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Mass Traceability for
an unbroken chain of comparisons all having stated uncertainties" (2). It is important to understand that traceability cannot be achieved by simple ownership of traceable standards; the measurement process and procedure must also be verified, and the people and equipment involved in a traceable measurement are as important as the standards themselves. In international commerce, traceability of mass measurements to the international prototype of the kilogram held by the Bureau International des Poids et Mesures (BIPM) in Sevres, France, closes the loop between vendor and client communities. In this article, we focus on the issues of proper mass measurement and how to determine the bias of mass measurements. Buoyancy effects
Analytical Measurements Measurements made in one place and time must be related unambiguously to those made by other workers at different locations and times
r
ass measurement is fundamental to most chemical determinations, including the mass of a sample, calibration of volumetric glassware, or dilution by mass. In the days of equal-arm balances, great pains were taken to ensure that an accurate set of weights was used to calibrate the balance. Today's electronic balances, however, usually include one or more built-in weights to facilitate calibration (1). Use of these balances assumes that built-in (and often sealed) calibration weights are sufficiently accurate to calibrate the balance to within its specified accuracy and that the balance has a linear response over the mass range derived from one weight at
M i c h a e l W . Hinds Royal Canadian Mint George Chapman National Research Council Canada 0003-2700/96/0368 -35A/$12.00/0 © 1995 American Chemical Society
one end of the mass range. Although a competent analyst would operate few analytical instruments without proper quality control samples to be sure of the proper functioning of the device, mass measurements are often assumed to be correct In many instances, this may be a valid assumption, but, ultimately, a mechanism to verify the operation of a balance by an external method that is entirely under the analyst's control should be available. Measurements made in one place and time must be related unambiguously to those made by other workers at different locations and times. This aim can be achieved only through the application of the concept of traceability.
The word "weight" in the English language is often used when "mass" is intended. Weight is a force that is generated by a mass as a result of the gravitational attraction of the Earth and varies from place to place, even at sea level, by up to 0.5%. Mass, however, is unaffected by location. The term "weight" has been accepted by the Consultative Committee on Mass and Associated Quantities (BIPM) as a term to be applied to a mass piece that is intended to be a standard (3). In air, the gravitational force or weight acting on an object is related to the mass, the density, and the buoyancy. The effective mass of an object is the mass that would be measured in a vacuum (often called the absolute mass) less the mass of the volume of air that it displaces. Calibrated mass values can thus be corrected for air buoyancy effects. As the densities of materials become greater, buoyancy decreases because they occupy smaller volumes (4), and one can conclude that, in an atmosphere, a pound of iron does indeed weigh more than a pound of feathers because of the greater buoyancy force of the feathers.
Aside from solving brain teasers, buoyancy does affect mass measurements. The magnitude of this effect depends on the What exactly is meant by "traceability"? The Vocabulaire International de Me-difference between the density of the reftrologie definition of traceability is "prop- erence weight and the density of the mateerty of the result of a measurement or the rial of interest. The dominant bias encountered in weighing is mat attributed to value of a standard whereby it can be related to stated references, usually through the buoyancy correction based on Analytical Chemistry News & Features, January 1, 1996 35 A
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Archimedes' Principle, in which the effective mass of an object is less than the absolute mass by the mass of air that the object displaces. Thus, for a stainless steel weight that has an absolute mass of exactly 1 kg and a density of 7900 kg/m3, the effective mass would be 999.848 g when the air density is 1.2 kg/m3. A summary of the equations used for these calculations can be found in a recent NRCC report (5). Bias from internal calibration weights
Despite the best efforts of balance manufacturers, internal weights inevitably have some (albeit small) bias. The tolerances for weights of various classifications are defined by organizations such as the American Society for Testing and Materials (ASTM), the National Institute of Standards and Technology (NIST), and the Organization Internationale de Metrologie Legal (OIML). Internal calibration weights typically conform to ASTM E-617 or NBS(NIST) class S, which can deviate as much as 2.5 ppm from the nominal value. Therefore, a comparison of two mass values determined for the same weight from different models of the same electronic balance can vary by as much as 5 ppm because the internal weights of each balance are at either end of the class tolerance. Calibration is affected by the internal electronics of the balance by fitting a straight line to two forces experienced by the load cell or nulling circuits. Zero is set under ambient conditions with the pan empty, and the output of the balance is set equal to the nominal mass of the calibration weight when the calibration weight is added to the weighing mechanism. If the linearity of the balance output is assumed, the operator who places an object on the balance pan expects a balance reading that is proportional to the effective mass of the object The absolute mass and the balance reading are then related to the buoyancy of the internal calibration weight and that of the object on the pan. When the densities of the calibration weight and the object being weighed are the same, the mass of the object is equal to the balance reading. At this point, it is instructive to consider the implications of this simple cali36 A
