Micro-homogeneity of Candidate Reference Materials Characterized by Particle Size and Homogeneity Factor Determination Thomas-Michael Sonntag and Matthias Rossbach* Institute of Applied Physical Chemistry, Research Centre J�ulich, KFA, 52425 J�ulich, Germany The IAEA Analytical Quality Control Services (AQCS) have made available two single-cell algal materials, IAEA-392 and IAEA-393, and an urban dust, IAEA-396, to study their use for analytical sample sizes in the milligram range and below.Solid sampling Zeemans effect AAS was applied to the determination of trace elements on the bases of 1026–1023 g amounts of the selected materials. The comparability of the mean values and the reproducibility of successive measurements is being evaluated in order to compare relative homogeneity factors for many elements in the investigated materials. From the reported results it seems that the algal materials IAEA-392 and IAEA-393 are extremely homogeneous biological materials for a number of elements with an extraordinarily sharp particle size distribution below 1025 m.A similar situation seems to hold for the urban dust material IAEA-396, which had been air-jet milled to a particle size distribution of around 4 3 1026 m. The introduction of these materials as CRMs with very small amounts needed to determine the certified concentrations will help to meet the needs of micro-analytical techniques for natural matrix reference materials.Keywords: Homogeneity; biological reference materials; particle size distribution; solid sampling atomic absorption spectrometry Certified Reference Materials (CRMs) from various producers are commonly used in trace analysis for method development and quality control purposes. Analytical techniques are becoming more and more sensitive and require smaller amounts of sample. Particularly the so-called ‘micro-analytical techniques’ such as m-PIXE, laser ablation MS, solid sampling AAS and Xray fluorescence techniques are especially sensitive to sample homogeneity.Determinations rely in some cases almost entirely on the availability of CRMs of proven homogeneity in the range of milligrams or below. Some of the producers of CRMs state in their certificates, however, that certified values are valid only if more than 100 mg of the material is used for analysis. Besides the fact that precious material is wasted if a homogeneous material is consumed in such a large quantity for the determination of a single element in one analytical run, a more precise evaluation of the homogeneity with regard to the element (or compound) considered in a given material would be desirable.The precision of an analytical measurement is a direct function of the stability of the instrument’s response and the material’s homogeneity, i.e., detecting the same chemical composition in successive aliquots. With decreasing mass of the aliquot the statistical probability of finding the same distribution of particles with identical overall composition decreases.Assuming a certain degree of heterogeneity of natural matrix materials, the homogeneity of a reference material at a level of 1026–1023 g aliquots is a direct function of its particle size distribution.1 Trace elements and compounds tend to be unevenly distributed throughout a biological or other environmental material. In the course of reference material production, homogenization of such materials is a critical step and generally results in a finely ground powder.The experimental determination of elementspecific homogeneity factors is tedious and time consuming. In many cases it is assumed from an exemplary survey analysis of one or two elements (with sometimes inadequate methods and/ or irrelevant sample mass) that all the certified elements behave in the same way. In order to be on the safe side, CRM producers generally quote the homogeneity of their materials to be satisfactory only at a high to very high (100–500 mg) sample mass.2 Precisely determined sampling constants3 or homogeneity factors for individual elements, which enable analysts to trace the material-inherent variability of concentrations to the level of material consumed for a particular analytical technique, would help to increase considerably the precision of results from such techniques and help to establish a higher degree of reliability of the results.The accurate applicability for quantitative analysis of micro-analytical techniques in biomedical, forensic, archaeological and palaeontological investigations would be greatly enhanced. Downscaling of sample preparation techniques and of digestion instruments would be feasible. If smaller amounts of reference materials could be used for quality assurance in various applications, these valuable materials could be used more extensively and the production of new materials could be concentrated on a greater diversity of matrices rather than on replacing exhausted materials.Experimental Three batches of single-cell