K. M.
64
MYLES A N D
A. T. ALDRED
Thermodynamic Properties of Solid Vanadium-Iron Alloys’
by K. M. Myles2 and A. T. Aldred Alloy Properties Group, Meletallurgy Division, Argonne .Vational Lahordory, Argonne, Illinoia (Received July I I , 1963)
The vapor pressure of iron over solid iron and over a series of vanadium-iron alloys has been measured by the torsion-effusion method in the temperature range 1500 to 1700’K. The chemical activities, as well as the free energies, entropies, and enthalpies of formation of the alloys have been computed a t 1600’K. from the vapor pressure data. The activities of iron exhibit fairly large negative deviations from Raoult’s law throughout the entire compositional range. The activities of vanadium, as determined by the Gibbs--nuhem relation, deviate negatively from ideal behavior in the iron-rich alloys but approach ideal behavior in the vanadium-rich alloys. The positive excess entropies and enthalpies of formation that are found at 1600’K. are considered in relation to the configurational, vibrational, and magnetic changes that occur upon alloying.
Introduction The thermodynamic properties of transition metal alloys have not been studied to any great extent. This is partly a result of the experimental difficulties encountered, but is due more to the difficulty in interpreting the properties in terms of existing models of metallic solutions. However, the recent emphasis on resolving the factors that govern transition metal behavior requires that the thermodynamics also be considered. The V-Ice alloy system was selected for the present study because of the extensive mutual solid solubility of the components at elevated temperatures. I n addition, other pertinent properties of the system were known. The torsion-cff usion technique was used because of the low vapor pressures involved and because the differences in the volatilities of vanadium and iron enable the design of the experimental apparatus to be simplified. This method also allowed the duration of the experimental runs to be appreciably shortened, and thereby minimized compositional changes in the alloys. The V--l‘e equilibrium diagram is shown in Fig. l e 3 At high temperatures, b.c.c. a-iron and a-vanadium form a continuous series of solid solutions; there is a narrow f.c.c. y-iron loop. Thr liquidas and solidus have a minimum a t about 33 atom yo V and 1740°K. I n the rquiatomic compositional region, a u-phase occurs, which dissolves congruently into the a solid sohThe Journal of Physical Chemistry
tion a t about 1470°K. When an alloy of approximately equiatomic composition is quenched from a temperature where the a-phase is stable and annealed for a short time at 870”K., a metastable CsC1-type ordered structure is formed, which transforms on further annealing to the u-phase. The only previous thermodynamic study of the V-Fe alloy system was made by S a ~ e rwho , ~ used the Knudsen effusion method over the temperature range 15.50 to 1725°K. The activities and free energies calculated from the vapor pressure data a t 1613°K. are in good accord with the present data, although there is disagreement between the two sets of entropy and enthalpy values.
Experimental Techniques The adaptation of the torsion-effusion method to the study of vapor pressures of metals and alloys has been described by previous a ~ i t h o r s . ~I,n~ the present arrangement, which has been described in detail elseThis work waa performed under the auspiccs of the U. S.Atomic Energy Commission. (2) This paper is based upon a thesis submitted by K. h l . IIylcs in partial fulfillment of the requirernrnts f o r thc 1’h.D. cicgrw at the University of Illinois, 1-rhana, 111. (3) 11. Hansen, “Constitution of Binary Alloys,” RIcGraw-1Iill Book Co., Iric., New York, N. Y.. 1958. (4) It. K. Saxcr, “The Chornical Activities of Iron and Vanadium in Binary Iron--Variadiurri .Alloys arid the Vapor 1’ressurt:s of Pure Cobalt, Iron. and Vanadium,” Ttiesia, The Ohio State C‘niversity, Columbus, Ohio, 1962. (1)
THERMODYNAMIC PROPERTIES OF SOLIDVANADIUM-IRON ALLOYS
65
hr. and degassed a t a temperature a t least 50” over the anticipated maximum temperature of the run until a constant deflection was noted. As the weight loss during a run generally did not exceed 0.275, the cornpositional changes of a specimen were considered to be insignificant. Chemical analyses indicated that the concentration of vanadium in the effusate was lesg than 0.1%.
