P. CH~NEBAULT AND A. SCHURENKAMPER
2300
The Measurement of Small Surface Areas by the B.E.T. Adsorption Method’
by P. Chsnebault Ddpartement de M&tallurgie, Service de Chimie des Solides, Seciwn des Combustibles Ceramiques, Chemin des bfartyrs, Grenoble, Isdre, France
and A. Schurenkamper Service de MMdtallurgie, Euratom, C C R Ispra
(Received January 18, 1966)
It is possible to measure surface areas of the order of a few square centimeters by using a mixture of natural xenon and 133Xeas the adsorbate. The vapor tension of xenon at the temperature of liquid nitrogen is equal to 2.15 X mm. The surface measured for glass is equal to the geometrical surface of the samples. I n the case of sintered uranium dioxide samples of different densities, the lower the density, the greater the surface area.
Introduction An important technological problem arising from the use of sintered uranium dioxide as a nuclear fuel is the migration and escape of krypton and xenon which are formed in situ as the result of fission.2 One mechanism governing the escape of these gases from UOz is volume diffusion. However, direct measurements of fission gas escape give only an apparent diffusion coefficient D’which is related to the volume diffusion coefficient D by the equation 2
D’
=
l/~(%)
D
where S is the specific surface area and V is the true volume of the sample. There is usually a large scatter in the results of such measurements and it is suspected that this may result from variations in S; thus it is desirable to know the actual specific surface of each microsample, the geometrical area of which is about 0.25 cni.2. This paper describes a method for measuring small surface areas with a sensitivity near 0.1 cm.2. 1. Choice of the Conditions of Measurement The method used is based on the application of the B.E.T. equation3to the isothermal adsorption of xenon. This equation
where p is adsorbate pressure, po is adsorbate vapor pressure, V , is adsorbed volume, V , is monomolecular layer volume, and C is a constant related to heats of adsorption and liquefaction, is applicable in the range of relative pressures ( p / p o ) from 0.05 to 0.35 and experimental conditions must be chosen to meet this requirement. A further limitation is that the surface area to be measured is sniall, so that the total volume of adsorbed gas is small. For measuring the gas volume adsorbed on a surface of 1 cm.2,it is necessary to use an adsorbate whose pressure is approximately torr a t the adsorption temperature and to reproducibly measure pressure variations of torr. Pressure Measurement. Pressures are measured by the y-activity of a radioactive isotope of the gas or vapor chosen as the adsorbate. The number of yphotons emitted per second is proportional to the number of molecules present; thus, it is also directly proportional to the pressure. If the radioactive properties of the adsorbate are suitable (half-life not too short, specific activity high enough) pressure measurements with a precision of 1% are quite feasible i n the range torr. (1) Work performed under contract No. 031.60.10 RDF between European Atomic Energy Community and the Commissariat B 1’Energie Atomique. ( 2 ) (a) A. H. Booth and G. T . Rymer, CRDC-720, August 1958; (b) W. B. Cottrell, et al., ORNL-2935, September 1960. (3) S. Brunauer, P. H. Emmett, and E. Teller, J . Am. Chem. SOC.,
60, 309 (1938).
T h e Journal of Physical Chemistry
MEASUREMENT OF SMALL SURFACE AREASBY
THE
B.E.T. ,METHOD
It should be noted that what is actually determined by this method is the partial pressure of a radioactive isotope which, if isotopic effects are negligible, is equal to the partial pressure of the adsorbate. Choice of the Adsorbate. Adsorption measurements a t 24" have been conducted with mercury and with bromonaphthalene activated in a neutron flux. Adsorption was followed by the y-activity of the isotopes z03Hgand **Br. The quantity of mercury adsorbed on the surface of glass or UOZ a t pressures lower than 2 X lov3torr represented only about 1% of the quantity necessary for the formation of a monomolecular layer; thus mercury vapor could not be used as an adsorbate. Tests using bromonaphthalene indicated a chemical reaction with UOZ. Bromonaphthalene is partially decomposed under neutron irradiation, and it is likely that the bromine formed reacts with UOz. On the other hand, adsorption isotherms a t 77.5"K. with a mixture of natural xenon and xenon-133 were found to be type I1 of B r ~ n a u e r . ~Techniques and results relativv to the xenon method are described in the following sections.
