Assessment of quality performance parameters for straight line calibration curves related to the spread of the abscissa values around their mean

In validation of quantitative analysis methods, knowledge of the response function is essential as it describes, within the range of application, the existing relationship between the response (the measurement signal) and the concentration or quantity of the analyte in the sample. The most common response function used is obtained by simple linear regression, estimating the regression parameters slope and intercept by the least squares method as general fitting method. The assumption in this fitting is that the response variance is a constant, whatever the concentrations within the range examined.The straight calibration line may perform unacceptably due to the presence of outliers or unexpected curvature of the line. Checking the suitability of calibration lines might be performed by calculation of a well-defined quality coefficient based on a constant standard deviation.The concentration value for a test sample calculated by interpolation from the least squares line is of little value unless it is accompanied by an estimate of its random variation expressed by a confidence interval. This confidence interval results from the uncertainty in the measurement signal, combined with the confidence interval for the regression line at that measurement signal and is characterized by a standard deviation s_x0 calculated by an approximate equation. This approximate equation is only valid when the mathematical function, calculating a characteristic value g from specific regression line parameters as the slope, the standard error of the estimate and the spread of the abscissa values around their mean, is below a critical value as described in literature.It is mathematically demonstrated that with respect to this critical limit value for g, the proposed value for the quality coefficient applied as a suitability check for the linear regression line as calibration function, depends only on the number of calibration points and the spread of the abscissa values around their mean.     

Calibration lines passing through the origin with errors in both axes

Linear regression of calibration lines passing through the origin was investigated for three models of y-direction random errors: normally distributed errors with an invariable standard deviation (SD) and log normally and normally distributed errors with an invariable relative standard deviation (RSD). The weighted (weighting factor is x ² _i ), geometric and arithmetic means of the ratios y _i /x _i estimate the calibration slope for these models, respectively. Regression of the calibration lines with errors in both directions was also studied. The x-direction errors were assumed to be normally distributed random errors with either an invariable SD or invariable RSD, both combined with a constant relative systematic error. The random errors disperse the true, unknown x-values about the plotted, demanded x-values, which are shifted by the constant relative systematic error. The systematic error biases the slope estimate while the random errors do not. They only increase automatically the slope estimate uncertainty, in which the uncertainty component reflecting the range of the possible values of the systematic error must be additionally included. Received: 9 May 2000 Accepted: 7 March 2001     

Distribution of geometrical current density inside a flow-by porous electrode: Effect of electrode parameters and electrochemical reactions

The effect of the difference between the equilibrium potentials of the target and side reactions, the solution flow rate, and specific surface area of porous electrode (PE) on the distribution of the geometrical current density along the solution flow i_g(y) at various average current densities is studied by the method of mathematical modeling. It is found that the largest range of the variation of i_g(y) (the exponential decrease along the solution flow) is typical for the conditions that provide the limiting current mode of the target reaction on the entire PE surface in the absence of simultaneous hydrogen evolution. All changes in the operation conditions, which reduce the uniformity of the distribution of the current inside PE along the X axis and hamper reaching the limiting current mode (for example, a decrease in the equilibrium potential difference, an increase in the flow rate or specific surface area of PE) lead to more uniform distribution of i_g(y).     

ESR evidence for structural rearrangements occurring upon MoO3 reduction

Reduction of polycrystalline MoO₃ in the course of heat treatmentin vacuo has been studied by means of ESR. The formation of two different Mo(V) centers has been identified: center A withg_x = 1.946, g_y = 1.960, g_z = 1.868; and center B characterized byg_x = 1.943, g_y = 1.954, g_z = 1.878. Center B exhibited a well-resolved hyperfine structure resulting from naturally abundant odd isotopes of Mo:A_x = 3.2mT, A_y = 3.0mT, A_z = 7.0mT. Species A formed at an early stage of reduction has been identified as Mo(V) in rhombically distorted square pyramidal surrounding, whereas center B appearing in strongly reduced samples shows a distorted octahedral coordination. The results have been interpreted in terms of the crystallographic shear mechanism.     

