High Temperature Equilibria Citation Brantley, Lee Reed (1930) High Temperature Equilibria. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/hwky-r736. https://resolver.caltech.edu/CaltechTHESIS:08202024-224826900 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1930 Record Number: CaltechTHESIS:08202024-224826900 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:08202024-224826900 DOI: 10.7907/hwky-r736 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16659 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 21 Aug 2024 18:20 Last Modified: 21 Aug 2024 18:38 Thesis Files PDF - Final Version See Usage Policy. 6MB Repository Staff Only: item control page

HIGH TEMPERATURE EQUILIBRIA Thesis by Lee Reed Brantley In partial fulfillment of the requirements for the degree of Doctor of Philosophy California Institute of Technology Pasadena. California 1930 CONTENTS Page I. !he High Temperature Equilibrium between Silieon Nitride. Silicon and Nitrogen. A. Plan of the Investigation l B. Apparatus and Procedure 2 c. The Equilibrium Measurements 2 D. Thermodynamic Calculations 4 Summary II. 5 The High Temperature Equilibrium between Titanium Dioxide end Carbon. A. Introduction 6 B. Apparatus and Procedure 1 c. Equilibrium Measurements 10 D. The Nature of the Solid Phases 16 E. Determination of the Size of the Unit Cell of TiC 18 F. Thermodynamic Calculations 20 Summary 21 References 22 [Reprint from the Journal of the American Chemical Society, 112, 48 (1930).) [CONTRIBUTION FROM GATES CHEMICAL LABORATORY, TECHNOLOGY, No. 224] CALIFORNIA INSTITUTE OIi THE HIGH-TEMPERATURE EQUILIBRIUM BETWEEN SILICON NITRIDE, SILICON AND NITROGEN BY w. B. HINCKE AND L. R. BRANTLEY RECEIVED JULY 6, 1929 PUBLISHED JANUARY 8, 1930 A • Plan of the Investigation This investigation is a continuation of the researches in progress in this Laboratory on high-temperature equilibria. 1 The method devised by Prescott and used by Prescott and Hincke1d in studying the equilibrium of the system aluminum carbide, nitrogen, aluminum nitride and carbon was employed. This method consists in heating by an electric current to various temperatures (measured by an optical pyrometer) the solid reaction mixture (in this case the silicon nitride and silicon) within a graphite tube a few millimeters in diameter and a few centimeters long placed within a pyrex bulb, and in measuring the pressures produced. In this article are described measurements made of the dissociation pressures of silicon nitride from 0.27 to 5.49 mm. through a temperature range from 1606 to 1802°K. 1 (a) Prescott, Tms JOURNAL, 48, 2534 (1926); (b) Prescott and Hincke, i bid., 49, 2744 (1927); (c) Prescott and Hincke, ibid., 49, 2753 (1927); (d) Prescott and Hincke ibid., SO, 3228 (1928); (e) Prescott, ibid., SO, 3237 (1928); (f) Prescott and Hincke, Phys. Rev., 31, 130 (1928). ') ,._, Jan., 1930 SILICON NITRIDE-SILICON-NITROGEN EQUILIBRIUM 49 It has been shown by Weiss and Engelhardt 2 and by Funk3 that the compound produced, when silicon is heated in nitrogen at 1300 to 1450° as long as the gas continues to be absorbed, is the normal nitride, SiaN4 • The nitride produced in the experiments here described presumably had this composition, since the conditions of heating were substantially the same. The authors wish to express their thanks to Dr. C.H. Prescott, Jr., whose suggestions and criticisms have been of great assistance. B . Apparatus and Procedure The temperature measurements in this investigation were made by means of an optical pyrometer with a disappearing filament; the details, corrections and limitations of these measurements have already been described. 