e with 5.3 to 8.5 # m 3/2 s -1/2 [14-17] for regular (lamellar or fibrous) eutectics based on Z n a n d values between 7 a n d 48#m3/Zs-l/z [18] for eutectics based o n A1. Predictions o f J a c k s o n a n d H u n t [19] (see A p p e n d i x B) give 2V~/2= 7 . 3 / / m 3/2 s -1/2 in excellent agreement with the experimental measurements. 4.3. Hardness measurements

4.2. Observed dependencies o f A and 2 on G and V

The eutectic cell size A was f o u n d to decrease with increasing solidification f r o n t velocity over the range 0.01 to 21 m m / s o b t a i n e d by B r i d g m a n g r o w t h a n d T I G weld traversing. B r i d g m a n results are consistent with those from T I G weld traversing a n d with the relationship: A V 1/2= K with K = 690 + 1 3 0 / / m 3/2 s-1/2.

While the values o f Ho from Figs 7 a n d 8 are identical at 58 ___4 k g / m m 2, the slope ky from the a p p a r e n t correlation with eutectic cell size A in Fig. 8 is ten times t h a t from the correlation with interlamellar spacing 2 in Fig. 7 consistent with the fact that A is ~ 902 for the conditions investigated.These values of H0 a n d ky are c o m p a r e d in Table 5 with results for eutectics in which ~ Z n or flA1 is one of the phases.

Table 3. Effect of Co and V on eutectic interphase spacing 2 and eutectic cell size A in Bridgman and Zn-5 wt% AI V 2 2 V 1/2 A A V 1/2 Solidification condition (mm/s) (#m) (#m3/2 s -I/2) (prn) (pro3/2s -'/2) 0.034 1.4 + 0.3 8.2 101 -t- 6 589 0.1 0.76 + 0.1 7.6 53.8 + 2.5 538 Bridgman 0.34 0.35 _ 0.I 6.5 38.9 _+ 1.8 717 1 0.24 + 0.05 7.6 21.1 -+ 2.7 667 3.4 0.15 ___0.03 8.7 14.8 + 1.3 811 4.4 . . . . 8.9 0.08 + 0.03 7.8 8.3 + 2.1 783 TIG 13.6 0.07-+0,03 7.8 6.1 -+ 1.8 711 18.1 0.06 -+0,02 7.7 5.2 -+ 1.8 700 21.8 0.05 -+0,02 7.5 4.5 -+ 1.3 664

TIG weld traversed samples Z n ~ wt% AI A A V tn (#m) (gm3/2s -1/2) ----40.2 -+ 3.5 741 26.6 + 2.8 841 16.6 _+2.1 909 9.0 1.2 599 7.4 -- 1.5 698 4.9--+ 1.1 571 3.3 -+0.9 444 ---

-

LIU and JONES: S O L I D I F I C A T I O N M I C R O S T R U C T U R E IN T H E Zn-A1 SYSTEM

lO I

2007

90

5 85 HV kg/mm 2

/Jm

80

75

O,

0.1 65 0.05

, 0-5 10 .4 10 .3 10 .2 10 "I 10 0 101

102

V mm/s

0

20

40

60

)C1/2

80

1 O0

mrn-1/2

Fig. 6. Eutectic interphase spacing 2 as a function of V for Bridgman and T I G weld traversing for Z n - 5 wt% A1 alloy in comparison with previous work. Key: • T I G weld traversing, present work, • Bridgman growth, present work; O Livingston et al. [5]; [] Cooksey et al. [6]; A Chadwick [7]; A Moore and Elliott [8]; ¢q Eruslu et al. [9].

Fig. 7. Macro (open points) and microhardness (solid points) H v as a function of eutectic interphase spacing 2 to the power minus one-half for Bridgman growth in Zn-5 wt% AI.