A mathematical model based on the limit dilution method to obtain linear calibration curves which eliminate the matrix effect in quantitative analysis by X-ray fluorescence

We propose a mathematical model from an analytical application viewpoint inspired in the limit dilution method. The theoretical development of the model and its results are given. The model shows that there is a linear relation between the inverse of fluorescence intensity and the inverse of the dilution factor; each analytic system (sample, diluent and analyte) is characterised by a general linear function which is easily obtained. The analytical applications arising from this linearity are of great importance in X-ray fluorescence analysis. The following immediate applications are proposed: direct procurement of the total correction factor Y/H, rapid calculation of the fluorescence intensity of the analyte in a sample (I_i^s) and direct calculation of the corrected fluorescence intensity (I_i^sF). The suggested model makes it possible to deduce a linear function between the fluorescence intensity of the analyte and the analyte concentration in successive dilutions of a standard; this straight line behaves as a calibration curve with direct application in X-ray fluorescence analysis. The proposed model may be applied to complex samples of geological origin, with elimination of the matrix effect. The results obtained in the determination of Ca, K, Fe and Ti in a standard soil show complete agreement with the certified reference values with a relative error about 0.5%, even using a standard shale with very different chemical composition as reference sample.     

A method for calibration and validation subset partitioning

This paper proposes a new method to divide a pool of samples into calibration and validation subsets for multivariate modelling. The proposed method is of value for analytical applications involving complex matrices, in which the composition variability of real samples cannot be easily reproduced by optimized experimental designs. A stepwise procedure is employed to select samples according to their differences in both x (instrumental responses) and y (predicted parameter) spaces. The proposed technique is illustrated in a case study involving the prediction of three quality parameters (specific mass and distillation temperatures at which 10 and 90% of the sample has evaporated) of diesel by NIR spectrometry and PLS modelling. For comparison, PLS models are also constructed by full cross-validation, as well as by using the Kennard-Stone and random sampling methods for calibration and validation subset partitioning. The obtained models are compared in terms of prediction performance by employing an independent set of samples not used for calibration or validation. The results of F-tests at 95% confidence level reveal that the proposed technique may be an advantageous alternative to the other three strategies.     

Application of direct calibration in multivariate image analysis of heterogeneous materials

Many scientific instruments produce multivariate images characterized by three-way tables, an element of which represents the intensity value at a spatial location for a given spectral channel. A problem frequently encountered is to attempt estimating the contributions of some compounds at each location of these images. Usual regression methods of calibration, such as PLS, require having a matrix of calibration X (n × p) and the corresponding vector y of the dependent variable (n × 1). X can be built up by sampling pixel-vectors in the images, but y is sometimes difficult to obtain, if the surface of the samples is formed by chemically heterogeneous regions. In this case, the quantitative analyses related to y may be difficult, if the pixels represent very small areas (for example on microscopic images) or very large ones (satellite images). This is for example the case when dealing with biological solid samples representing different tissues. Direct Calibration (DC), sometimes referred to as “spectral unmixing”, do not require having such a calibration set. However, it is indeed needed to have both a matrix of “perturbing” pixel-vectors (noted K) and a vector of the “pure” component spectrum to be analyzed (p), which are more easily obtainable. For estimating the contribution, the unknown pixel vector x and the pure spectrum p are first projected orthogonally onto K giving the vectors x_⊥ onto p_⊥, respectively. The contribution is then estimated by a second projection of x_⊥ onto p_⊥. A method, based on principal component analysis, for determining the optimal dimensions of K is proposed. DC was applied on a collection of multivariate images of kernel of wheat to estimate the proportion of three tissues, namely out-layers, “waxy” endosperm and normal endosperm. The eventual results are presented as images of wheat kernels in false colors associated to the estimated proportions of the tissues. It is shown that DC is appropriate for estimating contributions in situations in which the more usual methods of calibration cannot be applied.     

Paramagnetic resonance of interstitial mo5+ in a tio2 lattice

Paramagnetic absorption of Mo⁵⁺ has been studied in a polycrystalline TiO₂ rutile lattice, The g tensor (g_x = 1.897, g_y = 1.920, g_z = 1.857) and the hyperfine tensor (A_x = 32.7, (A_y = 51.2, (A_z = 58.5 (in 10^?4 cm^?1)) are in agreement with those expected for an nd¹ ion in an interstitial position.     

