Serum aluminum determination by instrumental neutron activation analysis in long-term haemodialysis patients

Serum aluminum levels were determined by instrumental neutron activation analysis in 31 patients undergoing long-term haemodialysis. Aluminum-28 1.778 MeV (T _1/2=2.24 min) γ-rays produced by the thermal neutron reaction²⁷Al(n,γ)²⁸Al were detected. Successive irradiation of the samples at epithermal neutron fluence was performed to correct for the interference from the fast neutron reaction³¹P(n,α)²⁸Al. Serum aluminum level in this group of subjects was adequately represented by a lognormal distribution with a mean and variance of 16.5 μg/l and 16.8 μg/l, respectively. The results obtained were found to be in agreement with serum aluminum determination performed by electrothermal atomic absorption spectrophotometry (r ²=0.97). Instrumental neutron activation can provide a rapid technique to routinely monitor long-term haemodialysis patients in order to identify individuals at greater risk to develop aluminum toxicity.     

Application of fast solvent extraction processes to studies of exotic nuclides

The nucleus²³Na has been investigated by studying the primary γ-rays emitted from 53 keV neutron capture in it using a high resolution and high efficiency (100%) HPGe detector and NaI(T1) detector for anti-Compton. 24 primary γ-rays were placed in the²⁴Na, in which 3 primary γ-rays were new ones from a (n, γ) reaction, and reported for the first time. In order to obtain an exact energy calibration within 7 MeV,⁵⁶Fe(n,γ)⁵⁷Fe reaction was used at thermal neutron energy. Intensity calibration was obtained from the²⁷Al(p,γ)²⁸Si reaction atE _p=2046 keV. The neutron binding energy of²⁴Na was determined to be 6959.75 keV.     

A quick method for the determination of the Al/Si weight ratio in alumino-silicates using an Am-Be neutron source

An irradiation procedure with fast and thermal neutrons from a 5 Ci Am-Be isotopic neutron source irradiation facility in combination with a 3'3' NaI(Tl) detector system has been used to determine Al/Si weight ratios in alumino-silicates. Samples were irradiated with and without Cd cover for 10 minutes and counted for 10 minutes after a waiting time of 1 minute. The peak area analysis of the 1779 keV gamma-ray line of ²⁸Al product radionuclide produced via ²⁷Al(n,γ)²⁸Al and ²⁸Si(n,p)²⁸Al reactions in combination with the neutron flux parameter at the irradiation site and nuclear data were used to determine Al/Si ratios. Due to discrepancy in literature data, Am-Be neutron source spectrum averaged cross sections of (n,p) reactions on ²⁷Al, ²⁸Si and ⁵⁶Fe were determined by the activation technique using ¹¹⁵In(n,n')^115mIn as the fast neutron flux monitor reaction. The method was tested using mixtures of high-purity Al₂O₃ and SiO₂ with known weight ratios of Al/Si and validated by a certified reference material BCS-CRM 348 (Ball Clay). Results are presented for bentonite, kaolin, bauxite, feldspar and ball clay samples from Nigeria. The method is non-destructive, rapid and suitable for use in-situ for large-scale exploration works and industrial process control. This revised version was published online in July 2006 with corrections to the Cover Date.     

Non-destructive bone aluminum assay by neutron activation analysis

A non-destructive method based on instrumental neutron activation analysis (INAA) for the assay of aluminum in bone samples is described. The²⁸Al signal obtained upon neutron irradiation includes contributions from both the reaction²⁷Al(n,)²⁸Al and³¹P(n,)²⁸Al. The first reaction is with the thermal neutrons and the second one is with the fast neutrons. The contribution from the³¹P reaction is calculated from the fact that Ca/P ratio in bone mineral is constant and the amount of calcium can be measured from the thermal reaction⁴⁸Ca(n, )⁴⁹Ca. The aluminum values obtained by the INAA procedure agreed within 10% of those obtained by atomic absorption spectrophotometry. With this assay the levels of aluminum in normal bones (<70 g g^–1 apatite) cannot be determined reliably but higher aluminum levles in bone biopsies associated with Al toxicity, e.g. some patients with renal osteodystrophy, can be determined with a precision of ±10%.     

