A Precise Method for Sieving Analyses M.WEBER, JR., AND RAYMOND F. MORAY1 The Mathieson Alkali Works (Inc.), Saltville, Va.
T
HE determination of the particle size distribution of a finely divided material by means of a sieving test is of
t o agree within wide limits. The work reported in this paper was done to sound out the possibilities of an absolute microscopic calibration of the testing sieves to be used on several specific products. It was desired particularly to avoid the
considerable industrial importance in testing materials for conformity to specifications and in control over manufacturing processes. Specifications for a finished product usually call for the use of one or two sieves, with limits on the amount of oversize or fines or both. However, when the primary product of an industrial operation is a crystalline material with wide distribution of particle size which is to be separated subsequently into several grades according to particle size, a more complete sieving test is necessary for the intelligent design and control of large-scale separating equipment. Sieving tests on commercial products, which are usually composed of irregularly shaped particles, are necessarily empirical and, in order to obtain reproducible results, all conditions of the tests must be rigidly standardized. But even under the best conditions, i t is frequently impossible to obtain comparable results with two sets of sieves which are apparently identical, in spite of mechanical shahing and standardized time and sample size. I n some cases, the retention of a product on two sieves which are nominally equivalent may vary by 20 per cent or more. F o r k done under the sponsorship of the American Society for Testing Materials (1) has resulted in the standardization of sieve sizes in the “U. S. Standard” scale, and variations are held within rather wide limits by microscopic measurements of wire diameter and ayerage number of wires per inch. In order to meet the A. S.T. 31. specifications, a sieve must have average and maximum openings within the tolerances shown in Table I. TABLE I.
TOLER4XCES ALLOW.4BLE UXDER
Sieve Nos. 4 20 50 140 230
SPECIFICATIOXS
use of standard samples, which is inconvenient and subject to cumulative errors, and which gives results that are empirical and of limited applicability.
Microscopic Calibration of Sieves
All the new U. S. Standard testing sieves which were on hand in the laboratory were examined under a microscope in an extension mounting that permitted making measurements over the entire surface of the sieve. (A binocular microscope was used in the first observations, but was found to give erroneous results due to the angle a t which the observations were made.) The microscope was equipped with a calibrated ocular micrometer, and combinations of scale and magnification were chosen so that a single opening of the sieve was equivalent to a t least 15 scale divisions, except for those finer than about 60 microns, for which the number of scale divisions per opening, and hence the accuracy of measurement, was proportionately less. Measurements were made on representative groups of fire adjacent individual openings along tn-o diameters of the sieve, parallel to the warp and shoot, respectively, taking the same number of measurements in each direction. A total of 100 measurements was found to give calibrations reproducible Tithin 1 per cent on sieves coarser than S o . 200. Two hundred measurements give approximately the same accuracy on sieves No. 200 and finer. The average opening, X, and the percentage standard deTiation, d = 100ajX, for each sieve, u being the standard deviation calculated by the method of grouping (8), are s h o r n in columns 3 and 4 of Table 11.
8.s. T. hl
4verage Opening
Mauiniunr Opening
%
570
t o 18 t o 45 t o 120 t o 200 t o 323
TABLE 11. SIEVECALIBRATIOSS AND RESULTS OF
u. 5.