green algae (Chlorella sp.) grown in cultivation media with different concentration levels of a number of environmentally relevant elements were produced at the Czech University of Agriculture, Prague, in large amounts.4 After harvesting 30–50 kg of fresh material with elevated, environmental and low levels of trace elements, the materials were air sprayed for drying.Without further grinding, the materials with elevated levels (IAEA-393) and the material with environmental levels (IAEA-392) were distributed among the participating laboratories of the first IAEA-AQCS meeting on ‘Reference materials for micro-analytical nuclear techniques’ held in Zagreb, Croatia, in December 1994.5 The third material, single-cell algae with low levels of trace elements (IAEA-391), was distributed only in early 1996 and could therefore not be fully implemented in this intercomparison.A second candidate reference material, ‘urban dust’, was distributed at the same time in two versions: one batch had been sieved through a mesh size of 70 31026 m (IAEA-396A/S) and the other was air-jet milled material (IAEA-396A/M). Both materials originate from a collection of air particulate matter extracted from the air conditioning filters of a Vienna hospital and should reflect the average loading of air particulates from an industrialized urban environment. The material was collected in Analyst, January 1997, Vol. 122 (27–31) 27a large enough amount and is intended to be used as a future air filter reference material.6 Solid sampling Zeeman-effect atomic absorption spectrometry (SS-ZAAS) is a well established technique within the AAS family of techniques.7,8 It allows the introduction of small amounts (0.02–20 mg) of solid materials for electrothermal atomization in a graphite furnace and single-element determination. Zeeman splitting of the specific absorption lines is performed by a strong magnetic field applied at the emission lamp and the instrument (SM 30, Firma Gr�un Optic, Wetzlar, Germany) is automatically tuned for zero adjustment and optimum sensitivity.Calibration was carried out using appropriate reference materials (NIES No. 9, sargassum for algae, and NIST SRM 1648, urban particulate matter for the IAEA dust materials). As it turned out that the peak height of the absorption signals gave more consistent results than the integrated peak area, peak height was used throughout the evaluation of our experiments for quantification.Whether this is due to a specific software problem or is a special feature of the direct solid sampling techniques could not be investigated. The technique is rapid (no sample digestion), inexpensive and sensitive for a large number of elements.9 The laser particle analyser Analysette 22 (Fritsch, Idar- Oberstein, Germany) contains an He–Ne laser and a detector system with 31 units each containing 10 channels.Particles between 0.1 and 1250 3 1026 m can be determined in intervals of 250 3 1026 m with a resolution of 310 channels. About 100 mg of dry sample are dispersed in propan-2-ol and agitated in a ultrasonic bath for about 10 min. The suspension is then pumped through the meast cell of the instrument with a built-in ultrasonic agitator.The diffraction pattern of the scattered laser light is used to calculate the particle size and the mean distribution of particle sizes is recorded.10 Results Particle Size Distributions In Figs. 1–5, the determined particle size distributions of the five materials [algae elevated level (IAEA-393), algae environmental level (IAEA-392), algae low level (IAEA-391), urban dust sieved (IAEA-396A/S) and urban dust jet milled (IAEA-396A/M)] are shown. From Figs. 1–5, it is clear that all materials exhibit fairly sharp particle size distributions with 90% of the particles smaller than 7, 15, 4.5, 20 and 25 mm for the respective materials.This finding points to very homogeneous materials where small amounts for analysis could show good reproducibility of replicate measurements11 provided that no systematic errors hamper the quantification. The systematic error of the technique was tested in performing replicate measurements with liquid standard solutions.It could be shown that SS-ZAAS does not add more than 3% to the overall standard deviation and is therefore well suited for this kind of homogeneity study. Homogeneity Factor and Sampling Constants According to Ingamells and Swizer,12 a sampling constant can be given by Ks = R2m (1) where Ks = sampling constant, R = relative standard deviation and m = mean sample mass (mg). This constant was originally intended to be used in geological sampling of larger amounts than are generally used for analysis, notably in microanalysis. Fig. 1 Particle size distribution in IAEA-393, algae elevated level. Fig. 2 Particle size distribution in IAEA-392, algae environmental level. Fig. 3 Particle size distribution in IAEA-391, algae low level. Fig. 4 Particle size distribution in IAEA-396A/M, urban dust air-jet milled. 