A new strategy of solution calibration in laser ablation inductively coupled plasma mass spectrometry for multielement trace analysis of geological samples

Because multielement trace analysis by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) is often limited by the lack of suitable reference materials with a similar matrix composition, a novel quantification strategy using solution calibration was developed. For mass spectrometric multielement determination in geological samples a quadrupole-based LA-ICP-MS is coupled with an ultrasonic nebulizer (USN). In order to arrange matrix matching the standard solutions are nebulized with a USN during solution calibration and simultaneously a blank target (e.g. lithium borate) is ablated with a focused laser beam. The homogeneous geological samples were measured using the same experimental arrangement where a 2% nitric acid is simultaneously nebulized with the USN. Homogeneous targets were prepared from inhomogeneous geological samples by powdering, homogenizing and fusing with a lithium borate mixture in a muffle furnace at 1050?°C. Furthermore, a homogeneous geological glass was also investigated. The quantification of analytical results was performed by external calibration using calibration curves measured on standard solutions. In order to compare two different approaches for the quantification of analytical results in LA-ICP-MS, measured concentrations in homogeneous geological targets were also corrected with relative sensitivity coefficients (RSCs) determined using one standard solution only. The analytical results of LA-ICP-MS on various geological samples are in good agreement with the reference values and the results of other trace analytical methods. The relative standard deviation (RSD) for trace element determination (N = 6) is between 2 and 10%.     

A new strategy of solution calibration in laser ablation inductively coupled plasma mass spectrometry for multielement trace analysis of geological samples

Because multielement trace analysis by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) is often limited by the lack of suitable reference materials with a similar matrix composition, a novel quantification strategy using solution calibration was developed. For mass spectrometric multielement determination in geological samples a quadrupole-based LA-ICP-MS is coupled with an ultrasonic nebulizer (USN). In order to arrange matrix matching the standard solutions are nebulized with a USN during solution calibration and simultaneously a blank target (e.g. lithium borate) is ablated with a focused laser beam. The homogeneous geological samples were measured using the same experimental arrangement where a 2% nitric acid is simultaneously nebulized with the USN. Homogeneous targets were prepared from inhomogeneous geological samples by powdering, homogenizing and fusing with a lithium borate mixture in a muffle furnace at 1050 degrees C. Furthermore, a homogeneous geological glass was also investigated. The quantification of analytical results was performed by external calibration using calibration curves measured on standard solutions. In order to compare two different approaches for the quantification of analytical results in LA-ICP-MS, measured concentrations in homogeneous geological targets were also corrected with relative sensitivity coefficients (RSCs) determined using one standard solution only. The analytical results of LA-ICP-MS on various geological samples are in good agreement with the reference values and the results of other trace analytical methods. The relative standard deviation (RSD) for trace element determination (N = 6) is between 2 and 10%.     

Determination of trace elements in zeolites by laser ablation ICP-MS

Laser ablation inductively coupled plasma mass spectrometry using a quadrupole-based mass spectrometer (LA-ICP-QMS) was applied for the analysis of powdered zeolites (microporous aluminosilicates) used for clean-up procedures. For the quantitative determination of trace element concentrations three geological reference materials, granite NIM-G, lujavrite NIM-L and syenite NIM-S, from the National Institute for Metallurgy (South Africa) with a matrix composition corresponding to the zeolites were employed. Both the zeolites and reference materials were fused with a lithium borate mixture to increase the homogeneity and to eliminate mineralogical effects. In order to compare two different approaches for the quantification of analytical results in LA-ICP-MS relative sensitivity coefficients (RSCs) of chemical elements and calibration curves were measured using the geostandards. The experimentally obtained RSCs are in the range of 0.2-6 for all elements of interest. Calibration curves for trace elements were measured without and with Li or Ti as internal standard element. With a few exceptions the regression coefficients of the calibration curves are better than 0.993 with internal standardization. NIM-G granite reference material was employed to evaluate the accuracy of the technique. Therefore, the measured concentrations were corrected with RSCs which were determined using lujavrite reference material NIM-L. This quantification method provided analytical results with deviations of 1–11% from the recommended and proposed values in granite reference material NIM-G, except for Co, Cs, La and Tb. The relative standard deviation (RSD) of the determination of the trace element concentration (n = 5) is about 1% to 6% using Ti as internal standard element. Detection limits of LA-ICP-QMS in the lower μg/g range (from 0.03 μg/g for Lu, Ta and Th to 7.3 μg/g for Cu, with the exception of La) have been achieved for all elements of interest. Under the laser ablation conditions employed (λ: 266 nm, repetition frequency: 10 Hz, pulse energy: 10 mJ, laser power density: 6 × 10⁹ W/cm²) fractionation effects of the determined elements relative to the internal standard element Ti were not observed. Received: 7 April 2000 / Revised: 25 May 2000 / Accepted: 31 May 2000     