Stand- S o m i ard nal No. Opening Microns ~~
Testing sieves having openings which fall within these tolerances are satisfactory for use on materials with a large average particle size, wide distribution of particle size, and regularly shaped particles. They become increasingly unsatisfactory, however, as the particle size distribution becomes narrower and as the particles become smaller and more irregular. This objection has been recognized by several in\ estigators a t the Bureau of Standards, especially in sieving tests on cement (2, 4, 5). TTig and Pearson, after making a survey of the subject, concluded that an empirical sieving test on a standard sample &-as preferable to any other method of standardization that had been investigated. They recognized the connection between variation in the individual openings of the sieve and variations in sieving results, but found no satisfactory means of correlating them. Sieving tests on finely divided materials other than cement have apparently received little or no attention from investigators. Many of these materials are being bought and sold on specifications, and in some cases they present considerable difficulty in that tests made by producer and consumer fail 1
1s 25 30 30 40 45 45 50 60 70 70 80 a0 100 100 100 120 120 140 140 140 170 200 200 200 200 230 c 230 230 c 270 5 270 C 325c 325C 0
Present address, Westvaco Chlorine Products, Inc.. South Charleston,
b c
W.\‘a. 180
1000 710 590 590 420 350 3,iO 297 230 210 210 177 177 149 149 149 12: 123 105 10 3 105 88 74 74 74 74 62 (j2 62 .5 3 .X3 44 44
X
d
io00 710 610 600 440 370 370 303 234 2230 221 187 180 151 148 141 13V 132 108 107 108
5.4 3.0 3 6 3 3 4.0 2 9
8i
6.4 7 4
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61 5SO 58” 44 41
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4 7 4.3 7 7
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Pample .-I
Sample
Sanipie
D
C
0 5
0.5 1.2 1.7 1.7 3.4
S:i
223
7.Sb
228 187 180 151 149 144 138 13’2 112 107 103 88 82 77 77 77 69 62 64 60 60 47 44
12.6 12.8
.... ...
93 3 96 0 96 2
23.1 24 6 28.7
.
40.5 43.4 58.4 64 0
. .. ..
87
(i
97 9 98 0
.
.
.... .. , .
.
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X3 1000 710 610 800 440 370 370 303 254
0 9 15.0 24 5 25.4 41 7 52.0 52.0 62.6 72 0 78 S 77.4b 87.3 88 3 94 7
3 ti
3 6 7 1 15 3 5 2 9 0 8.6 8 6 13 15
Sample B
TESTE4
...
...
69.7 69.4b 76.8
79.8 83:i 82.8 88.0 90.8
. . .
....
. . .
0 5 0.6 0.6 0.7
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8.9 133 6.5 7 76 3 b 87 0 87 1 85.26 89.9 93.8 94.5 95.2 95 1 96.0 96,s
.iverage opening outside A . 6. T . 11. specifications. Obviously o u t of line. Twill weave.
.
0.9
2 1 2 3 6 4 10.9 17.8 18.3 17.1b 26.4b 35.9 36.6 40.6 41.0 56.8 66.9
Xi 1000 7 10 610 600 440 370 370 303 254 223
233 187
IS0 151 150 147 138 132 114 107 105 89
84 77 77
78 72
62 e5 62
62 49 46
APRIL 15, 1938
-4XALYTICAL EDITIOS
181
SIEVE OPENING (MICRONS)- PRODUCT A
FIGURE 1 Xearly all the \le\ eb had ax eiage openings a hich differed to some extent from their nominal opening&. d few of the averages (as noted) fell outside the A. P. T. RI. tolerances. But although no individual opening was found outside the specified tolerances, the uniformity as measured by the standard deviation varied greatly, and increased as the openings became smaller, as is to be expected from the increased difficulty of manufacture of fine sieves. I n sieves for which the standard deviation is greater than 6 per cent, the nonuniformity is usually noticeable under casual inspection, especially in the spacing of the warp wires, which have more crimp and less accurate distribution.
