Stacking-fault energy of Al-21% Zn alloy

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Stacking-fault energy of AI-21% Zn alloy Deformation of the A1-21~ Zn alloy is distinctly different from that of aluminum in several respects. The activation energy for deformation of the alloy is several times greater than that of aluminum. A cell structure is readily formed in pure aluminum, but in the alloy cell structures are formed only at deformation temperatures exceeding 200°C. Such differences in deformation behavior are attributed to the changes in stacking-fault energy and dislocation interactions. This note reports on the stacking-fault energy of the A1-21% Zn alloy and its influence on the dislocation interactions in the alloy. Stacking-fault energies have been determined in a number of ways, either direct or indirect 1. The four common methods involve measurement of extended node radii z- 5 the pole intensity ratios in rolling textures 3 - 9, X-ray faulting probabilities 1o,t and the strain-rate dependence of ~3~2. Since extended nodes were not readily detectable by transmission electron microscopy of the A1-21~o Zn alloy, and since there is a superposition of the aluminum and second-phase X-ray reflections, the rolling texture technique was selected for this study. The rolling-texture method is essentially an empirical technique for determining the stackingfault energy of a metal or an alloy from the measured pole-intensity ratios in the pole figure. Two intensity ~/Gb x 103

Rh

L . C~'2At- 21./*Zn

~u

o.~

Pt

Au

o'.4 o15 o~6 o17 o18 o'.9 Io//( Io + I3o)

,

Co

6

C2

,.'3

C,

Irt)//I~o

Fig. 1. Calibration curves of 7/Gb vs. lo/(lo+13o ) and 7/Gb vs. 1TD/I20.

ratios, Io/(Io+I3o ) and ITD/I20, are derived from a {111} pole figure. Io is the pole intensity at 25° from the center of the pole figure in the rolling direction. 13o is the pole intensity at 25° from the center of the pole figure and 30° from the rolling direction. 12o and ITD are the pole intensities along the periphery of the pole figure at 20° and 90° , respectively, from the rolling direction. These pole intensity ratios are then related to the stackingfault energy, 7, through calibration curves. In this case, 7 was derived from reported values 3'9'13A¢ of the pole-intensity ratios and 7/Gb for Ni, Pd, Rh, Cu, Au, Pt andAg, rolled to 95% reduction at room temperature (Fig. 1). G is the shear modulus and b the magnitude of the Burgers vector. Specimens for texture measurements of the A12 1 ~ Zn alloy* were prepared by a two-step rolling procedure. Slabs, 0.5 in. thick, were machined from alloy ingots, hot-rolled to 0.050 in. thick sheet, solution-treated at 400° C and water quenched. The alloy sheet was then cold-rolled to a thickness of 0.0025 in. (95% reduction). Subsequently, the {111} pole figure of the as-rolled sheet was determined by combined X-ray reflection and transmission methods (Fig. 2), using a Siemens texture-goniometer and Co K, radiation. Tensile specimens 2 in. long with a 1/2 in. gage section (1/4 in. wide and 0.026 in. thick) were machined from rolled A1-21~ Zn alloy strip, solution-treated and quenched as previously described. These tensile specimens were elongated 10% at an initial strain rate of 0.2 min-t at room temperature or 150° C in an Instron testing machine. Thin foils of both rolled sheets and tensile specimens were prepared for transmission electron microscopy by electropolishing the specimens in a 20% solution ofperchloric acid in absolute ethanol at - 3 0 ° C. The microstructure and dislocation substructures of heat-treated and deformed specimens were examined in a JEM-7 electron microscope operated at 100kV. In addition to the electron microscope studies, as-quenched specimens were examined for evidence of G - P zones by small-angle scattering X-ray technique using a Kratky camera and Mo K, radiation. * Prepared by the Battelle Memorial Institute from 99.99~ AI and 99.99~ Zn.

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337

R.D.

+

Fig. 3. Helical dislocations, dislocation loops and black dots after solution-treating at 400 ° C and water-quenching in AI 21% Zn alloy.

Fig. 2. {111} Pole figure of AI 21~/ Zn alloy rolled 95% at room temperature (contour numbers represent relative intensity).

From the { 111} pole figure, the values of the two pole-intensity ratios are lo/(lo+13o)~-0.75 and 1TD/Izo--~0.67. The corresponding values of ?/Gb taken from the calibration curves are 7.3 x 10- 3 and 6.7 x 10-3. In the absence of appropriate data, the values of G and b were assumed similar in the alloy and aluminum. Using G = 2.70 x 1011 dyne/cm / and b = 2 . 8 6 x 10 -s cm, the average value of y is calculated to be 5 4 + 2 ergs/cm z. The stacking-fault energy for aluminum 7A~ is greater than 150 ergs/cm 2. Therefore, it is clear that the addition of 21~o Zn to aluminum significantly decreases the stacking-fault energy. Transmission electron microscope studies reveal that the defect structures in the water-quenched alloy include a small number of helical dislocations, dislocation loops and fine black dots (Fig. 3). Since the as-quenched specimens are expected to be supersaturated with respect to zinc atoms and vacancies, the black dots could be either (or both) G - P zones o r vacancy clusters. Results from the X-ray small-angle scattering study indicate the presence of G - P zones of about 150A diameter. After room-temperature tensile deformation, dislocations were observed to be confined in bands which follow {111} traces (Fig. 4). Tensile deformation at 150°C produced a high density of tangled dislocations distributed rather uniformly (Fig. 5). Room-temperature rolling of the alloy to 95~o reduction in thickness resulted in a higher density