Determination of trace elements in zeolites by laser ablation ICP-MS

Laser ablation inductively coupled plasma mass spectrometry using a quadrupole-based mass spectrometer (LA-ICP-QMS) was applied for the analysis of powdered zeolites (microporous aluminosilicates) used for clean-up procedures. For the quantitative determination of trace element concentrations three geological reference materials, granite NIM-G, lujavrite NIM-L and syenite NIM-S, from the National Institute for Metallurgy (South Africa) with a matrix composition corresponding to the zeolites were employed. Both the zeolites and reference materials were fused with a lithium borate mixture to increase the homogeneity and to eliminate mineralogical effects. In order to compare two different approaches for the quantification of analytical results in LA-ICP-MS relative sensitivity coefficients (RSCs) of chemical elements and calibration curves were measured using the geostandards. The experimentally obtained RSCs are in the range of 0.2-6 for all elements of interest. Calibration curves for trace elements were measured without and with Li or Ti as internal standard element. With a few exceptions the regression coefficients of the calibration curves are better than 0.993 with internal standardization. NIM-G granite reference material was employed to evaluate the accuracy of the technique. Therefore, the measured concentrations were corrected with RSCs which were determined using lujavrite reference material NIM-L. This quantification method provided analytical results with deviations of 1-11% from the recommended and proposed values in granite reference material NIM-G, except for Co, Cs, La and Tb. The relative standard deviation (RSD) of the determination of the trace element concentration (n = 5) is about 1% to 6% using Ti as internal standard element. Detection limits of LA-ICP-QMS in the lower microg/g range (from 0.03 microg/g for Lu, Ta and Th to 7.3 microg/g for Cu, with the exception of La) have been achieved for all elements of interest. Under the laser ablation conditions employed (lambda: 266 nm, repetition frequency: 10 Hz, pulse energy: 10 mJ, laser power density: 6 x 10(9) W/cm2) fractionation effects of the determined elements relative to the internal standard element Ti were not observed.     

Determination of platinum group elements and gold in geological materials: a review of recent magnetic sector and laser ablation applications

Inductively coupled plasma mass spectrometry (ICP-MS) has been used extensively as a rapid and accurate instrumental technique for determinations of platinum group elements (PGEs) and gold. Methods based upon ICP-MS have been important in analyses of many types of samples, and especially of geological materials containing very low concentrations of these elements. Recently, analytical methods based upon ICP-MS have been improved and widened in scope by the introduction of new magnetic sector (or high resolution) spectrometers, and laser ablation (LA) sampling. Detection limits attainable for PGEs and Au using magnetic sector instruments in analytical procedures cited here are as low as 0.01-0.02 pg g⁻¹; instruments have a dynamic range of up to nine orders of magnitude. This review describes applications of the techniques to analyses of PGEs and gold in minerals, nodules, meteorites, ice, sediments, airborne particulates and reference materials. The period covered is 1998-2002.     

Validation of multi-element isotope dilution ICPMS for the analysis of basalts

In this study we have validated a newly developed multi-element isotope dilution (ID) ICPMS method for the simultaneous analysis of up to 12 trace elements in geological samples. By evaluating the analytical uncertainty of individual components using certified reference materials we have quantified the overall analytical uncertainty of the multi-element ID ICPMS method at 1–2%. Individual components include sampling/weighing, purity of reagents, purity of spike solutions, calibration of spikes, determination of isotopic ratios, instrumental sources of error, correction of mass discrimination effect, values of constants, and operator bias. We have used the ID-determined trace elements for internal standardization to improve indirectly the analysis of 14 other (mainly mono-isotopic trace elements) by external calibration. The overall analytical uncertainty for those data is about 2–3%.In addition, we have analyzed USGS and MPI-DING geological reference materials (BHVO-1, BHVO-2, KL2-G, ML3B-G) to quantify the overall bias of the measurement procedure. Trace element analysis of geological reference materials yielded results that agree mostly within about 2–3% relative to the reference values. Since these results match the conclusions obtained by the investigation of the overall analytical uncertainty, we take this as a measure for the validity of multi-element ID ICPMS.     