Comparison of Test Results with Microscopic Calibrations Since there is no known method of obtaining an absolute calibration of a sieve on material composed of irregularly shaped particles, the best means of judging the validity of the calibration of a set of sieves is the graphical representation of the results of sieving tests on standard samples. It must be assumed, of course, that the samples are representative of the types of material to be tested, and that the size distributions of their particles are smooth and continuous; but these assumptions appear to be justified. The materials chosen as standard test samples were commercial products with various physical characteristics, as folloas: Sample A (denqe soda ash)--nide size distribution, regulai crystal shape Sample B (light soda ash)-smaller arerage size, more irregular particles Sample C (sodium bicarbonate, granular)-verv closely sized, monoclinic piisnis Sample D (sodium bicarbonate, pair dered)-very small particles (many subsiele size), mixture of monoclinic prisms and fragments of crystals The sieves were tested in groups of six, each group being selected to comprise a well-separated series covering as much of the range of particle size of the standard sample as possible, and in all tests the sieve. were shaken mechanically by
a Tyler Ko-Tap siemig iiiachiiie Samples A and B were h a k e n for 3 minutes, samples C and D for 5 . The resulte, reported as cumulative per cent retained on each sieve, are ehown in columns 5 to 8 of Table 11,and in Figures 1 and 2, in which the open and half-shaded circles represent retentions 1 8 . average openings The solid circles represent corrected values of several openings calculated by a n empirical method described below. The results furnish ample eiideiice of the futility of attempting to compare analyses made on two uncalibrated sieves, even though they may be of the same nominal size and in conformity with the A. S. T. l f . specifications. The variations which mag be expected in many iiistances are shown particularly well by the retention of samples C and D on the S o . 200, 230, and 325 sieves. If the average openings of the sieves are used in place of the nominal openings, the correlation is improved, but there still remains considerable irregularity in the sieving curves, especially in the finer sieve sizes. Those results which are most obviously out of line (Table 11) are all on sieves which have a relatively large dispersion of the size of opening &s indicated by the standard deviation of the measurements used to compute the averages. If the results on sieves having standard deviations greater than 6 per cent of the average are disregarded, the correlation of the remaining results is reinarkably good. The obvious solution to the pi oblem of getting concordant sieving analyses is therefore to use only those sieves for which the standard deviation of the openings is no more than 6 per cent of the average. This would probably be a satisfactory solution for sieves with openings down to about 100 microns, but the mechanical difficulties involved in the production of finer sieves of the required degree of uniformity are so great that costs of inspection and rejection would be prohibitive. Some means of correcting either the average sieve opening or the results of tests on sieves with greater dispersion would be much more economical, a t least until the technic of sieve manufacture is greatly improved.
INDUSTRI i L AND EYGIKEERING CHEMISTRI
182
FIGURE 2
It was noted from the sieving curves that sieves with relatively large dispersion of size of opening always behave as if their average opening were somewhat larger than that calculated from the measurements. Also, the difference between the average opening of a sieve with high dispersion and that of a sieve having the same retention but a small dispersion increases as the standard deviation of the former increases above 6 per cent. This suggests that the erratic behavior is due to the relatively larger proportion of oversized openings which are sought out and passed through by slightly oversized particles shaken on sieves of high dispersion. If such is the case, then the error must be also a function of shaking time, for a relatively small number of oversized openings would have an increasing effect as the time of shaking is increased. It is conceivable that a strictly theoretical treatment of the correctionmight be evolved for the ideal case in which the particles are perfect spheres with known size distribution, the openings perfect circles or squares, and the method of shaking produces a perfect random motion of all the particles over the entire surface of the sieve. But the difficulties of such an analysis are obvious, and since the practical utility of the results would be questionable, only an empirical treatment mas attempted, which resulted in the following approximation, developed by trial and error: 1
+ 0.002t
d - b
(&)l'2]
in which Xt is the effectire opening for a shaking tiiiie of t minutes. When d is less than 6, making the correction term imaginary, the average opening is used without correction. There is no apparent theoretical justification for this, but since sieves with standard deviations no greater than 6 per cent of the average give results sufficiently concordant to be used without correction, and the method of correction gives good results for the other sieves, the method appears to be justified on pragmatic grounds. The values for X 3 and X s calculated for the sieves used in this work are shown in columns 9 and 10 of Table 11, and the
VOL. 10, NO. 4
points representing the corrected values are represented on Figures 1 and 2 by the solid circles. The half-shaded circles represent sieves whose standard deviations are not more than 6 per cent of the average opening, and which therefore require no correction. An inspection of the graphical data shows clearly why sieve calibrations based on empirical corrections determined by check tests on standard samples have not proved satisfactory-the correction to be added to the percentage retention depends not only on the sieve itself but on the slope of the sieving curve of the sample a t the point in question. Thus, the correction on the 87-micron sieve is about 1 per cent for the finer sample and about 5 per cent for the coarser sample of the two shown in Figure 2. By applying the correction to the sieve opening, however, the sieve can be made to yield consistent results, as this correction is independent of the sample to be tested. It appears also that the effective opening is independent of the nature of the material to be tested within certain limits, but the data do not cover sufficient ground to determine these limits. TABLE 111. Identification Mark
V'eave
CALIBRATION O F N O .
