Quartz Microgram Balance PAUL L. KIRK, RODERICK CRAIG, J. E. GULLBERG,
AND
R. Q. BOYER, Uniuersity of California, Berkeley, Calif.
Using principles previously described, a refined quartz torsion balance was constructed. It was capable of weighing a sample as large as 300 micrograms, carrying a load of at least 0.1 to 0.2 gram and yielding a sensitivity of at least 1 minute of arc per 0.005 microgram. The balance was considerably more rapid and reproducible than the microchemical balance and was free of vibration effects.
I
Electrical or magnetic methods in which the gravitational force of attraction for the object being lveighed is opposed by a measurable electrostatic or magnetic force of attraction upon the balance system. The resistance of a current-bearing conductor in a magnetic field to displacement also belongs in the latter category. Mechanical balance in which the gravitational force of attraction is opposed by bending, torsion, stretching, or compression of some part of the mechanism. Fluid displacement or flotation mechanisms in which the gravitational force of attraction is opposed by an Archimedean force lyhose magnitude is determined by the mass of fluid (or gas) displaced. The most common form of this balance depends on evacuating the balance case until a small suspended bulb of gas sinks sufficiently to balance the sample.
S T H E course of certain investigations on the chemistry of
element, 94239, plutonium, it, became imperative to weigh samples of a few micrograms with an accuracy comparable to that which may be obtained by the use of analyt'ical or microchemical balances used with proportionately larger samples. A sensitivity of at least =t0.01 microgram was desired and the total load tvhich could be weighed had to be large enough to allow chemical manipulation on the pans-Le., at least 100 nig. These requirements are not greater t,han have been met by previously described balances. I t \vas desirable, however, that this balance be much more practical for rout'ine use than are the five or six earlier types iyhich have been described. Such a balance was designed and const,ructed. Its possible uses far exceed the purpose for which it n-as made, since it is of general utility in microgram analysis, and it should prove especially valuable in such quantit,ative biological investigations as those in the field of biological microchemist'ry. I t may also have wide application in the general field of isotope microchemistry, amd indeed, Tyherever especially small samples must be weighed. In operation, the balance is simple, considerably more rapid than the microchemical balance, and less subject' to disturbance by temperature changes, radiation, and vibrat'ion. (Its design and use are covered by a United States patent.) Weight differences as small as 0.005 microgram were detectable. This limit can probably he diminished to 0.001 microgram or less n-it,h a slight sacrifice in load capacity.
HISTORICAL
Although balances more delicate than the conventional microchemical balance are comparatively rare in modern laboratories, the cause does not lie in the absence of investigation and development in this field. From as early as 1882 to about 1912, a considerable number of balances ranging in sensitivity from 0.05 (4, 7 ) t o 4000 scale divisions per microgram (6) were described. Complete reviews of these developments, published by Gorbach (2) and Emich ( I ) , make unnecessary a detailed discussion here. Most significant to the development of the balance described m-as the work of Steele and Grant ( 9 ) , who first constructed a complete balance from fused quartz and employed fused-on fine quartz fibers for suspension of the pans, instead of the conventional knife-edge; Pettersson (6), who improved the design of the all-quartz balance and presented a detailed discussion of the theory of such instruments; and Seher (ii), who introduced the method of mounting the beam on a torsion fiber of quartz, which was used to balance the sample weight. The simple balance of Keher had a low load capacity, but with loads of less than 1 mg. it would yield a sensitivity of 0.1 to 0.001 microgram per scale division without the use of mirrors or microscopes.
THE PROBLEM
I t was unnecessary that the total load be weighed to the limiting sensit,ivity, since the samples might' be expected to L-ieigh from 1 to 100 micrograms, and only t,his sample weight had to be determined in the absolute sense to the full accuracy. I t rvas essent,ial, however, t,hat.the greater load composed of pans and supports be balanced by an opposing force of great constancy for at least 'the period of weighing, and ideally for an indefinite period. Assuming a t,ot,alload of 100 mg., the balancing force had to remain constant to 1 part, in 10,000,000. The reproducibility of t'he sample weight itself needed to he 1 part in 1000 for a sample weight of 10 micrograms or less and 1 part in 10,000 up t'o a weight of 100 micrograms, if the sensitivit,y or limiting accuracy was *0.01 microgram. Thus, the problem was resolved into two components:
This simple design had so many features to recommend it, that its principle was used in constructing the balance described in this publication. The optical system with which Seher dispensed was added to increase the relative sensitivity. The design was also altered considerably to incorporate greater strength and less distortion. il considerably more delicate and reproducible method was used to determine the amount of torque. By these means, it was possible to increase the load greatly and at the same time to maintain the high sensitivity. Sumerous designs of helical quartz balances have been constructed and used widely and effectively. Their principle is such that helical balances cannot be built to retain both a high load capacity and a high sensitivity. For this reason no detailed discussion of such instruments is included here.
