Fig. 2-Energy
vs interatomic distance in gold and in copper.
of copper (1.8) by an amount that predicts that the
bond will be 11 pct ionic. Thus, four bonds would
give each gold a charge of -0.44 and each copper,
+0.44. A transfer of '/z electron would approximately neutralize these charges, achieving electroneutrality.
Such a transfer increases the valence of gold to 6,
decreasing its single bond radius from 1.339A to
1.314A. The valence of copper decreases to 5 and its
single bond radius increases from 1.176A to 1.206A.
Hexavalent gold can form bonds with its 12
neighbors with n = 4/2. Copper would then use four
of its five valences in bonding with its eight gold
neighbors, leaving a single valence with n = ?4 for
its four copper neighbors. The bond distances for
unstrained bonds may be calculated from the formula
D. = Dl--0.60 log n
where Dlis the sum of the single bond radii of the
elements concerned. Results of the calculation are
given in Table VI.
For the superlattice AuCu, similar considerations
would lead to a transfer of 3h electron 'from the
gold, each copper receiving 4/4 electron. Gold would
then have a valence of 6 and a single bond radius
of 1.307A, while copper would have a valence of 5 4/4
and a single bond radius of 1.191A. Bond distances
would be those shown in Table VI.
The agreement in Table VI is remarkably good.
The Au-Cu bond in AuCu is practically strain-free,
as expected. The other bonds have most of their
strain removed; only about 100 cal per g atom remains. In AuCu,, strains have been reduced to about
300 cal per g atom. These results were attained by
simple and natural assumptions in the Pauling
theory.
However, for the other lattices of Table IV, Pauling's theory does not lead to a similar release of
strain. The transition metals involved, except nickel,
would change neither their valence nor their radius
appreciably on electron transfer. Two interpretations are possible. The estimated strain energy may
remain in the alloy. In this case, thermodynamic
measurements should show heats of formation that
are less negative than in AuCu; unfortunately, these
measurements are not yet available. The second possibility is that forces are involved that are not accounted for by any existing theory. Certainly this
is true at least to some extent; Fe-Pd and Fe-Pt
distances are unaccountably large and A1-Ti distances unaccountably small.
The question as to why Au-Ag alloys are less
exothermic than Au-Cu alloys may have an intriguing explanation. Silver has nearly the same electronegativity as copper and might be expected to
attract gold equally well. The size of the silver
atom is nearly equal to that of the gold atom, so that
misfit energy should be absent. As seen in this
paper, the size difference of gold and copper is overcome by a transfer of electrons, which is approximately the amount predicted by the difference of
electronegativity in order to produce electrical neutrality. Such a transfer cannot occur in Au-Ag without producing differences in size with consequent
misfit energy. This may produce a less stable bond,
accounting for the difference in heats of formation.
Electronic rearrangements are probably common
in alloys, so common that the ordinary calculation
of misfit energy from elasticity data may not be
correct even as to order of magnitude.
Acknowledgments
The author is indebted to Linus Pauling for advice and encouragement in this work. He thanks
Gunnar Bergman for calculating the uniaxial elastic constants from the constants for compressibility.
This work has been sponsored by the Office of Ordnance Research, U. S. Army.
References
A. W . Lawson: Journal of Chemical Physics, 1947, vol. 15, p. 831.
z B . E. Warren, B. L. Averbach, and B . W . Roberts: Journal o f
Applied Physics, 1951, vol. 22, p. 1493.
3 B . L. Averbach. P . A . Flinn, and M. Cohen: Acta Metallurgica.
1954 vol. 2 p. 92.
4 R. A . 0;iani: Research Laboratory ~ e ~ o No.
r t RL-1175. General
Electric Co. Schenectady, 1954.
" R . A . Oriani: Acta Metallurgica, 1956, vol. 4, pp. 15-25. C . Wagner: Acta Metallurgica, 1954, vol. 2, pp. 242-249.
