R. A. LAUDISEAND A. A. BALLMAN
1396
Vol. 65
THE SOLUBILITY OF QUARTZ UNDER HYDROTHERMAL CONDITIONS' BY R. A. LAUDISE AND A. A. BALLMAN Bell Telephone LabOTatOTieS, Ine., Murray Hill, New Jersey Received March 10, 1061
The solubility of 01 quartz as a function of temperature and density of the solvent has been measured between 300 and 400' and between a solvent density of 0.70 and 0.87 g./cc. in 0.51 m sodium hydroxide solutions and the results are compared with quartz solubilities in the systems H20-Si02, HZO-SiOrNazO and HaO-SiOz-NazC03. It is found that the van't l3off relation is obeyed and AE and A S for the respective solution processes are calculated. Itds further found that the logarithm of the solubility is linear with the solvent density which is shown to indicate weak solvent-solute interactions. It is shown that the reaction Si02 (2a 4)(OH) - e (Si0,).(z5-4)( a - 2)Hz0 goes essentially to completion in hydroxide solutions and nearly to completion in carbonate solutions. It is also shown that the species present in (OH)solutions in the one fluid phase region is (Sia07)z-while in (COJ*- systems (Sios)*- s e e m to predominate.
+
-
Introduction Single crystals of a-quartz12 sapphirela zinc oxide14zinc sulfide4 and yttrium iron garnet6 have been grown by the use of basic aqueous solvents at high pressure and temperahre which increase the solubility of these ordinarily insoluble materials. Experimental details of this t,echnique which is generally cztlled hydrothermal crystallization have been reviewed elsewhere6 and the kinetics of the crysta'llization of quartz under hydrothermal conditions have been studied in the system H20Si02-3C'a20.7 E. U. Franck8 and others9J0have discussed the solubility of solid substances under hydrothermal conditions and from a consideration of the thermodynamics of a constant volume system Franck has derived expressions predicting the dependence of solubility on the specific volume of the solvent. The only hydrothermal system for which solubility data exist in any quantity is the quartz system. However, even in the case of quartz all of the solubility data in the literature have not been evaluated and no consideration of the systems containing base has been made. Furthermore, comp1et)esolubility data over the pressure-temperature range where quartz is crystallized are not available. We therefore decided to measure the solubility of quartz in the system SiO2-H2O-Na2O at conditions where quartz crystallization rate studics have been made and by the use of Franck's treatment as a guide t.0 look for relationships which would allow int'erpolations a,nd extrapolations both in this and in similar systems. The validity of these relations was test'ed where appropriate wit>h the solubility data of Kennedy," Friedman,12
+
Morey'3 and Butuzov and Briatov14 in the systems SiO2-Hz0, SiOr H20-Na20 and SiOTHzO-Na2COa and finally the data were utilized to deduce where possible the nature of the silica containing species in the various hydrothermal systems. Quartz is ordinarily crystallized at temperatures between 300 and 400' from solutions where the specific volume is between 1.15 and 1.54 (corresponding to degree of fill of the free volume of the autoclave a t room temperature of 0.87 to 0.65). Under these conditions Morey's data13J6and preliminary experiments in these laboratories showed that but one fluid phase was present both in pure water and in the base concentration ranges described in this work.
Experimental
(1) Presented in part a t the 32nd National Colloid Chemistry Symposium, Lehigh Gniversity. June, 1960. (2) G. Speaia. dcad. Sci. Torino Atti., 40, 254 (1905); see also R. Nacksn, Captured German Reports, RDRC/13/18, February 28, 1946. (3) R. A. Laudise and A. A. Ballman, J . A m . Chem. Soc., 80, 2655
Several methods have been employed for the determinntion of solubilities under hydrothermal conditions. Fyfele has pointed out that in the sampling method unless the sample which is withdrawn from the autoclave at operating conditions is small, the system may be perturbed enough that the sample will not be representative. These errors were shown to be important in the solubility measurements made in the system SiOrHsO by Frederickson and COX." All other methods for determining solubility involve the examination of autoclave contents after quenching a t the conclusion of a run. Where only one fluid phsee exists the simplest technique to employ is the weight loss method. In our work this technique was used. Generally two weighed plates of quartz whose total surface area was about 15 cm.2 and whose principal face was (0001)were suspended near the middle of a suitably designed autoclave, the autoclave was filled to some predetermined fraction or per cent. of fill of its free volume with a NaOH solution of the desired concentration and sealed. The autoclave then was placed in a furnace capable of maintaining it isothermally a t the desired temperature and warmed up with special care being exercised to avoid overshooting in temperature. The vessel was maintained at temperature for a time in excess of that found to be required to establish equilibrium and then quenched. Provided only one fluid phase was present and provided quartz was known to be the stable phase under the conditions of the experiment, the loss in weight of the quartz plates was an excellent measure of the solubility of quartz.
