August 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
the alcohol vapor, the maximum activity in terms of conversion of the alcohol to acetaldehyde and other valuable by-products, was determined. A majority of the catalysts were fairly specific; copper alone gave the highest yields of the aldehyde. A constant small amount of ethyl acetate was formed as the chief byproduct with all the catalysts. For a sturdier type catalyst with fairly high activity, added cobalt and chromium as promoter agents were found beneficial; the former increased the percentage conversion of the alcohol and the latter contributed to a sustained high activity for a long continuous performance of the catalyst. From a practical viewpoint, the best catalyst was the one prepared by impregnation of short-fibered asbestos with a solution of copper nitrate containing 5% cobalt oxide and 2% chromic oxide, based on the weight of copper oxide equivalent. At a temperature of 275“ C. a maximum theoretical yield of 88% of acetaldehyde and 9.6%.of ethyl acetate was obtained with a 93% conversion of the alcohol per pass. After 100 hours under these conditions the catalyst lost only 16% of its initial activity, and reactivation b y a short air oxidation restored the activity to 105% of that initially present. Thus it was possible to obtain sustained activity, averaging gay0 of the initial activity, over a long period by reactivations. Based on the favorable results of this investigation, a potential process for the manufacture of acetaldehyde by the dehydrogenation of 95% ethyl alcohol is proposed. LITERATURE CITED
(1) Anderson, J. W., Beyer, G. H., and Watson, K. M., .Vatl. Petroleum News,36, R476 (1944). (2) Armstrong, E. F., and Hilditch, T. P., Proc. 2 2 0 ~ SOC. . (London), 97A, 259 (1920). (3) dssoc. Official Agricultural Chemists, “Tentative and Official Methods of Analysis,” p. 195, 1945. (4) Baladin, A. A., 2. physik. Chem., B2, 289 (1929); B3, 167 (1929). (6) Berthelot, M., Les Carbures d’hydrogene, 2, 202 (1901). (6) Constable, F. H., J . Chem. Soc., 1578, 2795 (1927).
1811
D a w . H.. Phil. Trans.. 97. 45 (1817). DogOIor, B. N., and Koton, M.‘ M.,‘J. Gen. Chem. (U.S.S.R.), 6, 1444-51 (1935).
Dunbar, R. E., Cooper, D., and Cooper, R., J . Am. Chem. Soc., 58, 1053 (1936).
Faith, W. L., and Keyes, D. B., IND.ENG.CHEM.,23, 1250 (1931).
Faith, Keyes, and Clark, “Industrial Chemicals,” New York, J. Wiley & Sons, 1950. Grimax, E., Bull. SOC.Chim. (II), 45, 481 (1886). Groggins, P. H., “Unit Processes in Organic Synthesis,” 3rd ed., p. 466, New York, McGraw-Hill Book Co., 1947. Hightower, J. V., Chem. & Met. Eng., 55, 7-105 (1948). Ipatieff, V. N., Ber., 34, 3579, 9596 (1901). Johnson, J. Y., Brit. Patent 331,883 (1930). Knoevenagel, E., and Heckel, W., Ber., 36, 2816 (1903). Kuhlman, F., Ann., 29, 286 (1839). Lorang, F. J. H., U. S. Patents 1,956,088 (1934) and 2,039,543 (1936).
Marchand, R. F., J. Proct. Chem., 15, 7 (1838). Neish, A. C., Can. J. Research, 23B, 49 (1945). Orloff, J. E., “Oxidation des Alcohols par L’action de Contact,” Paris (1901). Palmer, W. G., PTOC.Rou. Soe. (London). 98A, 13 (1920): 99A, 412 (1921); IOIA, 175 (1922).
Palmer. W. G.. and Constable. F. H.. Ibid.. 106A. 250: 107A I
,
255, 270 (1925).
Parks, G. S., and Huffman, H. M., “Free Energies of Some Organic Compounds,” New York, Reinhold Pub. Corp., 1932 Rideal. E. K., Proc. Roy. SOC.(London), 99A, 153 (1921). Sabatier, P., and Senderens, J. B., Compt. rend., 136, 738, 921, 983 (1903).