Zur Definition von Selektivität,Spezifität und Empfindlichkeit von Analysenverfahren

The three metric, functional concepts named in the title can be defined without arbitrariness and their values may be calculated for any multicomponent-analytical procedure from the relation of the measurable physical quantities x _ito the contents c _kwhich are to be determined. This relation is mathematically a “mapping” (achieved by systems of functions). The system of “analytical functions” (x _i→ c _k) is the inverse of the system of “calibration functions” (c _k→ x _i) which alone can be directly gained by experiments. The ‘calibration matrix” (γik) whose elements γ_ik are the “partial sensitivities” \(\tfrac{{\partial x_i }}{{\partial c_k }}\) represents the system in first approximation but only locally, i.e. for the respective constitution of the sample. The “sensitivity” of the analytical procedure as a whole, is numerically given by the determinant of this matrix; the “selectivity” is derived from the condition that the inversion of the calibration system to the analytical system (of functions) shall be possible by an iteration process. “Specificity” is defined in analogy to selectivity. In the appendix it is explained why selectivity is the strongest means to reduce the expenditure for the complete calibration of multicomponent analyses to a realistic and tolerable degree.     

Synthesis and electrochemical properties of sulfur doped-LixMnO2−ySy materials for lithium secondary batteries

Sulfur doped lithium manganese oxides (Li_xMnO_2−yS_y) were prepared by ion exchange of sodium for lithium in Na_xMnO_2−yS_y precursors obtained by a sol–gel method. These materials had the nano-crystallite size, which was composed of grain size of about 100–200 nm. Especially, Li_0.56MnO_1.98S_0.02 delivered the initial discharge capacity of 170 mAh g⁻¹ and gradually increased the discharge capacity of 220 mAh g⁻¹ until 50 cycles. Moreover, it showed an excellent cycling behavior, although its original structure transformed into the spinel phase during cycling.     

Determination of quality parameters of beers by the use of attenuated total reflectance-Fourier transform infrared spectroscopy

The estimation of important quality parameters of beers, such as original and real extracts and alcohol content, has been evaluated by attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) using a partial least square (PLS) calibration approach. Two sample populations, one consisting of 24 samples and other of 21 samples, obtained from the Spanish market and covering different types of beer were used. The first set was used for building and validating the model, whereas the second, measured 6 months after, was used for evaluating its robustness. The spectral range and the size of the calibration set and its suitability for building the PLS model have been evaluated.Considering a calibration set comprised of 12 samples, selected via hierarchical cluster analysis, and a validation data set of 11 samples, the absolute mean difference (d_x−y) and standard deviation of mean differences (s_x−y) of the real extract, original extract and alcohol content were 0.009 and 0.069% (w/w), −0.021 and 0.20% (w/w) and −0.003 and 0.130% (v/v), respectively. The maximum error for the prediction of any of these three parameters for a new sample did not exceed 2.5%. These values were practically invariant for both tested data sets.The developed methodology favourably compares with the automatic reference methodology in terms of speed and reagent consumption and waste generation.     

Single-crystal EPR study of a mixed-valence ruthenium dimer ion: the ground state of the creutz-taube complex

Single-crystal electron paramagnetic measurements have been carried out on an orthorhombic chlorotetrabromo salt of the mixed-valence μ-pyrazinc-decamminediruthenium(5⁺) ion (Creutz-Taube ion) Below ≈ 200 K the spectrum consists of two lines arising from two magnetically inequivalent but crystallographically equivalent centres. The resonances can be described by a g tensor with principal axes aligned with