Determination of silicon dioxide in iron and steel-making slags and fluorspars by 14 MeV neutron activation and high-resolution gamma-ray spectrometry

Silicon as silicon dioxide in iron and steel-making slags and fluorspars was analyzed by 14 MeV neutron activation high-resolution γ-ray spectrometry. Silicon was detected by measuring the 1.78 MeV γ-ray of²⁸Al, the product of the²⁸Si(n, p) reaction, using a 30 cm³ coaxial Ge(Li) detector. A modified TPA method was used for the calculation.²⁸Al is also produced from phosphorus by the³¹P(n,α) reaction, and from aluminium by the²⁷Al(n,γ) reaction. The contribution from the former reaction could be corrected experimentally when the P₂O₅ content of the sample was known, while the latter reaction could be neglected in this neutron energy region. The experimental correction coefficient for phosphorus agreed well with the theoretical value calculated from the nuclear properties of silicon and phosphorus. Yields of²⁸Al from SiO₂, P₂O₅ and Al₂O₃ of the same weight percentages were calculated as 1, 0.426 (experimentally 0.44) and 0.0022, respectively. The results of this method agreed well with the results of the usual chemical methods. The limit of detection of SiO₂ in iron and steel-making slags and fluorspars was calculated as 0.07%. The coefficient of variation of repeated experiments was compared with the statistical one.     

Method for determination of silicon in plant materials by neutron activation analysis

Silicon has been found to be an essential element for the growth and development of many ecomomically important plants such as sugarcane, rice, oats, and wheat. A method is described for the quantitative determination of silicon in plant samples. Measurements were made with two Ge(Li) detectors matched with a multiplexing unit to provide a single amplified signal to a computerized analyzer system. For those materials containing greater than 0.5 weight percent silicon, the reaction²⁹Si(n, p)²⁹Al (1273 keV) provides a direct measurement of the quantity of silicon provided the irradiation is done in a special boron nitride capsule to reduce interferences from thermal neutron reactions and a correction is made for the single escape line from²⁸Al (1268 keV). For lesser quantities of silicon, a technique which utilizes the fast neutron reaction²⁸Si(n, p)²⁸Al is preferred. Corrections for the interference produced by the presence of phosphorus³¹P(n, α)²⁸Al are made by determining the phosphorus content following the instrumental analysis using a unique application of neutron activation analysis, i. e., measurement of tungsten in tungstomolybdophosphoric acid produced when molybdate and tungstate ions are added to dissolved samples of the plant material containing phosphorus. Aluminum, which may also produce an interference by thermal neutron reaction²⁷Al(n, γ)²⁸Al, is determined directly from the original activation data after subtracting out the effect of the phosphorus. Thus, three irradiations in the pneumatic sample irradiator are necessary; one short irradiation (1 min) without thermal neutron shielding, a longer irradiation (6 min) in the boron capsule, and a final irradiation of the tungstomolybdophosphoric acid provide all data required to accurately determine silicon in plant materials. A computer program has been developed that provides rapid reduction of the data in final report format. Elements such as sodium, chlorine, calcium, manganese, potassium, and magnesium extrinsic to the analysis for silicon are also determined by this method. The method has been tested on a large number of samples and reliable results are obtained with less than 0.2 g of sample. This work was supported by Grant 533 from the Michigan Memorial—Phoenix Project.     

Determination of silicon in aluminium by 14 MeV neutron activation analysis

A method has been developed for determining silicon in aluminium by fast neutron activation. It is based on the separation of two gamma lines by a Ge(Li) detector: the 1.73 MeV line from the product of²⁷Al(n, α)²⁴Na and the 1.78 MeV line from the²⁸Si(n, p)²⁸Al reaction. In the case of aluminium-silicon alloys 100 μg silicon can be determined, with an error of 10% in an aluminium sample of 1 g. This work was supported in part by the International Atomic Energy Agency.     