11. Description of the Adsorption Apparatus Figure 1 shows a sketch of the apparatus used for surface area moasurement ; it includes a vacuum system capable of obtaining a pressure 5 X lov6 torr, connections for introducing both natural xenon and xenon-133, a IIcLeod gauge, a y-counting system, an adsorption section (volume VI)with a measuring bulb (volume Vz), a mercury trap, and a xenon trap. The xenon trap contains a few activated charcoal particles able to adsorb (at liquid nitrogen temperature) the total quantity of xenon in the adsorption section of the apparatus. This trap allows one to introduce or withdraw a given quantity of xenon from the adsorption section as required. The measuring bulb (Figure 1) was designed so that the surface on which adsorption occurs is not sensitive to variations of the liquid nitrogen level. Automatic regulation controls that level to *2 mm. 111. Procedure Preparation of the Adsorbate. A quartz bulb furnished with a fragile extension (see Figure l) containing a jO-mg. uranium chip is sealed under high vacuum. After a 120-hr. irradiation in a neutron flux of 5 X 1012 n. cm.-2 set.-' and after a decay time of some days, the uranium is melted by high frequency induction, the sample itself being used as the susceptor, to release the fission gases; the only radioactive isotope present in a measurable quantity is Isaxe. The bulb is put in the measuring apparatus, where it can be broken
2301
MEASURING
BULB
Figure 1. Apparatus for surface area measurements.
with a magnetic hammer and the 133Xemixed with the natural xenon. The activity of 133Xecan be adjusted a t such a level that the mixture can be used during the second and third weeks after irradiation. In operation, the apparatus is first carefully degassed, then natural xenon (99.94% Xe supplied by the Air Liquide Co.) is introduced a t about 5 X torr and the pressure is read with the IIcLeod gauge. The bulb containing 133Xeis then broken and pressure is calibrated in terms of the activity recorded by the counting system. The quantity of 133Xeis sufficiently small that the pressure measured by the IIcLeod gauge does not change. The volume of the apparatus is about 700 at 5 X torr; this corresponds to 4.2 X ~ m . ~ (NTP) of gas, a quantity capable of covering 250 cm.* with a monomolecular layer. Introduction of a Mercury T r a p . The vapor pressure of mercury is 2 X low3torr a t 24". The partial pressure of mercury vapor in the apparatus is therefore of the same order of magnitude as the partial pressure of xenon. When the measuring bulb is cooled with liquid nitrogen, mercury in the AIcLeod gauge evaporates and condenses on the walls of the measuring bulb. A trap cooled to -80" is therefore placed between the I I c Leod gauge and the adsorption section. During cooling of this trap, the counting device immediately records a 5-15% increase in the quantity of xenon in the adsorption section of the apparatus. This increase results from the equilibration of pressure on both sides of the trap and moreover it is possible for the xenon to be entrained by the mercury. Measurement of Adsorbed Volume. The calibration of pressure us. activity having been effected, and the mercury trap cooled to -80", a quantity VI of the natural xenon-xenon-133 gas mixture is introduced into the adsorption section. The bulb is then cooled to Volume 69, Number 7
J u l y 1966
2302
P. CHENEBAULT AND A. SCHURENKAMPER
liquid nitrogen temperature and the adsorption is followed until an equilibrium pressure, p , is obtained, as indicated by the activity recorder. After successive introductions of the gas mixture, a series of equilibrium states is obtained which allows the adsorption isotherm of xenon on the measuring bulb to be determined. Then the sample is introduced and the adsorption isotherm for the bulb plus sample is determined in the same way. The adsorption isotherm for the sample alone is given by the difference between the two experiments. Before plotting isotherms, the phenomenon of thermal transpiration must be accounted for. Values of the corrected pressure ( p * ) given by Podgurski and Davis4 have been used.
