of d,l-dibromosuccinic acid in 0.185ON hydrochloric acid were used. The run was carried out a t 70" C. and 0.1007N sodium hydroxide was used to titrate the hydrogen bromide formed. A plot of these data can be found in Figure 3, where k for slow isomer, meso, equals 1.4 X 10-3 niin.-' and k for fast isomer, d,l, equals 8.5 X 10-* min.-l The graphs show that a good extrapolation can be made using those points obtained when only the meso form remains; the amount of hydrogen bromide produced being calculated and then related to that which was formed from the mixture. For example, a value of 0.905 a t zero time, which corresponds to 8.05 ml., was obtained. The total hydrogen bromide expected was 15.33 ml., which gives a calculated value of 53% for meso-dibromosuccinic acid. The actual amount of the meso isomer present was 51%. I n other runs, the following results were obtained for per cent of mesodibromosuccinic acid: Found 53 80 TO
Actual
--
51 13
66
Table 111.
Time, 3llin. 30 90 180
Calculation of Rate Constant for the Fast Reaction Isomer, Using Figure 3 Fast Log Total Slow Titration, M1. (a - 2 ) (a - 2) (a - 2 ) (a - 2 ) 7.76 6.16 0,790 50.38 13.92
53.68 56.63
10.62 8.27
The individual components present may be identified from the data obtained in a run. The meso form can readily be identified from the rate constant calculated, using the latter portion of the curve. I n Figure 3, a k of 1.4 X 10-3 min.-l was found for the mesodibromo acid. I n the absence of the d,l form, a value of 1.2 X min.-' (Figure 2) was found, showing very good agreement. The d,l-dibromo acid can be identified in a mixture if the data are replotted subtracting that amount contributed by the meso form, as shown in Table 111. For example, a t 180 minutes, log(a - z) = 0.9175 (8.27 ml.), From Figure 3 a t 180 minutes log (a - z) contributed by the meso-dibromo acid is 0.812 (6.50 ml.). The amount due to the d,Zdibromo acid is therefore the difference, 1.77 ml., and the log = 0.248. This can be re-
3.38 1.77
7.24 6.50
0,529 0.248
peated a t 90 and 30 minutes, the data replotted, and a rate constant calculated (see last column in Table 111). Khen the last column is replotted, the rate constant calculated is 8.5 X 10-3 min.-' (using all three combinations), a value which is in good agreement with that obtained when only the d,l isomer was present (Table I). LITERATURE CITED
(1) Brown, H. C., Fletcher, R. S., J . A m . Chem. SOC.73, 1317 (1951). ( 2 ) Lee, T . S., Kolthoff, I. RI., Ann. N.I-. Acad. Sei. 53, 1093 (1951). 13) , , RlcKenzie. A.. J . Chem. SOC.101, 1146 ,
I
(1912). (4) Rhinesmith, H. S., "Org. Syntheses, Collected" Vol. 2, 177, Wiley, New York, 1944. RECEIVEDfor review -4pril 12, 1956. .iccepted February 28, 1957.
Pa rticle Size Determination by Radioac tiva tio n BERNARD M. ABRAHAM, HOWARD E. FLOTOW, and ROGER D. CARLSON Argonne National laboratory, Lemont, 111.
b A sedimentation method for pariicle size determination has been developed that can be used with reactive fluids, such as liquid metals, as well as with water and organic liquids. The powder to be analyzed is first activated by neutron bombardment and the resultant activity that radiates from a thin lamina of suspension is used as a measure of the weight of material in the lamina. A comparison was made between the radioactivation method and the more conventional fractional extraction method to demonstrate the reliability of the former, The radioactivation method has proved to be reliable, rapid, and capable of automatic operation.