Measurements of the thermal neutron cross-sections and resonance integrals for 186W (n,γ) 187W and 98Mo (n,γ) 99Mo reactions

The thermal neutron cross-sections and resonance integrals of the ¹⁸⁶W (n,γ) ¹⁸⁷W and ⁹⁸Mo (n,γ) ⁹⁹Mo reactions in the thermal and 1/E regions, respectively, of a thermal reactor neutron spectrum have been experimentally determined by the activation method using ¹⁹⁷Au (n,γ) ¹⁹⁸Au reaction as a single comparator. The high purity natural W, Mo, and Zr foils; and Au wire diluted in aluminum, were irradiated without Cd shield in two neutron irradiation sites, characterized with different values for the thermal-to-epithermal flux ratios, f at the Second Egyptian Research Reactor (ETRR-2). The induced activities in the samples were measured by high-resolution γ-ray spectrometry with a calibrated germanium detector. Thermal neutron cross-sections for 2200 m/s neutrons and resonance integrals for the ¹⁸⁶W (n,γ) ¹⁸⁷W and ⁹⁸Mo (n,γ) ⁹⁹Mo reactions have been obtained relative to the reference values, σ₀ = 98.65 ± 0.09 b and I ₀ = 1500 ± 28 b for the ¹⁹⁷Au (n,γ) ¹⁹⁸Au reaction. The necessary correction factors for thermal neutron and resonance neutron self-shielding effects, and the epithermal flux index (α) were taken into account in the determinations. The results obtained were: σ₀ = 38.43 ± 0.4 b and I ₀ = 502 ± 65 b for ¹⁸⁶W (n,γ) ¹⁸⁷W, and σ₀ = 0.137 ± 0.014 band I ₀ = 6.47 ± 0.8 for ⁹⁸Mo (n,γ) ⁹⁹Mo. These results are discussed and compared with previous measurements and evaluated data in literature. The traditional method of determining thermal cross-sections and resonance integrals via neutron irradiation with and without Cd shield in one irradiation position was avoided in this work by neutron irradiation without Cd shield in at least two different neutron irradiation positions. This method provides alternative way for determining thermal cross-sections and resonance integrals simultaneously.     

Neutron activation analysis for determination of trace elements in sediments in the Sea of Galilee,Israel

The feasibility of applying both thermal and epithermal neutron activation analysis for simultaneous determinations of elemental composition in sediments, collected from the Sea of Galilee (Kineret Lake), Israel, during 1988–1993, was experimentally investigated. In the present work, the concentrations of 30 elements (Al, Ba, Br, Ca, Ce, Co, Cs, Cr, Eu, Fe, Hf, K, La, Lu, Mg, Mn, Na, Nd, Rb, Sc, Si, Sr, Ta, Tb, Th, Ti, U, V, Yb and Zn) in sediments were determined. The validity of the method was checked by analyzing the U.S. NBS Standard Reference Material SRM-1633a; the elemental content found agreed well with the published certified data. Aluminium was determined by reactor neutron activation analysis (RNAA) taking into account the contribution of silicon to the total²⁸Al activity by the²⁸Si(n,p)²⁸Al reaction. Measurements of irradiated mixtures of Si and Al showed that the dependence of log SiAl mass ratio vs. log cadmium ratio (R _Cd) of²⁸Al is almost linear. The data can be analyzed more accurately by a parabolic correlation (log Si:Al mass ratio vs logR _Cd). The concentrations of fission radionuclide¹³⁷Cs, an activation radionuclide¹³⁴Cs (derived from Chernobyl accident) and the naturally occuring radionuclides⁴⁰K,²²⁶Ra and²³²Th in sediments were also measured by -ray spectrometry using Marinelli (Reentrant) Beaker-Sample Containers.     

Neutron induced reactions at the Athens Tandem Accelerator NCSR “Demokritos”

The neutron facility at the 5.5 MV tandem T11/25 Accelerator of NCSR “Demokritos” can deliver monoenergetic neutron beams in the energy range from thermal to 450 keV, 4–11.5 MeV and 16–20.5 MeV via the ⁷Li(p,n), ²H(d,n) and ³H(d,n) reactions, respectively. The flux variation of the neutron beam is monitored by using a BF₃ counter and a liquid scintillator BC501A detector. The ²³²Th(n,2n)²³¹Th and ²⁴¹Am(n,2n)²⁴⁰Am as well as (n,2n), (n,p) and (n,α) reactions on natural Ge and Hf isotopes, have been investigated from threshold up to 11.5 MeV, by using the activation method. The cross section values have been determined relative to the ¹⁹⁷Au(n,2n)¹⁹⁶Au, ²⁷Al(n,α)²⁴Na and ⁹³Nb(n,2n) reference reaction cross sections.     

