1080
J. A. CAHILLASD A. D. KIRSFIENBAUM
Vol. 66
THE DEKSITY OF LIQUID COPPER FROJI: ITS MELTISG POIST (1356'K.) TO %OO'K. AXD AN ESTIIIATE OF ITS CRITICAL COSSTXSTS'J BY J. A. CAHILL AND A. D. KIRSHENBAUM Research Institute of Temple University, Philadelphia 44, Pa. Received December 8 , 1961
The density of liquid copper was determined in an argon atmosphere by the immersed sinker method from 1356 t o 2500'K. Zirconium dioxide coated molybdenum sinkers with aluminum oxide and zirconium oxide crucibles were employed below 2100"K., while graphite sinkers and crucibles were used to 2500°K. The density, with respect t o temperature, is best e-: pressed by the equation D g . / ~ m .=~ 9.077 - 8.006 X T " K . The liquid density a t the melting point (1356°K.) IS 7.992 g . / ~ mand . ~ 6.792 g . / ~ m a. ~ t the normal boiling point (2855°K.). The molar volumes and thernial coefficients of expansion of liquid copper were calculated. Copper upon melting was found t o expand 4.517, of its solid volume. The ; M ~ ~=, ~61 . i critical constants of copper were estimated t o be: Tcrit. = 8900 f 900°K.; Dcrit. = 1.04 f 0.2 g . / ~ m . ~ V 10 cm.3/mole.
Introduction
of the upper section of the molybdenum and graphite suspension rods to maintain a stable immersion of the sinkers in the buoyant liquid copper. Procedure.-The density of liquid copper was determined come extremely important to many branches of by the immersed sinker method. The procedure, as depreviously, consisted in measuring the weight loss scientific investigation. It has been noted, how- scribed of a sinker in the liquid copper while simultaneously measurever, that many of these data for even our most ing the temperature of the copper with a calibrated optical abundant metallic elements have not been measured pyrometer. The temperature measurements were made over a temperature range which is concurrent with under black body conditions. The accuracy of the pyromwas found to be &0.2%. the temper:iture spread existing between their eter The volume of the sinker a t 20" was determined by the melting points and normal boiling points. Copper, loss in weight of the sinker when immersed in mercury, corwhich ranks high in importance and abundance rected for surface tension. The volumes of the sinkers alamong the common metals, is in this category. ways were corrected to the operating temperature. For the graphite sinkers the thermal expansion data reported by It is a liquid a t atmospheric pressure over a tem- Goldstein, el al.,lo were used together with data known for perature range of 1500OK. (m.p. = 1356'K., n.b.p. the graphite used"; while the coefficient of expansion values reported by Bockris, et a l . , l 2were used for the ZrOz-coated = 2S55'K.).3 sinkers. The volume of the sinker depended A literature search showed that the only measure- molybdenum upon its depth of immersion in the liquid copper. This was ments made over a range of temperature FTere those determined by the difference betveen the depth of the liquid made' by Bornemann and Sauerwald4and Widawski copper and the distance of the sinker from the crucible base.* The losses in weights were corrected for surface tension and Sauerwald.6 They determined the density by measuring the loss in weight of an immersed quartz using the values of Allen and Kingery'3 (1270 dynes/cm. a t 1373'K. and 1160 dynes/cm. a t li23'5.) extrapolated to sinker from the melting point to only 1873'K. 2500°K. with a contact angle of 170 . The correction Their data were reproducible to =t0.04 g . / ~ r n . ~varied from 0.600 to 0.800 g. The corrected density was calculated from the equation and only covered a 400' range. The authors have measured the density of liquid W A - Wm T d y cos 01 = D
A knowledge of the density of liquid metals which melt a t temperatures exceeding IOOO'K. has be-
copper from its melting point (1356'K.) to 2500'K. (an 1150' Experimental
Apparatus.-The temperature source used in these measurements vras the carbon tube resistance furnace described previously? operated in an argon atmosphere. For temperatures to 2100"K., molybdenum sinkers coated with zirconium oxide were used i s conjunction with aluminum oxide and zirconium oxide crucibles. At the higher temperatures (2100 to 2500°K) graphite crucibles and sinkers were employed.* Both the zirconium oxide coated molybdenum and graphite sinkers were 2 cm. long and were 1.3 cm. in diameter and tapered into a stem 0.20 om. in diameter and 3 cm. long. A steel counterweight was incorporated as part (1) Presented before the Physical and Inorganic Division of the 4th Delaware Valley Regional Meeting of the A.C.S.. Jan. 25, 1962. (2) This work was sponsored by the National Science Foundation under Grants 6278 a n d 15540. (3) D. R. Stull and G. C. Sinke, "Thermodynamic Properties of the Elements," A.C.S. Series No. 18 (1956), p. 82. (4) K. Bornemann and F. Sauerwald, Metallkunde, 14, 145 (1922). (5) E. Widawski a n d F. Sauerwald, 2.anorg. u. allgem. Chsna., 192, 145 (1930). (6) A. D. Kirshenbaum, "Second Annual Report on High Temperature Inorganic Chemistry," under Research Grant NSF-G 6278, Research Institute of Temple University, December 15, 1960. (7) A. D. Kirshenbaum and J. A. Cahill, J . Inorg. & Nuclear Chem., 14, 283 (1960). (8) A. D. Kirshenbaum, J. A. Cahill, and A. V. Grosse, ibid.. 22, 33 (1981).