6 W . Hume-Rothery and G . V. Raynor: The Structure o f Metals
and Alloys. Institute o f Metals. London, 1954.
7 P . M. Morse: Physical Review, 1929, vol. 34, p. 57.
6 J. Waser and L. Pauling: Journal of Chemical Physics, 1950. vol.
18. pp. 747-753.
OL. Pauling: Physical Review, 1938, vol. 54, p. 899.
loL. Pauling: Journal ACS, 1947, vol. 69, pp. 542-553.
L. Pauling: Proceedings Royal Soc., London, 1949, vol. 196A, p.
l
343.
l 2 L.
Pauling: Proceedings National Academy o f Science, 1950, v p l .
36, pp. 533-538.
13 L.
14 J.
Pauling: Journal Chemical Soc., 1948, vol. 15. p. 1461.
L. White. R. L. Orr. and R. R. Hultgren: Acta Metallurgica,
to b e published.
" R . A. Oriani: Acta Metallurgica, 1954, v o l . 2, p. 608.
16 R. L. Orr: Unpublished data. 1956.
Discussion o f this paper sent (2 copies) to AIME b y Dec. 1, 1957
will appear in A I M E Transactions Voi. 212. 1958, and in JOURNAL
OF
Technical Note
Temperature Dependence of the Tensile Properties of Vanadium
by J. W. Pugh
J. W . PUGH, Member AIME, formerly with Research Laboratory,
General Electric Co., is now associated with the Lamp Wire and
Phospors Dept., General Electric Co., Cleveland.
T N 424E. Manuscript, Jan. 30, 1957.
TRANSACTIONS AlME
v
ANADIUM has only recently received consideration with respect to structural application^.'.^
It would appear likely to find service where its
high electrical resistance and constant temperature
OCTOBER 1957, JOURNAL OF M E T A L S 1 2 4 3
Table I. Chemical Analysis of the Rolled Sheet
.25
Element
Wt Pet Present
.I5
.oo
Fig. 1-Tensile
parameters vs temperature for the
1273OK annealing
treatment.
I
,I
30
20
10
D
ELONGATION
I
Table II. Data for Cold Rolled Specimens
Test
Temperature, OK
0.2
Pot Yield
Strength.
Psi
Tenslle
Strength,
Psl
Elongatlon, Pet
Strain
Hardening. M
Rate
Sensitlvity, N
75
A similar relationship is used to evaluate rate
sensitivity.
50
25
TEST TEMPERATURE-.K
coefficient of resistance are advantageous. In addition, there are applications for vanadium which
exploit its resistance to attack by corrosive chemicals. The relatively high melting point, 2173"
225°K (1900" ?25°C),3 suggests good structural
strength at high temperature. Detailed information
about temperature dependence of strength has b d / n
lacking, although some data between room temperature and 1200°K are available.' In this report, an
analysis is made of the tensile properties of sheet
metal for constant strain rate and at temperatures
between 78" and 1500°K.
Arc melted ingots were cast in a rotating hearth
furnace described previously by Keeler.' These ingots were scalped and hot rolled in mild steel sandwzch jackets at 1073°K (800°C). Billets were removed from the jackets and cold rolled from 0.200
to 0.020 in. with a n intermediate vacuum anneal
(1073"K, % hr) at 0.100 in. thick. Chemical anafysis of the rolled sheet indicated the impurity cqntent shown in Table I. The temperature required, to
produce complete recrystallization for a '/z h r annealing treatment was approximately 1 2 0 0 : " ~
(927°C).
ensile test specimens were cut from the sh'eet
parallel to the rolling direction. These were tested
as cold rolled and as recrystallized at 1273°K
(1000°C) for 1 hr. The grain size for the recrystallized metal was 0.03 mm. An Instron testing machine was used at a nominal strain rate of 0.09. in.
per in. per min and a t temperatures from 78": to
1,500°K. In order to determine the effect of str,ain
rate on flow stress, the rate was changed momentarily to 0.009 during each test. Data were plotted
autographically. Elevated temperature tests were
made in vacuum, and temperatures were recorded
by means of a Pt-Pt-Rh
thermocouple positioned
a t the middle of the gage length. A description of
the test equipment can be found elsewhere." Evaluation was made in terms of ultimate tensile
strength, 0.2 pct yield strength, strain hardening,
and rate sensitivity of the flow stress.