230
.Average Openine
Xa
.Y5
Calcd.
Observed Micron ,$
Microns d R
c
11
E5 F G H I a Old sieve
Ti~ill
TU111 Plain Tnill Plain Twill Twill Flair1
ruLii
61
60 60 80 i!l
ti2 RO 61 i9
Standard Deviation
% 10 0 12 3 6 .i 11 4 10.4 8 3 9 3
6.1 11 1
.If
SIEVES
icroif s
66 66 62 66
64 66 65 62 1i4
68.9 tis. .5 62.8 69.9 61.9 71.9 71 0 61.2 IiY X
a i t h loose clotli
The corrections add but little to the accuracy of the sieving curves of samples 4 and B because of their wide size distribution and regular particle ehape. Sieve calibration is therefore unnecessary for tests of this type except to eliminate the possibility of the use of a sieve rarying widely from the rated opening. HoTyerer, the accuracy of the sieving curves of the closely sized and irregularly shaped particles of samples C and D is greatly increased when proper cognizance is taken of the calibrated openings and uniformity of the sieves. If sieves for use on products such as these are not calibrated and the nominal openings are used in determining the sieving curve, very grave errors may be obtained from sieves Fhich are considerably off-size or nonuniform. dl1 the sieves having standard deT-iations greater than 6 per cent gave direct results from 1 t o 12 per cent lower than the correct point on the sieving curve, while the corrected sieve openings (S3,X,) gave results that lay on the curve, m-ith the exception of the KO. 325 sieves and one of the KO. 230 on sample D. Although the use of the correction improves the concordance of the results on these finer sieves, i t was felt that further investigation was called for because the sieve which was most noticeably out of line after correction was the most uniform of all these finer sieves. For this purpose, a group of nine
APRIL 1 5 , 1938
4U.ILYTIC.4L EDITIOS
183
0
KO, 230 sieves was assembled, and each of them was calibrated and checked against a single standard sample on which results could be duplicated n 3 h i n 0.2 per cent. The data on this group of sieves are shown in Table 111, and the results of the tests on the standard sample are plotted in Figure 3, where the open circles again represent average openings, uncorrected for dispersion, and the solid circles tlie corrected values. Dat’a for ot’her sieve sizes are included t o establish the general form of the curve. The average openings of the entire group of KO.230 sieves were in the range 59 to 62 microns; but in their behavior, the pieves n’ere divided into tlvo distinct groups. Those in the group of threr, whose sieving characteristics fell in line n-ith the other sieves in the series. were all made up with plain-weave cloth, which is standard for sieves Xo. 200 and coarser. The data on the t.1T-osieve3 v d h effective openings of 62 microns are considered more accurate than those on the third member of the group, not, only becauqe the corrections for dispersion rwre smaller, but because the third sieve was old and its cloth wai loose. Those of the other group were made u p with twilled cloth, xhich apparently behaves aery differently; and since the correction formula is obvioucly inapplicable t o t b i ~type of cloth, the “effective openings” a‘: calculated by the correction formula are indicated as crosses, whoye locations apparently have no phyqical significance. In the light of t11e.e data the broken line ahon-n on the curve for product D (Figure 2 ) appears t o be a better approximation of the truth than the solid line which does nnt make allomances for the twilled sieves.