Results The vapor pressure of iron was measured over pure iron and over nine vanadium-iron alloys. Plots of log p us. 1/T were linear in form in accord with the Clausius-Clapeyron relation. The constants of the equations representing the plots were evaluated by the method of least squares and are given in Table I with the probable errors for 95% confidence limits. W
a Table I : Vapor Pressures of Iron over Vanadium-Iron Alloys
I-
+b
log p (mm.) = m/T
Temp. range,
Nre
1.000
___
600
0
20
40
60
80
100
ATOMIC PERCENT I R O N Figure 1. The vanadium-iron equilibrium diagram.
where,’ the specimen is enclosed in a tantalum effusion cell that has two eccentrically located orifices. The cell is suspended vertically from a fine tungsten wire in which an elastic torsional strain is induced as the vapor effuses through the orifices. The vapor pressure p is related t o the angle e through which the cell rotates by the expression p = 2 ~ 8 / Z A d f . Here T is the torsion constant of thc wire, A is the cross-sectional area of the orifice, d is the horizontal distance of the orifice from the suspeinsion axis, and f is the Freeman-Searcy correction factor for an orifice of nonzero length.8 The alloys were prepared by arc-melting on a water-. cooled copper hearth under a helium-argon atmosphere 99.96% pure iron, obtained from the Metals Manufacturing Control Laboratory, and 99.88% piire vanadium, supplied by the Union Carbide Metal Co. Although weight Ijosses were small, chemical analyses were performed on aJl the alloys. The arc-melted buttons were machined into the form of coarse turnings, which were loosely packed into the cells to ensure a large surface-to-volume ratio. Each cell was homogenized for 3
0.913 ,807 ,704 ,596 ,501 ,399 ,304 ,206 ,0951
-20908 -20751 -20096 -19984 -19810 -20087 -20774 -21070 -21238 -23411
= K.
b
m
f 109 f 117 f 110 f 115 119 f 127 f 125 f 100 f 66 f 190
10.036 9.888 9.373 9.178 8.952 8.920 9.161 9.118 8 943 9.331
jz
0.070
f ,109
,070 f ,074 f ,075 f ,080 f ,079 f ,081 f ,040 f ,110
&
1451- 1677 1467-1672 1472-1666 1468-1629 1454-1668 1469-1669 1468-1704 1474-1 756 1527-1767 1631-1 800
The vapor pressure data were used to calculate the thermodynamic properties of the solid alloys a t 1600“E:. with hypothetical pure a-iron as the reference stat(!. No corrections were made for the difference in free energy between y- and c ~ - i r o n ~since v ~ ~ a t 1600’K. it falls within the experimental accuracy with which the free energies can be determined. The chemical activities of iron were computed a t 1500, 1600, and 1700°K The activities of vanadium were determined by means R. Speiser and J. W. Spretnak, “Determination of the Vapor Pressures of Metals and Alloys,” “Vacuum Metallurgy,” Electrochemical Society, Inc., 1955. ( 6 ) J. N. Pratt and A. T. Aldred, J . Sci. Instr., 36, 365 (1959). (7) K. M. Myles, Argoiine National Laboratory, Argonne, Ill., ANL-6657 (1963). (8) R. D. Freeman and A. W. Searcy, J . Chem. Phys., 2 2 , 762 (1954). (9) J. C. Fisher, Trans. A I M E , 185, 688 (1949). (10) R. J. Weiss and K. J. Tauer, Phys. Rev. 102, 1490 (1956). (5)
Volume 68,ivumber 1
January, 1964
Table I1 : Thermodynamic: Properties of Vanadium-Iron Alloys a t 1600°K. AFF.., NFa
up,
nv
0.9 .8 .7 .6 .5
0.856 ,695 ,534 ,387 256 ,155 ,0870 ,0460 .0207
0.0138 ,0466 . 103 ,188 ,312 ,470 634 787 . (300
.4
.3 .2 .1
t
----Cal./y.
AP\!