IV. Results Adsorption Isotherms-Values
o i PO. Adsorption isotherms for the glass bulb and for a sample of sintered UOz were determined by plotting the adsorbed volume V aas a function of the equilibrium xenon pressure p * after correction for the thermal transpiration effect as shown in Figures 2 and 3. The isotherms show no hysteresis effects, but for a sample with a density of
9.92 g./cc. (theoretical density of UOZ is 10.96) there is an important amount of open porosity (about 5% by volume) and equilibrium is slowly obtained; in this case it is difficult to distinguish between a false equilibrium and a hysteresis effect. The values obtained for po (vapor tension of xenon a t liquid nitrogen temperature) are slightly different in the curves of Figures 2 and 3; this could result from a variation of the liquid nitrogen temperature. The value of po has been determined by a series of measurements made with measuring bulbs having an internal diameter of 3.2 or 3.3 mm. and also with a 20cm. long glass tube of 3.3-mm. internal diameter; this diameter was selected in order to have similar thermal transpiration correction factors each time. The agreement between results obtained with the tube and with the bulbs is good and gives confidence in the thermal transpiration correction factor applied to the measuring bulbs. The result of these measurements torr. is p o = 2.15 f 0.1 X Adsorption Measurements. Figure 4 shows results of four different measurements with the same glass
Figure 2.
The Journal of Physical Chemistry
(4) H. H. Podgurski and F. N. Davis, J . Phys. Chem., 6 5 , 1343 (1961).
MEASUREMEKT OF SMALL SURFACE AREASBY
THE
B.E.T. METHOD
2303
Table I : Results of Surface Area Measurements on Glass and UOz
V , (NTP), cm.8
C
Measuring bulb 24 Measuring bulb glass sample about 1 cm.2 21.5 RIeasuring UOU:9 . 9 2 g./cc., fragment 68 mg. 100 100 Rleasuring UO2: 10 g./cc., fragment 25 mg. Measuring U02: 1 0 . 2 g./cc., cylinder 70 mg. 13 Measuring UOZ: 1 0 . 5 g./cc., parallelopiped 167 mg. 22
+
I
5.95 x 7.17 x 2.16 x 1.54 X 3.08 x
0.6
x
10-6 10-6
10-4
Surface area, cm.2
4 4.8 14.5
1.0 10-6 10-5
2.2 0.4
Geometric surface area, cm.2
-4.1 -5.1 2 1 8.3 1
II
40
Figure 5. 5
Figures 6, 7, and 8 show the B.E.T. curves obtained for the xenon adsorption on glass (bulb and sample) and on uranium dioxide samples. Table I summarizes the values of C and V, and the surface areas S calculated from these curves.
V. Discussion of Results Precision and Sensitivity of
Figure 4.
bulb and of two measurements with a glass sample having a geometric surface area of about 1 cmS2. For each sample of U 0 2 the adsorption was determined as the difference between the gas volume adsorbed on the “bulb U02” and on the “bulb” alone. Results are shown in Figure 5 . Calculation of Surface Area. The parameter p * / V,(p, - p * ) was plotted as a function of p * / p , to obtain values for the monomolecular layer volume, V,, and the constant C in the B.E.T. equation (2). Taking the value for the atomic cross section of xenon a t liquid nitrogen temperature as u = 25 A.2 (the mean value proposed in the literature5), the surface area is given by the relation S = 6.7 X 104V,, when S is . ~ expressed as cm.2and V , as ~ m(NTP).
+
the Measurements. Apart from any systematic error caused by calibration of the AIcLeod gauge, pressures measured from the activity of 133Xeare known with a precision of f 1%. The volumes V1 and Vz calibrated with mercury are known with the same precision. This results in a total uncertainty of about h 7 y 0 for the value of the first adsorbed volume. B.E.T. curves used for determining the surface area (Figures 6-8) are obtained from the difference between two adsorption curves. Not enough results are available to have a statistical analysis of the resulting errors. Also, unknown experimental variations may result from variations in bulb surface area during an experiment (by dust accumulation, for example) from temperature uncertainties resulting from the low rate ( 5 ) W. A. Cannon, A’atuTe, 197, 1000 (1963).