(4) R. A. Laudise and A. A. Ballman, J . Phys. Chem.. 64, 688 (1960). (5) R. A. Lautlise. J. C. Crocket and A. A. Ballman, ibid., 65, 359 (1961). (6) R. A. Lacdise and J. W. Nielsen in "Solid State Physics," Ed. F. Seitz, t o be published. (7) R. A. Laudise, J . Am. Chem. SOC.,81, 562 (1959). (8) E. U. Franck. 2. p h y a k . Chem. (Neue Folge), 6 , 345 (1956). (9) R. Mosebach. Neuea J b . Mineralog. Abb., 87, 351 (1955). (10) J. A. Wood, Jr., Amar. J . Sci., 266, 40 (19.58). (11) G . C. Kennedy, Econ. Geol.. 46, 629 (1950). (12) I. L. Friemdman, Am. M i n e d , 34, 583 (1949).
(13) G . W. Morey and J. M. Hesselgesser, Amer. J . Sci., Bowen Volume, 343 (1952). (14) V. P. Butuzov and L. V. Briatov, "Soviet Physics-crystallography," 2 [51, 670 (1957). (Translated b y American Institute of Physics, p. 662.) (15) Phase Diagrams for Ceramists, Ed. b y E. M. Levin. H. F. McMurdie and F. P. Hall, Publ. b y American Ceramic Society, Columbus, Ohio, 1956, p. 259. The phase diagrams of reference 12 and other diagrams of interest to this work are a180 given in t h i s compendium. (16) W. S. Fyfe, A m . Mineral, 40, 520 (1955). (17) A. E'. Frederickson and J. E . Cox, ibid., 39, 886 (1954).
(1958).
August, 1961
SOLUBILITY O F
QUARTZUNDER HYDROTHERMAL
CONDITIONS
1397
Morey's dat ala show a-quartz to be stable over the region of our experiments and all of those in the literature which we have discussed. Since no glasses were observed in the quenched vessels we assume that the heavy liquid phase region was not entered. The vessels were either welded closure vessels of the sort described by Walker and BuehlerlB or modified BridgmanlQvessels. Their internal length was 12' and their internal diameter was 1'. The furnace was a nichrome wound ceramic tube long enough to avoid end effects when the vessel was placed in its center. This ceramic tube was surrounded by Vermiculite insulation and arranged in such a way that it could be rocked through about 30" to further aid in obtaining temperature equilibration within the autoclave. Temperature was controlled by a Leeds and Northrup Micromax Controller and r p ported temperatures are felt to be accurate within A3 Degree of fill as reported is felt to be accurate within &l%. Although the bomb volumes and solution volumes were known with a. greater precision at room temperature the bomb volume at operating tem erature was known with less certainty This is especialyy true of the laminated type design of the welded closure vessel. Concentration of the sodium hydroxide solutions used was determined by titration against potassium acid phthalate and was adjusted to0.500 f0.0015 N . Equilibrium time was estimated by determining apparent solubility as a function of time while all other variables were held constant. It would be expected that equilibrium time would be greatest a t the lower temperatures and preasures. Under these conditions i t was found IO that there waH essentially no change in apparent solubility 1 0K-l x IO-^ between two and six days. The minimum time employed T ' for the runs of this work was three days. Quenching was effected by plunging the vessels into a Fig. 1.-Log S us. 1 / T at several degrees of fill where the solvent was 0.50 N in KaOH a t room temperature. bucket of water arranged behind a barricade. The vessels were consequently brought from operating temperature to ambient in less than 5 minutes. Several runs were allowed 0 54 to cool in the 'urnace' over ~1 period of several hours and no difference in %eight loss of the quartz plates was observed. The plates were also examined under 50 X magnification 0 52 for evidence of growth hillocks, growth steps, precipitated foreign phases, etc. No evidence of growth was ever observed but on the contrary etch pits and other evidences of 0 50 dissolving always were found.
.