Shreve, R. Norris, ”Chemical Process Industries,” 1st ed., p. 918, New York, McGraw-Hill Book Co., 1945. Steverson, H., Chem. Eng. News,27, 1182 (1949). Strecker, A., Ann., 93, 370 (1855). Trillatt, A,, Bull. SOC.Chim. (III),27, 96, 797 (1902). U. S. Tariff Commission, Washington 25, D. C., “Production and Sales of Synthetic Organic Chemicals,” 1948. Whitmore, F. C., “Organic Chemistry,” p. 243, New York, D. Van Nostrand Co., 1937. Young, C. O., U. S. Patent 1,977,750 (1934). RECEIVED September 15, 1950. In partial fulfillment of the requirements for the Ph.D. degree granted in June 1949. Contribution No. 19 from the Chemical Engineering Labs., Columbia University,. New York, N. Y.
Equilibrium Relations of Two MethaneAromatic Binarv Svstems at 150° F. J
J
M. ELBISHLAWI’ AND J. R. SPENCER Texas Petroleum Research Committee, University of Texas, Austin, Tex. Previous work on mixtures of methane and hydrocarbons indicated a correlation between the chemical nature of the sol\ent and the solubility of the methane, the chemical nature being expressed by the Universal Oil Products characterization factor (13). The purpose of this work was to test the correlation for low values of the U.O.P. characterization factor and for systems containing aromatic hydrocarbons. Equilibrium constants for the systems methane-benzene and methane-toluene which were studied bear out the correlation even to extreme ranges of the factors. If, as these binary systems suggest, the solubility of methane in crude oil-natural gas systems has a similar dependence on the chemical character of the solvent, the prediction of phase behavior in petroleum reservoirs would be greatly facilitated. This prediction is of great economic importance in the petroleum industry, especially during the national emergency when oil and gas must be piocluced at maximum rates consistent without sacrifice of ultiniate recovery.
B
ECAUSE of their importance in predicting the phase behavior of hydrocarbon systems, vapor equilibrium data for hydrocarbons have been extensively studied in the petroleum industry over the past two decades. Such data are usually used in the form of vaporization equilibrium constants as these can be applied directly to problems involving the effect of temperature and pressure on the compositions of liquid and vapor in two phase systems. This constant is defined as
where y is the mole fraction of the component in the vapor phase, and x, the mole fraction of the same component in the liquid phase. Simplified systems of two and three components have been studied to provide a basis for the consideration of complex problems of more practical interest and thus enable the production 1
Bureau of Minea, Cairo, Egypt.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1812
Vol. 43, No. 8
the data obtained during this study would substantiate and extend the correlation proposed by Clark ( 9 ) between the equilibrium constant for methane in binary hydrocarbon systems and the Universal Oil Products (C.O.P.) characterization factor of the heavier component. APPARATUS
Phase compositions of binary mixtures can be established if the gas densities of the vapor and liquid phases are known. T o provide the relation between the gas density and composition for the mixtures studied, the apparatus described by Clark ( 3 ) was used in Khich known gaseous mixtures of the components could be prepared and from which samples could be taken into a Dumas bulb and the density determined. The apparatus used in establishing equilibrium conditions was originated by Webber (IC) and used by Weinaug and Cordell (16). MATERIALS
COMPOSITION-MOL FRACTION METHANE
Figure 1. Isobaric Density of Gas at 150" F. in MethaneBenzene Systems
technologist to predict the phase properties of a given crude oilnatural gas or condensate-natural gas system. The behavior of crude oil-natural gas mixtures as found in the field has undergone little investigation, the moet comprehensive work on this subject being that of Katz and Hachmuth (S), who reported results on samples taken from a well in the Wilcox sand of the Oklahoma City field.
METHANE.Methane used in this work was a Phillips Petroleum Company pure grade product containing not less than 99 mole % methane, approximately 0.5 mole % ethane, 0.3 mole yo nitrogen, and traces of carbon dioxide. The molecular weight, 16.042, from the literature was corrected for the impurities, ethane and nitrogen, to 16.164. AROMATICS.Commercial benzene and toluene were purified by fractional distillation in a column packed with aluminurn helices and operating under conditions of high reflux ratio. The purity of the distillate was determined by checking the refractive index of the middle fraction with an Abbe refractometer; refractive indexes obtained for the D line of sodium for benzene arid toluene were 1.4956 and 1.4825, respectively, a t 30.5" C , METHOD
Before charging, the equilibrium cell was evacuated t o an absolute pressure of less than 1 mm. of mercury. A small portion of aromatic liquid was then bled into the cell for purging
I 1033
I
I
d ' 0
01
02
03
04
05
06
a7
RE
09
io
COMPOSITION-MOL FRACTION METHANE
Figure 2. Pressure and Composition of Methane-Benzene System at 150' F.