Csl./g. atoiii-
- 1995
- 13616 - 9747 - 7226
-3018 -4332 - 5'327 - 7763 -!)788 - 12327
-5313 -3702 - 2400 - 1449 -761 -335
- 494
- I157
ASF,
ASV atom-dey.-
1 46 2 54 3 32 3 82 4.06 4 12 4 04 4 67 7 55
of the Gibbs-Duhem integration. The activities as well as the, calculated partial and integral free energies, entropies, and enthalpies of formation are assembled in Table 11. The precision of the activities is estimated to be about +3% and that of the integral free energies about f300 cal./g. atom. Because the calculation of the entropies and enthalpies involves the difference between two large numbers, their precision is considerably lower. A reasonable estimate is about f 1.50 cal./g. atom-deg. for the entropies and about f1500 cal./g. atom for the enthalpies. Possible systematic errors, although believed to bc small, preclude an estimation of the accuracy.
Discussion The vapor pressure of iron, as determined by this study, is plotted in Fig. 2 . Values of the latent heat of sublimation a t 298.15°K., calculated by means of the third-law test equation, showed no systematic temperaturc dependence. The average value of A H ~ W O99,000 , =t 150 cal./g. atom, agrces favorably with the value compiled by €iultgren,'l 99,550 f '200 cal./g. atom. As seen in Fig. 3, the activities of iron exhibit fairly large negative deviations from ideality. The activities of vanadium are also characterized by negative deviations in the iron-rich alloys, brit ideal behavior is approached in the vanadium-rich alloys. The most iriterest,ing thermodynamic properties in the present context are the excess quantities, which depict deviations from ideal behavior. The integral excess functions arc shown in Fig. 4. The minimum in the excess free energy occurs a t approximately 55 atom yo Fc!, that is, near the composition of the congruent maximum of the c-phase. However, in view of the noncorifiguratiotial factors that appear to dominate thc! excess entropies arid enthalpies, it is not believed that thc excess frce energies cat1 bo considered simply i n terms of a tendency toward conipound formation. The Journal of Physienl Chemistry
11.26 4.82 2.36 1.46 0.985 1.09 1.13 0 . '335 0.220
AHFe
--Cal./g.
Ajjv atorn-
1842 2907 3317 3094 2164 665 - 1299 -2316 247
4400 - 2035 -3450 - 2977 -2126 650 359 735 17
-
Ab----Cal./g.
-1806 -2875 -3564 3936 -4017 -3811 -3343 - 2566 - 1534
-
AH atom-
2098 1925 1284 672 15 -131 - 143 122 -9
AS C s l . / a . atom-deg.
2.44 3.00 3 03 2.88 2.52 2 .30 200 1 68 0 . 953
-2.40b -2.60 -2.80 -
-
-3.00-
v
-3.20-
E E y
-3.40-
Q
0 -3.60-
3
-3.80 -4.00
-
-4.20-4.40
1700'K
-4.605.60
1500%
1600%
I I
600
6.40
6.80
bT x io4vK')
7.20
Figure 2. The vapor pressure of iron.
Although the excess free energies are rcgarded as more reliable, the excess entropies are more amenable to discussion. The excess entropy of formation may be correlated with the nonidcal changes that occur in the atomic and electronic structures of the component metals upon alloying, as manifested by the configurational, vibrational, and magnetic characteristics of the alloys. ~
(11)
~~
~
R. €rdtgrell, 11. 1,. Orr, P. D. Auderuon. and K. K. Kclley. "Srlccted Values of Thermodynamic Properties of hIetalv and Alloys," John Wiiley and Sons, Inc., New York, N. Y.. 1963.
THERMODYNAMIC PROPERTIES
OF 'SOLII) ~'ANADIUM-IRON
NF*
Figure 3. Actlvities of iron and vanadium at 1600°K.: X , experirnentd values; 0, calculated values.