amined, whereas the Tvarp and shoot art’ usually at right angles in plain-weave cloth. It would appear, therefore, that in any attempt to determine the effective opening of twilled cloth from its dimensions one must include correction factors for the ratio of w r e diameter to average opening and for tlie angle between the warp and shoot wires. The determination of these factors would be rather involved, and would require either a large number of sieves or facilities for producing sieves in ~ l i i c l i these variables can be controlled. It seems more practicable. therefore, t o calibrate twillweave sieves by comparison 11ith calibrated plain-weave sieves in actual sieTing tests. Cnfortunately, however, such standards for comparison are not available a t present. Sieves finer than ?\To.200 are produced only in twilled cloth, and the three plain-weave KO.230 sieves used for the work were found only with considerable difficulty. Two of the S o . 230 plainweave sieres have been preserved as standards, but none finer than this has been located. Further refinement of the method of measurement xi11 probably be required for calibration of the very fine sizes, such as the use of a filar micrometer and selection of microscope objectives of small aperture to increase the depth of focus, bringing the wires on opposite sides of the opening& in twilled cloth into focus simultaneously.
Influence of Method of Sicwing
F I G ~ R3E
Two possible causes for the erratic behavior of the tnilletl cloth suggest themselves at once: (1) I n the t d l e d cloth. only two of the four wires which bound each opening traverse the thickness of the cloth, the other two lying entirely on one side, one on the top and the other on the bottom; whereas all four wires of the plain-weave cloth traverse the cloth thickness at each opening. Hence, the distance between the projections of two adjacent wires on the plane of the cloth is somewhat less than the actual distance between them a t the center line of the opening, and the effective opening is greater than that for a plain-weave cloth with the same horizontal spacing between the wires. (2) The axes of symmetry of the twill weave are not parallel to the wires, but a t an angle of 45”, wherefore there is a tendency for the cloth to warp, throwing the warp and shoot wires out of their normal rectangular relation. This is noticeable in all of the twilled cloth ex-
The technic (mode of sieving, sieve sizes, sample size. and time of sieving) for the test sieving must be standardized for each type and size of product. Some form of mechanical sieve shaker must be used for reproducibility, economy of time, and convenience. The Tyler Ro-Tap used in this work gave very satisfactory results. The sieve sizes must be selected to include the limits of the size distribution and enough intermediate sieves to give a welldefined curre. They muet be selected far enough apart in mesh opening so that their full effect can be obtained within a short sieving time. Five properly selected sieves should be sufficient t o determine accurately the size distribution curve of even a widely distributed product. The retention on any other standard sieve can be predicted accurately from the curve. The sieving time required to obtain reproducible results decreases with sample size, but accuracy is lost in both sampling and weighing. The optimum size may best be fixed by determining the smallest sample that will give reproducible results. One hundred grams is a very convenient size, as the fractions are reported directly in percentages. The influence of time of shaking is very important, being greatest when the particles are small and irregular. Enough time must be allon-ed for the fractions retained on the several sieves to approach constancy, but a protracted time only allows additional opportunity for the closely sized particles to seek out the openings slightly larger than average in each sieve. A balance between these effects can be obtained by sievinp the same sample for time periods increasing in steps of one minute. The period after which the greatest sieve fraction begins to lose a constant amount for each succeeding minute is the optimum period on which to standardize.
Summary Testing sieves available on the market, even though they may conform to A. S. T. N. specifications, cannot be trusted to give accurate results without calibration. Methods of calibration by checking on standard samples are not generally satisfactory.