A simple method of target preparation for the bulk analysis of powder samples by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS)

A simple and rapid procedure using a glue technique has been developed for the preparation of stable targets from powder samples for bulk analysis by LA-ICP-MS. The procedure was evaluated for the analysis of trace elements in SiC, of rare-earth elements in different types of silicate (rocks, sediments, and soils), and of Au and platinum-group elements in geological silicates. The test analysis was conducted using an IR laser in combination with a quadrupole mass spectrometer. The recommended preparation procedure offers the possibility of different types of calibration, for example application of certified reference samples in combination with prepared spiked samples on a base of a natural or synthetic matrix, or addition calibration. The resulting calibration functions are linear over a range of several decades. The trueness of the results was evaluated by use of certified reference samples. Analytical concentration ranges, detection limits, and the relative standard deviations are reported.     

A simple method of target preparation for the bulk analysis of powder samples by laser ablation inductively coupled plasma mass spectrometry (LA–ICP–MS)

A simple and rapid procedure using a glue technique has been developed for the preparation of stable targets from powder samples for bulk analysis by LA– ICP–MS. The procedure was evaluated for the analysis of trace elements in SiC, of rare-earth elements in different types of silicate (rocks, sediments, and soils), and of Au and platinum-group elements in geological silicates. The test analysis was conducted using an IR laser in combination with a quadrupole mass spectrometer. The recommended preparation procedure offers the possibility of different types of calibration, for example application of certified reference samples in combination with prepared spiked samples on a base of a natural or synthetic matrix, or addition calibration. The resulting calibration functions are linear over a range of several decades. The trueness of the results was evaluated by use of certified reference samples. Analytical concentration ranges, detection limits, and the relative standard deviations are reported. Received: 20 November 2000 / Revised: 13 March 2001 / Accepted: 17 March 2001     

Direct Determination of Aluminum in Archaeological Clays by Laser‐Induced Breakdown Spectroscopy

Abstract

Instrumental techniques that allow the direct analysis of solids with little or no sample preparation are particularly important for the evaluation of samples that are difficult to analyze such as refractory or geological materials. Laser‐induced breakdown spectroscopy (LIBS) is a promising technique for the direct, rapid analysis of elements in solid materials with minimal sample preparation. The main advantages over wet techniques are virtual nondestructiveness and analysis speed. The goal of this work is the direct determination of aluminum of archaeological pieces using laser‐induced breakdown spectroscopy. The corresponding signals of metals were interpolated from calibration graphs of different salts of the metals. The matrix effects from the direct determination of these elements were thoroughly investigated. The potential of this technique for direct quantitative analysis of real archaeological materials (from Department of Ancient Science, University of Zaragoza) was evaluated, and the reproducibility of LIBS spectra from different archaeological samples was measured as a function of the number of laser shots. Finally, the results from LIBS are compared with those obtained by laser ablation inductively coupled plasma mass spectrometry.     

Laser Ablation Inductively Coupled Plasma Mass Spectrometry for Determination of Trace Elements in Geological Glasses

 Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) was used as a powerful multielement analytical method for trace analysis of geological glasses which are useful as reference materials for geochemical in-situ microanalytical work. The quantification of the analytical results was carried out using the BCR-2G and NIST 612 glass standard reference material (SRM). The experimentally determined relative sensitivity coefficients (RSC) for both SRMs vary between 0.2 and 3 for most of the elements, with increasing mass an increasing of relative sensitivity coefficients was observed. The relative standard deviation (RSD) for determination of trace element concentration of most elements (N=3) are between 2 and 10%. The determination of trace elements in various geological glasses by LA-ICP-MS yielded a good agreement with the reference values and those results of other trace analytical methods. Received October 15, 1999. Revision April 14, 2000.     