ALLOYS
67
short-range ordering or clustering, will resiilt in entropies whose values are lower than ideal. In the V-Fe alloy system, the existence of a series of disordered b.c.c. solid solutions a t 1600°K. implies that this contribution should he very small, although the occurrence a t lower temperatures of CsCl type ordering in the a-phase, and a t higher temperatures of a liquidus-solidus minimum suggests that some nonrandomness may exist in the alloys a t 1600°K. The changes in the electronic configurations of the component atoms that occur on alloying12-14could also contribute to the excess entropy, although no theoretical basis for their effect has yet been put forward. The vibrational entropy, which is associated with the change in t,he atomic and electronic bonding charT acteristics upon alloying, is expressed by J0 ACp d In T, where AC, represents the deviation of the specific heat from Keumann-Kopp behavior. Although no hightemperature specific heats have been measured in this system, an approximate cvaluation of this relation may be made near room temperature by mcans of the I h b y e theory of heat capacity and the Debye temperatures and electronic specific heat coefficicrits determined by Cheng, et ~ 1 . ~ The 2 rntropies thus calculated, listed in Table 111, are mainly negative. This trend is consistent with the negative deviations of the room temperature lattice pararnetcrs from Vegard's law15 and the decrease in the diffusion rates of a number of solute eltments into V-Fe alloys as compared with pure iron." However, it has been suggested'g that deviations from Neumann-Kopp behavior become more positive SLS melting temperatures are approached. This is partjcularly truc when a minimum occurs in the liquidussolidus, as a minimum signifies that the deviations of the activities from ideality in the solid are more positive than in 1he liquid. The expected misfit energy in the solid leads to an increase in the vibrational frequencies of the atoms in the alloys as compared to those in the pure components, so that the vibrational entropy a t high temperatures (1GOO"K.) may in fact be positive with a maximum value a t the composi-
c. 11. (;ht:ug, c. T. Wei, and P. A. Reek. Phgs. Rev., 120, 426 (1960). (13) D. J. Lain, D. 0. Van Ostc,nhurg, H. 1). Trapp, and D. E. MacLcod, J . Jlctalu, 14, 691 (1962). (14) L). 0. Van Ostcsriburg. 1). ,J. Idam, IT. D. Trapp, and D 17. Mac1,iwd. P h g Y RPI!.,128, 1550 (19132). (15) 1-1. XIartriis and 1'. I>UJWZ, Trans. Am. SOC..Wet&, 44, 484 (12)
Figure 4. Integral exceas free energies, entroples, and enthalpies of formation of vanadium-iron alloys a t 1600°K.
The configurational contribution to the exc~"ssentropy must of necessity be negative since departures froni completely random mixing, whether toward
(16)
( I 952). A. I,. Sutton arid iV. Ilulric.-ILotll(.r,~. P h i l , M a g . , 46, 1295 ( 1 955).
(17)
SI. A. Krishtnl, Fiz. .tfdo( i . l l c f d ( o w d . . 9 , GXO (1960).
(18)
11. A. Oriarii, Acid Met., 3 , 2 3 2 (1955).
T'olun~68, .Vumher 1
Januurg; I964
68
K.
tion of the liquidus-solidus minimum, in spite of the indications that a t lower temperatures it is negative. The magnetic ~ r i t r o p yis' ~dependent upon the degree of randomness in the orientation of the atomic magnetic moments that are associated with the iron atoms in all but the vanadium-rich alloys. Above the Curie temperature, the total entropy of hypothetical paramagnetic iron with no atomic mcments is lower than that of paramagnetic iron with randomly oriented moments by an amount R In ( p n 1) = 2.3 cal./g. atom-deg.'" Here, p~ is equal to 2.2, the average atomic magnetic moment per iron atom in Bohr magnetons. Upon alloying either of these two forms of paramagnetic iron with vanadium, which has been assumed to carry no magnetic moment,2°-22 ideal behavior occurs, insofar as the magnetic entropy is concerned, when the magnetic moment per iron atom remains constant a t either 0 or 2.2. This is illustrated by the dashed lines in Fig. 5. Neither of these relations is to be expected in the real
+
n.