Logarithmic plots of true stress-strain were quite
straight so that hardening could be evaluated in
terms of the slope, m, of these logarithmic curves.
I
ai0gu
m
aloge 2 , T
where m is called the strain hardening exponent,
u is the flow stress, and E is the strain.
-
=-I
€1
log i21€,T
where n is called the strain rate sensitivity; ul is the
flow stress a t the faster rate; U* is the flow stress at
the slower rate; h, is the faster rate, 0.09; and i2is
the slower rate, 0.009. There are no data to indicate
that the logarithmic relationships between strain
rate and stress for vanadium should be linear. In
view of the temperature dependence of stress, they
may be presumed not to be linear. Hence, the values
for n are not expected to apply to rates other than
those listed above.
Table I1 lists data for the cold rolled specimens,
and Fig. 1 shows the tensile parameters vs temperature for the conditions resulting from the 1273°K
(1000°C) annealing treatment. Fractures were observed to be transgranular a t all temperatures.
Vanadium has a temperature dependence of tensile properties which is characteristic of bodycentered-cubic metals. There are several features of
this dependence. For example, strength is exceedingly dependent on temperature in the low temperature range. Below 300°K strength rises very
rapidly as temperature is diminished. Yield points
and discontinuous yielding, observed a t low and intermediate temperature,. respectively, indicated
strain aging behavior. Other strain aging indicators
are the minima in strain rate sensitivity and elongation, and the maxima in strain hardening and
strength relationships at about 700°K. Similar temperature dependences have been observed for iron
and ~ t e e l , ' ~ h o l y b d e n u m , \ n d tantalum."
References
J. L. Everhart: Titanium, Zirconium Molybdenum Tungsten
Tantalum, Columbium, Vanadium, ~ a f n i L mas ~ n g i n e L r i n ~
rials. Materials and Methods 1951 vol. 39 p. 89.
PA. R. Gardner: Fitting your broduct 'to the Atomic Age, Part
11. Dun's.Review and Modern Industry 1955 vol. 66 p 39.
SH. K . Adenstedt, J. R. Pequignot, akd J.'M. ~ a y k e ; : The Titanium-Vanadium System. ASM Trans. 1952 vol. 44 p. 990.
W. Rostoker A. S. Yamamoto anh R. E. ~ i l e y : ' ~ hMechanical
e
s.
Trans., 1956, vol. 48, p.
Properties of v a n a d i u m - ~ a s e. ~ l < o ~ASM
1
at el
3bU.
5 J. H. Keeler: The Tensile Characteristics of Unalloyed Zirconium at Low and Moderate Temperatures. ASM Trans., 1955, vol.
..
47.
- ., n.
. -157.
- ..
V. W. Pugh: How to Test Refractory Metals. Steel, 1955, vol.
137. No. 16, p. 114.
7 J . L. Everhard et al.: Mechanical
Properties of Metals and
Alloys. Circular C 447, p. 265. National Bureau of Standards. Washineton. D. C.. 1943.
x ~ 'w.. ~ e i l - a n dN. L. Carwide: Tensile Properties of Ingot Iron
at Low Temperatures. Journal of Research National Bureau of
Standards, 1950, vol. 45, p. 129.
J. W. Pugh: The Tensile Properties of Molybdenum at Elevated
Temperatures. ASM Trans., 1955, vol. 47, p. 984.
10 J. W. Pugh: The Tensile Properties of Tantalum. ASM Trans.,
1956, vol. 48, p. 677.
'
I
1244-JOURNAL
OF METALS, OCTOBER 1957
I
TRANSACTIONS AlME