1h' 1 The furnace, the devices for introducing nitrogen and the McLeod gages have also been described. ld The silicon used was a c. P. Eimer and Amend preparation which had been ground to pass a 200-mesh sieve. The preparation upon treatment with hydrofluoric and nitric acids, evaporation with nitric acid and ignition of the residue yielded 2% of oxides, corresponding to about 1 % of metallic impurity. In the procedure adopted there was placed loosely in the middle zone of the graphite tube a charge of 0.1 g. of finely powdered silicon. After complete evacuation, the apparatus was filled at one atmosphere with (tank) nitrogen that had been passed through a purifying train, and the furnace was heated to 1675°K. for thirty minutes. This converted about 75% of the charge to silicon nitride.' The apparatus was then evacuated, after which it was ready for the equilibrium measurements. In all of the determinations the temperature of the furnace was held constant, and the equilibrium pressure was found by taking the mean of the final pressures of a forward and a reverse reaction wherein the pressure in the glass bulb containing the graphite furnace increased and decreased, respectively. To hold the furnace at a constant temperature it sufficed to keep the current through it constant, which was done by means of a standard resistance and a potentiometer. A shower of tap water was caused to play continuously over the glass bulb containing the graphite tube while equilibrium measurements were being made. This prevented excessive outgassing of the glass walls and contamination of the nitrogen. A gas micro-analysis apparatus 1d was used to determine the partial pressure of nitrogen at the end of each experinient. In all the satisfactory runs the nitrogen formed more than 92% of the gases in the bulb. For the preliniinary formation of silicon nitride the current was drawn from a 1kilowatt transformer. During the measurements it was taken from storage batteries. To maintain the furnace at 1802 °K. about 80 amperes at 10 volts was required. C • The Equilibrium Measurements The first equilibrium determination was made at 1675 °K. The pressure of the nitrogen in the bulb built up from a vacuum to 0.47 mm. in the course of one hour, the gas then containing 92% of nitrogen. The apparatus was then again evacuated and filled to 0.90 mm. of nitrogen, as measured when the furnace had become hot; in this case the pressure of the gas decreased Weiss and Engelhardt, Z. anorg. Chem., 65, 78 (1910). Funk, ibid., 133, 67 (1924). . 'No silicon carbide was formed at this nitrogen pressure by the reaction of silicon with the graphite furnace; moreover, it was found that silicon carbide is inert to nitrogen under the conditions of these experiments. 2 3 -- . 3. 50 Vol. 52 W. B. HINCKE AND L. R. BRANTLEY in one hour to 0.762 mm., and the gas contained 95% of nitrogen. Two one-hour runs were then made, one at 0.57 mm. and the other at 0.675 mm. of nitrogen, but these showed no measurable change in pressure. Finally a run of two hours with increasing pressure was made, starting from an initial pressure of 0.336 mm. and stopping at 0.553 mm. of nitrogen. The gas analysis showed 100% of nitrogen in this run, which was to be expected because of the pumping off of the outgassed impurities in the previous runs. It was observed that a pellet reacted more slowly after some hours of heating, probably owing to loss of some of the silicon from the charge by volatilization and to sintering of the silicon nitride into a more compact mass. The pellets removed from the furnaces after each equilibrium determination always gave the characteristic ammonia test on heating with concentrated alkali, and under a low powered microscope showed a white sintered mass speckled with darker particles of silicon. In each determination the true equilibrium pressure