Silver containing sol–gel derived silica thin films: effect of aluminum incorporation on optical,microstructural and bactericidal properties

Silver containing silica (Ag–SiO₂) thin films with and without aluminum (Al) were prepared on soda-lime-silica glass by spin coating of aqueous sols. The coating sol was formed through mixing tetraethyl orthosilicate [Si(OC₂H₅)₄]/ethanol solution with aqueous silver nitrate (AgNO₃) and aluminum nitrate nonahydrate [(AlNO₃)₃·9H₂O] solutions. The deposited films were calcined in air at 100, 300 and 500 °C for 2 h and characterized using x-ray diffraction, UV-visible and x-ray photoelectron spectroscopy. The effect of Al incorporation and calcination treatment on microstructure and durability of the films, and chemical/physical state of silver in the silica thin film have been reported. The bactericidal activity of the films was also determined against Staphylococcus aureus via disk diffusion assay studies before and after chemical durability tests. The investigations revealed that the optical, bactericidal properties and chemical durability of Ag–SiO₂ films can be improved by Al addition. The Al-modified Ag–SiO₂ thin films do not exhibit any coloring after calcination in the range of 100–500 °C, illustrating that silver is incorporated within the silica gel network in ionic form (Ag⁺). Al incorporation also improved the overall durability and antibacterial endurance of Ag–SiO₂ thin films.     

Die Bestimmung von53Mn,Welches in Meteoritischem Material Durch Kosmische Strahlung Erzeugt Wurde,mit Hilfe der Neutronenaktivierung

Among a number of stable and unstable nuclides formed in material exposed to cosmic radiation the spallation nuclide⁵³Mn (T=2·10⁶ a) is investigated in meteoritic manganese by combined techniques of neutron activation and advanced γ-spectrometry. The need for an economic use of precious meteorites is so ensured best. Intense neutron bombardment transforms the long-livedK-emitter⁵³Mn into⁵⁴Mn, which is detected by its 0.84 MeV γ-rays. Using the (n,γ) cross section—recently derived byMillard—⁵³Mn-values in the range of 60–600 dpm/kg (10⁻¹¹ g/g) are found in a larger number of iron meteorite samples, which are only 1–3 g in weight. The determination is very specific and under appropriate conditions unaffected by side reactions. The attempt to use the⁴⁴Ti (n,γ)⁴⁵Ti reactions for the analysis of spallogenic titanium failed, because the σ_therm of⁴⁴Ti was found to be unexpectedly low (10 barns). Additionally,⁴⁵Sc was determined after (n,γ) reaction by the⁴⁶Sc γ,γ-cascades.      

Non-destructive determination of aluminum in biological reference samples using neutron activation analysis

The non-destructive methods of thermal and epithermal neutron activation analysis have been employed to determine the aluminum concentration of seven National Institute of Standards and Technology certified biological reference materials. Through the judicious use of both thermal and epithermal neutron activation analysis using bare and boron-lined irradiation carriers, the major and minor contributions of the³¹P/n, /²⁸Al and of the²⁸Si/n, p/²⁸Al reactions, respectively, to the²⁷Al/n, /²⁸Al reaction could be corrected for explicitly. Based on replicate determinations precision of the analysis ranged from 2.5% for citrus leaves determined at the 75 ppm level to 18% for bovine liver measured at the 1 ppm level. Accuracy was demonstrated whenever possible by comparison to existing published data.     

Potentiometric and Multinuclear Magnetic Resonance Study of the Solution Equilibria Between Aluminium(III) Ion and L-Aspartic Acid

Solution equilibria between aluminium(III) ion and L-aspartic acid were studied by potentiometric, ²⁷Al, ¹³C, and ¹H NMR measurements. Glass electrode equilibrium potentiometric studies were performed on solutions with ligand to metal concentration ratios 1:1, 3:1, and 5:1 with the total metal concentration ranging from 0.5 to 5.0 mmol/dm³ in 0.1 mol/dm³ LiCl ionic medium, at 298 K. The pH of the solutions was varied from ca. 2.0 to 5.0. The non-linear least squares treatment of the data performed with the aid of the Hyperquad program, indicated the formation of the following complexes with the respective stability constants log β_p,q,r given in parenthesis (p, q, r are stoichiometric indices for metal, ligand, and proton, respectively): Al(HAsp)²⁺ (log β_1,1,1 = 11.90 ± 0.02); Al(Asp)⁺ (log β_1,1,0 = 7.90 ± 0.03); Al(OH)Asp⁰ (log β_1,1,−1 = 3.32 ± 0.04); Al(OH)₂Asp⁻ (log β_1,1−2 = −1.74 ± 0.08), and Al₂(OH) Asp³⁺ (log β_2,1,−1 = 6.30 ± 0.04). ²⁷Al NMR spectra of Al³⁺ + aspartic acid solutions (pH 3.85) indicate that sharp symmetric resonance at δ∼10 ppm can be assigned to (1, 1, 0) complex. This resonance increases in intensity and slightly broadens upon further increasing the pH. In Al(Asp)⁺ complex the aspartate is bound tridentately to aluminum. The ¹H and ¹³C NMR spectra of aluminium + aspartic acid solutions at pH 2.5 and 3.0 indicate that β-methylene group undergoes the most pronounced changes upon coordination of aluminum as well as α-carboxylate group in ¹³C NMR spectrum. Thus, in Al(HAsp)²⁺ which is the main complex in this pH interval the aspartic acid acts as a bidentate ligand with –COO⁻ and –NH₂ donors closing a five-membered ring.     