S e v e r a l p o i n t s e m e r g e f r o m a n a l y s i s o f this d a t a . Firstly, t h e r e s u l t s f o r Z n ~ d s h o w a v a l u e o f ky f r o m e u t e c t i c cell s p a c i n g w h i c h is 18 t i m e s t h a t f r o m i n t e r l a m e l l a r s p a c i n g b e c a u s e A w a s ~ 1302 in t h a t p a r t i c u l a r case. S e c o n d l y , v a l u e s o f k y f r o m interl a m e l l a r s p a c i n g a r e l a r g e s t (i> 2 k g / m m 3/2) w h e n vol-

u m e f r a c t i o n o f t h e s e c o n d p h a s e is l a r g e ( ~ 0.5), a n d s m a l l e s t (~< 1 k g / m m 3,~2) w h e n m i n o r p h a s e v o l u m e f r a c t i o n is s m a l l (~< 0.3). T h i r d l y , o u r v a l u e o f ky f r o m i n t e r l a m e l l a r s p a c i n g o f Z n - A I is i n t e r m e d i a t e bet w e e n t h e v a l u e s for g r a i n size h a r d e n i n g o f Z n a n d AI. T h i s is c o n s i s t e n t w i t h t h e m a j o r c o n t r i b u t i o n to

Table 4. Macrohardness H v (kg/mm2) as a function of V and Co for the Bridgman experiments V (mm/s)

2wt% AI

4wt% AI

3.4 1 0.34 0.1 0.034 0.01

84.7_+2.5 83.1_+3.1 79.5_+1.8 74.5_+2.2 74.8 -+ 3.6 69.7_+3.7

81.1_+2.1 77.1_+1.8 71_+1.4 67.3_+3.0 66.8 _+ 3.4 58.8_+2.7

Alloy concentration Co 5wt% AI 6wt% AI 86.2_+1.8 78.4_+3.1 76.3_+2.8 70.6_+3.7 67.9 _+ 3.1 62.3_+3.0

85.5+4.5 a 82.9+2.2 a 75.6_+2.8 ~ 72.1_+1.8 ~ 69.3 _+ 2.7~ 66.4_+2.7"

86.8_+3.1 84.4_+2.5 79.2_+2.7 69.8-+3.9 65.7 _+ 1.8 59.2_+2.2

7wt% AI

10wt% AI

72.9_+2.9 69.4_+3.1 65.5_+3.4 72.8-+3.7 65.8 _+ 1.9 69.3_+2.9

63.2_+3.1 58.6_+2.7 56.3_+4.1 61.0-+2.1 62.7 _+2.9 66.8_+3.2

~Microhardness. Table 5. Values of constants H 0 and ,~ from results of H = H o + ky2 ~/2 for c~Zn or aAl-based eutectics, where 2 is eutectic interphase spacing Eutectic morphology

Volume fraction of minor phase

7Zn-/::A1

Lamellar

0.26 (flA1)

Cd-Zn

Lamellar

0.18

Fibrous Complex regular Lamellar Fibrous Fibrous ---

0.5 0.5 0.5 0.1 0.1 0 0

System

~Zn Mgz Zn H ~AI T 2 :~AI AI2Cu ~AI-AI3Ni ~AI AI6Fe Pure Zn Pure AI

/4o (kg/mm2) 58.6 _+ 1.2 (57.7 _+ 1.5a) 27 _+3.7 (4.5_+ 12.8") 135 -+ 6.9 96.3 _+ 13.2 67.3 _+ 10 15.0 _+4.2 0.7 _+2.8 9.9 ~ 21.9 ~4.8

"These values of H 0 and k, are from the apparent relationship H = H o + k,.A (in Ref. [14] described as a grain size).

k~ (kg/mm3/2)

Reference

0.34 _+0.02 (3.4 _+0.3~) 0.56 _+0.05 (9.9+_2.1a) 2.2 -+ 0.2 2.9 _+0.4 2.5 _+0.3 0.96 _+0.08 0.89 _+0.04 0.71 ~ 1.17 0.22

Present work Present work [14] [14] [4] [20] [21] [22] [23] [24] [24]