8 I
c
&-I-
\
$E
cn Q
-2-
I
MOMENTS
\
The enthalpirs of formation are also composed of several additive terms related to the changes that occur in the atomic and electronic structures of the component metals upon alloying. According to the usual nearest neighbor approximations, the configurational contribution to the enthalpy may be expressed in tcrms of the pairwise bond energies E between nearest neighbors. In a binary alloy that exhibits some degree of clustering, E12 is less than 'lp(E11 &2) and the enthalpy is positive; similarly, if ordering occurs Elzis greater than 1/2(Ell EZ2),and the enthalpy is negative. Therefore, a t 1600°K. the small configurational enthalpy term may be positive a t the composition of the liyuidus-solidus minimum and negative near the eyuiatomic composition. The vibrational enthalpy is related to the thermal excitations of the atoms and electrons through JoTAC,dT. Both the Debye temperatures and the electronic specific heat coefficients indicate that the deviations from Neumann-Kopp behavior a t about room temperature are negative; this leads to negative thermal enthalpies (Table 111). However, a t elevated temperatures, the occurrence of a liquidus-solidus minimum suggests the existence of a misfit energy in the solid alloys. Application of the calculation proposed by Wagner23 suggests that a positive contribution (about
+
Table 111: Computed Values of the Vibrational Entropy and Enthalpy of Formation a t 298'K." NF.,
\
PARAMAGNETIC \ >F WITH NO ATOMIC MOMENT S
\
1.o 0.67 .45 .34 .20 .15 .08
.o Figure 5.
alloys as the paramagnetic moment per iron atom gradually decreases with increasing vanadium concentration and disappears at about 22 atom To k ' ~ . ~ ~The ' resultant magnetic entropy should be approximatrd by the solid line in Fig, 5. In summary, the positive exccss rntropies found experimentally have the wrong sign to bc either ronfigurational or magnetic in origin. 'l'hrrc is some basis for a belief that a strong vibrational contribution may be made a t elevated temperatures.
---Cal./g.
0.00
+O. 38 -1.26 -0.38 -2.23 -2.12 -1.33 0.00
Asvitr e l .
atom-deg.---
0.00 .l9 .12 .04 .30 .22 .13
-
.oo
AHvib at.
----Cal./g.
0 +45 - 130 -31 - 242 - 224 - 131 0
A H v i b 01.
atorn-
0 - 42 - 17 -6 - 44 - 33 - 19 0
Assuming C, = C.,
Plot of the magnetic entropy.
The Journal of Physical Chemietry
+
A s v i b at.
\
M.MYLESAND A. T. ALDRED
+870 cal./g. atom) may be made to the vibrational enthalpy of alloys near this composition. Hence, there R. A. Oriani, J . Chem. Phys., 28, 679 (1958). S. Arais, 11 V . Colvin, H. Chcssin. and J. I1 I'cwk J . Appl. Phys., 33, 1353 (1962). (21) >I. V. Nevirt atid A. T. Aldred. ibid., 34, 463 (1903). (22) 13.,J. Lam, D. 0. Van Ostenburg, .\I V. Nevitt. 11. D. Trapp, and D. W , I'mcht. Phys. Reu., 131, 1428 (1963). (23) C. Wagner, Acta M e t . , 2, '242 (1954). (19)
(20)
THERMODYNAMIC PROPERTIES OF SOLID VANADIUM-IRON ALLOY~
is some basis for positive values of the vibrational enthalpy at 1600°K. The magnetic contribution to the enthalpy could be discussed in a manner similar to the contribution to the mtropy, but the theoretical basis is not as well establishrd. However, since the magnetic ternl affects thc heat capacity, the signs of the related entropy and twthalpy contributions must be the same. Although thtx activities and free energies of formation obtained a t 1800°K. appear to be reliable and selfconsistent, the eiitropies and enthalpies of formation are considerably more difficult to rationalize. The apparent positive exccss entropies and enthalpies have
69
been discussed in terms of the known properties of the alloy system. The present work tends to demonstrate the importance of nonconfigurational contributions to the thermodynamic proprrties of transition metal alloys. E'urther elucidation of the thermodynamics of the V-I+ alloy system must await direct measurements of the enthalpics of formation and high temperature heat capacities. Acknowledgments. The authors arc grateful to Professor li. W. Bohl of the University of Illinois and to nr. &I. V. Nevitt of the Argonne National Laboratory for their many helpful discussions during the course of this investigation.
Volume 68, Sumber 1
January, 1964