28 Analyst, January 1997, Vol. 122Kurf�urst et al.13 therefore took the square root of this factor to calculate the relative homogeneity factor, HE: HE = sHOMAmºº (2) where sHOM = relative standard deviation and m = mean sample mass (mg).The difference between the two factors can be illustrated graphically as shown in Figs. 6 and 7. Whereas Ingamell and Switzer’s factor ends up with very large numbers at moderate sample mass, Kurf�urst et al.’s factor is suitable particularly for the description of low sample masses but not so much for higher sample masses. For application of milligram sample inputs to the SS-ZAAS instrument we preferred Kurf�urst et al.’s approach to describe the relative homogeneity as HE in mg1 2.11,14 Homogeneity Testing The systematic error of the SS-ZAAS method was checked using liquid standard solutions for several elements.It was found that, related to the absolute mass of element introduced into the graphite furnace, the reproducibility of repetitive measurements varied only between 2 to 3%. The pipetting error can be estimated (by weighing) to be < 1%. Weighing of the solid materials using a Sartorius 4503 microbalance with a maximum loading of 4.1 g and a weighing error of d = ±0.001 mg assures a maximum weighing inaccuracy of < 1% at a sample mass of 0.1 mg.A few examples of the reproducibility of repetitive (20) measurements of the investigated materials using the SS-ZAAS approach are shown in Figs. 8–11. It can be seen that the reproducibility of repetitive measurements varies with the element analysed in a particular sample material and the standard deviation varies with the mass of the sample analysed Fig. 5 Particle size distribution in IAEA-396A/S, urban dust sieved. Fig. 6 Proportionality between sampling constant and sample mass at different fixed standard deviations. Fig. 7 Proportionality between the relative homogeneity factor HE and the sample mass at different fixed standard deviations. Fig. 8 Lead homogeneity in IAEA 393, algae elevated level, mean sample mass 0.193 mg. Fig. 9 Copper homogeneity in IAEA-392, algae environmental level, mean sample mass 0.458 mg.Fig. 10 Copper homogeneity in IAEA 396A/M, urban dust, mean sample mass 0.34 mg. Analyst, January 1997, Vol. 122 29(e.g., Cu in dust at a sample mass of 0.34 mg is reproducible with RSD = 5.5% and at a level of 0.08 mg with RSD = 10%). In order to achieve relative homogeneity factors related to the sample mass used for analysis, a number of measurement series all following the same routine (20 measurements, same calibration, same wavelength) were carried out and the results were plotted [RSD versus sample mass (mg)] as shown in Figs. 12 and 13. Fitting the parabolic curves yields a function of x depending on a factor times m21 2. The factor is the relative homogeneity factor of Kurf�urst et al. (HE) and it is related to this particular element’s homogeneity in the investigated material. In Table 1, the HE values for the four materials are given for all the elements investigated.The Cd concentration in IAEA-392 is very low and close to the detection limit of the method (0.015 ± 0.006 mg kg21) at a sample mass of 1.3 mg. For this reason, only one measurement series of 20 measurements could be carried out. Within these 20 measurements one outlier of about three times the mean of all other results was recorded. This value was not rejected and hence the RSD reached about 50%. Cadmium therefore cannot be considered to be homogeneously distributed in this particular material (IAEA-392, algae, environmental level).Lead concentrations could not be determined at all in this material at such a sample mass level. Increasing the sample mass by a factor of ten resulted in a more sensitive determination. Discussion and Conclusion It was shown that the particle size distributions of all five materials are exceptionally narrow and peak at very low particle sizes, compared with the normal range of other biological reference materials.From this finding, the assumption of good to very good homogeneity for trace elements can be drawn. Using the approach of Kurf�urst et al. a numerical description of element-specific homogeneity of the materials was experimentally elaborated. As Kurf�urst and co-workers pointed out,13–16 HE < 10 indicates very good homogeneity. All the materials investigated for the investigated elements show HE values in this range (with the exception of Cd in IAEA-392) and can be considered suitable as reference materials for micro-analytical techniques analysing samples with masses between 0.1 and 10 mg.For techniques using even smaller amounts of sample, natural matrix reference materials still have to be investigated. As the relative homogeneity factors HE are determined in an accurate way for individual elements in a given material, they can be used to assign the uncertainty of a certified concentration which is due only to material heterogeneity. Today