Determination of minor elements in steelmaking flue dusts using laser ablation inductively coupled plasma mass spectrometry

Element determination in solid waste products from the steel industry usually involves the time-consuming step of preparing a solution of the solid. Laser ablation (LA) inductively coupled plasma mass spectrometry (ICP-MS) has been applied to the analysis of Cr, Ni, Cu, As, Cd and Sn, elements of importance from the point of view of their impact on the environment, in electric arc furnace flue dust (EAFD). A simple method of sample preparation as pressed pellets using a mixture of cellulose and paraffin as binder material was applied. Calibration standards were prepared spiking multielement solution standards to a 1:1 ZnO + Fe₂O₃ synthetic matrix. The wet powder was dried and mechanically homogenised. Quantitative analysis were based on external calibration using a set of matrix matched calibration standards with Rh as a internal standard. Results obtained using only one-point for calibration without matrix matched, needing less time for standardization and data processing, are also presented. Data are calculated for flue dust reference materials: CRM 876-1 (EAFD), AG-6203 (EAFD), AG-6201 (cupola dust) and AG-SX3705 (coke ashes), and for two representative electrical arc furnace flue dusts samples from Spanish steelmaking companies: MS-1 and MS-2. For the reference materials, an acceptable agreement with certificate values was achieved, and the results for the MS samples matched with those obtained from conventional nebulization solutions (CN). The analytical precision was found to be better than 7% R.S.D. both within a single pellet and between several pellets of the same sample for all the elements.     

Rapid and precise determination of Sr and Nd isotopic ratios in geological samples from the same filament loading by thermal ionization mass spectrometry employing a single-step separation scheme

Thermal ionization mass spectrometry (TIMS) offers the excellent precision and accuracy of the Sr and Nd isotopic ratio analysis for geological samples, but this method is labour intensive, expensive and time-consuming. In this study, a new analytical protocol by TIMS is presented that aims at improving analytical efficiency and cutting down experimental cost. Using the single-step cation exchange resin technique, mixed Sr and rare earth elements (REEs) fractions were separated from matrix and evaporated to dryness. Afterwards, mixed Sr + REEs fractions were dissolved and loaded onto the same Re filament using 1 μL of 2 M HCl. Then, Sr and Nd were sequentially measured without venting using TIMS. In contrast to conventional TIMS methods, the merits of this analytical protocol are its cost- and time-saving adaptations. The applicability of our method is evaluated by replicated measurements of ⁸⁷Sr/⁸⁶Sr and ¹⁴³Nd/¹⁴⁴Nd for nine international silicate rock reference materials, spanning a wide range of bulk compositions. The typical internal precision in this study is ca. 0.001% (RSE) for ⁸⁷Sr/⁸⁶Sr and ¹⁴³Nd/¹⁴⁴Nd; the analytical results obtained for these standard rocks show a good agreement with reported values, indicating the effectiveness of the proposed method.     

Multi-element trace determinations in pure alkaline earth fluoride powders by high-resolution ICP-MS using wet-chemical sample preparation and laser ablation

Four alternative analytical procedures for the determination of ten important trace impurities (Mg, Cr, Fe, Cu, Zn, Sr, Zr, Cd, Ba, and Pb) in pure alkaline earth fluoride powders were applied using high-resolution inductively coupled plasma mass spectrometry (ICP-MS). Two procedures are based on a wet-chemical microwave digestion with boric acid and quantification by the standard addition technique and isotope dilution mass spectrometry (IDMS), respectively. In addition, analyses are also performed by laser ablation as a direct solid sampling technique applying matrix-matched external calibration as well as isotope dilution of the powdered sample. For most elements good agreement between the different methods is found. Detection limits for laser ablation vary between 0.05 ng g^–1 for Zr and 20 ng g^–1 for Mg. They are about one to two orders of magnitude lower than those of the wet-chemical procedures, which is mainly due to the high dilution factor during the sample preparation step. Advantages and restrictions of the different analytical procedures are discussed with respect to their routine applicability. Due to its relatively high accuracy, low detection limits, and time-efficiency LA-ICP-IDMS is the preferred choice if no standard reference materials are available.     

