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Letters to the EditorGrain Growth in Alpha-Brass
J. E. BURKEInstitute for the Study of Metals, University of
Chicago, Chicago, Illinois
June 30, 1947
AN extensive series of data on isothermal grain growthin
alpha-brass has recently been published byWalker.l Plotting from
these data 10gD (grain diameter inmm), vs. log time, one obtains a
series of isothermal curves.An example for 42.4 percent deformation
prior to recrystallization is shown in Fig. 1. One should like to
know whethertime an d temperature for this process ar e related by
aheat of activation Q. I f so, times at temperature Tl shouldbe
related to times at temperature T2 by th e equation:
In(tt/t2) = (Q/R) (T2-1- T1- l).This equation can be solved to
give values of t1/t 2 to
convert times at a given temperature to times at an y
IomL02. LO 40 .. eo 240FIG, 1. Isothermal grain growth at
various temperatures in alpha-brass.
reference temperature. By taking Q as 60,000 cal. permole it is
found that the data taken at all temperaturescan be p l o t t ~ d
on a smooth curve at a single referencetemperature, with only a
reasonable experimental scatter.Figure 2 shows this for the curves
of Fig. I, at a referencetemperature of 500C, I t thus seems proper
to assign aheat of activation to the process. This curve is not
astraight line.
..
FIG. 2. Solid line: composite grain-growth curve at 500C
referencetemperature; Dashed line: composite curve corrected by
subtracting0.03 mm.
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Beck, Kremer, an d Demer2 report that their data forgrain growth
in high purity aluminum follows the relationship:
D=ktn,where k is a constant and the exponent n increases
linearlywith temperature. Obviously this relationship cannot
holdfor short times, for, at 1=0, D has'a finite value, Do.
The present data are expressed reasonably well by.therela
tionship:D-Do=klt",
where Do is the grain size a t the time of recrystallization,k
is a temperature-dependent constant, an d the exponentn has the
value 0.425 until late in the growth process. Thedotted line in
Fig. 2 was obtained by subtracting thprecrystallized grain size
reported by Walker for this series(0.03 mm ) from the solid curve
through the experimentalpoints. I t can be seen that it is a
straight line until thplate stages of growth, but that the slope
definitely fallsoff then. Similar results are obtained from other
series ofdata in Walker's work,
This work was supported by the Office of Research andInventions,
U. S. N. (Contract No. N60ri-20-IV),1 Harold L. Walker, University
of Illinois Eng. Exp. Sta. Bull.No. 359 (Nov. 1945).2 Paul A. Beck,
Joseph C. Kremer, and L. Derner, Phys. Rev. 71.555 (1947).
'Comments on "Grain Growth in Alpha-Brass"PAUL A. BECKUniversity
of Notre Dame, Notre Dame, Indiana
September 12, 1947I N the above note J. E. Burke calculated a
heat ofactivation value from grain-growth data on brassobtained by
H. L. Walker.l Considering the scatter of thedata, his value of 60
kcal./g of atom is in reasonableagreement with the heat of
activation value of 73.5 kcal./gatom previously calculated for
brass by Beck, Kremer,and Demer,2 by an essentially identical
method, from otherpublished grain-growth data. Thus, Burke's result
tendsto confirm Beck, Kremer, an d Derner's conclusions withregard
to the heat of activation value from grain-growthdata on brass.
Burke states that the relationship,(1 )
found by Beck, Kermer, an d Derner for isothermal graingrowth in
high purity aluminum cannot hold for shorttimes, for at t=O, D has
a finite value, Dr, the grain size as
r e c r y ~ t a l l i z e d , O b v i o u s l y , Burke uses t
to denote the timefor grain growth. The zero point of his time
scale is at themoment when recrystallization is just complete.
However,in the nomenclature used by Beck, Kremer, an d Derner
tdenotes the total time of annealing, which includes thetime for
recrystallization.* Clearly, Burke's objection isbased on a
misunderstanding of the nomenclature.