the uncertainty given for certified reference materials is a composite of several uncertainties, such as (i) the systematic error of the analytical technique, (ii) bias from different standardizations of all the techniques used for certification and (iii) the materials’ inherent heterogeneity.By assigning a certified value with the homogeneity factor related to the sample mass consumed in analysis it is possible to calculate a mass-dependent uncertainty which derives strictly from the quality of the material itself.Hence systematic errors and bias of analytical techniques will be easier to recognize and the analytical process will be more transparent. The accurate determination of element-specific homogeneity factors for certified reference materials is essential for all CRMs to be used for quality control in micro-analytical trace element determinations. Suitable techniques such as INAA and SSZAAS with no sample digestion and accurate control over the total sample mass analysed are available and should be applied regularly in the course of certification of CRMs for the quantification of trace element distributions in natural matrix materials.The ‘true value’ of an element in a matrix is not a very useful parameter unless reliable information on the probability of obtaining exacue in repetitive measurements (repro- Fig. 11 Copper homogeneity IAEA 396, urban dust air-jet mulled, mean sample mass 0.08 mg. Fig. 12 RSD versus sample mass for Pb in IAEA 393, algae elevated level. The data points can be fitted as f(x) + 4.68 m21 2. Fig. 13 RSD versus sample mass for Cu in IAEA 393, algae elevated level. The data points can be fitted as f(x) + 8.67 m21 2. Table 1 Relative homogeneity factors, HE, for individual elements in the four materials investigated No. of Material measurements HE (Cu) HE (Cd) HE (Pb) IAEA-392 20 8.9 45.3 —* IAEA-393 80 8.7 4.0 4.7 IAEA-396A/M 20 3.0 4.6 6.8 IAEA-396A/S 20 8.9 8.4 6.7 * Pb in IAEA-392 was below the limit of determination. 30 Analyst, January 1997, Vol. 122ducibility) of the same material is attached to it. This probability is clearly dependent on the number of particles with potentially differing concentrations in an analytical aliquot and hence on the sample mass consumed for analysis. Hitherto certified values were given with a conservative estimate (amounting to 50% in some cases) of the overall uncertainty. The empirical statement ‘a minimum sample mass of 250 mg of the dried material .. . is necessary for any certified value . . . to be valid within the stated uncertainty’ is misleading and may only have a commercial background. Precisely determined individual homogeneity factors for each element would therefore help CRM users to (i) save precious material, (ii) determine the systematic error of the applied analytical technique and (iii) test the reliability of the sample preparation techniques more accurately and should therefore be endorsed also by CRM producers.We are grateful for and greatly appreciate the intensive work of D. Koglin in particle size analysis. M.R. acknowledges the financial support of the Bundesminister f�ur Umwelt, Naturschutz und Reaktorsicherheit, Bonn, and the Bundesumweltamt, Berlin. Many thanks are due to the IAEA (Dr. R. Zeisler, Dr. V. Valkovic) for letting us participate in this interesting AQCS programme. References 1 Rossbach, M., Ostapczuk, P., Schladot, J.D., and Emons, H., UWSFZ. Umweltchem. � Okotox., 1995, 7(6), 365. 2 Pauwels, J., and Vandecasteele, C., Fresenius’ J. Anal. Chem., 1993, 345, 121. 3 Chatt, A., Jayawickreme C. K., and McDowell, L. S., Fresenius’ J. Anal. Chem., 1990, 338, 399. 4 Mader, P., Stejskalova, I., and Slamova, A., Fresenius’ J. Anal. Chem., 1995, 352, 131. 5 Report of the Research Co-ordination Meeting on Reference Materials for Microanalytical Nuclear Techniques, IAEA/AL/083, IAEA, Vienna, 1994. 6 Zeisler, R., personal communication. 7 L�ucker, E., K�onig, H., Gabriel, W., and Rosopulo, A., Fresenius’ J. Anal. Chem., 1992, 342, 941. 8 Mohl, C., Grobecker, K. H., and Stoeppler, M., Fresenius’ J. Anal. Chem., 1987, 328, 413. 9 Kurf�urst, U., Fresenius’ Z. Anal. Chem., 1982, 313, 97. 10 Friedrich, H., and Mansour, A., Nachr. Chem. Tech. Lab., 1995, 43, 87. 11 Sonntag, Th.-M., Homogenit�atsstudien f�ur ausgew�ahlte Elemente in verschiedenen Materialien der Bank f�ur Umweltproben und der Internationalen Atomenergiebeh�orde mit der Solid-sampling-Zeeman- Atomabsorptionsspektrometrie, Diplomarbeit, Fachhochschule Aachen, Abteilung J�ulich, 1996. 12 Ingamells, C. O., and Swizer, P., Talanta, 1973, 20, 547. 13 Kurf�urst, U., Grobecker, K.-H., and Stoeppler, M., Trace Elem., 1984, 3, 591. 14 Stoeppler, M., Kurf�urst, U., and Grobecker, K.-H., Fresenius’ J. Anal. Chem., 1985, 322, 687. 15 Kurf�urst, U., Fresenius’ Z. Anal. Chem., 1983, 315, 304. 