1515
V O L U M E 26, NO. 9, S E P T E M B E R 1 9 5 4 neodymium impurity in the praseodymium of 0.4%. Since the very low gamma counting rate of the praseodymium sample could easily be bremsstrahlung rays produced by the interaction of beta particles and the aluminum absorber, there is reason to believe that the purity of the praseodymium fraction exceeds 99.6%. I n order to check the purity of the neodymium fraction, a sample of inactive neodymium and active praseodymium containing 100,000 counts per minute of activity were analyzed by the lactate technique. The final sample had a counting rate of 800 counts per minute and an 80% yield indicating about 1% praseodymium contamination. While this error does not exceed the error involved in counting, recycling would give neodymium 99.9% pure. ACKNOWLEDGMENT
The author wishes to express his thanks to Rose Tirrell, Walter Small, and John Goresh for their contributions. Special thanks are due to J.-4. Marinsky for his valuable advice and instruction.
LITERATURE CITED
(1) Ballou, N. E., Natl. Nuclear Energy Ser., Div. I V , Vol. 9, Paper 292 119.51). ~~. .-,. (2) Boldridge, W. F., and Hume, D. N., Ibid., Paper 294 (1961). (3) Fitch, F. T., and Russell, D. S., ANAL.CHEM.,23, 1469 (1951). (4) Fitch, F. T., and Russell, D. S., Can. J. Chem., 29, 363 (1951). (5) Harris, D. H., and Tompkins, E. R., J . Am. Chem. Soc., 69, 2792 (1947). (6) Ketelle, B. H., and Boyd, G. E., Ibid.,69, 2800 (1947). (7) Spedding, F. H., and Fulmer, E. I.. Ibid., 72, 2354 (1950). (8) Spedding, F. H., Fulmer, E. I., Butler, T. A., Gladrow, E. M., Gobush, M., Porter, P. E., Powell, J. E., and Wright, J. M., Ibid.,69, 2812 (1947). (9) Spedding, F. H., Fulmer, E. I., Butler, T. .4.,and Powell, J. E., Ibid.. 72. 2349 (1950). (10) Spedding, F. H., boigt, A. F., Gladrow, E. M.,Sleight, N. R., Powell, J. E., Wright, J. M., Butler, T. A., and Figard, P., Ibid.,69,2777 (1947). (I1) Ibid., P. RECEIVED for review August 6, 1953. Aocepted June 1, 1954.
Determination of Density of Small Fragments WILLIAM PRIMAK and PAUL DAY Chemistry Division, Argonne National Laboratory, Lemont,
T
HE extension of the flotation method of Hutchison and Johnston for determining crystal densities to the determination of the densities of small fragments in the fractional milligram weight range is shown to involve an entirely different set of limitations on precision from the original method. Control of temperature and freedom from convection and vibration no longer limit the precision, but rather the viscosity of the flotation liquid, the size of the particle, the length of observation of the crystal, and the heat diffusivity of the vessel and liquid. The adhesion of foreign matter becomes of greater importance while the presence of voids becomes a lesser problem. INTRODUCTION
The method of determining the density of a crystal by determining the temperature a t which it will neither float nor sink in a liquid whose density and temperature coefficient are determined was developed into a method of high precision by Hutchison and Johnston (4, 6 ) . Using crystal fragments 3 to 4 mm. on edge (3) and organic liquids with a temperature coefficient about 10-8 gram per cc. per degree, these authors determined the flotation temperature to 0.002' C. and found that they could compare densities to about 5 X 10-6. Thus their precision was limited by their temperature control. When the method is extended to smaller particles, other factors limit the precision. The flotation vessel can be decreased in diameter t o eliminate convection difficulties. The motion of the particle in the flotation chamber is observed with the aid of a telescope fitted with a cross hair, while the chamber is set in a thermostat. Khen the temperature of the thermostat is adjusted so that the density of the liquid is close to that of the particle, the hydrostatic force is small and the particle executes viscous motion according to a generalized Stoke's law applicable to its shape. I t attains a velocity, T',
V
=
kAA/p
where A is the difference in density between solid and liquid, A is a measure of the size of the particle with the dimensions of area, p is the viscosity, and k is a constant having a value near 70 when the other quantities are in c.g.s. units. [This equation for the steady-state motion follows by equating the viscous drag to the hydrostatic force (2). If A is taken to be the square of the
111. principal dimension, k must be adjusted by a shape factor. Alternatively, an A suitable to the size and shape of the particle may be chosen. The equation as written is probably good to within a factor of 2 without these refinements and is entirely adequate for this discussion of precision where orders of magnitude are involved.] In accordance with Johnston and Hutchison's procedure, the temperature of the bath is successively altered to reverse the motion and decrease the speed of the particle-Le., to reverEe the sign of A and decrease its magnitude. Assuming perfect instantaneous temperature control, the smallest difference in density which can eventually be detected, Am, is seen to be Am = pS/ktA where 6 is the smallest reliable displacement which one can detect and t is the effective time of observation. I n practice, in the absence of stirring, unless the diameter of the flotation chamber is small and its walls are thin, the bath temperature can be altered very much more quickly than the flotation liquid responds; hence the heat diffusivity of the flotation chamber becomes a factor, and its thermal relaxation time must be subtracted from the total time of observation to obtain t. [The effect of the thermal lag of the chamber probably explains the character of the flotation curve presented by Johnston and Hutchison ( S ) . ] In practice, the determinations become tedious when