-
VT
where TVA and 117, is the weight of the sinker in air and melt, respectively, d i s the diameter of the stem of the Pinker, y the surface tension, and a the contact angle between the stern and the liquid copper. Materials Used.-The samples used in these studies were electrolytic copper with a purity of 99.97% metalljc copper. Analysis of the copper after use in a graphite crucible up to 2500°K. showed a carbon content of 0.02170 carbon. This is in good a reement with that reported by Ruff and BergdahlI4 (O.Ozf% a t 2488OK.). This required a correction of only +0.001 g./cm.3 at 2495'K.
Results Using the apparatus and procedure described above, the density of liquid copper was determined (9) A. D. Kirshenhaum, J. A. Cahill, and C. S. Stokes, ibid., 16, 297 (1960). (10) A. Goldstein, T. E. Waterman, and H. J. Hirschhorn, "Thermophysical Properties of Solid Materials," Vol. I, WADC Technical Report 58-476, Aug., 1960, pp. 59-158. (11) Dixon E-821, fine grain petroleum coke base stock with a transverse linear coefBcient of expansion from 100-600" of 35 X lo-' and a parallel expansion of 20.8 X lo-'. (12) J. O'M. Backris. J. L. White, and J. D. Mackenzie, "PhysicoChemical Measurements a t High Temperatures," Academic Press, New York, N. Y., 1959, p. 347. (13) B. C. Allen and W.D. Kingery, Traris. ;Metal. Soc. AIIME, 216, 30 (1959). (14) 0. Ruff 5nd B. Bergdahl, 2. ~ ~ O T u. Q . allgem. ChPm., 106. 91 (1919).
June, 1902
DESXITY OF LIQUIDCOPPER FBOM ITS MELTING POINT TO 2500"IL
1081
90
85
0
ye0
m
8 *k L-J z
75
IU
a
70
65
1400
1500
1600
1700
I800 1900 TEMPERATURE 'K.
2000
2100
2200
2300
2400
25
Fig. 1.-Density of liquid copper.
TEMPERATURE,
Fig. 2.-The
OK,
liquid range diagram for copper.
from its melting point (1356OX .) to 2500OK. The results obtained fall on a straight line as shown in
Fig. 1when density is plotted against temperature, The equation of this line as determined by the
J . I?. CONSOLT~Y
1082
method of least mean squares is D g./cc. = 9.077 - 8.006 X T'K. zk 0.011 Thus, the liquid density is 7.992 g . / ~ m at . ~ the melting point (1356OK.) and 6.792 g . / / ~ ma.t~the boiling point (2855'K.). This is equivalent to a change in liquid density with temperature (dDldt) of -8.006 X loF4. Extrapolation of the solid density reported by Sauerwald4.j gives a solid density of 8.350 g./cc. at the melting point. Therefore, the volumetric expansion on melting, AVlV,, is 4.51%. The atomic volumes were calculated for various temperatures from the smoothed density values obtained from the liquid copper density equation. They are summarized in Table I together with the cubical coefficient of expansion values calculated from the equation
- do dt
pDt
where dD/dt is the change in density with temperature, p is cubical coefficient of expansion, and Dtis the density at temperature t. Estimate of the Critical Constants.-A method of estimating the critical constants of metals has been described lately by Grosse.I5 From this method, the critical temperature was calculated to be 8900 + 900'K. while the critical density and atomic volume are 1.04 zk 0.2 g./cm.3 and 61 + 10 ~rn.~/mole, respectively. The rectilinear diameter DS = 4.538 - 4.003 X TOK. in g . / ~ m . ~ . (1;) A. \ . Grosse, J . Inorg. & .Yuclear Chem., 2 2 , 23 (1961).