Fig. 4. Band structure after tensile deformation at room temperature in AI-21% Zn alloy.

of tangled dislocations distributed in a less uniform manner (Fig. 6). In no case were cell structures observed in the alloys deformed at room temperature and 150°C. The preceding observations indicate that little or no cross-slip occurs during deformation at room temperature and at 150°C. The lack of cross-slip is traceable to the low stacking-fault energy of the alloy among other factors. The decreased stacking-fault energy in the AI 2 1 ~ Zn alloy signifies an increased separation of the partial dislocations, which is the result of enhanced solute atom concentration at the stacking fault 15'16. The enhanced concentration of solute Mater. Sci. Eng., 8 (1971) 336- 339

338

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fault energy of zinc is (55 ergs/cm2). C1 is calculated to be about 18 at. ~ (35 wt. ~ ) , which indicates that the concentration of zinc at the stacking fault is nearly twice the average zinc concentration of the alloy. The separation of the partial dislocations, r, was calculated from the equation 15 Ga 2

r - 24~7,

Fig. 5. Tangled dislocations after tensile deformation at 150°C in A1-21~ Zn alloy.

Fig. 6. Densely tangled dislocations after rolling 95~ at room temperature in AI-21 ~ Zn alloy.

atoms at stacking faults and the increased separation of partial dislocations in the A1-21~ Zn alloy were estimated by independent calculations. The concentration of zinc at the stacking faults, C,, was calculated from the equation 1~ C1

Co

[1

-

(1 - Co) {1 - exp ( - H/R T)}_]

(1)

k-

where

F H = ~(~Zn--~AI).

(2)

Co is the average concentration of zinc in the alloy, i.e., 9.9 at. ~ (21 wt. ~o), v the volume of the alloy per tool (8.72 cm3/mol), h the spacing of closepacked planes (2.34 × 10- 8 cm), and 7z, the stacking-

(3)

where a is the lattice parameter and the other terms are as defined above. Using values of G = 2.70 x 101 dyne/cm 2, a = 4.0403 x 10- s cm and y = 54 ergs/cm 2, r in this alloy is calculated to be 11 x 10- 8 cm, whereas that in aluminium is 4 × 10- s cm. Thus, r is larger in the alloy by a factor of almost three. The thin foil work reveals the presence of numerous G - P zones, and these are known to have a great influence on the deformation mechanisms. The dominant role of G - P zones in controlling deformation of the A1-21 ~ Zn alloy is discussed more fully by Lee et al. 19. The decrease in stackingfault energy may hinder cross slip, but the effect is secondary when compared with the effects of coherent precipitates. This general conclusion has been reached by Gallagher and Liu 4 in their comparison of methods for obtaining the stackingfault energy. On the'oasis of these findings, it is concluded that an addition of 21 wt. ~ Zn to aluminum results in: (1) A reduction of stacking-fault energy of from > 150 ergs/cm 2 to 54 ergs/cm 2. (2) A zinc atom concentration at stacking faults approaching twice the nominal alloy composition. (3) A threefold separation of partial dislocations. (4) An inhibition of cross-slip due to a reduction in stacking-fault energy and the effect of G - P zones. The sponsorship of this study by the Office of Naval Research under Contract N00014-67-C-0503, NR 031-723, with the technical cognizance of Dr. W. G. Rauch, is gratefully acknowledged. Appreciation is also extended to W. E. Krull for assistance with the X-ray small angle scattering and rolling-texture experiments, to Drs. C. C. Feng and E. A. Starke for helpful discussions and to A. D. Friday for assistance with the electron microscope. E. U. Lee, H. H. Kranzlein and E. E. Underwood

Lockheed Georgia Company Research Laboratory, Marietta, Ga. (U.S.A.) Mater. Sci. Eng., 8 (1971) 336-339

SHORT COMMUNICATIONS REFERENCES 1 P. C. J. GALLAGHER,Met. Trans., 1 (1970) 2429. 2 P. C. J. GALLAGHERAND J. WASHBURN,Phil. Mag., 14 (1966) 971. 3 R. E. SMALLMANAND D. GREEN, Aeta Met., 12 (1964) 145. 4 P. C. J. GALLAGHERANDY. C. LIU,Acta Met., 17 (1969) 127. 5 T. V. NORDSTROMANDC. R. BARRETT,Aeta Met., 17 (1969) 139. 6 P. S. KOTVALAND O. H. NESTOR, Trans. AIME, 245 (1969) 1275. 7 B. E. P. BEESTON, I. L. DILLAMOREAND R. E. SMALLMAN, Metal Sci. J., 2 (1968) 12. 8 B. E. P. BEESTONAND L. K. FRANCE,J. Inst. Metals, 96 (1968) 105. 9 I. L. DILLAMORE,R. E. SMALLMANAND W. T. ROBERTS, Phil. Mag., 9 (1964) 517. 10 M. S. PATERSON,J. Appl. Phys., 23 (1952) 805. 11 B. E. WARRENANDE. P. WAREKOIS,Acta Met., 3 (1955) 473.