bration relationship. Consider a balance with an internal weight with a density of 7700 kg/m3 that has been adjusted to exactly nominal absolute mass. A service technician, using a check weight made by the same manufacturer and with the same density as the internal calibration weight, checks the balance operation in situ and declares it to be operating within specifications, a repeatability of 2 mg. If a staff member of the laboratory then produces a 1-kg weight made to the same Grade S specifications and adjusted to exactly 1 kg absolute and places it on the balance pan, the output of the balance may range from exactly 1 kg to 1 kg plus 7.7 mg, because the second kilogram may have a density in the range 7700 to 8100 kg/m3 and still be within Grade S specifications. Unless air buoyancy is properly accounted for, deviations from expected results may be observed even when all
Mass values determined for the same weight from different electronic balances can vary by 5 ppm. components of a measurement system are thoroughly inspected and passed as being within tolerance. Although the user usually has little or no access to information about the density of the internal weight(s) or whether it has been adjusted properly, if a reference weight whose attributes are well known is used, more accurate mass comparisons can be made. Approaches to weighing
It is evident that buoyancy does affect the accuracy of a mass determination. Mass measurements are also limited by the assumption that the internal weight within the balance is absolutely accurate. Although in many situations these factors may not be of significant concern, it is useful to examine some different approaches to mass measurement. Direct weighing. For most analysts, this is the method of choice: A sample can
Analytical Chemistry News & Features, January 1, 1996
be placed on the balance pan and the mass recorded from the display on the electronic balance. The analyst assumes that the internal weights within the balance are absolutely accurate, that the balance gives a linear response throughout the operating range of the balance, and that no buoyancy effects exist. Because the absolute accuracy of a sealed internal weight cannot be guaranteed, a bias of a few ppm can be expected in this procedure. Although it is reasonable to expect a linear response over most of the range of the balance, it would be prudent to verify this response periodically with a set of external weights. It is also clear from the earlier examples that substantial buoyancy effects do occur. Weight by difference. Another common method is to record the mass of a container and then place the appropriate amount of sample or substance into the container and record the mass again. Although this approach gets around the problem of any bias or offset of the linear calibration by subtracting the two weights, it cannot account for buoyancy effects and also assumes that the balance response is linear. Comparative weighing. The final common approach is to measure the difference between a sample of interest and reference weight whose mass is very well known and then add this difference and the known mass of the reference weight to arrive at an accurate mass value. This approach overcomes any bias in the internal weight of the balance, minimizes error due to nonlinear response because of the small differences that are measured, and eliminates buoyancy effects if the reference sample is made of the sample material. Although this method is not as convenient as the direct weighing method, it is far more accurate. Choice of approach. The choice of weighing procedure is entirely dependent upon the situation. Whether an approach introduces a significant bias depends on the importance of the measurement, precision of other analytical methods that affect thefinalvalues assigned to a sample, and the resources that are available to assign to this task. Another important consideration is that the procedure by which the mass values are determined must be accepted by the industrial community
concerned. If this is not the case, a decision must be made to either maintain the status quo or communicate the accuracy of the new approach to the end user. Why bother w i t h mass traceability?
There has been a growing trend toward ensuring traceability in chemical measurements to primary reference standards (6). The adoption of International Organization for Standardization (ISO) standards has prompted many organizations to re-evaluate their procedures in terms of repeatability (Can we make or measure things consistently?) and in terms of accuracy (Can we conform to the specifications? Do our measurements agree with national or international standards?). Obviously the extent to which an analyst is concerned with mass traceability depends on the method of analysis and importance of the measurement. In the case of the Royal Canadian Mint (RCM), mass traceability is very important for the weighing of precious metal products and for the gold bullion fire assay, a gravimetric method in which a set of eight 500-mg samples are used to determine the gold content of 800 tr.oz. gold bullion bars valued up to $320,000. It also assists in the certification of precious metal reference materials produced at RCM. Although current electronic balances are very precise, it is difficult to judge their accuracy, and there is generally no documentation on the traceability of the internal weight nor any way to evaluate the weight because it is sealed within the balance. In addition, there is no built-in mechanism to assess the bias in the mass measurements from a particular balance caused by its reference weight's density or calibration. This must come from procedures that use external weights of known mass that can be traced to the international prototype of the kilogram. The single most serious bias is that attributed to buoyancy effects, especially when there are great differences between the densities of the reference weight and the unknown.