of the nitrogen corresponding to any temperature was assumed to be the average of the two pressures which had been attained in a forward and a reverse run. Each of the two pressures always approached a limiting value that seemed to be as far as the reaction would go within a reasonable time. These pressures, however, did not differ very greatly from one another. At temperatures above 1800 °K. sublimation of the silicon and sintering of the silicon nitride were so rapid that a pellet became only slowly reactive after a few runs. This permitted, nevertheless, a range of about 200° over which the equilibrium could be studied. Table I gives the final pressures (in millimeters) observed at each temperature. There are shown in each case the highest pressures (marked TABLE I EQUILIBRIUM PRESSURES OF Tira REACTION AT VARIOUS TEMPERATURES AND THE Absolute temp., T 10'/T 1606 1638 1675 1709 1739 1779 1802 6.225 6 .110 5 .971 5.850 5.750 5.625 5.550 CORRESPONDING FREE ENERGIES Final pressure in mm. Increasing Decreasing Mean 0 .179 .382 .553 1.110 2 .215 3.560 5.05 0.361 .537 .762 1.335 2.675 4.65 5 .93 0 .27 .46 .66 1.22 2.44 4 .11 5.49 Pressure Free energy X lO•inatm, llF 3 .5 6 .0 8 .7 16 .1 32 .0 54 .0 72.0 50,800 48,300 46,900 43,700 39,700 36,900 35,300 "increasing") which were attained by the forward reaction (decomposition of the nitride) and the lowest pressures (marked "decreasing") which were attained by the reverse reaction. These pressures are always the partial pressure of the nitrogen in the gas (found by multiplying the total pressure by the fraction of nitrogen present). The mean values of these two pressures for each pair are taken as the equilibrium pressures. The correspond- 4. Jan., 1930 SILICON NITRIDE-SILICON-NITROGEN EQUILIBRIUM 51 ing values expressed in atmospheres are given in an adjoining column. In the last column of the table are given also the values (derived as described below) in calories of the free-energy increase (t:.F) attending the reaction SiaN4(s) = 3Si(s) or (1) + 2N2(g). In Fig. 1 are plotted as full circles the mean values of log1o p (in mm.) against 10 4/ T . The straight line was drawn so as to fit best the full circles. The corresponding observed "increasing" and "decreasing" values are shown by half-circles. T-+. 1818 1739 1667 1600 5.50 5.75 6.00 6.25 +1.0 ,,-.. d "§ ~ 0.0 ~ i;i 0 H -1.0 10 4 / T. Fig. 1. The final relation between the equilibrium pressures in atmospheres and the absolute temperature is given by the equation 2.3 log,o p (in atm.) = 19.75 - 44 ,;00 Since the melting point of silicon is approximately 1687°K., there should be a slight change in slope of the line at this temperature due to the heat of fusion of the silicon, but the data are not accurate enough to show this change in slope. D. Thermodynamic Calculations The chemical reaction is SiaN4 = 3Si + 2N2. The free-energy increase (t:,,.F) attending it when the nitrogen pressure is one atmosphere may then be derived from the equilibrium pressure p in atmospheres by the familiar equation t:.F = -RT ln K, where K = p 2 and R = 1.987. From the determinations of the equilibrium pressure p are thus obtained the values of t:.F given in the last column of Table I. From these values of the free-energy increase one obtains the function 5. 