Results Figure 1 shows the dependence of solubility, S expressed as g./100 cc. of free volume of the autoclave on temperature. Figure 1 shows that over the temperature411 range investigated van? Hoff's relation is obeyed and that while the heat of solution is nearly independent of temperature, it is strongly dependent on degree of fill. The heats and entropies of solution found from Fig. 1 were AE, kcal./niole (in 0.51 m NaOH)
87% f 2.68'f 0.50 8 5 % j 1.82 f 0.50 80% f 1.03 3z 0.50
0 48
w 0 046
s
044
042
A S cal./"mole (in 0.51
m NaOH) 2.68 % 0.50/T X 10s 1.82 f 0.50/5" X IOs 1.03 =t0.50/T x 108
040
0 38 t
The entropies were calculated on the assumption that 4E/T = 45' since 4 A a t equilibrium is zero. It has bem shown that for small temperature differences the supersaturation can be considered R linear function of the temperature difference for crystal growth purposes.' Tn Fig. 2 made with the data of Fig. 1, we have wpressed the solubility S' as g./100 cc. of solution at rooin temperature which is nearly proportional to the weight fraction silica in solution. S is related t3 S' by the equation S' = S / d
(1)
where d is the degree of fill or, to a reasonable (18) A. C. Walker and E. Buehler, Sci. Monthly, 69, 148 (1949). (19) F. Gaschs, Ind. Rng. Chem., 48, 883 (1956).
P E R CENT F I L L .
Fig. 2.-Log S' us. per cent. fill a t several temperatures where the solvent was 0.50 N in NaOH at room temperature.
approximation in the one-fluid phase region, the solvent density or the reciprocal of the specific volume. I n accordance with the convention used in hydrothermal crystal growth studies, these solubilities were measured at constant molality (0.51 m) or nearly consbant weight fraction of NaOH. As can be seen from Fig. 2, while there may be some tendency for a departure from linearity a t the higher fills within experimental error log S' is a linear function of degree of fill. It might be noted that the van't Hoff relation would, of course, be obeyed equally well in terms
It. h.L44UDISE AND A. A. BALLMAN
1398
of S or S' with only the y-intercept of the log S 1,/T curves being affected by a change to S' and that in all of the figures of this paper equally good fits of the experimental data were found when either S or X' was plotted. Discussion Dependence of Fill.-According to Franck8 the solution of quartz in pure water may be represented by the reaction 77s.
Q
+ n.Hp@
SiOs.nH20
( 2)
where Q is solid crystalline a quartz. Equation 2 assumes the silicic acids formed are essentially un-ionized. If n is non-integral equation 2 describes the formation of polysilicic acids. Since a t equilibrium AA = 0 we may write PSiOz.nHz0
=
PQ
-k
in water vapor obeys equation 4. The authors treated the solubility data of Kennedy in a variety of ways and found that the best fit was to equation 6 as can be seen in Fig. 3. While a reasonable fit to more sophisticated equations could be obtained, in no case was a better fit discovered. This would then indicate that the H z O S i 0 2 interactions in this system are weak. Unfortunately the association factor, n, cannot be calculated from a plot of the form of Fig. 3. -0.40~
(3)
nPHzO
Vol. 65
I
I
I
I
I
I
I
I
where bsIoz" ~ ~PQ, 0 ,etc., are the chemical potentials (of SiOs.nH20, quartz' etc. Franck has shown that equation 3 is consistent with either of the two well-known equations for solubility interactions involving virial expansions 1
log xz = a log -
+b
( 4)
or 1 l0gXz = c -V
+s,
1
+q
(5 )
which as a first approximation may be written log S' =
ccl + g
( 6)
- 1 201 I 1 I 48 52 56 60 64 68 72 76 where a, b , c, f and g are constants, XT is the P E R C E N T FILL, analytically determined mole fraction of the dissolved substance and v is the specific volume of the Fig. 3.-Log S' us. per cent. fill a t 460 and 380" in pure water (made with the solubility data of Kennedy"). solvent. Equation 4 is derived for the case of large solIn a similar manner as can be seen in Fig. 2 the vent-solute interactions and equation 5 for small solubility data indicate weak interaction in the interactions and both equations are strictly appli- H20-SiO2-?Jaz0 system. The data of Butuzov cable only in dilute solutions. However, as Franck8 and Briatov14 which we have plotted in Fig. 4 has shown and this work indicates they are ap- indicate weak interactions in the system HzOparently valid for the concentration ranges ob- SiOz-NazCOS. taining in Si02 solutions in water and dilute bases. Franck also pointed out that a more exact form of Equation (4) for quartz might be
where K is the association constant for equation 2 VQis the molar volume of solid quartz, V is the molar volume of the fluid phase, and P is the total pressure. Franck tested this form with the data of Kennedyll in the system Si02-H20. For this purpose the. association value, n, of equation 2 and the association constant, K , were adapted to the measured values. Franck deduced the value of n to be 2 which suggests Si(OH)4 as the principal species present in pure water. However, the fit of Kennedy's solubility data to equation 7 as found by Franck a t densities greater than 0.30 was not entirely satisfactory. h40sebachg neglected the term VQPIRT and is reported to have obtained a $,ornewhat better fit and to have again deduced n t o be 2. Jasmund2" reports that the solubility of quartz (20) K. Jasmrind. He&lhergPr (1952).