Potentiometric and Multinuclear Magnetic Resonance Study of the Solution Equilibria Between Aluminium(III) Ion and L-Aspartic Acid

Summary. Solution equilibria between aluminium(III) ion and L-aspartic acid were studied by potentiometric, ²⁷Al, ¹³C, and ¹H NMR measurements. Glass electrode equilibrium potentiometric studies were performed on solutions with ligand to metal concentration ratios 1:1, 3:1, and 5:1 with the total metal concentration ranging from 0.5 to 5.0 mmol/dm³ in 0.1 mol/dm³ LiCl ionic medium, at 298 K. The pH of the solutions was varied from ca. 2.0 to 5.0. The non-linear least squares treatment of the data performed with the aid of the Hyperquad program, indicated the formation of the following complexes with the respective stability constants log β_p,q,r given in parenthesis (p, q, r are stoichiometric indices for metal, ligand, and proton, respectively): Al(HAsp)²⁺ (log β_1,1,1 = 11.90 ± 0.02); Al(Asp)⁺ (log β_1,1,0 = 7.90 ± 0.03); Al(OH)Asp⁰ (log β_1,1,−1 = 3.32 ± 0.04); Al(OH)₂Asp⁻ (log β_1,1−2 = −1.74 ± 0.08), and Al₂(OH) Asp³⁺ (log β_2,1,−1 = 6.30 ± 0.04). ²⁷Al NMR spectra of Al³⁺ + aspartic acid solutions (pH 3.85) indicate that sharp symmetric resonance at δ∼10 ppm can be assigned to (1, 1, 0) complex. This resonance increases in intensity and slightly broadens upon further increasing the pH. In Al(Asp)⁺ complex the aspartate is bound tridentately to aluminum. The ¹H and ¹³C NMR spectra of aluminium + aspartic acid solutions at pH 2.5 and 3.0 indicate that β-methylene group undergoes the most pronounced changes upon coordination of aluminum as well as α-carboxylate group in ¹³C NMR spectrum. Thus, in Al(HAsp)²⁺ which is the main complex in this pH interval the aspartic acid acts as a bidentate ligand with –COO⁻ and –NH₂ donors closing a five-membered ring.     

Features of Formation of Mixed-Ligand Complexes of Aluminum Tetraphenylporphine

Formation of extra complexes of aluminum tetraphenylporphine was studied by spectrophotometric titration. The effect of the nature of acido ligands on the stability of mixed-ligand complexes of aluminum tetraphenylporphine was determined. The stability constant (log K _st) of sterically unstrained complexes (Cl)Al(L)TPP and (OH)Al(L)TPP increases linearly with increasing basicity of the extra ligand (log KBH⁺); in the case of sterically distorted complexes (OAc)Al(L)TPP and (Acac)Al(L)TPP changes in log K _st and log KBH⁺ vary in the same direction. The geometries and energy characteristics of six-coordinate complexes of aluminum porphyrins were calculated quantum-chemically. The calculated enthalpies and Gibbs energies of formation of the complexes are consistent with the experiment. The possibility of the bidentate coordination of acetate and acetylacetonate in the porphyrin extra complexes was proved.     