a variety of classifications of mass stanmore sets of working weights. The referdards, and each classification outlines the ence set is used only to verify the working type of material and tolerances that can sets at least twice a year. The mass of the be expected from the manufacturer. reference set is verified by comparison to One-piece vs. two-piece weights. traceable weights by an accredited mass Although a single-piece weight is more dif- laboratory or a national standards laboratory. An ideal schedule has the masses of ficult to manufacture, if properly handled it will maintain its mass for a very long the whole reference set verified for two consecutive years. If no excessive deviatime. Two-piece weights, which are generally more easily manufactured and used tions are observed, a quarter of the weights are reverified in succeeding years. for masses above 1 g, can be classified This schedule ensures that the reference into two categories: plug type and screw (or cavity) type. The plug type consists of weights maintain their mass calibration over a long period of time in an economia cylinder of metal with the center bored cal manner. Because a fair amount of time, out and a lead plug inserted and fastened into the bore to bring the weight to its effort, and money have been invested in the reference set, it is not in the analyst's nominal mass value. The screw type consists of a cylinder of metal with an empty long-term best interest to use this set too frequently. Working sets are generally cavity containing metal trim weights to used on a more regular basis (daily or bring the weight to its nominal value; a weekly) at balances at one particular screw top (whose mass is also measured) weighing station or within a laboratory. is fastened to complete the weight. The Therefore, these weight sets should be cleaned, and the mass values checked regularly against the reference set values.
Mass standards
Handling practices for weights. As a general rule, no weight should come into direct contact with skin or abrasive material because this may alter the mass of the weight, mar the finish, and lead to corrosion of the surface, which will also change the mass of the weight. Weights should be kept in a lint-free lined box that has indentations (or holes) for each weight Only plastic forceps and/or lintscrew-type two-piece weights tend to main- free gloves should be used to handle the weights. Stainless steel weights should be tain their masses for longer periods of cleaned in a 1:1 mixture of ethyl alcohol time and can be adjusted by adding or removing metal trim weights if necessary. and diethyl ether; a clean piece of chamois leather can be used to rub off any (One screw-type weight set, still in use at RCM, is 120 years old!) Plug and screw- marks that do not dissolve. As afinalstep, weights should be rinsed in distilled type weights are acceptable for many deionized water and air dried. Cleaning weight classifications. Other factors that frequency is dictated by frequency of use must be considered, especially in an inherand how many different people use the ited set of weights, include thefinishand weight set. Any inadvertent damage, depth of lettering. A machined finish is such as from dropping the weight, should preferable to a platedfinishbecause with be noted, and the piece should be cleaned continued use a plated finish may deterioand recalibrated or replaced. rate. Avoid using weights that show obvious wear on the finish or corrosion. The smaller the indentation of any identificaCalibration tion marks or numbers (lettering), the Once you have made a decision (a wise smaller the chance of picking up partione!) to have a set of weights calibrated, cles and altering the mass over time. how do you go about it? National mass
The foundation of any mass traceability program is the procurement and maintenance of a set of mass standards. There is
Reference and working sets. As a general rule, at least two weight sets are recommended: a reference set and one or
The single most serious bias is that attributed to buoyancy effects.
standards laboratories will either calibrate weights or refer you to properly accredited laboratories. Each national mass
Analytical Chemistry News & Features, January 1, 1996 3 7 A
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Figure 1 . Mass metrology pyramid. The numbers represent approximate relative uncertainties available at each level.