It has been realized for some time that the distribution of methane between the liquid and vapor phases of field hydrocarbon mixtures is dependent on the properties of the heavy component-e.g., pentanes (+), hexanes (+). Information on the behavior of methane binary systems in which the heavy component is another member of the paraffin series, is available from numerous sources in the literature and to a smaller extent also is available on methane-naphthene mixtures ( 2 , l a ) . However, with the exception of a paper by Schoch and coworkers (11) on the solubility of methane in benzene, no comprehensive data have been available on methane-aromatic binary systems. In addition to providing useful information to the literature, it was hoped that
COMPOSITION-MOL
FRACTION METHANE
Figure 3. Pressure and Composition of Methane-Toluene Systems a t 130" F.
any air remaining and a second evacuation carried out. Following completion of the purging process, an amount of aromatic hydrocarbon sufficient t o provide for later sampling was sucked into the cell. An amount of methane, calculated to give approximately the bubble point desired, was added, and the pressure on the resulting system was raised above this value by forcing mercury into the cell from the calibrated positive dis-
August 1951
INDUSTRIAL AND ENG INEERING CHEMISTRY
1813
I n addition to the data for these two systems, the equilibrium constants for the equivalent paraffinic and naphthenic systems were obtained from the literature ( 1 , 2, 5 ) (Figures 4 and 5). The data for methane in these systems and for several other binary systems (6,4 , 6, 9, 10) containing methane were studied in relation t o the U.O.P. characterization factor (10)at constant prewure (Table I1 and Figure 6). The U.O.P. factor is defined as follows:
where
= U.O.P. characterization factor T B = normal atmospheric boiling point, G = specific gravity at 60°/600 F.
O
F. absolute
Assuming Dalton's law of partial pressures, Henry's law for mctharie can be stated as follows: IC=- 1
where IC = C = P =
Figure 4. Equilibrium Constant and Pressure of Methane-Benzene, Methane-n-Hexane (7), and MethaneCyclohexane (2)
placement pump. After thermal equilibrium was established, the cell was rocked manually for about 15 minutes t o ensure uniformity of the contents. Portions of mercury then were withdrawn and a curve relating pressure to the change in volume was obtained. A sharp break in the curve indicated the bubble point pressure of the particular mixture in the cell. Mercury wa8 added to maintain the pressure a t a t least 1500 pounds square inch absolute above that corresponding to the b u b E i point and samples were taken from the single phase through a throttling valve into an evacuated glass balloon for measurement of the density of the mixture. Other increments of methane were injected into the cell and the process repeated, until the bubble point pressure of the particular system as a function of composition was determined over a pressure range from 100 pound8 per square inch absolute t o a pressure as close to the critical point as was feasible with the equipment used. The composition of the vapor was obtained by sampling from the vapor phase while maintaining constant pressure in the cell by the addition of mercury. Triplicate samples were taken a t each point, and several extra runs were made to eliminate random errors in sampling as far as possible, and to establish the pressure-composition diagram with certainty. EXPERIMENTAL RESULTS
Density data obtained on known mixtures of methane and benzene were cross-plotted to give the composition as a function of gas density for lines of constant pressure (Figure 1). A similar plot was constructed for the methane-toluene system. The curves obtained appear to be nearly straight lines in the range of high methane content and show slight curvature when the concentration of the heavy component becomes great; the latter effect may be due to deviation of the mixture from the ideal gas laws or to slight error in the original compositions since mixtures containing only a small amount of methane were difficult t o synthesize accurately. In any case, the deviation is small compared with errors in the equilibrium determination. Compositions were taken from Figures 2 and 3 at various pressures and the vaporization equilibrium constants computed for the methanebenzene and methane-toluene systems (Table I).
(3) CP vaporization equilibrium constant for methane Henry's law constant for methane total pressure of the system, pounds per square inch absolute
The plotting of this equation on logarithmic coordinates results in a series of parallel lines of negative slope inclined 45" to the coordinate axis. Data on the systems containing naphthenes and aromatics show that the law holds for methane in these systems to pressures above 1000 pounds per square inch absolute. In several of the systems containing normal paraffins the IC values for methane appear to deviate considerably from HenryJs law in the low pressure range where the law normally would be expected to hold. ' As a matter of interest, data on the equilibrium constant for methane in four multicomponent systems ( 3 , 7 , 8, 1 4 ) were studied in this way (Figure 6). The calculation of the U.O.P. characterization factor for heavy fractions in these systems can-
TABLEI. EQUILIBRIUM CONSTANTSOF METHANE-BENZENE SYSTEM AND METHANE-TOLUENE SYSTEMAT 150' F. pressure,
Lb./Sq. Inch Abs. 100 150 200 400' 600 800 1000 1500 2000 2500 3000 3500 4000 4200 4400 4600 4800
Mole Fraction of Methane Liquid Vapor
0.014 0.022 0.030 0.060 0.090 0.118 0.146 0.213 0.278 0.340 0.400 0.455 0.514 0.538 0.565 0.603 0.695
.