and x₁.y₁:x₂.y₂ in the ab plane. At 113 K the comp of the g tensor are g_x = 2.779(5). g_y = 2.489(5). g_z = 1.334(10). The point-group symmetry about the centre of unit is C₂h (m/2) with the c axis being the two-fold axis. The g_z component is aligned perpendicular to the plane of the pyrazine ring and perpendicular to the Ru-Ru axis (X). The remaining components should be aligned closely wilh X.Y. The angle between the X axes for the two sites as determined by X-ray measurements, is 85.8° compared with 82.5 ± 1° between the x₁.x₂g tensor axes. Magnetic exchange coupling between the dimer ions is very small. The tetragonal approximation to the observed g tensor is g₁ = 2.632 ± 0.005. g₁₁ = 1.334 ± 0.010. The theory of the g tensor for this complex is discussed, it is shown that these values are within the range predicted for an ion with a symmetrical delocalized ground state, the orientation of the g₁₁ component normal to the plane of the pyrazine ring is also predicted for a delocalized ground state. The EPR results arc thus consistent with a stable single-minimum ground state for the Creutz-Taube ion Powder EPR experiments on a tosylate salt of this ion have previously been reported by Bunker et al. A g₁₁ signal was not observed and it was assumed to be very small (? 0.6) and oriented along the Ru-Ru axis, however the absence of a signal at g ≈ 1.3 (in fact oriented perpendicular to the Ru-Ru axis) was presumably due to poor statistics for g₁₁ in EPR measurements on powder samples. The proposal of these authors that EPR measurements provide evidence for a trapped-valence ground state for the Creutz-Taube ion thus cannot be accepted.     

Dependence of calibration sensitivity of a polysulfone/Ru(II)-tris(4,7-diphenyl-1,10-phenanthroline)-based oxygen optical sensor on its structural parameters

The optimum performance of an optical oxygen sensor based on polysulfone (PSF)/[Ru(II)-Tris(4,7-diphenyl-1,10-phenanthroline)] octylsulfonate (Ru(dpp)OS) was checked by carefully tuning the parameters affecting the membrane preparation. In particular, membranes having thickness ranging between 0.2 and 8.0 μm with various luminophore concentrations were prepared by dip-coating and tested. The membrane thickness was controlled by tuning the solution viscosity, and was measured both by secondary ion mass spectrometry (SIMS) and by visible spectroscopy (Vis). Luminescence-quenching-based calibration was a single value of the Stern-Volmer constant (K^′SV) for membranes containing up to 20 mmol Ru(dpp) g⁻¹ PSF (1.35 μm average thickness). The K^′SV value decreased for larger concentration. The highest sensitivity was obtained with membrane thickness around 1.6 μm, having a response time close to 1 s. Thicker membranes exhibited an emission saturation effect and were characterized by longer response time. The K^′SV behavior was interpreted on the basis of a mathematical approach accounting for the contribution of luminescence lifetime (τ₀), oxygen diffusion coefficient (DO₂) and oxygen solubility inside the membrane (sO₂) establishing the role of all of them and allowing their experimental determination. Moreover, a simple experimental way to estimate K^′SV without needing calibration was proposed. It was based either on the light emission asymmetry or on the percent variation of light emission on passing from pure nitrogen to pure oxygen.     

Theory of depolarization dispersion of inversely polarized modes in heme proteins

A new polarization phenomenon observed recently in resonance Raman scattering from heme proteins is explained by vibronic interactions between split Q_x, Q_y, and B_x, B_y electronic states in porphyrin rings. Analytical formulas are presented which account well for the observed depolarization dispersion of the 1585 cm^?1 and 1310 cm^?1 a_2g modes in ferrocytochrome c.     

Chemical shifts of the protons of the primary amine group and its structure

In the NMR spectra of a series of amine-containing organic compounds, a linear dependence has been found to exist between the chemical shifts of the signals for the primary amino group protons, δ_NH2 values, and the s-character (b²) of N-H bonds. The points for the amines (aliphatic and aromatic) lie on a straight line of equationS(%) = 2.1δ_NH2 + 18.4The corresponding correlation for amides is a straight line parallel to the abscissa, on a level of (b²) = 0.33, i.e. the value characterizing the pure sp² hybrid state on the N atom.     