16 Kurf�urst, U., Fresenius’ Z. Anal. Chem., 1983, 316, 1. Paper 6/05396C Received August 1, 1996 Accepted October 21, 1996 Analyst, January 1997, Vol. 122 31 Micro-homogeneity of Candidate Reference Materials Characterized by Particle Size and Homogeneity Factor Determination Thomas-Michael Sonntag and Matthias Rossbach* Institute of Applied Physical Chemistry, Research Centre J�ulich, KFA, 52425 J�ulich, Germany The IAEA Analytical Quality Control Services (AQCS) have made available two single-cell algal materials, IAEA-392 and IAEA-393, and an urban dust, IAEA-396, to study their use for analytical sample sizes in the milligram range and below.Solid sampling Zeemans effect AAS was applied to the determination of trace elements on the bases of 1026–1023 g amounts of the selected materials. The comparability of the mean values and the reproducibility of successive measurements is being evaluated in order to compare relative homogeneity factors for many elements in the investigated materials.From the reported results it seems that the algal materials IAEA-392 and IAEA-393 are extremely homogeneous biological materials for a number of elements with an extraordinarily sharp particle size distribution below 1025 m. A similar situation seems to hold for the urban dust material IAEA-396, which had been air-jet milled to a particle size distribution of around 4 3 1026 m. The introduction of these materials as CRMs with very small amounts needed to determine the certified concentrations will help to meet the needs of micro-analytical techniques for natural matrix reference materials.Keywords: Homogeneity; biological reference materials; particle size distribution; solid sampling atomic absorption spectrometry Certified Reference Materials (CRMs) from various producers are commonly used in trace analysis for method development and quality control purposes. Analytical techniques are becoming more and more sensitive and require smaller amounts of sample.Particularly the so-called ‘micro-analytical techniques’ such as m-PIXE, laser ablation MS, solid sampling AAS and Xray fluorescence techniques are especially sensitive to sample homogeneity. Determinations rely in some cases almost entirely on the availability of CRMs of proven homogeneity in the range of milligrams or below. Some of the producers of CRMs state in their certificates, however, that certified values are valid only if more than 100 mg of the material is used for analysis.Besides the fact that precious material is wasted if a homogeneous material is consumed in such a large quantity for the determination of a single element in one analytical run, a more precise evaluation of the homogeneity with regard to the element (or compound) considered in a given material would be desirable. The precision of an analytical measurement is a direct function of the stability of the instrument’s response and the material’s homogeneity, i.e., detecting the same chemical composition in successive aliquots.With decreasing mass of the aliquot the statistical probability of finding the same distribution of particles with identical overall composition decreases. Assuming a certain degree of heterogeneity of natural matrix materials, the homogeneity of a reference material at a level of 1026–1023 g aliquots is a direct function of its particle size distribution.1 Trace elements and compounds tend to be unevenly distributed throughout a biological or other environmental material.In the course of reference material production, homogenization of such materials is a critical step and generally results in a finely ground powder. The experimental determination of elementspecific homogeneity factors is tedious and time consuming. In many cases it is assumed from an exemplary survey analysis of one or two elements (with sometimes inadequate methods and/ or irrelevant sample mass) that all the certified elements behave in the same way.In order to be on the safe side, CRM producers generally quote the homogeneity of their materials to be satisfactory only at a high to very high (100–500 mg) sample mass.2 Precisely determined sampling constants3 or homogeneity factors for individual elements, which enable analysts to trace the material-inherent variability of concentrations to the level of material consumed for a particular analytical technique, would help to increase considerably the precision of results from such techniques and help to establish a higher degree of reliability of the results.The accurate applicabimicro-analytical techniques in biomedical, forensic, archaeological and palaeontological investigations would be greatly enhanced. Downscaling of sample preparation techniques and of digestion instruments would be feasible. If smaller amounts of reference materials could be used for quality assurance in various applications, these valuable materials could be used more extensively and the production of new materials could be concentrated on a greater diversity of matrices rather than on replacing exhausted materials.Experimental Three batches of single-cell green