Methane-Benzene System 0.925 0.985 0.075 0.947 0.978 0.053 0.957 0.970 0.043 0.977 0.940 0.023 0.980 0.910 0.020 0.980 0.882 0.020 0.977 0.854 0.023 0.974 0,787 0,026 0.969 0.722 0,031 0.963 0.660 0.037 0.956 0.600 0,044 0.950 0.545 0.050 0.935 0.486 0.065 0.923 0.462 0.077 0.900 0.435 0.100 0.865 0.397 0.135 0.775 0.305 0.225
Mole Fraction of Methane Liquid Vapor
100 300 500 700 1000 1500 2000 2500 3000 3500 4000 4500 5000 5100 5200 5300
0.017 0.052 0.085 0.120 0.173 0.252 0.325 0.393 0.452 0.505 0.554 0.604 0.664 0.680 0.700 0,729
Mole Fraction of Benzene Liquid Vapor
Mole Fraction of Toluene Liquid Vapor
Methane-Toluene System 0.973 0.983 0.027 0.987 0.948 0.013 0.915 0.990 0.010 0.990 0.880 0.010 0.827 0.989 0.011 0.748 0.987 0.013 0.675 0.985 0.016 0,607 0.980 0.020 0.548 0.976 0.024 0.971 0.495 0.029 0.446 0.962 0.038 0.396 0.945 0.055 0.919 0.336 0.081 0.320 0.910 0,090 0.300 0.895 0.105 0.271 0.870 0.130
E uilibrium 8onstant Methane Benzene 63.8 43.0 31.9 16.2 10.8 8.30 6.69 4.67 3.48 2.83 2.39 2.09 1.82 1.72 1.59 1.43 1.12
0.076 0,054 0.045 0,024 0,022 0,023 0.027 0,033 0.043 0,056 0.073 0,092 0.134 0.166 0.229 0.341 0.737
Equilibrium Constant Methane Toluene
57.2 19.0 11.6 8.25 5.71 3.91 3.02 2.49 2.15 1.92 1.74 1.56 1.38 1.34 1.28 1.19
0.027 0.014 0.011
0.011 0.013 0.017 0.023 0.033 0.044 0,059 0.085 0.139 0.241 0.281 0.350 0.479
INDUSTRIAL AND ENGINEERING CHEMISTRY
1814
Vol. 43, No. 8
1
TABLE 11. EQUILIBRIUM CONSTAXTS O F M E T H A N E BINARYSYSTJCMS AT 150" F. Heavy
component Benzene Toluene Cyclohexane Cyclopentane Methyloyclohexrtne n-Decane n-Heptane n-Hexane n-Pentane ?&-Butane iso-Butane Crude oil Distillate Absorption oil Crystal oil
10
I-
z
I z 0 2
2
s
Ia
-
8
.IO
.01 PRESSURE- eSlA*.