Volume 69, Number 7
J u l y 1066
P. CHENEBAULT AND A.
2304
SCHURENKAMPER
Figure 7 . Figure 6.
p. V d p.-c]
of thermal equilibration under the experimental conditions used6 or from variations in po resulting from changes in the liquid nitrogen temperature. However, the starting and final (desorbed) volumes of xenon always were found equal within &3%, the experimental B.E.T. curves (Figures 6, 7 , and 8) are linear, distinctly different adsorption curves were found for the bulb alone and the bulb plus a sample of known surface area of about 0.4 cm.2, and the measured and geometrical surface areas of fully dense UOz and glass samples agree within hO.1 cm.2. As a result we believe that the reported measurements are reliable within about f 10% for a 1-cmS2sample.
(0.
5a
Results The values obtained from the measuring bulb and for the glass sample show that the B.E.T. surface area obtained is practically equal to the geometrical surface area. However, for UOZ we find that the surface area is much larger than the geometrical area for low density samples. This presumably results from the presence of open porosity in the sintered UOZ. The The Journal of Ph~8icalchemistry
Figure 8.
(6) C. Moreau, Rapport CEA No. 1878, 1960.
ENTHALPY OF FORMATION OF YTTRIUMTRIFLUORIDE
values obtained for the constant C in the B.E.T. equation are larger for the lower density UOz samples. This may indicate that heat of adsorption for the first layer of xenon is higher when densities are low, which is in agreement with Smith's results' for krypton adsorption on UOZ.
Conclusions It is possible to measure small surface areas of about 1 cm.2with a precision of h O . 1 cm.2 using a mixture of natural xenon and xenon-133. The xenon vapor pressure a t liquid nitrogen temperature was found to be 2.15 torr after a thermal transpiration correction. X The surface area measured for glass samples is equal
Fluorine Bomb Calorimetry, XI.
2305
to the geometrical surface area. For sintered UOe, the B.E.T. surface area is much larger than the geometrical surface area, and the ratio between these increases as the density decreases. The described technique makes it possible for one to measure the surface areas of high activity samples (irradiated U0z for instance).
Acknowledgment. The authors thank 1Iiss Y. Carteret (CEN Saclay) very much for her kind collaboration. They are grateful for the critical comments of their colleagues of their laboratory (CEN Grenoble). (7) T. Smith, NAA-SR-53, October 1960, p. 19.
The Enthalpy of Formation
of Yttrium Trifluoridel
by Edgars Rudzitis, Harold M. Feder, and Ward N. Hubbard Chemical Engineering Division, Argonne National Laboratory, Argonne, Illinois
(Received January 19, 1965)
The energy of formation of yttrium trifluoride was measured by direct combination of the elements in a bomb calorimeter. The standard enthalpy and Gibbs free energy of formation a t 298.15"K. were determined to be -410.7 f 0.8 and -393.6 f 1.0 kcal. mole-', respectively .
This work, which is part of a series of fluorine bomb calorimetric studies, was prompted by the unavailability of thermochemical data on YF3, an important intermediate in the production of metallic yt,trium. The combustion method employed was developed earlier.2 An yttrium metal sample was suspended in a fluorine-filled combustion bomb and ignited electrically. The interior surfaces of the bomb werc protected by a tamped liner of YF3. Extensive experimentation showed that adequate combustion of yttrium in fluorine could be achieved only if the temperature of the burning metal was well in excess of its melting point (1509") and high enough to volatilize the reaction product YFa (b.p. -2300").
Experimental Materials. (a) Y . An yttrium ingot (Lunex Co., nuclear grade) was rolled to a sheet approximately 1 mm. thick. Chemical and spectrochemical analysis showed the following significant impurities (in p.p.m.) : Ta, 2500; 0, 1390; C, 188; H, 42. If the impurities are assumed to be present as the chemical species, Ta, Y203, YCZ, and YH2, the calculated content of elemental yttrium in the sample is 99.37 mole yG. (1) Work performed at Argonne National Laboratory, operated by the University of Chicago under the auspices of the U. S. Atomic Energy Commission, Contract No. W-31-109-eng-38. (2) E. Rudzitis, H. M. Feder, and W. N. Hubbard, J . Phys. Chem., 68, 2978 (1964).
Volume 69, A'umber 7
J u l y 1965