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Since most of the annealing periods used by Beck,Kremer, and
Demer are very long in comparison with thetime for
recrystallization, the error committed by using"grain-growth time"
instead of "totartime," as a result ofthe above misunderstanding,
is negligible, except for theshortest annealing periods at the
lowest annealing temperatures. Consequently, the whole matter would
be lackingin significance were it not for another mistake in
Burke'snote. He uses the time data from Walker's paper as ifthese
meant "time for grain growth" in the above sense.;\ctually, Walker,
like Beck, Kremer, and Demer, uses the"total time" of annealing. As
some of the times of recrystallization in Walker's work are
relatively long (such as16 min. at 450C), the error resulting from
this misinterpretation is significant.
The dotted line in Burke's Fig. 2 gives 10g(D-D r ) as afunction
of logt, where t is supposed to be the time forgrain growth, bu t
it is actually the total time of annealingof Walker's specimens, as
explained above. Although theinitial portion of this line was so
selected across the"reasonable scatter" of the transposed
experimental pointsthat it is straight, Burke admits that deviation
from th estraight line definitely occurs at longer annealing
periods.Nevertheless, he considers that the data are reasonablywell
expressed by the relationship:
(2)A comparison of relationships (1) an d (2), by \,IsingBeck,
Kremer, and Derner's grain-growth data on high
purity aluminum at 400C, is given in Fig. 1. I t is clearthat
the plot of 10gD vs. logt closely approximates astraight line.
Plotting the same data as D -;- D r vs. t. (to isused here to
designate "grain-growth time" in order toavoid confusion) results
in a curve which asymptoticallyapproaches th e above straight line
at very large to values.Similar curves are obtained for other
annealing temperatures. Obviously, relation (2) does no t fit the
grain-growthdata for high purity aluminum, but formula (1)
does.
I t can be easily shown that the initial portion of th ecurve in
th e figure approaches a slope of n = 1. I f t. approaches zero,
D/D. approaches 1, that IS D/D r= l+d,where d is a very small
number, and
D-Dr=dD r. (3)In Eq. (1) th e constant k can be eliminated if
one putsD=Dr for t=R, where R is the time for just
completerecrystallization. The following formula is then
obtained:
D/D r= (t/R)nor, substituting to = t - R,
(4)From (4), with the above relations,
and from this, for a small value of to,d=(n/R)ta (5)
By substituting (5) into (3) one obtainsD -Dr=n(Dr/R)t . (6)
VOLUME 18, NOVEMBER, 1947
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to AND Lg.M1N . LOG SCAU
FIG. 1.
Formula (6) shows that for small values of to the relationshi p
between D - D. an d to is linear. This means that atvery short
times in the logarithmic plot the curves for alltemperatures
approach the slope of n = 1. At long annealingtimes they approach
the D = k tn straight lines, where theslope, n, increases with the
temperature.**A fuller discussion of these questions is included in
a detailedpaper by Beck. Kremer. Derner. and Holzworth to be
published inMetals Technology. September. 1947.1 Harold L. Walker.
University of Illinois Eng. Exp. Sta. Bull.No. 359 (1945).2 Paul A.
Beck. Joseph C. Kremer. and L. Derner. Phys. Rev. 71.555
(1947).
Electron Micr-oscope and Electron-DiffractionStudy of Slip in
Metal CrystalsR. D. HEIDENREICH AND W. SHOCKLEY
Bell Telephone Laboratories. In c Murray Hill. New JerseyAugust
20. 1947T HE process of plastic deformation in metal crystalshas
been the subject of many investigations, both
experimental and theoretical, over a long period of years.Th e
new experimental results to be described briefly inthis letter have
been presented orally before two differentgroups* bu t have no t
appeared in print. A fuller account ofthe methods and results will
appear in a British publication.
The current experiments concerning the structure of slipbands
were carried ou t using 99.99 percent aluminum castin the form of
small single crystals (20X6X2 mm). Theas-cast crystals were
mechanically polished through 4/ 0French emery to produce a flat, 6
X 20 mm surface and thenelectropolished to remove the heavily
worked layer. Th esamples were then annealed 3--4 hours above
600C,
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