12

,

where A is eutectic cell size

2008

LIU and JONES: SOLIDIFICATION MICROSTRUCTURE IN THE Zn-A1 SYSTEM

/

90

Hv8s

/

value between those for grain size hardening of the pure constituents Zn and A1. Acknowledgement---One of us (H J) would like to acknowledge financial support from the Brite Euram Directorate, Brussels, for continuing work on solidification microstructure selection.

kg/mm 2 8O

REFERENCES

75

70

65

I

600

2

4

6

J

I

8

10

A'1/2 ram'1/2 Fig. 8. Macro (open points) and microhardness (solid points) Hv as a function of eutectic cell size A to the power minus one-half for Bridgman growth in Zn-5 wt% AI.

Icy for Z n - A I eutectic deriving from the interlamellar spacing rather than from the eutectic cell size. The alternative possibility that solid solution hardening of ~Zn and flAl in the eutectic has increased ky for the eutectic cell size to as high as 3.4 k g / m m 3/2 can be ruled out on the basis that solid solution hardening evidently affects H0 much more than Icy, as borne out by Table 5.

5. CONCLUSIONS I. A solidification microstructure selection diagram has been determined for Z n - A I alloys containing 2-10 w t % A1 by Bridgman and T I G weld traversing over the growth velocity range 0 . 0 1 - 2 1 m m / s at temperature gradients 15 and 95 K / m m . 2. Secondary arm spacing 22 of primary ccZn and flA1 depends on growth velocity V for Bridgman growth in the range 0.01-3.4 mm/s according to the relationship 22VI/3=A where A is 9 0 + 6, 3 6 + 3, 37 _+ 2 and 57 ___5 / t i n 4/3 s -1/3 for alloy concentration 2, 4, 7 and 10 wt% AI respectively. 3. F o r eutectic cell size we find AV~/2=690__+ 130/~m 3/2 s-1/2 for Bridgman and T I G weld traversing o f Z n - 5 and 6 wt% AI while for eutectic interphase spacing 2, we find 2V~/2 = 7.1 __+0.8/tin3/2 s -1/2, both values in good agreement with previous data. 4. Macro/microhardness of the ~ Z n - f l A l eutectic exhibited a Hall-Petch relation with eutectic interphase spacing 2 and eutectic cell size A. The value of ky from the interphase spacing is intermediate in

1. A. Kofler, Ber. Deutsch. chem. Ges. 77, 110 (1944). 2. W. Kurz and D. J. Fisher, Int. Metals Rev. 177 (1979). 3. H. Jones, Mater Sci. Engng A 133, 33 (1991). 4. H. Y. Liu and H. Jones, Acta metall, mater. 40, 229 (1992). 5. J. D. Livingston et al., Acta metall. 18, 399 (1970). 6. D. J. S. Cooksey et al., Phil. Mag. 10, 745 (1964). 7. G. A. Chadwick, J. Inst. Metals 92, 18 (1963). 8. A. Moore and R. Elliott, in The Solidification o f Metals, p. 167. Iron and Steel Inst., London (1968). 9. N. Eruslu and A. Altmisoglu, in Advanced Materials and Processes (edited by H. E. Exner and V. Schumacher), Vol I, p. 153, DGM Informationsgesellschaft (1990). 10. H. Y. Liu and H. Jones, J. Mater. Sci. Lett., in press. I1. U. Feurer and K. Wunderlin, DGM Fachbereicht, Oberursel (1977). 12. N. Tunca and R. W. Smith, J. Mater. Sci. 23, 111 (1988). 13. H. Jones, in Rapid Solidification o f Metals and Alloys, Inst. of Metallurgists, London (1982) and Mater. Sci. Engng 65, 145 (1984). 14. B. J. Shaw, Acta metall. 15, 1169 (1967). 15. V. De L. Davies, 3. Inst. Metals 93, 10 (1964). 16. D. Jaffrey and G. A. Chadwick, J. Inst. Metals 97, 118 (1969). 17. W. A. Tiller and R. Mrdjenovich, J. appl. Phys. 34, 3639 (1963). 18. J. A. Juarez and H. Jones, Acta metall. 18, 399 (1970). 19. K. A. Jackson and J. D. Hunt, Trans. metall. Soc. A.LM.E. 236, 1129 (1966). 20. Y. Li, H. Jones and D. H. Warrington, J. Mater. Sci. 25, 835 (1990). 21. I. G. Davies and A. Hellawell, Phil. Mag. 19, 1285 (1969). 22. R. S. Barclay, H. W. Kerr and P. Niessen, J. Mater. Sci. 6, 1168 (1971). 23. I. R. Hughes and H. Jones, J. Mater. Sci. 11, 1781 (1976). 24. R. W. Armstrong, Adv. Mater. Res. 4, 101 (1970). 25. J. L. Murray, Bull. Alloy Phase Diagr. 4, 55 (1983). 26. W. Kurz and D. J. Fisher, in Fundamentals of Solidification. Trans. Tech., Aedermannsdorf (1986). APPENDIX A Prediction of 2 2