0
techniques (9, 4, 9, 10) developed for determining
F THE VARIOUS
particle size by sedimentation analyses, none are easily adapted for use with liquid metal dispersants. The difficulty in all cases is the determination of the amount of material in suspension as a function of time. A modification of
1058
ANALYTICAL CHEMISTRY
the light scattering method that substitutes gamma rays for visible light is not entirely satisfactory because it is fairly insensitive to small changes in composition. Furthermore, it requires the stopping power of the suspensoid be much different from the stopping power of the dispersant. The method presented here can be used for any powder that can be made radioactive and can be performed with any fluid. It was developed specifically to determine the particle size of uranium dioxide (VOZ) powders suspended in sodium-potassium alloy a t various temperatures up to 800" C., and is now used in this laboratory on a routine basis to determine particle size in water and organic solvents as well. The method is rapid and yields results that are in satisfactory agreement with the more conventional fractional extraction method ( 2 ) . METHOD A N D APPARATUS
The radioactivation method uses the
activity generated in the particles by neutron bombardment to measure the weight of material in suspension. During irradiation the activity generated in a particle is proportional to the number of atoms in the particle; consequently, the relative activity between two particles will be equal to their relative weights. Similarly, in a lamina of a settling suspension the relative activity in the lamina a t two different times will be equal to the relative weight of material in the lamina a t those times. When the lamina is defined by a collimating slit a t a fixed distance from the top of the suspension, then one can calculate from Stokes' law the time, t,, for a particle of diameter z i microns to settle past the slit. The ratio of the activity a t time t , to the initial activity, when the suspension was uniform, will be equal to the weight fraction of material less than zi microns in diameter. The data yield directly a cumulative distribution of weight fraction of undersized particles from which the differential distribution is readily obtained. A schematic diagram of the apparatus is shown in Figure 1. The collimating
-lit in the lead shield mas 0.25 cm. high by 4 cm. wide by 23 cm. deep. A square sedimentation tube, 2.5 cm. on a side by 30.4 cm. long, was used in order to eliminate vortex formation while the suspension was being stirred; it is essential to the method t h a t the initial concentration be uniform with height and that the surface of the liquid I cmain at a constant level. To mininiize resuspension by convection currents, the tube was thermally iiisulatc,d so that the temperature \ aried by no more than 0.1O C. during :t determination The time constant for tlie counting rate meter \\as set for 2000 counts; for the activity level used this means that the time constant n a s about 6 seconds a t the beginning of a determination and increased to 1 niinute toward tlie end. The viscosity of the medium arid the settling depth ~’ierechoscn so that a 10-micron particle fell past the slit in 80 to 90 seconds. The 1)article range to be determined c:iu cn5ilj t r changed by
adjusting the viscosity of the suspending medium. Uranium dioxide (Mallinckrodt Chemical Co.) was around in a ball mill with toluene’as t h e lubricant, washed with 3-pentanone, and vacuum dried. About 2 grams were irradiated in the Argonne CP-5 reactor for a period of 24 hours a t a neutron flux of 2 X 10.12 After a 2-day cooling period the resulta n t activity in the sample was about 108 disintegratioiib per minute; a t 6 inches from the sainple the radiation level was 20 mr. per hour. When the sample was unifornily dispersed a counting rate of approximately 20,000 counts per minute m-ah recorded. The irradiation had no effect on the particle size, nor did the activity leach iiito the cuspending medium. Prior to the analysis all samples were shaken for 16 hours in 50 cc. of the suspending medium, 0.05% sodium pyrophosphate solution or 3-pentanone, to ensure deflocculation. The suspension was transfcrred t o the sedimenta-
tion tube and the total volume brought to 100 cc. so t h a t the resultant uranium dioxide concentration was never greater than 0.2 volume yo. A settling height of 5 cm. \$-as generally used with the water suspensions and 10 cm. with the 3-pentanone suspensions. With the stirrer on, the counting rate was rccorded for 5 minutes; then the stirrer was stopped and the counting rate was recorded for an additional 40 minutes, slightly longer than the time required for a 2-micron particle to settle past the slit. Thc values used for the constants in Stokes’ law arp: 3-Pentanone Density, 0.810 gram per cc. (6) Viscosity, 0.443 cp. (8) Rater Density, 0.99797 gram per cc. ( 6 ) Viscosity, 0.8936 cp. ( 7 ) Uranium dioxide, density, 10.793 gi ams per cc. ( 1 ) Local acceleratioii of gravity, 980 28 cm. per aec.* RESULTS AND DISCUSSION
--
S t rter
I
3 Codnt ng R a t e Meter IO rn” OJtPUf
r e c o r d ;~-~‘,“;~nt
Sed m e n t o t t o n
O-eter
Tu be
I S c o l e r 8 Pb s e Height Selector
Figure 1.
