the first column. The retention of strontium-90 was calculated from the yttrium-90 measured in the final product. The sum of the two quantities of strontium40 agreed, for each sample, with the known quantity of this activity introduced a t the start of the analysis. It may be seen from Table I11 that there is no loss of strontium-90, if the solution passed through the resin column is less than about 0.5V in chloride or nitrate ion or 1.OJf in perchlorate ion. Radiochemical Punty of Product. The radiochemical purity of the yttrium40 from analyses of fissionproduct samples Ivas determined by ?-ray spectruni analysis and study of t’he decay rate of the samples. Samples obtained froiii an analysis of 11-day-old fission products showed no signs of foreign activity. However, during development of the procedure, a number of contaminants \yere observed in the vttriuni-90 activity. An attempt to shorten the procedure by elimination of the hydroside step resulted in contamination of the product by about 0.01% each of the zirconium-95 and ruthenium103 actiJ.it#iesn.hich were present in the
sample at the time of analysis. Failure to evaporate the sample to perchloric acid resulted in contamination of the product by about 0.01% of the possible iodine-131 activity. On several occasions about 1% of the product activity was due to iodine-132 which had appaiently grown in from tellurium-132 adsorbed on the cation resin. The short half life (2.3 hours) of iodine-132 renders this contaminant harmless, if sample is not counted earlier than about 12 hours after separation. Analysis of Fission Products. The precision and accuracy of the strontium-90 procedure were tested by analyses for strontium-90 and molybdenum-99 performed on a series of samples of uranium-235 which had been irradiated with thermal neutrons. The results (Table IV) indicate that the procedure is suitable for the determination of strontium-90 in fission for products. The value of 6.08 X D(SrgO)/A(Mogg) is in reasonable agreement with the value 6.26 X 10-4 obtained previously by a conventional strontium-90 procedure ( 2 ) . The corresponding values for the fission yield of
strontium-90 are 5.45% and 5.61%, respectively. LITERATURE CITED
(1) Glendenin, L. E. Paper 236, Sational Nuclear Energy deries, Div. IV, Vol. 9, hlcGraw-Hill, New York, 1951. (2) Kleinberg, Jacob, et al., U’. S. Atomic Energy Comm.,. ReDt. - LA-1721,2nd ed. (August 1958). (3) Martell, E. A., “Chicago Sunshine Method. Absolute Assav of Srwin Biological Materials, Soils,“ Waters, and Air Filters,” Enrico Fermi Institute for Nuclear Studies, University of Chicago, May 1956. (4) Salutsky, M. L., Kirby, H. IT., ANAL. CHERT. 27, 567 (1955). (5) Smith, H. L., Hoffman, D. C., J . Inorg. and Nuclear Chem. 3, 243 (1956). (6) Stanley, C. TT., Kruger, P., “Determination of SrgOActivity in Katers with Ion Exchange Concentration,” Pittsburgh Conference on Analytical Chemistry, Pittsburgh, Pa., Feb. 29, 1956. ( 7 ) Sunderman, D. S . , Rleinke, IT. W., ANAL.CHEM.29, 1578 (1957). RECEIVEDfor review May 31, 1998. Accepted December 15, 1958. Division of Analytical Chemistry, Symposium on Radiochemical Analysis, 133rd Meeting, ACS, San Francisco, Calif., April 1958. Work done under the auspices of the U.S. Atomic Energy Commission.
Particle Size Analysis by Gamma-Ray Absorption CHARLES
P. ROSS
Savannah River Laboratory, E. I. du Pont d e Nemours & ,Accurate particle size analyses of uranium oxide were obtained by a y-ray absorption method. As particles settled from a uniform suspension, their concentration a t a fixed depth was continually determined by measuring the transmittance of yrays from an americium-241 source. The data were readily converted to a standard curve of particle fractions under a certain size vs. the diameter obtained from Stokes’ law. For the uranium oxide particles that were tested, the absorption of y-rays depended only on the mass of suspended material. The fraction undersize was determined with a 95% confidence limit of about A 0 . 0 4 , and the average diameter according to Stokes’ law was determined to about A0.3 micron. The method can b e used for any subsieve particles having an absorption coefficient significantly different from that of the suspending liquid.