t exceeds 5 X lo2 seconds (although in some of the present work, times as long as 3 X lo3 seconds were employed). . Zreasonable value for 6 is 0.1 cm. For organic liquids 1.1 may be 10-2 poise; hence for Hutchison's fragments ( 3 )A,,, is a fraction of 10-6, smaller than can be conveniently obtained by regulating the bath temperature. On the other hand, for a fragment 0.04 cm. across corresponding to a temperature de(about 40-mesh) A, is termination of 0. l ' C., and temperature regulation more precise than to within a few hundredths degree is pointless! Thus, the low precision quoted by Lewis and McDonald (a), who gave no experimental details, probably does not represent a lack of care but is intrinsic in the the hydrostatic methods. In working with particles of density beyond the range of organic liquids it is necessary to use an aqueous solution like thallous formatemalonate (9). At the density of diamond the viscosity of the solution a t about 30" C. is about 0.06 poise and a t the density of corundum about 0.44 poise, and A,,, is correspondingly incremed.
1516
ANALYTICAL CHEMISTRY
However, in planning temperature control in this case it must be remembered that the temperature coefficient of the density of these solutions is some threefold smaller than for the organic liquids. I n work with small fragments, the presence of flaws may be expected to be of lesser importance than in work with large fragments; small crystals would be freer of flaws, and if the small fragments were prepared by crushing crystals or aggregates, the flaws would be expected to break out. Since fragments of interest wcre in the range 40 to 100 mesh and weighed but a fraction of a milligram, in a density determination to several parts in lo4, the adhesion of several hundredths of a microgram of foreign substance could materially affect the results. No ordinary mode of examination could be expected to detect this, and hence consistency among a series of determinations after successive washings was used as a criterion of cleanliness. Similarly, consistency in a series of determinations on different fragments from the same source was used as a criterion of suitabilitj of the fragments; any results which showed a large deviation were discarded. The handling of these small fragments required special precautions through many determinations, which made I t necessary to devise special apparatus and techniques. Some that proved to be of special value are described here,
1
-a -b
I mm
1.2mm A
Fd G
B
SPECIAL APPARATUS AND PROCEDURES
The most satisfactory of the procedures tried utilized the apparatus shown in Figure 1. It was necessary in this work to provide for the determination of a wider range of densities than Hutchison and Johnston’s ( 4 ) , and hence to adjust the temperature of the liquid over a greater range. I n order to minimize evaporation, the thermostat was operated below room temperature. I t was found necessary to maintain a dry atmosphere above organic flotation liquids, for otherwise dissolved water precipitated a t the l o w r temperatures, giving a cloudy solution a t first, through which Observation was difficult; then later, a suspension of inhomogeneous density with which determinations were impossible. Referring to the figure, the capillaries, A , were freshly drawn, about three times the diameter of the crystals. One end was partially closed by holding it in a flame for an instant to prevent the crystal from falling through. The capillaries were handled only with gloves. The crystal fragments were dropped into their respective capillaries, and left there during the operations of determining the flotation temperature and of washing and drying. The washing was performed by setting a capillary in the washing tube, C, introducing the solvent around the inside and outside of the capillary by means of a hypodermic syringe, and then sucking the liquid off by means of an aspirator. A final washing with doubly distilled acetone was used and the capillary was then set into the drying chamber, D, in which it was maintained a t 110”C. while air which had been dried over Drierite and filtered through cotton was aspirated over i t a t a flow rate of about 100 cc. per minute. The flotation chamber, B , convenient for determining the flotation temperature of the crystal contained in its capillary, was made by simultaneouslv blowing and drawing the softened end of a glass tube and sealing it off. The flotation temperature was often found to alter after first washing and drying, but after several washings and dryings became reproducible and only occasionallv shomd a large variation. For storage, the crystals contained in their capillaries were placed in chambers like the one shown in E to prevent them from accumulating moisture. The temperature coefficient of the liquid was obtained bv determining its density a t several different temperatures over the range of interest and fitting the results to a line by the method of least squares The density was determined by weighing a weighted glass bob suspended in the liquid and in water in a manner similar to that used by Hutchison and Johnston ( 4 ) Johnston and Hutchison ( 7 ) and Hutchison ( 5 ) . Bobs filled u i t h lead shot were found to be as suitable as mercury-filled ones except a t the highest densities. Because 4-mil platinum wire was frequently broken with the heavy bobs required for the thallium solutions, the suspension was altered to 5-mil rhodium-platinum alloy, and a special arrangement for withdrawing the bob was devised. However, even then an occasional break was experienced. To prevent destruction of the chamber (a serious hazard in working with thallium solutions and a nuisance otherwise) a short section of
D Figure 1. Apparatus for Determination of Density 6f Small Crystal Fragments A. 8.