I n the follon ing tables, the detnminations on four different samples of uranium dioxide by the radioactivation technique are compared with determinations on the same samples by fractional extraction. Because the slit a a s only 0.25 cm. high, no correction was applied to the data for resolution error. A small correction for scattered radiation arising from Compton recoils was applied to the data, the magnitude of this correction was just outside the mean devintion given in Table I, column 2, for sample 1. The correction was determined experimentally by measuring, with the sample on the bottom, the amount of radiation scattered into the slit as the vertical distance between t h e slit and bottom of the sedimentation tube was varied. By keeping the bottom of the sedimentation tube a t least
Apparatus for particle size determination
30
Table 1.
20
$
z
IO
K w a
O
5
20
[L
io
w 0 W
a
z
o
L2 20 IO
‘0
Figure 2.
I
2
4 5 6 7 DIAMETER IN MICRONS
3
8
9
IO
Particle Size Determinations
Particle Weight Fraction Range, Fractional Microns Radioactivation extraction Sample 1 Oto2 0 641 A 0 010 0 676 = k O 011 0 179 i 0 010 0 168 z!= 0 011 2 to 3 3 to 5 0 114 i 0 010 0 107 A 0 003 5 to 10 0 042 =k 0 010 0 025 & 0 010 0 023 i 0 010 0 024 i 0 006 >10 Sample 2 0 to 2 0 443 0 467 2 to 3 0 050 0 043 3 to 5 0 163 0 145 5 to 10 0 202 0 171 > 10 0 144 0 175 Sample 4 0 to 2 0 035 0 028 2 to 3 0 206 0 230 3 to 5 0 199 0 138 5 to 10 0 544 0 604 >10 0 017 0 000
Histograms of particle size distribution of samples VOL. 29, NO. 7, JULY 1957
1059
10 mi. below the slit and adjusting the pulse height selector on the scintillation counter, the necessity for making the correction can be eliminated. Sample 1, Table I, n a s taken from the material as it came from the ball mill. The distribution of particle size is nearly linear when plotted on lognormal paper, with the n eight mean size a t 1.3 microns. The distribution as obtained by radioactivation is illustrated graphically as the upper histogram in Figure 2. The radioactivation analysis in Table I is the average of five runs on t w o different I ortions of sample 1 and the fractional extraction analysis is the average of three different portions of sample 1. The agreement between thc two niethods is considered satisfactory. Samples 2 and 4, Table I, and sample 3, Tahle 11, were prepared from a large batch of saniple 1 by fractional extraction. I n these samples the distributions of particle size were distorted in order to give an additional test of the radioactivation method. The distortion introduced into the distributions is illusstrated graphically in Figure 2 where the histograms for saiiiples 2 and 4 are plotted to compare with the distribution of sample 1 , The results for sample 2, 3, and 4 alqo skion excellent agreement between the two methods. The sources of error peculiar to the radioactivation niethod are counting statistics, inconiplete dispersion. and scattered radiation. 4 s mentioned above, scattered radiation can be largely eliminated by suitable geometrical arrangement and electronic discrim-
Table 11.