12 13 14 15 16 17 18

19

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E. PEISSKER,Acta Met., 13 (1965) 419. R. E. SMALLMAN,J. Inst. Metals, 84 (1955-56) 10. S. R. GOODMANANDHSUNHu, Trans. AIME, 242 (1968) 88. A. H. COTTRELL,Relation of Properties to Microstructures, ASM, Cleveland, 1954, p. 131. HIDEJI SUZUKI,Sci. Rept. Res. Inst., Tohoku Univ., Japan, A4 (1952) 455; J. Phys. Soc. Japan, 17 (1962) 322. HIDEJISUZUKI,in J. C. FISHER,W. G. JOHNSTON,R. THOMSON AND T. VREELAND,JR. (eds.), Dislocations and Mechanical Properties of Crystals, Wiley, New York, 1957, p. 361. R. L. GEGEL,Calculation of stacking fault energies for facecentered cubic metals, Teeh. Documentary Rept. No. ASDTDR-62-388, Wright-Patterson Air Force Base, Ohio, May 1962. E. U. LEE, H. H. KRANZLEINAND E. E, UNDERWOOD,Met. Trans., to be published.

R e c e i v e d A p r i l 28, 1971 ; in revised form June 8, 1971 Mater. Sci. Eng., 8 (1971) 336-339

Analysis of sintering equations pertaining to constant rates of heating

A , = f(v, a, Q, R) A 2 = f(y, (2, D'v, k, a, Qv, R)

D e n s i f i c a t i o n kinetics of " p o w d e r " c o m p a c t s of vitreous as well as crystalline m a t e r i a l s have been s t u d i e d when the c o m p a c t s were h e a t e d at c o n s t a n t h e a t i n g rate. A t t e m p t s have been m a d e with some success to c o r r e l a t e such d a t a with d a t a o b t a i n e d u n d e r i s o t h e r m a l c o n d i t i o n s 1-4. Since the c o n s t a n t heating rate e x p e r i m e n t s simulate m o r e closely the i n d u s t r i a l practice, it w o u l d be beneficial if the m e c h a n i s m or m e c h a n i s m s r e s p o n s i b l e for densification can be d e c i p h e r e d f r o m such d a t a . T h e c o n d i tions u n d e r which it is possible to do so are examined. The general expressions relating the fractional s h r i n k a g e (y) with t e m p e r a t u r e ( T ° K ) 1-4 in cons t a n t - r a t e - h e a t i n g sintering e x p e r i m e n t s are as follows : In ( y / T 2) _~ In A t c

Qv

A:, c

(1)

QI 2RT

(lattice diffusion c o n t r o l l e d ) l n ( y / T ~) ~ In A3 c

a n d ? = t h e surface energy, c = the heating rate, ( 2 = t h e v a c a n c y volume, k = t h e B o l t z m a n n constant, D ' = p r e - e x p o n e n t i a l factor in diffusion terms, a = particle radius, R = gas constant, a n d b = grain b o u n d a r y width. A1, A2 and A 3 are a s s u m e d to be i n d e p e n d e n t of t e m p e r a t u r e . It will be shown b e l o w that a linear fit between the l o g a r i t h m o f the a p p r o p r i a t e function of y a n d T versus the reciprocal t e m p e r a t u r e is a necessary but not sufficient c o n d i t i o n to differentiate a m o n g the sintering mechanisms. Let us a s s u m e that a given set of d a t a relating to y a n d T fits eqn. (1). It is instructive to see w h e t h e r the same set of d a t a fits eqns. (2) and (3) and, if so, how well. A d d i n g n In T to b o t h sides of eqn. (1), we get

RT

(viscous-flow c o n t r o l l e d ) In ( y / T ~) ~ In

A3 = f(7, (2, Db, R, b, k, a, Qb)

(2)

Qb 3RT

(grain b o u n d a r y diffusion c o n t r o l l e d ) where

(3)

in ( y / T 2 -") = In -A1 - +nlnTc

-Qv --

RT

(4)

F o r the t e m p e r a t u r e range n o r m a l l y used in sintering (873°K to 2073°K), the plot of In T versus I / T is linear with a c o r r e l a t i o n index of 0.982. The m a x i m u m d e v i a t i o n from the best straight line is within one percent. The r e l a t i o n can be expressed as In T = 8 . 2 - 1298/T

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(5)