M
practical methods of particle size analysis depend on the fact that the size and density of particles govern the settling velocity in a fluid. Many methods have been described (1, 2, 5 , 7 ) . One of the most accurate
Co., Inc.,
Aiken, S. C.
consists of drying and weighing samples that are drawn from a certain distance below the surface at various times after settling begins from a uniform suspension. If the sampling procedure r e r e replaced by a method of continuous measurement which would not disturb the suspension, the speed and accuracy of the particle size analysis mould be vastly improved. Such a method, based on the attenuation of an x-ray beam by the suspended particles, was briefly described in 1954 ( 1 ) . S o data were given, but because the method appeared to be fast and reliable, it was investigated a t the Savannah River Laboratory for the particle size analysis of high density material. -4y-ray source was substituted for an x-ray tube, because a source is more compact and it is stable over longer periods of time. The attenuation of gamma radiation has previously been used to determine the concentration of heavy metals in solution and in suspension (3,8 ) .
as expressed by the following equation
( 4 ): where
Zro
=
Z
=
p/p =
C
=
2
=
The fraction of the particles that are of a size that will not settle from the surface to the depth of the beam in time t is gil en by
where
Ct
=
C,
=
OST
THEORY
The absorption of a monoenergetic gamma beam by a suspension of particles of a given chemical composition in a cell should obey the Beer-Lambert law
intensity of gamma beam emerging from cell with no particles in suspension intensity of gamma beam emerging from cell with particles in suspension mass absorption coefficient of particles for the energy of the beam, sq. em. per gram concentration of particles, gram per cc. path length of cell, cm.
concentration of particles a t time t , gram per cc. concentration of particles in initial uniform suspension, gram per cc.
Expressed in terms of gamma ray absorption, this fraction becomes VOL. 31, NO. 3, MARCH 1959
337
IO 9-
I
I
a - I~I,,,/I:(E)c~
I
-
I
-
P
76
-
0
-
SOLUTIONS
A PARTICLES A ,
MEDIAN DIA., 18,'. 90% BI WT. 3 10 2 3 p 0 PARTICLES B. MEDIAN DIA., 22p.90% BY WT. 16 l o 32p x = 10 Crn.
54-
A B S O M I O N COEFFICIENT 15 CONSTANT AND EQUAL
b where
I,
=
Io =
intensity of emerging gamma beam a t time t intensity of emerging gamma beam from initial uniform suspension
Thus a settling rate curve can be obtained without knowing the absorption coefficient or the concentration. In practice only the settling height must be known. The particle size is calculated from the settling height and time by Stokes' law.