Lead determination in whole blood by laser ablation coupled with inductively coupled plasma mass spectrometry

This work describes a simple procedure for blood lead level determination. The proposed method requires little sample pretreatment and subsequent direct analysis of a dried blood spot on a filter membrane using laser ablation coupled with inductively coupled plasma mass spectrometry (LA-ICP-MS). In general, LA-ICP-MS studies are somewhat limited by the lack of matrix-matched standards for calibration purposes. Here we describe aqueous standard calibration and matrix-matched calibration methods. This method was validated by analysis of the reference materials. With the matrix-matched calibration method, the recovery ranged from 97.8% to 112.8%, while the aqueous standard calibration method ranged 90.4% to 122.4%. The lower detection limit was estimated as 0.1 ng mL⁻¹. The determination precision, expressed as the relative standard deviation (RSD), was not worse than 10% for all results. A sample throughput of approximately 5 min per sample made it possible to rapidly screen a large number of samples.     

Direct determination of major elements in solid plant materials by electrothermal vaporization inductively coupled plasma atomic emission spectrometry

The present work demonstrates the capability of electrothermal vaporization (ETV) to become an important tool of solid sample introduction in ICP-AES for plant sample analysis. Direct determination of Al, Ca, Fe, K, Mg, Mn, Na and Zn was investigated in powdered plant samples. Obtaining good results for major elements in plant samples was governed by some special operating conditions. The sensitivity of the method necessitated the use of ICP in radial view configuration. The behavior of elements during vaporization was studied between 500 and 2600 °C. External calibration was carried out using solid external (cellulose) spiked with aqueous standard solutions. However, performances of the analytical method were found dependent of argon flow rates. Analytical accuracy of the method was tested in three reference materials. Analytical results agreed with certified values when cellulose was used in calibration. However, K could not be determined because of excessive sensitivity. Without cellulose, it was found that Fe results were underestimated and Zn results overestimated. Relative standard deviations varied from 3 to 23%. Limits of detection varied from 1 to 80 ng g⁻¹ from one element to the other for a typical mass sample of 2 mg.     

Laser-induced breakdown spectroscopy for quantitative spectrochemical analysis of geological materials: effects of the matrix and simultaneous determination

A microscopic laser-induced breakdown spectrometer was used to evaluate the analytical matrix effect commonly observed in the analysis of geological materials. Samples were analyzed in either the powder or pressed pellet forms. Calibration curves of a number of iron and aluminum compounds showed a linear relationship between the elemental concentration and peak intensity. A direct determination of elemental content can thus be made from extrapolation on these calibration curves. To investigate matrix effects, synthetic model samples were prepared from various iron and aluminum compounds spiked with SiO₂ and CaCO₃. The addition of these matrices had a pronounced analytical effect on those compounds prepared as pressed pellets. However, results indicated the absence of matrix effects when the samples were presented to the laser as loose powders on tape and results were compared to certified values, indicating the reliability of this approach for accurate analysis, provided the sample particle diameters are greater than ≈100 μm. Finally, the simultaneous analysis of two different elements was demonstrated using powders on tape.     

On-line double isotope dilution laser ablation inductively coupled plasma mass spectrometry for the quantitative analysis of solid materials

We report on the determination of trace elements in solid samples by the combination of on-line double isotope dilution and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). The proposed method requires the sequential analysis of the sample and a certified natural abundance standard by on-line IDMS using the same isotopically-enriched spike solution. In this way, the mass fraction of the analyte in the sample can be directly referred to the certified standard so the previous characterization of the spike solution is not required. To validate the procedure, Sr, Rb and Pb were determined in certified reference materials with different matrices, including silicate glasses (SRM 610, 612 and 614) and powdered samples (PACS-2, SRM 2710a, SRM 1944, SRM 2702 and SRM 2780). The analysis of powdered samples was carried out both by the preparation of pressed pellets and by lithium borate fusion. Experimental results for the analysis of powdered samples were in agreement with the certified values for all materials. Relative standard deviations in the range of 6–21% for pressed pellets and 3–21% for fused solids were obtained from n = 3 independent measurements. Minimal sample preparation, data treatment and consumption of the isotopically-enriched isotopes are the main advantages of the method over previously reported approaches.     