Determination of sodium and phosphorus in organophosphorus compounds by fast-neutron activation

A method is described for the determination of sodium and phosphorus using the NG-160 neutron generator and an automated pneumatic transport device. The reactions²³Na (n, p)²³Ne and³¹P(n, α)²⁸ Al are utilized for the determination of sodium and phosphorus, respectively. For the determination of sodium, hermetically sealed vials are indispensable. The time required for one determination is 6 to 8 min. A rapid method for the determination of macro-amounts of sodium against a phosphorus background is also described, leading to the general conclusion that isotopes with γ-quantum energies close to 0.51 MeV can be determined against a background of positron radiation sources in a well-type crystal.     

Simultaneous determination of silicon and phosphorus in cast iron by 14 MeV neutron activation analysis

A fast (10 min), non-destructive simultaneous determination of silicon and phosphorus in cast iron and steel by 14 MeV neutron activation was developed. The 1.78 MeV²⁸Al activity (T=2.24 min) induced by the reaction²⁸Si(n, p)²⁸Al is counted on a NaI(Tl) detector. Two measurements are made to correct for the 1.81 MeV⁵⁶Mn activity (T=2.58 hr) from the iron matrix. However,²⁸Al is also produced via³¹P(n, α)²⁸Al. By (n, 2n) reaction, phosphorus yields also³⁰P (T=2.6 min), the 0.511 MeV annihilation radiation of which is counted by two opposite NaI(Tl) detectors in coincidence. Again, two successive coincidence measurements are carried out in order to take into account the⁵³Fe activity (β⁺; T=8.9 min) from⁵⁴Fe(n, 2n)⁵³Fe. The²⁸Al measurement is appropriately corrected via the computed phosphorus content. An oxygen flux monitor was used to normalize to the same flux. Nuclear interferences have been examined. Special attention has been paid to the presence of copper. The standard deviation for phosphorus being as high as ca. 0.09% P for a single determination, this technique can only be practical as an independent phosphorus analysis for high phosphorus cast irons. The precision on the²⁸Al measurement is 5% relative for 0.2% Si and 2.5% above 1% Si. Aspirant of the N.F.W.O.     

Measurement of neutron-induced activation cross sections of lanthanum at 14.8 MeV

Cross-sections for (n,p), (n,α), (n,n′α), (n,t) and (n,2p) reactions have been measured on ¹³⁹La isotope at the neutron energy 14.8 MeV using the activation technique in combination with high-resolution gamma-ray spectroscopy. Neutrons were produced via the ³H(d,n)⁴He reaction using a solid tritium–titanium target. The neutron fluences were determined using the monitor reaction ²⁷Al(n,α)²⁴Na. The neutron energy in this measurement was determined by cross section ratios for the ⁹⁰Zr(n,2n)^89m+gZr and ⁹³Nb(n,2n)^92mNb reactions. Data are reported for the following reactions: ¹³⁹La(n,p)¹³⁹Ba, ¹³⁹La(n,α)¹³⁶Cs, ¹³⁹La(n,n′α)^135mCs, ¹³⁹La (n,t)^137mBa, and ¹³⁹La(n,2p)¹³⁸Cs. The cross sections were discussed and compared with experimental data found in the literature, and with the comprehensive evaluation data in ENDF/B-VII.0, JENDL-3.3, JEFF-3.1/A, and TENDL-2008 libraries.     

Determination of silicon in cast iron by 14 MeV neutron activation

Silicon in cast iron was analyzed by 14 MeV neutron activation—high-resolution γ-ray spectrometry. Silicon was detected as²⁸Al, the product of the²⁸Si(n, p)²⁸Al reaction. Interference of⁵⁶Mn was separated using a Ge(Li) detector and a biased amplifying system. The 1. 81 MeV gamma-radiation of⁵⁶Mn, which is the product of the⁵⁶Fe(n, p)⁵⁶Mn reaction of the matrix of cast iron, was used as an internal standard and for correction of the self-absorption of the 1. 78 MeV gamma-radiation of²⁸Al by the sample. The interferences of aluminum, phosphorus and manganese could be neglected according to the results calculated from their nuclear properties and contents in the cast iron of this experiment. The results of this method agreed well with the results of the usual chemical method, with errors less than 5% of the results, and the precision of the method was satisfactory with a C. V. of less than almost 6% for rapid analysis of silicon in cast iron. The analytical line through the origin with a slope of the mean value of the repetition experiments could be used as the analytical line with almost the same precision and accuracy of the results as for the analytical line calculated by the least squares method.