Capillary tube, about 0.06-mm. wall Flotation chamber
C. Washing t u b e s e t i n t o a n adapter
D . Drying chamber
E.
F. a.
b. c. d. C.
f.
Storage t u b e Capillary flotation chamber Drierite Glass wool To aspirator From d u s t filter a n d drying tube To drying c o l u m n a n d aspirator Nichrome wire 26, to Variac
standard wall tubing of not much larger internal diameter than the outer diameter of the bob was sealed on the end of the flotation chamber to serve as a hydraulic brake. The general arrangement is shown in Figure 2, B . The bob is attached to a short length of platinum-rhodium wire which is hooked to the gold chain passing upward to a hole in the base of the balance through tm-o sections of glass tubing, the lower of which is shown in the figure. The lower tube telescoped within the upper and in the process caught a wire cross bar attached a t the proper location on the chain and ~ i t h d r e wthe bob from the liquid. The liquid of chamber z4 could be stirred by thus moving the bob, but in some cases (especially with viscous liquids) there was evidence of a “dead” region in the lower portion which was avoided in chamber B in Rhich rapid temperature equilibrium was achieved by controlled forced convection. A fine capillary was inserted into the side tube, c’, depressing the glass bead (the densities of most of the liquids used were greater than glass), and for some minutes introducing a slow stream of small bubbles of dried nitrogen The side tube was a satisfactor:flotation chamber in manv instances. When it was not, it served as a tubulation for insertion of a pipet to transfer liquid to another flotation chamber.
To achieve a reasonable precision in determining the densities with thallium formate-malonate solutions, these procedures were modified. To decrease the viscosity, the thermostat was operated a t a higher temperature. To increase the heat diffusivity (much smaller for the thallium solutions than for the organic liquids) the crystals were floated directly in the 2-mm. walled chamber, F , Figure 1. Then, even with the time of observation increased some fourfold, a precision only within
V O L U M E 26, NO. 9, S E P T E M B E R 1 9 5 4
1517
to 1 / 1 3 ~ ~could be achieved; and a large number of erratic results obtained were attributed to the increased handling of the crystal fragments and the need for transferring the flotation liquid. No correction was made for the effect of surface tension on the wire suspending the bob in the density liquid. This is 2 ~ r T case M here r is the radius of the wire, T is the surface tension, and 0 is the contact angle. For the bob used in the present work suspended by a 5-mil wire wThose volume was determined from its weight in air and in water to be about 6.8 ml., the density of a n organic liquid would be about 1 / 3 0 0 ~ less than stated. ILLUSTRATIVE RESULTS
Two substances xere studied which permitted the use of organic liquids of loiv viscosity. Silicon Carbide. Commercial silicon carbide, 6O-?esh, was washed with hydrochloric acid, hydrofluoric acid, and water. Two series of determinations of the temperature coefficient of the density liquid, methylene iodide to which about 37, 0dichlorobenzene had been added, taken a month apart gave t h r recults for the density, D
D
= 3.23562 - 0.002644T
n
=
3.24724 - 0.0026457'
ii.i least squares fits to four and three points over the range about 9" to 23" C. Thus, although the density had increased by evaporation, the temperature c o e f f i c i e n t r e mained sensibly constant and was taken as 0.002645 gram per cc. per O C. A silicon carbide grain was floated in the chamber along with the bob a t each time. During the first set of determinations it floated a t 8.75" C., during the .econd a t 9.10" C., correcponding to the r e s p e c t i v e densities 3.2125 and 3.2131, average 3.2128 grams per cc. T n o other grains were compared with the first grain in a smaller flotation chamber, and the densities computed from the flotation temperature and the density of the f r a t crystal were 3.2134 and 32133 grams per cc. Reproducibility on individual grains after successive washings tl-as found to be within about l / s ~ ~ ~ . The deviations between grains of this sample were found to be somewhat larger. Boron Carbide. Using the same methods with methylene bromide in the temperature range 10" to 15" C. the densities of three fragments from a sample of boron carbide whose respective weights were 30, 440, and 280 y were found t o be 2.5164, 2.5168, and 2.5160 grams per cc., respectively.