Evaluation of a rapid semi-quantitative analysis approach using inductively coupled plasma optical emission spectrometry with axial viewing

This work describes a rapid screening procedure for simultaneous determination of multiple elements by inductively coupled plasma optical emission spectrometry with axial viewing. The process requires no calibration reference solutions, and therefore requires a shorter analysis time per sample. The “Rapid Quant for Axial” worksheet contains stored calibration functions that are not adjusted between analyses. These functions were applied to the analysis of standard reference materials to demonstrate the effectiveness of the screening tool. Quantitative recoveries were obtained for most elements in a variety of biological materials. Aluminum, Cu, Mn, P, and Zn were determined in spinach leaves, for example, with errors ranging from − 45% (Al) to + 23% (Cu). A simulation of the worksheet procedure was also tested. With this technique, a single user-specific, multi-element reference solution was used to prepare a new set of calibration parameters to replace those stored in the worksheet. This procedure proved to be useful for sample screening when the analytes of interest were not present in the original calibration file, or when their concentrations differed significantly from those previously stored.     

Applications of inductively coupled plasma mass spectrometry and laser ablation inductively coupled plasma mass spectrometry in materials science

Inductively coupled plasma mass spectrometry (ICP-MS) and laser ablation ICP-MS (LA-ICP-MS) have been applied as the most important inorganic mass spectrometric techniques having multielemental capability for the characterization of solid samples in materials science. ICP-MS is used for the sensitive determination of trace and ultratrace elements in digested solutions of solid samples or of process chemicals (ultrapure water, acids and organic solutions) for the semiconductor industry with detection limits down to sub-picogram per liter levels. Whereas ICP-MS on solid samples (e.g. high-purity ceramics) sometimes requires time-consuming sample preparation for its application in materials science, and the risk of contamination is a serious drawback, a fast, direct determination of trace elements in solid materials without any sample preparation by LA-ICP-MS is possible. The detection limits for the direct analysis of solid samples by LA-ICP-MS have been determined for many elements down to the nanogram per gram range. A deterioration of detection limits was observed for elements where interferences with polyatomic ions occur. The inherent interference problem can often be solved by applying a double-focusing sector field mass spectrometer at higher mass resolution or by collision-induced reactions of polyatomic ions with a collision gas using an ICP-MS fitted with collision cell. The main problem of LA-ICP-MS is quantification if no suitable standard reference materials with a similar matrix composition are available. The calibration problem in LA-ICP-MS can be solved using on-line solution-based calibration, and different procedures, such as external calibration and standard addition, have been discussed with respect to their application in materials science. The application of isotope dilution in solution-based calibration for trace metal determination in small amounts of noble metals has been developed as a new calibration strategy. This review discusses new analytical developments and possible applications of ICP-MS and LA-ICP-MS for the quantitative determination of trace elements and in surface analysis for materials science.     

Determination of cadmium and lead in reference materials by volatile species generation with in situ trapping flame atomic absorption spectrometry

The analytical performance of coupled volatile species generation-integrated atom trap (VSG-IAT) atomizer flame atomic absorption spectrometry (FAAS) system was evaluated for determination of Cd and Pb in reference materials. Lead using formation of PbH₄ and Cd⁰ vapors are atomized in air-acetylene flame-heated IAT. A new design of VSG-IAT-FAAS hyphenated technique that would exceed the operational capabilities of existing arrangements (a water-cooled single silica tube, double-slotted quartz tube or an “integrated trap”) was investigated. A dramatic improvement in detection limit was achieved compared with that obtained using either of the above atom trapping techniques separately. The concentration detection limits, defined as 3 times the blank standard deviation (3σ), were 0.05 and 0.40 ng mL^− 1 for Cd and Pb, respectively. For a 120 s in situ pre-concentration time, sensitivity enhancement compared to flame AAS, was 500 and 575 folds for Cd and Pb, respectively, using volatile species generation-atom trapping technique. The sensitivity can be further improved by increasing the collection time. The precision, expressed as RSD, was 4.4% and 4.1% (n = 6) for Cd and Pb, respectively. The designs studied include slotted tube, single silica tube and integrated atom trap-cooled atom traps. The accuracy of method was verified using certified reference materials (PLANTS 3 and IAEA/W-4) by standard addition calibration technique. The measured Cd and Pb contents in two reference materials were in satisfactory agreement with the certified values.