laboratory has at least one kilogram that has been calibrated in terms of the international prototype of the kilogram (Le Grand K) held by the Bureau International des Poids et Mesures and maintains sets of reference weights verified in terms of the national prototype. Several working sets are then verified in terms of the reference sets. A set of weights sent to the laboratory is calibrated by direct comparison to one of the working sets. Figure 1 illustrates how relative uncertainty increases as one moves away from the prototype kilogram. Depending on your requirements, you may wish to have a single weight calibrated. More sophisticated work may require calibration of a set of weights. If your application involves only the measurement of the same mass, calibration of a single weight may be adequate. For most laboratories, however, a set of weights ranging from 1 mg to 100 g is usually required. Such a set normally contains 22 weights which, in combination, will produce nomi38 A
nal masses from 1 mg to 211.12 g in 1-mg steps. The cost of calibrating a single weight is lower than calibrating a set, but the utility of having a calibrated set is, in our opinion, worth the extra cost Air buoyancy and density corrections. Mass values for calibrated weights, termed absolute values, are usually quoted for the weights in a vacuum because air buoyancy effects differ with time and location. A weight calibrated at sea level can be then be used in a mountainous region when the barometric pressure, temperature, and relative humidity are measured to calculate the air density. For accurate mass calibration, the density of the metal the weight is made of must be known. There is a large difference (390 mg/kg) between the buoyancy effects of aluminum compared with the platinum-iridium alloy from which kilogram prototypes are made. Even when comparing stainless steel weights, the most accurate mass calibrations involve determining the densities of each weight
Analytical Chemistry News & Features, January 1, 1996
because the density of steel alloys used for weights often varies by 12%. For careful work, air density can either be measured or computed from temperature, barometric pressure, and relative humidity using the definitive formulas given by Davis (7). If accuracy better than 2 or 3 ppm is required, air density must be computed. Uncertainty. A statement of uncertainty for mass measurement is an essential requirement for traceability. Uncertainty can be estimated by following an internationally recognized set of rules (8) that rigorously defines standard uncertainty, which can be either statistically based (standard deviation) or knowledgebased (uncertainty of stainless steel densities). Standard uncertainties can be combined by adding the squared individual standard uncertainties and then taking the positive square root of the resultant sum. There are four main sources of uncertainty: reference mass and density values, unknown object density values, air density values, and uncertainty in the measurement process. If calibrated by an accredited mass laboratory, each reference weight comes with a stated uncertainty for both mass and density. Weighing uncertainty refers to the imprecision of the measurement process and can be calculated from the standard deviation of several weight measurements of the same weight. Balance QA
Quality assurance is a way to confirm that a given balance at a given time is performing as expected. A quality assurance program involves regular checks of the operational balance performance, including the zeroing function, the linear response over a weight range, and response of a check weight at different pan positions. Any obvious damage and the steps taken to repair the balance should also be noted for each balance. The scheduling of these checks depends on the frequency of the balance use and the importance of the measurements. For example, at RCM, balances used for fire assay determinations of gold bullion are checked daily with a check weight and weekly for linear range. A quality control chart can then be used to establish a normal operational range (± 3 8) and determine if the balance is performing as expected. This program has
been very useful in assuring RCM customers and auditors that mass measurements are accurate. Alternatively, some laboratories hire outside contractors to verify balance operations and verify mass measurement accuracy. The laboratory should expect the contractor to provide a set of procedures for verifying balance operation and a written report from each visit. If the laboratory is relying on the contractor to assess mass measurement accuracy, the contractor should produce documents outlining the traceability of the weights used for assessment and the procedures used in the assessment process. Finally, a written statement (dated and signed) indicating the mass measurement bias should be produced from each visit. Admittedly, the implementation and maintenance of this program takes time and effort, but this is offset by the assurance that the balances in a program operate properly and within the accuracy of the external reference weights. References (1) Schoonover, R. M. Anal. Chem. 1982,54, 973 A. (2) Vocabulaire International de Metrologie, 2nd ed., International Organization for Standardization, Geneva, Switzerland, 1993. (3) Consultative Committee on Mass and Associated Quantities, Bureau International des Poids et Mesures, Sevres, France, 1981. (4) Schoonover, R. M; Jones, F. E. Anal. Chem. 1981,53,900. (5) Chapman, G. Weighing with Electronic Balances; National Research Council Canada: Ottawa, NRCC 38659,1995. (6) Taylor, H. K. Quality Assurance of Chemical Measurements; Lewis Publishers: Chelsea, MI, 1987. (7) Davis, R. S. Metrologia 1992,29, 67. (8) ISO Guide to the Expression of Uncertainty in Measurement, 1st ed.; International Organization for Standardization: Geneva, Switzerland, 1995. Michael W. Hinds, an assay chemist at the Royal Canadian Mint, is involved in developing precious metal reference materials and conducts fundamental and applied research in atomic spectrometry. George Chapman, group leader of mechanical metrology for the Institute for National Measurement Standards at NRCC, is responsible for the INMS mass standards program. Address correspondence about this article to Hinds at the Royal Canadian Mint, 320 Sussex Dr., Ottawa, Ontario, K1A 0G8, Canada.
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