52 W. B. HINCKE AND L. R. BRANTLEY Vol. 52 11F = 176,300 - 78.35Tfor absolute temperatures between 1600 and 1800°. From this it follows that the heat-content increase 11H is 176,300 calories in this temperature range. The function shows also that at an absolute temperature of 2250° (assuming it to hold up to this temperature) the freeenergy increase becomes zero and therefore that the dissociation pressure becomes one atmosphere at this temperature. Summary The pressure of nitrogen at which equilibrium prevails between silicon nitride, SiaN4, and its elements at absolute temperatures ranging from 1606 to 1802 °K. has been determined by an experimental method previously described. This pressure is 0.27 mm. at 1606°K. and 5.5 mm. at 1802°K. Within this temperature interval the free-energy increase 11F at one atmosphere attending the reaction SiaN4 = 3Si + 2N2 was found to be expressed by the function 11F = 176,300 - 78.35 T calories. From this it follows that the heat-content increase 11H at 1700°K. is 176,300 cal.; also that the dissociation pressure of the nitride becomes one atmosphere at about 2250°K. PASADENA, CAI.IFORNIA 6. THE HIGH TEMPERATURE ~QUILIBHIUM BETll'iEEN TITANIUM DIOXIDE Al\1D CARBON A,. IM'rRODUCTION This investigation is a continuation of the reset1 rches on high temperature equilibria which have been carried out in this l Laboratory. The high-pressure apparatus previously used in study- ing the equilibria between ziroonium oxide and carbon la • thorium oxide and oarbon10 _ and aluminum oxide and carbon1 b was employed. The method used consists in electricall;y heating a small graphite tube furnace which contains the solid reaction mixture, determining the temperature by an optical pyrometer, and measuring the gas pressure on a mercury manometer. The measurements described in this thesis include the pres- sures of c a rbon monoxide in equilibrium with the solid phases Ti02 , TiC and Cover the pressure range 0.8 to 2.0 atmospheres and the temperature range 1000° to 1150°C. The composition of the solid reaction mixture was determined by X-ray powder photographs. The author wishes to express his thanks to Dr. Arnold a.Beckman for his advice e.nd sugg estions, to Dr. W.B.Hincke f or his interest in t his work and to l';1r. 1''.J.Ewing for his assistance in obtaining the X-ray photographs. 7. B. APPARATUS AND PROCEDURE The apparatus was substantially the same as that used in the previous high pressure investigationso la , o , d A more convenient furnace assembly was used, however, which had been developed by Dr. Hinoke and the author during the course of an investigation (unpublished) of the calcium oxide- carbon equilibri'Ulll. As is sho?m in Fig. lA the graphite furnace A was supported by tungsten leads which were in turn connected t hrough tlexible copper oa.bles to the water-cooled copper tubes B o.nd C which were held rigidly co-linear by attachment to the heavy rod D. Electrode B was held in place by a miearta insulative support E; electrode C was held by a similar brass support F fitted with a thumbscrew H. The Pyrex furnace bulb was sealed to the electrodes at G with sealing wax. A side- tube with an inverted oup connection also sealed with sealing wax. connected the furnace bulb with the manometer and auxiliary gas apparatus. Since the entire furnao~ was immersed in a water thermostat it was neces- sary to protect the exposed sealing wax with paraffin. To insert a furnace tube. the glass bulb was slipped over the lmvered electrode J. which was thon raised to allow the insertion of the furnace tube. after which thumbscrew H was tightened and the glass furnace bulb raised and sealed in position. It was found that the sealing wax seals were gas tight even at t,vo atmospheres pressure and a furnace temperat ure of 2000°1. The furnace tubes, Fig. 1B, were turned from Acheson graphite with a groove near each end to provide a central region of nearly uniform temperatHro within which the change was held by graphite plugs. Two types of charge were used~ one consisting of Tic and the other consisting of 3 . Furnace Bulb aGd Grarh~te F~rn2ce B E G A D rt .I C F Tt'ig. lb. 9 . equal quantities of 'li02 and gra.