Feurer and Wunderlin [11] predicted 22 from a coarsening model to obtain 22 = 5.5(ktl) 1/3 where, for alloy concentrations COabove the solid solubility limit at the eutectic temperature TEu 22 = q~[DF ln( CEu/Co)/( l - k )G V]1/3 with ~b = 5.5, where D is diffusivity of solute in the melt, F is Gibbs-Thompson parameter, CEt~ is eutectic concentration and k is solute partition coefficient. For primary ~Zn, we take D =2.04 × 1 0 - 9 m 2 / s [4], F = 1.1 × 10 - 7 mK [4], CEv = 5 wt% A1 [25] and k = 0.234 [25]. For primary flA1, we take D = 3 x 10-9m2/s [26],

LIU and JONES: S O L I D I F I C A T I O N M I C R O S T R U C T U R E IN T H E Zn A1 SYSTEM F = 0 . 9 × 10 7inK G = 15 K/mm:

[26]

and

k =0.8748,

giving

for

2009

and b = m Pac,,!Lft~ D

Co (wt% AI) 2 4 7 10 ,~2V13 (prediction) 144 90 80 109 ;teV ~ (experimental results) 90 _+ 6 36 4- 3 37 _+_2 57 + 2

with

p = ~ [sin2(n~f~)]/(n~) ~. n

APPENDIX B

Prediction q f 2Vl2,for Eutectic Growth Jackson and Hunt [19] predicted for eutectic interlamellar spacing 2, on the assumption that growth occurred at m i n i m u m undercooling and m a x i m u m velocity V, that ,].V 1'2 = (a/b) t/2 where

a = ma~TEu [l/f~m~AH~ + 1/f~m~AH~]

1

Here a ~ is interfacial energy between ~ and/3 phases, .1~,,m~ and AH~ are volume fraction, liquidus slope and enthalpy of fusion for the ~-phase (and.f/~, ml~ and AHI~ correspondingly for the fl-phase), AC is concentration difference between and fl phases at TEu, and P is tabulated in Ref. [16]. For the lamellar ~Zn-flA1 eutectic, we take .1~-0.74, f~ = 0.26 [25], m~ = 10.1, m s = 7.4 K / w t % [25], T~:v = 660 K [25], A C = 1 5 . 7 2 w t % A 1 [25], A H ~ - 7 . 9 × I0SJ/m ~ [4], D = 2 . 0 4 x 10-gm2/s, AHI~= 9.5 x 108J/m 3 [26] and % l t 0 . 1 J / m 2 giving a = 2 . 0 2 × 1 0 7 K m and b = 3 . 7 8 x 109 K s / m 2 so that ).V I/2= 7.3 ~m3'2 s ~2 in excellent agreement with our experimental value 7.1 _+ 0.8 p m v2 s ~~.