algae (Chlorella sp.) grown in cultivation media with different concentration levels of a number of environmentally relevant elements were produced at the Czech University of Agriculture, Prague, in large amounts.4 After harvesting 30–50 kg of fresh material with elevated, environmental and low levels of trace elements, the materials were air sprayed for drying.Without further grinding, the materials with elevated levels (IAEA-393) and the material with environmental levels (IAEA-392) were distributed among the participating laboratories of the first IAEA-AQCS meeting on ‘Reference materials for micro-analytical nuclear techniques’ held in Zagreb, Croatia, in December 1994.5 The third material, single-cell algae with low levels of trace elements (IAEA-391), was distributed only in early 1996 and could therefore not be fully implemented in this intercomparison.A second candidate reference material, ‘urban dust’, was distributed at the same time in two versions: one batch had been sieved through a mesh size of 70 31026 m (IAEA-396A/S) and the other was air-jet milled material (IAEA-396A/M).Both materials originate from a collection of air particulate matter extracted from the air conditioning filters of a Vienna hospital and should reflect the average loading of air particulates from an industrialized urban environment. The material was collected in Analyst, January 1997, Vol. 122 (27–31) 27a large enough amount and is intended to be used as a future air filter reference material.6 Solid sampling Zeeman-effect atomic absorption spectrometry (SS-ZAAS) is a well established technique within the AAS family of techniques.7,8 It allows the introduction of small amounts (0.02–20 mg) of solid materials for electrothermal atomization in a graphite furnace and single-element determination.Zeeman splitting of the specific absorption lines is performed by a strong magnetic field applied at the emission lamp and the instrument (SM 30, Firma Gr�un Optic, Wetzlar, Germany) is automatically tuned for zero adjustment and optimum sensitivity. Calibration was carried out using appropriate reference materials (NIES No. 9, sargassum for algae, and NIST SRM 1648, urban particulate matter for the IAEA dust materials). As it turned out that the peak height of the absorption signals gave more consistent results than the integrated peak area, peak height was used throughout the evaluation of our experiments for quantification. Whether this is due to a specific software problem or is a special feature of the direct solid sampling techniques could not be investigated.The technique is rapid (no sample digestion), inexpensive and sensitive for a large number of elements.9 The laser particle analyser Analysette 22 (Fritsch, Idar- Oberstein, Germany) contains an He–Ne laser and a detector system with 31 units each containing 10 channels. Particles between 0.1 and 1250 3 1026 m can be determined in intervals of 250 3 1026 m with a resolution of 310 channels. About 100 mg of dry sample are dispersed in propan-2-ol and agitated in a ultrasonic bath for about 10 min.The suspension is then pumped through the measurement cell of the instrument with a built-in ultrasonic agitator. The diffraction pattern of the scattered laser light is used to calculate the particle size and the mean distribution of particle sizes is recorded.10 Results Particle Size Distributions In Figs. 1–5, the determined particle size distributions of the five materials [algae elevated level (IAEA-393), algae environmental level (IAEA-392), algae low level (IAEA-391), urban dust sieved (IAEA-396A/S) and urban dust jet milled (IAEA-396A/M)] are shown.From Figs. 1–5, it is clear that all materials exhibit fairly sharp particle size distributions with 90% of the particles smaller than 7, 15, 4.5, 20 and 25 mm for the respective materials. This finding points to very homogeneous materials where small amounts for analysis could show good reproducibility of replicate measurements11 provided that no systematic errors hamper the quantification.The systematic error of the technique was tested in performing replicate measurements with liquid standard solutions. It could be shown that SS-ZAAS does not add more than 3% to the overall standard deviation and is therefore well suited for this kind of homogeneity study. Homogeneity Factor and Sampling Constants According to Ingamells and Swizer,12 a sampling constant can be given by Ks = R2m (1) where Ks = sampling constant, R = relative standard deviation and m = mean sample mass (mg).This constant was originally intended to be used in geological sampling of larger amounts than are generally used for analysis, notably in microanalysis. Fig. 1 Particle size distribution in IAEA-393, algae elevated level. Fig. 2 Particle size distribution in IAEA-392, algae environmental level. Fig. 3 Particle size distribution in IAEA-391, algae low level. Fig. 4 Particle size distribution in IAEA-396A/M, urban dust air-jet milled. 