µhite. In each case the materials were ground to pe.ss through a 20()..raesh sieve. The 1'iC we.s prepared by heat- ing in vacuo an equ5molal mixture of' powdered 'l'i and graphite to a temperature (1950°K) sufficiently hi gh t o volatilize a~ unoombined titimium metal. The Ti02 and Ti metal were Eimer and lunend C.P. pre- parations. vrnen the chG.rge consisted of Tic. the furnace was baked out in va.cuo at a high t~perv.tUT'o after whie!h the temperature v.u.s lowered to 1275"- l 350°K,, end the hea ting continued for 6 to? hours with carbon monoxide present at a pressure of' about 2 at::iosphores. eonsisted of 1'102 r1nd When t he eharge graphite. the f urnace wa s heated in vaeuo at a dull red heat for a few seconds. The apparatus wns then filled with carbon monoxide at a pressure of about 2 atmospheres ~nd the f'urnaoe hoated to about 1750°1( for half an hour, near enuf to the equilibrium pressure that the chG-rge would not all b@ used up. to drive off adsorbed oxygen. The furnace was then evacas ted and r efilled with fresh carbon monoxide to the desi!'ed press,u re for the equiiioi·ium. measurements. It w~s found that under these eondit1ons reaction mixtures were produced which gave sntis!'aetory rates of reaction for the equilibrium met.laurements. For preliminary \l'Ork the furnace was heated by alternating currant .frooi a low-voltage one-kilo.watt transformer but tor the final mee.sure:aenta direct current from storage batteries was used. l'o main- tain e. t emperature 0£ 1330°K a current of about 70 amperes at 6 v~lta was required. C. THE EQUILIBlHUM MEASUREMENTS The equilibrium pressures were determined by measuring the rate of reaction (i.e.~ rate of change of carbon monoxide pressure) at constant temperature for different pressures of carbon monoxide. By ob- taining a series of both forward and reverse rates with the same furnace charge, the equilibrium pressure was found graphically as the pressure corresponding to zero rate. Typical graphs are shown in Figures 2 and 3. In. Figure 2 a.re shown the carbon monoxide pressures plotted as ordinates age.inst the time as abscissae for si.x successive runs at the temperature 1278°K with different initial carbon monoxide pressures • .F'or each run the average rate of pressure oharge was determined. rejecting values which were obtained during the first 30-40 minutes of the run when the syutem was attaining temperature equilibrium. These aix. rates are shown as o:rdinatee in li'ie,-ure 3 wit,h the average pressure durirlt; the run aa ab .. scisss.e. The intersection with the zero-rate ordinate of the best straight line t hrough these points shows the equilibrium pressure to be 60.5 om. at t hi s temperature. Six sets of · runs of this kind werli made over the temperature range 1278tl to 1428°K and pressure range from a few oentimeters to two atmospheres. I n s~~e cases the initial furnace charge consisted of Ti02 and C a...~d in other cases of Tic. The equilibrium pressures and corres- ponding temperatures are given in Table I. where e is the observed tem- perature and r is the true temperature after corrections have been made for the transmission of the window and the emissivity of carbon. In Figure 4 the logarithms of the equilibrium pressures are shown plotted 11. R8.te of Change of Pressure vd th 'l'ir.ie (1278°K) 120,3 0 0 )...20• 2 mm/min 120,2 CCT A • -,0236 m IC 0 • 0 9 , 5 L.. l G -e !ks. I~ -;• • s 10 (0 Q) 0 0 0 0 0 0 0 0 0 ----: 00424 :mm/min 43.5 cm C Zero Rate 68.9 cm D 1• fi:68,9 g. 5 mm/min cm B ,01080 0 0 0 101..l l -,00?!l? mr:i/min '-----,------,.----------.--------.---l ..:. O__l _._1_ .c:..m :.:;;___:::E:_ •00385 mm/min 0 33 • ? 33,? cm F -------.-----------.--------r--------- 136,5 -.01473 mm/m,in 136.4 ___.....,,__ _ ____,,...,,....---....;._----------.