1. Means whereby a relatively large mass could be balanced with very high reproducibility but without an absolute determination of the mass. 2. Means whereby a small superimposed lqad (the sample) could be balanced by an absolutely determinable force (or weight) with an accuracy of about 1part in 10,000.
Requirement' 1 was best, met, by the use of gravitation, which may be assumed to he sufficiently uniform throughout a small volume and not subject, to sudden variations. Thus a counterweighted beam could most, easily maintain constancy of balance of the large component of the niass. The sample itself is not conveniently balanced in t'his manner, because of the excessively small size of any weight or rider vhich may be used for the' purpose. In addition to the common gravit'ational balance, a number of other balancing principles have been used.
CONSTRUCTIOR
The balance which was finally constructed combined the torsion principle of Seher, the pan suspension of Steele and Grant, the pan well of Pettersson, and a comparison microscope for determining the beam position. By using a cantilever beam of great rigidity, the main portion of the load-viz., the pans and pan suspensions- 1yei-e balanced by gravity. The sample contained in one of the pans was balanced by rotation of the wheel to apply 427
V O L U M E 19, NO. 6
428 sufficient torsion to the fiber to restore the beam to the horizontal as determined by the comparison microscope. The overall design is shown in Figure 1. Quartz Assembly. The quartz assembly consisted of a beam, of cantilever or upright triangle form with pan supports or hangdowns; a torsion fiber; a bow attached to one end of the torsion fiber; end attachments; and pan support cradles. With tlie exception of the latter, all the quarts pieces were fused together into a single assembly. The beam had to be as rigid as possible under all weighrtble loads, and as light in weight as uossible. Massive construction t o
lected was "the simple &tilever
used an as~indexfor det;&ning
shown in Figure 2. Themain
the beam~positionwas
F&L:
structed from fiber apprnximately 15p in diameter. The brace
portion of the vertical member was used for adibsting thecenter
which allowed accurate reproduction of beams and a gr'eat re&& tion in construction time over other methods which have been described (6). Details of the jig method of constructing quart5 fiber device may be the subject of a later publication. Fibers were drawn by a variety of methods, depending an the size desired. I n penerd the larger fibers-greater than 50p in
arrow shot from a cross how into a targkt from 4.6 to 7.5 meters
crtised bv raging t h e center of gravity of the beam above the
to 1 minute of arc on the wheel per 0.005 microgram. The sensitivity varies inversely with the fourth pnwer of the diameter, so that a very slight change in diameter produces a large change in sensitivity. This is fsvorable for an ultradelicate balance because the tensile strength of the fiber is about proportional ta the square of the diameter. A slight decrease in diameter increases the sensitivity much more rapidly than it lowers theload capacity. Cdculation indicates that a 17p fiber mill yield a sensitivity of approximately * 0.001 microgram. I t has long been known that quartz bas B tendency to crystallize with alteration of its physical properties, particularly with regard t o tensile strength. While this effect might be expected t o be significsut in the use of these balances, intermittent though frequent use over a period of nearly two years did not lead to spontaneous breakage under load, nor did the sensitivity of the balance change markedly. Further atudy of this effect should definitely be made over a longer period of time, a study whieb was not possible under the existing conditions of use. Several designs of pan support cradle were used. A satisfactory one, which was also constructed on a jig, is shown in Figure 2 (right). A single side Suppwt may be used instead of the double one shown, as may also various other designs, which give the requisite strength and reasonable rigidity without adding excessively to the weight.
Figure 1. Balance with Cover Removed
Support and Case Assembly. The supporting mechanism and case assembly were constructed chieRy of brass. These metal parts served to support the optical system and the ends of the quarta torsion fiber nn which the beam was suspended. Since the load was so small, no distortion due t o the metal parts had to be considered. The supports were made comparatively heavy to increase the inertia. and thus avoid vibration. The metal parts consisted essentially of a rectangular frame mounted in a vertical position, carrying the supports of the quartz assembly, the frame being fastened t o a rectangular metal base plate provided with leveling screw6 on which it rode. The uprights and base of the frame were ConstNCted of brass 1.25 X 5 em. (0.5 X 2 inches) and the top member was of brass 1.25 x 1.25 em. (0.5 x 0.5 inch). The base was about 25 X 17.6 X 1.25 em. (10 X 7 X 0.5 inch). A little consideration will show that as long a6 the temperature of the whole frame was uniform, no error was introduced by dimensional changes. Variation of the axis of the torsion fiber also could introduce no error, so the restriction on the graduated wheel was that the angle of rotation could he measured with sufficient wcuracv. This r d d be read t t i 1 minute ( i f arc with u vernier wl.icli kcquired that the a x i d of rotxtirm correjpond with the