Synthesis and characterisation of the SrxBa1−xFeO3−y-system and the fluorinated phases SrxBa1−xFeO2F

Compounds in the system Sr_xBa_1?xFeO_3?y have been prepared under different partial pressures of oxygen. In this system, different perovskite-type structures are found depending highly on the values of x and y. Fluorination using polyvinylidenedifluoride (PVDF) gives oxyfluoride materials of composition Sr_xBa_1?xFeO₂F, which normally crystallize in the cubic perovskite structure. Rietveld refinement results provide information about the packing density for oxide and oxyfluoride samples and allow a general comparison between these two different types of materials. Furthermore, the determination of the average iron oxidation state also showed that the oxygen deficiency, y, depends significantly on the value of x and the structure determined by the Sr/Ba ratio.     

Excellent Performance of Few‐Layer Borocarbonitrides as Anode Materials in Lithium‐Ion Batteries

Borocarbonitrides (B_xC_yN_z) with a graphene‐like structure exhibit a remarkable high lithium cyclability and current rate capability. The electrochemical performance of the B_xC_yN_z materials, synthesized by using a simple solid‐state synthesis route based on urea, was strongly dependent on the composition and surface area. Among the three compositions studied, the carbon‐rich compound B_0.15C_0.73N_0.12 with the highest surface area showed an exceptional stability (over 100 cycles) and rate capability over widely varying current density values (0.05–1 A g^?1). B_0.15C_0.73N_0.12 has a very high specific capacity of 710 mA h g^?1 at 0.05 A g^?1. With the inclusion of a suitable additive in the electrolyte, the specific capacity improved drastically, recording an impressive value of nearly 900 mA h g^?1 at 0.05 A g^?1. It is believed that the solid–electrolyte interphase (SEI) layer at the interface of B_xC_yN_z and electrolyte also plays a crucial role in the performance of the B_xC_yN_z .     

Diffusion aspects of lithium intercalation as applied to the development of electrode materials for lithium-ion batteries

The creation of new electrode materials and the modification of existing ones are important trends in the development of lithium-ion batteries. Of special significance is to evaluate their diffusivity, i.e., the ability of providing transfer of the electroactive component. Such electrochemical techniques as cyclic voltammetry, electrochemical impedance spectroscopy, potentiostatic intermittent titration technique, and galvanostatic intermittent titration technique are used for this purpose. The values of chemical diffusion coefficient D estimated in similar electrode materials are shown to scatter by several orders of magnitude. Principal causes of this rather considerable scattering are discussed, including the uncertainty of diffusion area estimations and the use of various approaches to deriving equations to calculate D. Our conclusions are illustrated by examples of D estimations in the electrode materials Li _x C₆, Li _x Sn, Li _x TiO₂, Li _x WO₃, LiM _y Mn_2?y O₄, and LiFePO₄.     

Electrophysical and electrochemical properties of Y1 − x Ca x Cr1 − y Me y O3 (Me = Mg, Cu)

Structure, thermal elongation coefficient, and conductivity of Y_{1 ? x} Ca _x Cr_{1 ? y} Me _y O₃ (Me = Mg, Cu) in air are studied at 100–1000°C. Electrochemical activity of electrodes made of most conducting compositions Y_{1 ? x} Ca _x Cr_{1 ? y} Me _y O₃ (Me = Mg, Cu), contacting solid electrolyte 0.9ZrO₂ + 0.1Y₂O₃, is studied over a wide range of polarizations, in air, at 700–900°C.     

Preparation and thermoelectric properties of AgPbmSbSem+2 materials

Hydrothermally synthesized AgPb_mSbSe_m+2 (m=10, 12, 16, 18) nanoparticles with diameters of 20-50 nm were compacted by pressureless sintering. The Seebeck coefficient and electrical conductivity of the samples were measured from room temperature up to ∼750 K. The samples show large and positive values of the Seebeck coefficient and moderate electrical conductivity. The thermoelectric properties of Ag_xPb₁₈SbSe₂₀ (x=0.8, 0.85) and AgPb₁₈SbSe_20−yTe_y (y=1, 3) samples have also been studied. It has been found that Ag_0.85Pb₁₈SbSe₂₀ sample has a higher thermoelectric power factor. A significant difference in thermoelectric properties has also been observed for the AgPb₁₈SbSe₂₀ samples prepared with pressureless sintering and spark plasma sintering.