where
V
settling velocity, em. per second acceleration of gravity, 980 cm. per P = density of particles, gram per cc. pl0 = density of liquid, gram per cc. d = diameter of partielr, em. '1 = viscosity of water, gram/cm.-sec. g
= =
Thus a size distribution curve can be obtained if the density of the particles and the density and viscosity of 6he liquid are known. EQUIPMENT
Figure 1is a photograph of the equipment used in the particle size studies. The four main units were: source of gamma radiation, cell containing suspension of particles, radiation detector, and count rate meter and recorder. The source of gamma radiation was a 0.lbcurie sample of americium-241 prepared a t the Savannah River Laboratory (6). This source of 60-k.e.v. energy and 470-year half life presented no great radiation hazards and was especially suitable in the analysis of particles of heavy metals or heavy metal compounds. The cell was a rectangular glass container 20 inches high having a path
338
ANALYTICAL CHEMISTRY
Figure 2. Absorption of gamma rays by uranium oxides
'
lZcL2-d 0.005
IO
0.010
0.015
CONCENTRATION OF URANIUM OXIDES,
length of 4 inches and a width slightly greater than 1 inch. Perfectly clean glass was the only material t o which the uranium oxides did not adhere strongly. The cell was made by shrinking glass tubing on a graphite mandrel of the required size. The cell was placed betmeen the Source and detector so that the gamma beam passed through the suspension about 4 inches above the bottom of the cell. The settling height was about 14 inches. The radiation detector was a sodium iodide-thallium scintillation crystal 1.5 inches in diameter and 0.5 inch thick, connected through a photomultiplier circuit to the count rate meter and recorder, which measured directly the intensity of the emerging gamma beam. The maximum beam height was Q/,s inch. The count rate with water in the cell but with no particles in suspension (I.) was about 2000 counts per second. PROCEDURE
The count rate meter and recorder were set so that the reading with only water in the path, I,, was near full scale. Then a lead sheet was placed between the source and detector while the suspension of particles was thoroughly shaken. The lead sheet was removed as the cell was returned to its position between the source and the detector. The instrument was allowed to record I continuously until the intensity reading again leveled off. It usually leveled off at a value slightly below I , in 10 to 15 minutes. Because of some extremely small particles in each sample, i t took several hours for the intensity to return to I,. Calibration experiments were performed to verify that Equations 1and 3 are valid for the system examined. These experiments were considered nec-
0.020
(1.
-
-
f
0025
UO,/CC
essary, because of the following uncertainties: Pure americium-241 is not strictly a monoenergetic source. In addition, there were present in the source small amounts of acOive impurities which contributed gamma energies other than the main energy. It was not known whether the size of the particles had any effect on the absorption coefficient. During most of the runs, slowly moving eddy currents nppearcd new the top oi the cr11 nfter mnst of the p:inirlcs had settled out. T h r ternpcrutiire rise of tlicsusprnsiim diiringn run wnsless than 0.2" C., Init this temperntiirc chnngc could urcuunt for the formntion of the rddies, nhicli nffrrtcd only the tinrst particle?. All NIIS w r e mnilis ut room ternprrnturv, 23 C . In order to ohtnin pcrkct disprrrnl of partirlrs, it is oftm desiral,le to add a sninll amount of n dispersing ngent to the suspension. In t h c present vsperiments. however. tlic i n t m x t ivns mnuily in thit h r h v i o r of the matrrinl in pure water, and no disperingngent wns usrd. RESULTS
Figure 2 is a plot of experimental data showing the dependence of ln(Iw/I) on C for a constant path length, 2. The data include experiments with aqueous uranyl nitrate solutions as well as with aqueous suspensions of the following fractions of a uranium oxide sample: Median Stokes' law diameter, 18 microns. 90% by weight, 3 to 23 microns Median Stokes' law diameter, 22 mjcrons. 90% by weight, 16 to 32 microns
i ::
so that wall effects will be negligible. The path length then must be a t least 1 inch, and for concentrations up to 0.02 gram per cc. should be as long as is practical-say 4 to 6 inches-so that the ratio I,/Io will be as large as possible. Particles of any composition can be analyzed by the technique described here, provided that the absorption coefficients of the particles and the SUSpending medium differ significantly. Other gamma ray sources or an x-ray machine may be used to provide radiation of the required energy. Particles which are soluble in water can be suspended in other liquids for the particle size analysis.
100
8
70
5 t
60
f
50
5
40
I
30 20
I 'f-l
TIME, ONE MINUTE DIVISIONS-
Figure 3.