Be&.
Mznernlog
Petrogr., 3, 380
I
044L 68
I
I
72
76
I
1
80
84
PER CENT
A
I
88
I
I 92
I
I
96
FILL.
Fig. 4.-Log 8' us. per cent. fill a t 400' where the solvent was 57, NazC@a a t room temperature (made with the solubility data of Butuzov and BriatovI4)).
August, 1961
SOLUBILITY O F QUAHTZ U S D E l t
The fact that a similar dependence of solubility on density is found both in pure water and in the basic systems is a t first sight surprising. One might assume, for instance, that the generalized reaction describing the interaction of quartz with (OH)- in aqueous solution would be Q
+ ( 2 a - 4)(OH)-
Si0a(2a-4)-
+ (a - 2)Hz0 (8)
where a is greater than two. The value. a, like that of n in equation 2 may be non-integral but must be a small rational fraction for the case of the formation of disilicates and anionic species of higher catenation. Equation 8 assumes a complete ionization of the sodium silicates formed. While the ionization is surely not complete, it is probably reasonable to assume near completeness in solntions of the alkalinity studied in this work. The solution of quartz in aqueous NaOH obviously involves equation 2 and equation 8. However, since the loss of weight of quartz plates will not allow the separate determination of the concentrations of SiOz.nHnOand SiOa(2a-4)- we may not directly apply a treatment of the data analogous to Franck's. However, if we examine (see Figs. 2, 3 and 4) the density dependence of solubility in XaOH, Na2C03 and pure water we may deduce several generalizations. First we see that a t nearly comparable conditions the solubility in the basic media is about an order of magnitude greater than in pure water. Consequently, SiOa(2a-4)must be the principal species present in Na2C03or NaOH. Next we see that a t nearly comparable conditions the solubility in (COY)- is somewhat less than in (OH)-. If me consider the equilibrium (CO,)"
+ HLO
(HC0a)- t (OH)-
(9)
and remember that a t 25' the concentration of (OH)- in a 0.5 m Na2C03 solution as calculated from the hydrolysis constant for equation 9 is about 0.01 m then it is not surprising that the solubility in (COa)=solutions is less than in (OH) solutions since most of the solubility occurs because of equation 8. Finally we should examine the slope of the solubility density curves of Figs. 2, 3 and 4, that is, the values of ( blog S ' ) / ( byo fill)^ = a. For nearly comparable conditions C Y H ~ O> CrNaOH > L Y N ~ ~ C QThe ~. relatively large positive value for CYH~Ois commensurate with equation 2 and the treatment which leads to equation 6. The values of C Y N ~ O Hand ~ N ~ , are c o ~of course determined both by equations 2 and 3. The overall equation in a basic solution can, therefore, be represented as 2Q
+ nHzO + (2a - @(OH)SiOz.nHzO + SiO,(2"-4)- + (a - 2)HzO
(10)
Therefore, provided n > (a - 2 ) , ffNaOH and ffNa&Oa mould be expected to be positive. Franck,* Mosebachg and BradyZ1have all determined n to be equal to two. Consequently for CYNaOH > L Y N ~ ~ C aON~a,O H < aNanCO, < 4. It will be shown below that a N a O H = 7/3 and aNa2COs = 3. Dependence on Base Concentration.-Data on 121) E L. Brad?, J f h g s Chem , 67, 706 (1953)
HYDROTHEKMAL ' & ~ D
I ~ T ~ ~ s
1399
the dependence of solubility on base concentration are somewhat limited in the literature. The ratio SiOz/NazO was plotted as a function of Na2,O concentration for hydroxide12 a t 55% fill and carbonatel4 a t 80% fill. I n (OH)- a t 450' and in (COS)- a t 350" the ratio is essentially constant suggesting that the concentration of SiOz(za- 4)- is essentially limited only by the available (OH)-. The ratio SiOz/Na20 is about 1, in hydroxide and one in carbonate. These values for the ratios suggest (SiO8)- in carbonate solutions and (SiaOr)-* in the hydroxide solutions as the predominant species and leads from Equation (10) to values of aNarCOa = 3 and a N a O H = 7,'3. Dependence on Temperature.-As we have seen in the NazO-SiOz-H20 system (Fig. 1) the van% Hoff equation describes the temperature dependence. Likewise under generally similar conditions in the Si02-Hz012and Si0z-Hz0-Na2C0314 systems the van't Hoff equation is obeyed. The heats of solutions and entropies found were A E N ~ ~ c=o 3.42 ~ f 1.0 kcal./mole A S N ~ ~ C=O3.42 ~ zk LO/T X lo3 Gal./" mole
(80% fill, in 5 wt.