---~ 1~s~6__,__s; ___ c __ m:...___G:;._ 30 60 Time (in minutes) 90 Fig. 2. -. 0 -.02 - ~ ~01 . G ~ ~ Cl! 4> t) .p ....~ .oo - ~ - } ,..t.Ol • ~ 25 50 Pressure (ui ems .) 76 Fig . S 100 0 ' 125 Change of Reaction Rate with Pressure Ave. Temp . 1278.A Equilib . Press . 60.& cm. ' 150 .r-v r' ,-f 1. 75" 2.00· ....0 i ~ - 9 ....s= Ill - 2.25- 7.00 7.25 10 /f Fig . 4· 6 7.60 '1. 75 Relation between ~quil~~ • Pr,ae ~ of' 00 and Absolute, Te,perature Cirolea - TiO~-c as original reacting ~a~eriala Triangles TiC-CO as original '19acting. materiala TiOc + 30 • TiC + 200 Log p • 3'!829 .. 51 024/t 8.00 • vJ t-' 1 4. T.ABLE I Equilibrium Pressures and Free Energies at Various Temperatures T °K l x 10• p (atm) log p (atrn) 6-F (cal) 1250 12'1i '7.825 o.796 -0.099 +11 57 1293 132-3 7.559 1.081 0.034 -411 1294 1324 7.553 1.114 .047 -569 1318 1349 'T.413 1.216 .085 -1048 1353 1386 7.215 1.634 .213 -2703 1!93 1428 7.003 l.995 .300 -3917 'l 15 . age.inst the reciprocal of the absolute temperatures,, and it is to be seen that all of the points fall upon a straight line within the experimental error. The relation be·tween the equilibrium pressures and absolute tem- perature is given by the equation log10 P(at"m.) • 3.829 - 5024ft. The pellets were never used for more than two equilibrima pressure dt:rtennina tions and usually for only one. One run was attempted at 1246°K but the reaction rates ware too slow to measure accurately. The dissociation of carbon monoxide into carbon dioxide and carbon is appreciable in this temperature range, being approximately 0.6% at 1278°K and 0.1% at 1428°K. It is well known, however,, that the reac- tion a:ttains equilibrium only very slowly. In blank experiments, using an entirely empty graphite furnace at temperatures,, carbon monoxide pressures and over time intervals similar to those used in the equilibrium measur ements, no measurable rates were observed, showing that the carbon monoxide dissociation oould be entirely neglected. D. THE NATl11(E OF' THE SOLID PHASES To determine the nature of the solid phases an analytical method was attempted but the small quantities of materials available and th-e lnek of information regarding th"O chemistry of the lower oxides of titanium led to the abandonment of this method. X-ray powder photo- graphs were finally takell o i' the rea ction mixtures and of the various subst ances. namely Tio2 (both the rutile and brookite modifications). Tic. graphite. Ti metal. and Tio. ·,;hose prese nce would be suspected in the reaction mixtures. 'l'he Tio was prepared by heating in the graphite furnace to 1775°K for half an hour in vacuo a mixture of finely ground Ti0 2 and Ti in a pproximately st.oi ehiometrio proportions. The work of 2 Billy has shown that !10 is formed under these conditions. although perhaps there may be some uncombined 1102 or Ti as well. The diameters of the rings (i.e •• the distance between corresponding lines on either side of the position of &ero deflection) o'btained on the eight photographs are represented in Figure 6. Photographs were ta.ken of two reaction mixtures. one (Fig. 5a) in wh ich the initial charge was Ti02 and graphite and one (Fig. 5b) in which t he initial cha.rge was 'liC. The results of this investigation showed t ht.i.t the solid phases in the reaction mixture were Tio£ (rutile modification), TiC and graphite. Metallic Ti, the brookite modification of 710 2 • and the lower oxide TiO were dei'i nitely shown to be absent. 17. Re3~lts of X-ray Powder Photographs Fig. 5a . initially Ti 0 2 - C Fig . 5b . initially (?) I I 11 I Ti C-CO Fig . 5c . 11 i:.... . ,... Tl. __. Ill t:l ~ +> '1 H' . . _1g 5d . 1-4 ....+>• ► Graphite QI r-4 0 ~ I Fig . 5e. Rutile I Fig . 5f . Brookite Fig. 5g . Ti metal 2· I 4' I 6' I I I 8 I I Diameter of Rings {in cm . ) '· 10 Fig . 