Gamma ray transmittance of settling uranium oxides
Figure 4. Particle size distribution of uranium oxides
ACKNOWLEDGMENT
72
02 A
The oxide was principally uranium dioxide. It probably contained some uranium octaoxide and small amounts of lighter impurities. The measured density of the oxide was 9.6 grams per cc. Because the experimental data points are best fitted by a straight line, the absorption coefficient can be considered constant and Equations 1 and 3 are valid over the range of zero to 21.5 grams per liter (0 to about 0.2% by volume). The value of the absorption coefficient for these uranium oxides is about 5.9 sqxm. per gram. A typical settling curve for the uranium oxide particles, in which I is recorded against the time after settling begins, is given in Figure 3. The fraction undersize, C/Co, was calculated for various settling times from the value of I , and the values of I on this curve. The Stokes' law diameter of the particles was calculated from the settling time and height, and was plotted against the fraction undersize in a particle size distribution curve. Such a curve appears in Figure 4. The 95% confidence intervals for the fraction undersize a t various particle sizes are s h o m . These were obtained from the data from six runs on the same sample, and vary from k0.015 to h 0 . 0 5 9 . The experimental data, as taken from the recorder charts for these six runs, are given in Table I. The confidence interval a t the 50% size is fairly large, because the slope of the curve is steep a t this point. However, the 50% size itself can be determined to about 1 0 . 3 micron. These results were obtained with particles from 5 to 50 microns in diameter and concentrations from 8 to 20 grams per
The information contained in this paper was developed during the course of work under contract AT(07-2)-1 with the Atomic Energy Commission, whose permission to publish is gratefully acknowledged.
-------
Table 1.
Transmittance
% a t Various Times for Six Runs on the Same Sample I a t Various Times
0
Run 1 2 3 4 5 6
3
4
6
6
10
I,
min.
min.
min.
min.
min.
min.
min.
96.25 97 97 95.25 95.25 95.25
55 56 56 56 55.5 56
57.5 58 58 58 57.5 58
59 59 59 59 59 59
62 62 63 62 62 61
73 72.5 75 72 73 72.5
82.5 83 83.5 81.5 82 82
89 89 89 87.5 87.5 87.5
Run conditions Settling height Temperature P
2
34 cm. 23' C. 9 . 6 grams/cc.
liter (0.08 to 0.20% by volume). Microscopic examination of samples taken during some of the runs showed that there was very little agglomeration of the settling particles. The method is applicable to particles up to about 74 microns in diameter (200 mesh). For large particles of high density the settling height can be increased to ensure an adequate settling time. The largest particles in the suspension should settle from the surface to the gamma beam in no less than about 1 minute. During this time the initial turbulence dies out. It is generally agreed that hindered settling can be avoided by keeping the concentration of the suspended particles less than 0.2% by volume. This corresponds to about 2% by Keight, or 20 grams per liter for uranium oxides. As the concentration decreases the precision decreases, because the intensity term in Equation 3, ln(Iw/I), is subject to error as I approaches I,. The cell should be a t least 1inch wide,
LITERATURE CITED
( 1 ) Brown. J. F.. Skrebowski, J. K., Brit. J.' A p p l . Phys. Suppl.; NO. 3; 527 (1954). (2) Cadle, R. D., "Particle Size Deter\
,
mination," Interscience, New York,
1955. (3) Furman, S. C., U. S. Atomic Energy Comm., Rept. KAPL-1648 (Jan. 8, 1957). (4) Glasstone, S., "Textbook of Physical Chemistry," p. 581, Van Nostrand, New York, 1946. (5) Lapple, C. E., "Fluid and Particle Mechanics," p. 272, University of Delaware, Newark, Del., 1951. (6) Milham, R. C., U. S. Atomic Energy Comm., Rept. DP-173 (August 1956). (7) Tennessee Valley Authority, Rept. 7 (June 1943). (8) Thurnau, D. H., U. S. Atomic Energy Comm., Rept. DP-249 (November 1957).
RECEIVEDfor review April 19, 1968. Accepted October 6, 1958. Conference on Analytical Chemistry in Nuclear Technology, Gatlinburg, Tenn., October 1958. VOL. 31, NO. 3, MARCH 1959
339