28 Analyst, January 1997, Vol. 122Kurf�urst et al.13 therefore took the square root of this factor to calculate the relative homogeneity factor, HE: HE = sHOMAmºº (2) where sHOM = relative standard deviation and m = mean sample mass (mg). The difference between the two factors can be illustrated graphically as shown in Figs. 6 and 7. Whereas Ingamell and Switzer’s factor ends up with very large numbers at moderate sample mass, Kurf�urst et al.’s factor is suitable particularly for the description of low sample masses but not so much for higher sample masses.For application of milligram sample inputs to the SS-ZAAS instrument we preferred Kurf�urst et al.’s approach to describe the relative homogeneity as HE in mg1 2.11,14 Homogeneity Testing The systematic error of the SS-ZAAS method was checked using liquid standard solutions for several elements. It was found that, related to the absolute mass of element introduced into the graphite furnace, the reproducibility of repetitive measurements varied only between 2 to 3%.The pipetting error can be estimated (by weighing) to be < 1%. Weighing of the solid materials using a Sartorius 4503 microbalance with a maximum loading of 4.1 g and a weighing error of d = ±0.001 mg assures a maximum weighing inaccuracy of < 1% at a sample mass of 0.1 mg. A few examples of the reproducibility of repetitive (20) measurements of the investigated materials using the SS-ZAAS approach are shown in Figs. 8–11. It can be seen that the reproducibility of repetitive measurements varies with the element analysed in a particular sample material and the standard deviation varies with the mass of the sample analysed Fig. 5 Particle size distribution in IAEA-396A/S, urban dust sieved. Fig. 6 Proportionality between sampling constant and sample mass at different fixed standard deviations. Fig. 7 Proportionality between the relative homogeneity factor HE and the sample mass at different fixed standard deviations.Fig. 8 Lead homogeneity in IAEA 393, algae elevated level, mean sample mass 0.193 mg. Fig. 9 Copper homogeneity in IAEA-392, algae environmental level, mean sample mass 0.458 mg. Fig. 10 Copper homogeneity in IAEA 396A/M, urban dust, mean sample mass 0.34 mg. Analyst, January 1997, Vol. 122 29(e.g., Cu in dust at a sample mass of 0.34 mg is reproducible with RSD = 5.5% and at a level of 0.08 mg with RSD = 10%).In order to achieve relative homogeneity factors related to the sample mass used for analysis, a number of measurement series all following the same routine urements, same calibration, same wavelength) were carried out and the results were plotted [RSD versus sample mass (mg)] as shown in Figs. 12 and 13. Fitting the parabolic curves yields a function of x depending on a factor times m21 2. The factor is the relative homogeneity factor of Kurf�urst et al.(HE) and it is related to this particular element’s homogeneity in the investigated material. In Table 1, the HE values for the four materials are given for all the elements investigated. The Cd concentration in IAEA-392 is very low and close to the detection limit of the method (0.015 ± 0.006 mg kg21) at a sample mass of 1.3 mg. For this reason, only one measurement series of 20 measurements could be carried out. Within these 20 measurements one outlier of about three times the mean of all other results was recorded. This value was not rejected and hence the RSD reached about 50%.Cadmium therefore cannot be considered to be homogeneously distributed in this particular material (IAEA-392, algae, environmental level). Lead concentrations could not be determined at all in this material at such a sample mass level. Increasing the sample mass by a factor of ten resulted in a more sensitive determination. Discussion and Conclusion It was shown that the particle size distributions of all five materials are exceptionally narrow and peak at very low particle sizes, compared with the normal range of other biological reference materials. From this finding, the assumption of good to very good homogeneity for trace elements can be drawn.Using the approach of Kurf�urst et al. a numerical description of element-specific homogeneity of the materials was experimentally elaborated. As Kurf�urst and co-workers pointed out,13–16 HE < 10 indicates very good homogeneity.All the materials investigated for the investigated elements show HE values in this range (with the exception of Cd in IAEA-392) and can be considered suitable as reference materials for micro-analytical techniques analysing samples with masses between 0.1 and 10 mg. For techniques using even smaller amounts of sample, natural matrix reference materials still have to be investigated. As the relative homogeneity factors HE are determined in an accurate way for individual elements in a given material, they can be used to assign the uncertainty of a certified concentration which is due only to material heterogeneity.Today