5h . Ti 0 i2 r,, • ,.!lg. 5 . 18 . E. DETiill.~INATION OF THE SIZE OF THE UNIT CELL OF TITANIUM CARBIDE The structure of titanium carbide has been worked out by AeEo van Arkel3 and by K.Beaker and F. Ebert~ Both investigators reported the carbide to be cubic but v&n Arkel reported a100 to be 4.29 1 while Bushman and Ebert reported 4.60 lt. During the study of the na:-ture of the solid phases in the titanium oxid~-carbon equilibrium. a redetermination of the value for d 100 for titanium carbide was made. X-ray powder photographs were t aken of a 1nixture of titanium carbide and sodium chloride. tion with NaCl. Table II shows the results of the calibra- The values of e in radians for various planes were taken from ivyokoff • "The Structure of Crystals"• page 198. TABLE II Sodium Chloride Calibration Plane Diameter of Ring (ems) e in radians Weight 100 (2) 2.54 .1266 3 110(2) 3.62 .1794 3 5.046 111(2) 4.43 .2203 1 5.028 100(4) 5.15 .2551 1 5.048 120(2) 6.78 .2860 1 5.053 112(2) 6.30 .3142 2 6.014 Distance of PO\vder to F'i lm (oms) 6.016 Weig hted .mean 5.032 oms. 19., Table III shows the results of TiC measurements TABLE III Titanium Carbide Data from NaCl Comparison Plane Di Qllleter 01' h ing (in cm) 4iuc1 (in 1) Weights d1ee (in!) 111 (1) 2.89 2.479 3 4.294 001 (2) 3.34 2.149 3 4.298 011 (2) 4.71 1.531 3 4.330 113 (1) 5.57 1.299 2 4.308 111 (2) 5.78 l.253 1 4.341 001 ( 4) 6.78 l.0'14 1 4.294 133 (l) 7.40 .9875 2 4.304 012 (2) 7.61 .9618 2 4 . 301 112 (2) 8.35 .880'1 2 4.315 111 115 8.91 .8289 l 4.307 a~ Weighted mean 4.308 .ff. ·r hus powder photographs have shown the siH of the unit cell for titanium carbide to be 4.Sl l. in fair agreement with 4.29 reported by van Arkel and not in agree:,,ent with 4 .. 60 reported by Bushmal'l and Evert. 20 •. F. THERMODYNAMIC CALCULATIONS From the results of the X-ray investigation the equilibrium studied is undoubtedly that expressed by the equation Ti02 + 30 • TiC + 2co. The value of LJ F 6 the free energy increase attending this reaction. may be derived !'rom the thermodynamic equation L\ Jo' • •RT ln K, where K • p 2 • The values of L1 F correspond!~ to the equilibrium pressures at various temperatures are given in the last colwnn of Table I. From the expression for log10 p given in the p-revious section, the relation may be obtained L1 F • 45.,930 - 35.0l T for the temperature range 1278 to 1428°K. From this it follows that the increase in heat content., LlH., is 45.930 calories. At 1312°K the free energy is zero and the equilibrium pressure is one atmosphere. SUiJ!MARY Deterni.ini,; tiona have been m.ade of the equilibrium pressures ot CO for the reaction T102 +SC• TiC + 200 in the temperature range 1278° to 1428°K. fied by X-ray powder photographs. The solid phases were identi- The length of the unit cube for Tic was found to be 4.31 !. With t his temper ature range the inorease in free energy and heat content that attend this reaction at one atmosphere pressure were f nund to b e given by the e~pressions .6 F • 45,930 - 36.0l 1' ealories end 6 H • 45.930 calories. l312"K. The equilibrium pressure is one atmosphere at References l a. Prescott , J. A.rn. Chem . Soc., 48, 25:')4 (1 926). b. Prescott, ibid., 5 o, 3237 ( 1928 ). c, Prescott and Hincke , ibid ., 49, 2744 (19 27 ). " . r1 Prescott and Hinc ke , i bid . , 4i, 275:3 (1 9:~7). e. Prescott and Hinc ke , ibi d. , f. Presc0tt and Hincke , Phys . Re v., ;i_L L'lO (1928). g. Hincke ,':. ncl Fr a nt l ey , J. 1-\m .Chem.Soc., 52 , 48 (1930). 2. Bi lly, Ann.i;him., 1 6 , ·:i. . ,., vvan 4. Bec "-er e. ncl :i;be:r t, Z .Physik , 31, 2fs6 (1 925 ). A rKe. , ' l nys i c 0,~, .:_, P' • 4 t) , 5 o, :s22s ( l o ')8 ) ..1 ~~ (1 92 1). P :J ,· ,•--:i, ., 0 ( l r. ~• ~ 4 ) • •