Figure 5. Equilibrium Constant and Pressure of Methane-Toluene, Methane-n-Hexane ( 8 ) , and Methane-Methplcyclohexane (2)
U.O.P. Charaoterilation
IN
SEVERAL
-Pressure, Lb./Sq. Inch Abs.100 200 400 600 1000 1trier-
~~~t~~ x q d i b r i u m Constants of Methane ellce 9.75 63.8 31.9 16.2 10.8 6.7 ... 10.14 11.05 11.20 11.40 12.67 12.70 12.80 12.00 13.50 13.82 12.0 12.1 11.5 12.14
57.2 50.9 45.5 44.1 35.0 28.5 28.: 30.2 28.0 24.5 40.7 39.0 37.5 30.5
28.9 26.8 23.2 22.5 17.7 15.0 15.5 15.8 14.24 12.2 20.4 19.6 18.8 15.25
15.0 13.0 11.6 11.4 8.76 7.8 8.3 7.8 7.01 6.11 10.03 9.8 10.1 7.40
9.7 5.7 8.6 5.2 7.8 4.7 7.6 4.6 6.13 4.00 5.4 3.5 5.8 3.6 5.2 3.2 4.69 2.80 4.05 2.35 7 . 0 4.62 6.6 4.5 6.85 4.38 5.75 3.80
. . ,
(2)
(Z) (2) (6) (6) (1) (IO) (9)
(4) (3) (7)
(14) (8)
with the U.O.P. characterization factor, subst'antiate his rcsults and extend the range of the correlabion. -4simple empirical relationship has been found whereby the equilibrium constant for niet,hane in a binary system a t 150' F. and moderate pressure can be computed knowing the pressure and the U.O.P. characterization factor for the heavy component. Data from the literature on met.hane-parafin systems suggest that similar correlations might be found at other temperatures, but few reliable data on binary systems of methane-aromatic and methmenaphthenic compounds are 1mon.n. ACKNOWLEDGMENT
not be made with certainty so that little emphasis can be placed on the fact that these multicomponent systems have the wine gelieral behavior as t'hat of binary systems. The solubility of methane in binary systems a t 150 F. appears to be a simple function of the U.O.P. characterization factor of the heavy component for a given pressure, the following empirical relationship being found:
The experimental data were obtained by hf. Elbishlawi in partial fulfillment of the requiremeiits for the M.S.degree in petioI ~ u mengineering a t the University of Texas. The authors rrish
O
log,& = 0,0953E - 1.732
(4)
is the U.O.P. Characterization factor of the heavy component. Equation 4 substituted in Equation 3 yields loglok = (4.732
- 0.0953z)
- 10gioP ( 5 )
Equation 5 can be plotted easily (Figure 6) and the relationships appear to hold satisfactorily for pressures up to approximately 1000 pounds per square inch absolute when deviations from Henry's law become great enough to nullify Equation 5. CONCLUSION
-
Vaporization equilibrium constant6 for the binary systems Of methane-benzene and methane-toluene a t 150 O F. have been determined over a range of pressure from atmospheric almost to the critical for each system. Application of the results obtained to the Clark's ( 2 ) correlation of the equilibrium constants for methane
.o U.O.P. C H A R A C T E R I Z A T I O N FACTOR i(
Equilibrium Constant for Methane and U.O.P. Characterization Factor of the Heavy Component at Several Pressures
Figure 6.
System at 150° F. 1. Benzene 2. Toluene 3. Cyclohexane ( 2 ) 4 C clopentane(2) 5: ethylcyclohexane (2) 6. Absorption oil (14) 7. Natural gapcrude oil (3)
J
8. Natural gas-condensate (7) 9. Crystal oil ( 8 ) 10. n-Decane (6)11. n-Heptane (a) 12. n-Hexane (I) 13. n-Heptane (IO) 14. n-Butane ( 9 ) 15. iso-butane (4)
August 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
to express appreciation to the Texas Petroleum Research Committee and the Petroleum Engineering Department of the University of Texas for financial support and for the use of the necessary laboratory equipment. Also, W. D. Rose is thanked for his helpful suggestions in the preparation of this paper. LITERATURE CITED
Boomer, E. H., and Johnson, C. A,, Can. J. Research, 16, 328 (1938).
Clark, G. A., unpublished M.S. thesis, University of Texas, 1949.
Katz, D. K., and Hachmuth, K., IND.ENG.CHEM.,29, 1072 (1937).
Olds, R. H., Sage, B. H., and Lacey, W. N., Zbid., 34, 1008 (1942).
Poyner, H.F.,unpublished M.S. thesis, University of Texas, 1949.
1815
H.9 Fiskin, J. M.3 and Lacey, W- N.9 I N D - E R G CHEM.,41,2871 (1949).E,, and Kaveler, (7) Roland, c, H., Smith, oil J., 39, 128 (March 27,1941). (8) Sage, B. H., Backus, H. S., and Lacey, W. N., IND. ENG.CHEM., 27, 686 (1935). (9) Sage, B. H., Hicks, B. L., and Lacey, W. H., Ibid., 32, 1086. (1940). (10) Sage, B.H., and Lacey, W. N., Ibid., 34, 1108 (1942). (11) Schoch, E. P., Hoffman, A. E., Kasperik, A. S., Lightfoot, J. H., and Mayfield, F. D., Ibid., 32,788 (1940). (12) Schoch, E. P.,Hoffman, A. E., and Mayfield, F. D., Ibid., 32,. 1351 (1940). (13) Watson, K. M., and Nelson, E. F., Ibid., 25,880 (1933). (14)Webber, C. E., Trans. Am.Znst. Mining Met. Engrs.,Petroleum Div., 136 (1940);142,381 (1941). (15) Weinaug, C. F.,and Cordell, J. C., Ibid., 179,303 (1949). RECEIVED September 16, 1950. This paper was prepared under the spon(6) Reamer,
sorship of the Texas Petroleum Research Committee
a8
contribution No. 6.