Particle Size Determination of Sample 3
Particle Keight Fraction Range, RadioFractional Microns activation Extraction 0
0 to 2 2 to 3
0.372 0 073
0.379
b
0.395 0 059
0.053 3 to5 0.180 0.221 0.213 5 to 10 0 08T 0 079 0.100 0.268 0.232 > 10 0.287 a Prior t o radioactivation analysis. Xfter radioactivation analysis.
in :ic.curnc>- \\-it11 a i i i r ~conventional ~ scdinientation technique. The method is rapid, capable of being adapted to automatic operation, and to taking close size intervals. I t is particularly suited t'o reactive systems that must be handled in vacuo or in an inert atmosphere. An additional application suggests itself-namely, the deterniination of the particle distribution of the components in a niisture by elect'ronic discrimination of the respective radiations. thereby avoiding the necessity of separating tlie pon-der into its components. LITERATURE CITED
ination. If nonuniforni dispersion isuspected, this can easily be checked by scanning the length of the tube with tlie counter while stirring. The counting statistics actually limit the accuracy of the method; this means that the largest weight fractions are known with the greatest precision. Here the activation technique has a distinct advantage over fractional extraction or pipet methods, for if the bulk of tlic material in a particular size interval is found near the point where a cut is to be made. there can he c:trry-over to the adjacent size brackets. Furthermore. close size intervals may be obtained n-ith the activation method without the tinieconsuming tediousness required by the other methods. SUMMARY
The radioactivation method for particle size deteriiiination is coniparalile
(11 Gronv@ld, F., J . Inorg. ie. Sziclear C h e m , 1,357-70 (1955). ( 2 ) Herdan, G., "Small Particle Statistics,' ' Eleevier, S e w York, 1953. ( X , Inst. Chem. Engrs., (London) and Soc. Chem. Ind., Road andBuilding Materials Group, Symposium on Particle Size A\nalysis, Trans. Inst. C'hem. Engrs. (London) Suppl., pp. 128-45 (Feb. 4, 1947). (4) Inst. of Physics, Brit. J . .Ippl. Phys. Suppl. s o . 3 (1954). ( 5 ) "International Critical Tables,'' Vol. 3; p. 25, 3IcGraw-Hill, Set? l o r k . 1928.
Co.. Sew'Tork. 1954.
-
RECEITEDfor review October 20, 1956. Accepted 1Iay 1, 1957. Presented at the Second Annual Meeting of the American Nuclear Society, Chicago, Ill., June 1956. V o r k performed under the auspices of the IT,S.Atomic Energy Commission.
High-Frequency Determination of Ferromagnetic Metals FRANCIS J. SCHMIDT1 Nickel P rocessin~Corp., Nicaro, Orienfe, Cuba
The ferromagnetic metal content of reduced oxide i s determined b y its magnetic permeability, which i s measured b y its influence on the induction of a coil forming p a r t of a tuned oscillator circuit. The method i s calibrated in an empirical manner b y use cf chemically analyzed samples. Large, coarsely crushed samples reduce sample preparation time, and permit completion of a determination in several minutes.
I
s THE ferrous metals industry the reduction of oxides to metals is a common process. Many process variables must be closely controlled to ob1060
e
ANALYTICAL CHEMISTRY
tain products within specified limits of reduced metal content. iinalytical determinations lose much of their effectiveness for process control TI hen they require considerable tinip. If sintering occurs, a product does not lend itself to rapid analytical niethodi, such as spectrography, because of sampling difficulties. Individual particles range from coarse pieces to finc dust :tnd the chemical compositions of the fractions vary. Fine dust is incvitahly lost during size reduction :ind splitting. Brittle particles are miwd together with soft, malleable metallics; the latter have a tendency to flatten out during crushing. Frequently many hours are required for the preparation
of 1-gram samples, and the sampling error is often several times greater than the analytical error. This pa1:cr describes a method capable of using larger arid coarser laboratory samples. I t is based on permeability inpasuremerits at high frequencies and i4 suitable fur the determination of iron, nickel. or cobalt, when only one of these nietals is pre*ent as a major constituent. The composition and temper of the eventual alloys formed can be regarded as constant. Smong the magnetic properties, permeability measurements offered the adl Present addresp, Rey1101ds 1Ietals Co., Sheffield, .\la.