I
'
The densities of samples of diamond, spinel, and corundum were determined using thallous formate-malonate solutions and the modifications of procedure described above which were found to be necessary in using these viscous solutions. Diamond. Crushed diamond powder 80 to 100 mesh, termed "bort" in the trade, was employed. It was washed with hydrofluoric acid, hydrochloric acid, and water, then dried. It consisted mainly of transparent colorless and yellow fragments. The larger colorless fragments were selected under a microscope. Four determinations (washing with water and acetone and dl ying between each) on each of three selected fragments were performed. The densities of the first two fragments were determined a t 20" to 22" C., where the viscosity of the solution n a s about 0.1 poise. For the first fragment the results 3 5175 (3.5150, discarded), 3.5169, and 3.5174 (average 3.5172), \ V P ~ P obtained; and for the second fragment the results 3.5181, 3.5187, 3 5176, and 3.5179, (average 3.5181) grams per cc. were obtained. The density of the third fragment was determined a t about 2" t o 4 ' C., where the viscosity of the solution was near 0.2 poise and the results were 3.5144, 3.5160, 3.5148, and 3.5134 (average 3.5147), grams per cc., shoming deviations about twice as great as a t the higher temperature. The differences between the densities of the fragments are evidently greater than the precision of the determinations and cannot be accounted for by the temperature roefficients of the fragments which would only affect the fifth decimal place. However, since different fragments from this sample of diamond floated a t different temperatures \Then dropped into the flotation chamber simultaneously, it is concluded that there are real differences in the average densities of these fragments. Thp results may be compared with Beardon's precision value, 3.51540 a t 20" C. (1). Spinel. The densities of four fragments of acid-washed 40- t o 60-mesh powder obtained b3; crushing part of a boule of artificial, caolorless, transparent spinel were found to be 3.6272, 3.6272, 3 6269, and 3 G284 grams per cc , respectively, a t about 20" C. Corundum. The densities of four fragments of acid-washed 10- t o 60-meqh powder obtained by crushing part of a boule of artificial, colorless, transparent corundum (sapphire) were determined as: 3.9897; 3 9869; 3.9888, 3.9862; and 3.9888, 3.9872, at 27" to 30" C. Thta precision attained in these determinations conforms n i t b the anul\qis given above. 4CKiYOWLEDGMEYT
The author. are indebted to G. R. Finlay, The Sorton Co., Siagai-a Falls, Canada, for supplying the sample of boron carbide on which results are reported here, and to D. -4.Hutchison for photographs of the apparatus he used in his density determinationq and for advice. A
e
Figure 2. Apparatus for Determining Density of the Liquid -4.
First chamber chamber showing float mounted i n position a. Drierite 6 . , Glass wool C,C T h i n r-all sections C. Bob suspension chamber c'. Side chamber for removal of liquid and for insertion of convection stirring capillary d . Bob e. Pt-Rh wire 5-mil diameter f. Fine old chain g. G l a s s s e a d float valve h . Hydraulic brake region
H. Second
.
LITERATURE CITED
(11 Beardon, J. A , , P h y s . Rea.. 54, 698 (1938). ( 2 ) Dodge. R. A., and Thompson, 11. J., "Fluid LIechanics," Xew York, 1st ed., Articles 158, 87, hlcGraw-HI11 Book Co., 1937. (3) Hutchison, C. h.,private communication. (4) Hutchison, C. -i., and Johnston, H. L., J . Am. Chem. Soc., 62, 3165 (1940).
( 5 ) Hutchison. D. A , , Phus. Rev.,66, 144 (1944). (6) Johnston, H. L , and Hutchison, C. A , , J . Chem. Phus., 8, 869 (1940).
(7) Johnston, H. L., and Hutchison, D. 8 . , P h y s . Rev., 62, 32 (1942). ( 8 ) Lewis, G. S., and McDonald, R. T., J . Am. Chem. Soc., 58, 2519 (1936). (9) O'Meara, R. G., and Clemmer, T. B., E. S. Bur. Nines, Report, Invest. 2817 (October 1928).
RECEIYED for review January 18, 1954. Accepted May 27, 1954.