181
IZDUSTRIAL AXD ENGINEERISG CHEhIISTRI-
A method has been developed for determining microscopically the effective opening of plain-weave sieves and it has been shown that this value is independent of the size distribution of the material to be tested. This method corrects for both the deviation of the average opening from the nominal and the variations between the individual openings of a single sieve. There still remain discrepancies in the case of twillweave sieves, wherefore these should be checked by comparison with calibrated plain-weare sieves if the accuracy of the results is of great importance. Further work is needed to check the applicability of the method of calibration to sieves used on niore varied materials and to improve the accuracy of the method. Such a program might well be undertahen in collahoration with qieve manufacturers.
VOL. 10, NO.4
Acknowledgment The authors are very grateful to William B. Kent for his valuable suggestions and criticism, and to the W.S. Tyler Company for t,he loan of some of t'he sieves used in this n-ork. Literature Cited (1) Am. Soc. Testing Materials, Standards, 1936, Part 11, Nonnietallic Xaterials, p. 1413. ( 2 ) Judson. L. V.. B7u. Standurds Technol. Paper No. 321 (1926). (3) Shewhart,, W. A,,, "Economic Control of Quality of Manufactured Product, S e w York, D. Van Nostrand Co., 1931. (4) Wig, R. J., and Pearson, J. C., Bur. Standards Technol. Paper N o . 29 (1913). (5) Ibid., No. 42 (1914). RECEIVEDJanuary 17, 1938. Presented before the Division of Industrial and Engineering Chemistry a t t h e 94th Meeting of t h e American Chemical Society, Rochester, S . T., September 6 t o 10, 1937.
~~
~
Observations on the Rare Earths Quantitative Estimation of the Rare Earths by Means of Their Arc Spectra C. N. ;\IcC4RTY, L. R. SCRIBNER,
~ N M D 4RGIRET
LIWRESZ,
WITH
B. S . HOPKINS
University of Illinois, Urbana, Ill.
The determination of some individual rare earths in complex rare earth mixtures, by means of the Hilger E1 quartz-type spectrograph using an internal standard, has been studied. Magnesium, zirconium, and cerium oxides were tested as possible internal standards. Of these, zirconium oxide was found to be most suitable with respect to position and intensity of lines and rate of volatilization. 0 The region between 2300 and 3300 A. was found to be the most suitable in number and intensity of lines and degree of dispersion. The effects of other rare earths on the line intensities of an individual rare earth were found to be of similar magnitude, no matter which rare earth was added. Duplicate standard plates for lanthanuni, neodymium, samarium, gadolinium, dysprosium, ytterbium, and yttrium were prepared by photographing the arc spectrum of rare earth-zirconium mixtures of various ratios containing sufficient added lanthanum or neodymium oxides to keep the total rare earth content constant at all ratios. The arc spectra of the rare earth oxides extracted froni a number of typical rare earth ores with added zirconium oxide were photographed in a manner similar to that employed in preparing the standard plates.
The intensity ratios between the selected line pairs of rare earth and zirconium lines were determined on both the standard and the ore plates by means of a recording microphotometer. The percentages of the rare earths in the extracts of the ores were estimated by interpolating the ratios of the line pairs obtained from the ore plates on a logarithmic plot relating the intensity ratios and concentration of rare earths obtained from the standard plates. The percentages of individual rare earths present in the ores were found to vary both with the type of ore and with its geographic origin. The method was applied to the determination of the individual rare earths in an artificial mixture of rare earth oxides of known composition. The maximum error as calculated from the results was found to be * 15 per cent.
THE
selection of a suitable ore as the starting material for the preparation of a pure rare earth has always been attended by difficulty and uncertainty because of the lack of methods of analysis for the individual rare earths. This has been particularly unfortunate since, because of the lengthy and difficult processes of fractional crystallization and precipitation required to prepare a rare earth in a pure form, it is probably more important to choose as rich as possible a source in preparing the rare earths than in preparing any other elements. Early analysts, recognizing this, made such separations as were practicable and reported the rare earths in ores in percentages of cerium and yttrium groups and of cerium present. KOvery great advance in methods of analysis for