Thermodynamic Functions of Iron J
L. S. DARKEN AND R. P. SMITH Research Laboratory, United States Steel Co., Kearny, N. J.
F o r the thermodynamic treatment of metallurgical systems a knowledge of the thermodynamic functions of the pure components is essential. In view of the numerous data on the heat capacity and t h q m a l properties of iron that have appeared in the literature since the collation of Austin in 1932 and the review of Cleaves and Thompson in 1935, it seemed desirable to review this subject and to compile a consistent set of thermodynamic functions. The thermal properties of iron are reviewed and combined with equilibrium data to obtain a consistent tabulation of the thermodynamic functions C,, H' HZ and
F' - HX
-
for body-centered cubic and face-centered cubic
iron from 298' to 2000' K. and for liquid iron from 1300' to 2000" K. ' Kelley, in his recent compilation, includes equations for the heat aapacity and enthalpy of iron as well as a table of
T
HE general method used in this work was to establish the heat capacity, C,, for each modification and the heats of transition, A H , as a function of temperature; the enthalpy and free energy functions were then obtained by successive integrations, Direct measurements of C, and AH could not be used exclusively since the experimental errora, particularly the experimental uncertainty in the heat capacity of y-iron, led to values that failed by a large margin to satisfy the equilibrium'conditions (23,29). Rather, a method of successive approximations was used. The heat capacity of a-iron, up to about 850" C., which now seems reasonably well established, was adopted from direct experimental data. The difference in the heat capacity of bodycentered cubic (bcc) and face-centered cubic (fcc) modifications was calculated principally from equilibrium measurements in the range 723" to 1400" C. by a method described later. From these two quantities heat capacity of y-iron in the vicinity of 800' C. was determined. The remainder of the curve for the heat capacity of y-iron was selected by consideration of direct experimental data, the heat capacity of similar metals, and the condition imposed by the third law; a linear relation with temperature was chosen. The heat capac.ity curve for a-iron wag then adjusted slightly in the vicinity of 850' C. to be nearly consistent with the linear reIation for y-iron and ACpa-'Y; the process was repeated until all-around consistency was attained for the bcc and
enthalpy and entropy. The table, however, covers each modification only in the region in which i t is stable in pure form. His equations are not intended for application to. equilibria in alloy systems and are inadequate for this purpose. The authors present a consistent set of thermodynamic functions for iron, at one atmosphere pressure, which may be used for determining the enthalpy, entropy, and free energy change accompanying a change of state at any temperature. Such a table is particularly useful in dealing with the thermodynamics of alloy systems, as has been illustrated by Zener. The enthalpy and free energy changes of the transformation from the body-centered cubic (a, 8 ) to the face-centered cubic (y) modifications are so small that the consistency of the table is very important. Moreover, it is necessary to express the tabular functions to several more figures than the absolute precision warrants. fcc modifications. The remainder of the functions were calculated in the usual way. The entire procedure reported here wag carried through several times until, by successive approximations, a consistent table was obtained. TEMPERATURE OF TRANSFORMATION AND MELTING
The temperature of equilibrium between CY- and y-iron via8 taken as 910' C. This value is identical with that selected by Cleaves and Thompson (7) and is supported by the dilatometric work of Wells, Ackley, and Mehl (sa), who give the temperature as 909.5 f '1 C.; by Mehl and Wells (23); by the magnetic determination of Rogers and Stamm (37); and by x-ray measurements by Wangsgard (32). The carefuil magnetic investigation (27) of the transformation of high purity iron disclosed considerC.) and able gap between the thermal crest on heating ( A c ~(910.5" ) that on cooling (Ar8) (902.5' C.). The authors suggest, however, that the transformation tends to be reversible a t about the temperature of the Ac3 change. X-ray measurements give AcB as 910.5' f 0.6 and Ar8 as 908' C. The melting point (1539" C.) was taken from the determination of Wensel and Roeser reported by Cleaves and Hiegel (6). The temperature of the equilibrium 7 - 6 transformation (1400' C.) is in agreement with the value selected by Cleavesand Thompson (7). Adcock (1)reports 1388 f