yo Na2C03, dependent on fill)
AEH~o= 8.8 i 1.0 kcal./mole A S H ~ O= 8.8 i l.O/T X lo3 tal./" mole
(71.5% fill but independent of fill within experimental error). The lack of dependence of AR on T in all these systems implies that over the temperature intervals st idied ACv of each of the systems was small or the change was balanced by other effects. The dependence of AE on fill in the basic solutions but not in the pure water and the relative values of AE in the three systems can be explained by a con. sideration of the solution process in a stepwise manner, The heat of solution in a constant volume process is a measure of the change in the internal energy of the system and may be considered t o be composed of two parts: the first, an endothermic reaction as the solid silica goes to a gaseous state, and the second, an exothermic reaction as the gaseous silica reacts with the solution. The first part of the process will require the same energy input regardless of the solvent used; the second part, however, will release energy dependent on the reaction of the gaseous silica in combining with a particular solvent. In the case of silica reacting with pure water, part two can produce a hydrated or hydrolyzed silica molecule of one sort or another. For silica reacting with sodium hydroxide or sodium carbonate, however, part two can produce a hydrated silica molecule or, as we have seen, any one of a variety of silicate complexes. Since the second part is an exothermic reaction and thus has negative value relative to the system, the greater the reaction in part two, the smaller the over-all value for AE. This is demonstrated in a comparison of the SiOz-HzO and the SiOs-HzO-;?;azO systems where AE for the sodium hydroxide is about l/lo that in the pure water system indicating a greater release of energy in part two and thus a lower value for LE. In sodium carbonatr the over-all heat of solution is only obtained when the
1400
H. W.GOLDSTEIN, P. K.WALSHA N D D. WHITE
endothermic heat, of hydrolysis of equation ‘3 is added to parts one and two. Consequently, AE for the solutiori process in carbonate solution will be greater than in hydroxide. The first part of the process is density iridepeadcrlt while the second part is apparently more
Vol. 65
strongly density dependent when canform. Acknowledgments.-‘rhe authors \vi& to thank G. T. Kohman and M. Tannenbaum for advice arid elicouragement in this work. R. A. L. also wishes to acknomledge discussions with E. U. Franck and R. Mosebach.
RA:RE EARTHS. I. VAPORIZATIOS OF Ls20a AND Sd,03: DISSOCISTION ENERGIES OF G-4SEOUS La0 AND NdOl B Y HAROLD IT.GOLDSTEIN, PATRICK 3.JfrALSH
.4SD
DAVID WHITE
Cryogenic Luborutory, Department of Chemistry, ?’he Ohio State University, Columbus, Ohio Recehed March 19. 1981
The vaporization of the rare earth oxides, La208 and Ndz03, a t elevated temperatures has been studied by a combination of Knudsen effuaiion and mass spectrometric techniques. Both vaporize almost stoichiometrically to the monoxide and oxygen. The heizta of formation, AHoa, in kcal. mole-’, and dissociation energies, Doo, in e.v. are: Lao, -29.8 2~ 4,8.08 f 0.2; NdO, -30.0 f 6, 7.18 f 0.3, respectively.