the uncertainty given for certified reference materials is a composite of several uncertainties, such as (i) the systematic error of the analytical technique, (ii) bias from different standardizations of all the techniques used for certification and (iii) the materials’ inherent heterogeneity. By assigning a certified value with the homogeneity factor related to the sample mass consumed in analysis it is possible to calculate a mass-dependent uncertainty which derives strictly from the quality of the material itself. Hence systematic errors and bias of analytical techniques will be easier to recognize and the analytical process will be more transparent.The accurate determination of element-specific homogeneity factors for certified reference materials is essential for all CRMs to be used for quality control in micro-analytical trace element determinations.Suitable techniques such as INAA and SSZAAS with no sample digestion and accurate control over the total sample mass analysed are available and should be applied regularly in the course of certification of CRMs for the quantification of trace element distributions in natural matrix materials. The ‘true value’ of an element in a matrix is not a very useful parameter unless reliable information on the probability of obtaining exactly this value in repetitive measurements (repro- Fig. 11 Copper homogeneity IAEA 396, urban dust air-jet mulled, mean sample mass 0.08 mg. Fig. 12 RSD versus sample mass for Pb in IAEA 393, algae elevated level. The data points can be fitted as f(x) + 4.68 m21 2. Fig. 13 RSD versus sample mass for Cu in IAEA 393, algae elevated level. The data points can be fitted as f(x) + 8.67 m21 2. Table 1 Relative homogeneity factors, HE, for individual elements in the four materials investigated No.of Material measurements HE (Cu) HE (Cd) HE (Pb) IAEA-392 20 8.9 45.3 —* IAEA-393 80 8.7 4.0 4.7 IAEA-396A/M 20 3.0 4.6 6.8 IAEA-396A/S 20 8.9 8.4 6.7 * Pb in IAEA-392 was below the limit of determination. 30 Analyst, January 1997, Vol. 122ducibility) of the same material is attached to it. This probability is clearly dependent on the number of particles with potentially differing concentrations in an analytical aliquot and hence on the sample mass consumed for analysis.Hitherto certified values were given with a conservative estimate (amounting to 50% in some cases) of the overall uncertainty. The empirical statement ‘a minimum sample mass of 250 mg of the dried material . . . is necessary for any certified value . . . to be valid within the stated uncertainty’ is misleading and may only have a commercial background. Precisely determined individual homogeneity factors for each element would therefore help CRM users to (i) save precious material, (ii) determine the systematic error of the applied analytical technique and (iii) test the reliability of the sample preparation techniques more accurately and should therefore be endorsed also by CRM producers.We are grateful for and greatly appreciate the intensive work of D. Koglin in particle size analysis. M.R. acknowledges the financial support of the Bundesminister f�ur Umwelt, Naturschutz und Reaktorsicherheit, Bonn, and the Bundesumweltamt, Berlin. Many thanks are due to the IAEA (Dr. R. Zeisler, Dr. V. Valkovic) for letting us participate in this interesting AQCS programme. References 1 Rossbach, M., Ostapczuk, P., Schladot, J. D., and Emons, H., UWSFZ. Umweltchem. � Okotox., 1995, 7(6), 365. 2 Pauwels, J., and Vandecasteele, C., Fresenius’ J. Anal. Chem., 1993, 345, 121. 3 Chatt, A., Jayawickreme C. K., and McDowell, L. S., Fresenius’ J. Anal. Chem., 1990, 338, 399. 4 Mader, P., Stejskalova, I., and Slamova, A., Fresenius’ J. Anal. Chem., 1995, 352, 131. 5 Report of the Research Co-ordination Meeting on Reference Materials for Microanalytical Nuclear Techniques, IAEA/AL/083, IAEA, Vienna, 1994. 6 Zeisler, R., personal communication. 7 L�ucker, E., K�onig, H., Gabriel, W., and Rosopulo, A., Fresenius’ J. Anal. Chem., 1992, 342, 941. 8 Mohl, C., Grobecker, K. H., and Stoeppler, M., Fresenius’ J. Anal. Chem., 1987, 328, 413. 9 Kurf�urst, U., Fresenius’ Z. Anal. Chem., 1982, 313, 97. 10 Friedrich, H., and Mansour, A., Nachr. Chem. Tech. Lab., 1995, 43, 87. 11 Sonntag, Th.-M., Homogenit�atsstudien f�ur ausgew�ahlte Elemente in verschiedenen Materialien der Bank f�ur Umweltproben und der Internationalen Atomenergiebeh�orde mit der Solid-sampling-Zeeman- Atomabsorptionsspektrometrie, Diplomarbeit, Fachhochschule Aachen, Abteilung J�ulich, 1996. 12 Ingamells, C. O., and Swizer, P., Talanta, 1973, 20, 547. 13 Kurf�urst, U., Grobecker, K.-H., and Stoeppler, M., Trace Elem., 1984, 3, 591. 14 Stoeppler, M., Kurf�urst, U., and Grobecker, K.-H., Fresenius’ J. Anal. Chem., 1985, 322, 687. 15 Kurf�urst, U., Fresenius’ Z. Anal. Chem., 1983, 315, 304. 16 Kurf�urst, U., Fresenius’ Z. Anal. Chem., 1983, 316, 1. Paper 6/05396C Received August 1, 1996 Accepted October 21, 199