Vol. OG
AA.TOiVICVOLUMES BND
TABLE I EXPANSION COEFFICIENTS
OF
LIQUID
COPPER
Temp., OK.
Density, g./cm.a (smoothed values)
Atomio volume, cm.a/mole
7,992 7.956 7.797 7,636 7.476 7.316 7.156 6.792
7.952 7.990 8.152 8.324 8,503 8,688 8.883 9.359
1356 (m.p.) 1400 1600 1800 2000 2200 2400 2855 (b.p.)
Cubical expansion coefficient P x 105, OK.-
100,2 100.6 102.7 104.8 107.1 309.4 111. 9 117.9
Figure 2 shows the whole liquid range diagram from melt'ing point to critical t'emperature. The densities of the liquid copper above the normal boiling point are presented in Table 11. TABLE I1 THELIQUIDDEXSITY OF COPPER ABOVE IXG POIKT Temp.,
O K .
ITS
NORMAL BOIL-
Liquid density, g./cm.3
3000 4000 5000 6000 7000
6.675 5.87 5.03 4.16 3.2
Acknowledgment.--We wish to thank Dr. A. V. Grosse for his helpful advice and Lucia Streng for the analytical determinations.
IDEALITY OF YZ-BUTANE :ISOBUTANE SOLUTIOSS BY J. F. CONNOLLY Research and Development Department, American Oil Company, Whiting, Indiana Re~eibedDecember 9, 1962
Gas compressibilities were measured for the isobutane: i-butane system up to the saturation pressures, in the temperature range 70 to 170", and 2nd and 3rd virial coefficients were derived. Mixed 2nd virial coefficients calculated on the basis of Amagat's law agreed with the experimental values to 1 cc./mole on the average. Phase boundaries were meaeured for the same system from 70" t o the critical temperature of i-butane. The phase-boundary pressures computed using the idealsolution laws and the virial coefficients agreed with the observed values within 0.2%.
Introduction Solutions of compounds as closely related to one another as n-butane and i-butane might well be expected to form nearly ideal solutions as long as the critical region is not approached too closely. Redlich's vapor-liquid equilibrium measurements, made near atmospheric pressure, have shown that a number of isomers come close to forming ideal solutions1 below a reduced temperature of 0.7. Because of the higher saturation pressures at temperatures nearer the critical, an accurate knowledge of gas compressibilities mould be a necessary addition to vapor-liquid equilibrium data in testing the ideal solution laws. The present work was done in the reduced temperature range from 0.8 to near 1 in order to ascertain whether or not ideality continued to hold at higher temperatures. Phase-boundary pressures (1) 0. Redlioh and A. T. KiEter, J . A m . Chem. Soc., 71, 505 (1949).
mere measured for both compounds and three mixtures in the temperature range 70' to near the critical temperature of i-butane. Gas compressibilities were measured from 4 atm. to close to the saturation pressures for both compounds and a 50: 50 mixture in the temperature range 70 to 170'. Experimental The n-butane and i-butane were Phillips research grade materials with stated purities of 99.99 and 99.96 mole 70. They were not purified further except to remove the air present by distillation in oarno. The purities of the resulting products were confirmed by the small pressure rises, 0.01 atm., observed beta een the two phase boundaries, i.e., between the dew (first trace of liquid) point and the visual bubble (last trace of gas) point. In the experimental method,2 a sample was confined above mercury in a calibrated glass capillary and stirred with a magnetically driven steel ball. Volumes were determined by measuring lengths tr-ith a cathetometer. Pressures were measured with a dead weight gage; temperatures with a (2) J. F. Connolly and G. A. Kandalic, Phys. Fluids, 3, 463 (1960).