Introduction The question of the identity and stability of the vapor species formed in lanthanon-oxygen systems has been of considerable interest for many years and has becoime increasingly important as rare earth compounds have become more readily available. The existence of gaseous monoxides of several of the rare earth elements has been inferred from stellar and arc spectraza and L a 0 has been observed in the mass spectrometer.2b Only in the latter invwtigation has a dissociation energy been determined with an uncertainty of less than one e.v. Dissociation energies estimated for other rare earth monoxides by Birge-Sponer3 or modified Birge-Sponer4 extrapolations of the observed vibrational levels have such large uncertainties connected with them ( A l - 3 e.v.) that the thermodynamic properties of chemical systems a t elevated temperatures containing the elements of these compounds cannot be determined with sufficient accuracy for most purposes. The positive identification of the monoxides or other simple gaseous oxides of the rare earth metals and the determination of their thermodynamic properties are also of considerable interest from the chemical standpoint. The heats of formation of the solid sesquioxides of these metals are unusually large6; in terms of enthalpy of formation per oxygen atom, they are equaled only by Li20 and some of the Group I1 oxides.6 It is possible that the origin of this strong bonding energy can be inferred from the properties of the gaseous species formed on vaporization of the sesquioxides. The gaseous (1) This work wa3 supported by the Air Force Office of Scientific Research. (2s) B. Rosen, “Donnees Spectroscopiques Concernant les Molecules Diatomiques,” Herman et Cie, Paris, 1951. (b) U‘. A. Chupkn, 11. G . Inghrsm a n d R. F. Porter, J . Chem. Phys., 24, 792 (1956). (3) G. Herzberg, ‘Molecular Spectra and Molecular Structure. I Spectra of Diatomic Molecules.” D. Van Nostrand Co., Inc., Princeton, N. J.. 1957. (4) A. G . Gaydon, “Dissociation Energies and Spectra of Diatomic hloiecules.” Chapman and Hall, Ltd., London, 1953. (5) E. J. Huber, Jr., E. L. Head a n d C. E. Holley, Jr., J . Phys. ChPm., 64, 1708 (19CO) and earlier papers. (C) J. P. (‘oughlin, r.S Bur. Mines Bull., 542 (19.54).
oxides of the rare earths (in particular the monoxides) constitute a unique set of compounds in the sense that the electronic structure of the elements suggests that the chemical bonding should be nearly the same for all. It is, however, well known that there exist large variations in the binding energies4 of these compounds. Before any generalization can be made concerning these variations, it is necessary to establish quantitatively their magnitude In the present paper the dissociation energies of gaseous L a 0 and KdO are determined through Knudsen effusion and mass spectrometric measurements of the dissociation pressures of the corresponding solid sesquioxides. This is the first paper of a series concerned with the determination of the thermodynamic properties of gaseous rare earth oxides. Experimental Materials.-The lanthanum and neodymium oxides were the same materials previously used for heat capacity measurements.’ They were dried before use by firing a t 1000O in air. Apparatus and Procedure.-The effusion experiments were carried out in vacuum induction furnaces of the type described by Hoch and Johnston.* Tantalum and tungsten crucibles, machined bv Fanstcel Metallurgical Company, were used as Knudsen cells. These were right circular cylinders I/*‘‘ 0.d. by ”4’’ high; the tantalum crucibles were S / g “ i.d., the tungsten l/*‘‘. Each was covered with a thick lid of the same material machined to b t inside the crucible (with a tolerance of 0.002”) to a depth of l/Jz”. A 1/168 diameter hole, drilled axially through the lid, served as the effusion orifice. In the calculations, dimensions measured to f 0.001 ” and corrected for thermal erpansiong werc used. Temperatures were measured by Biphting directly into the effusion orifice, through an optical flat a t the top of the furnace. with an XRS calibrated optical pvrometer or with one that had been compared with it under the conditions of these experiments. With an appropriate window correction, the temperature so measured equals the “black (7) H. W. Goldstein, E. F. Neilson, P. i T.Walsh a n d D. White, J . Phys. Chem., 6 3 , 144R (19.59). (8) M. Hoch and H. L. Johnston, J . A m . Chem. Soc.. 7 6 , 4833 (1954). (9) H. A. Jonesand I. Langmuir, Gen. Elec. Rev., 30, 351 (1927); W. J. W. Edwards, R. Speiser and H. L. Johnston. J . A p p l . Phys., 22. 421 (1951). Ta.
