Investigation of plasma-related matrix effects in inductively coupled plasma-atomic emission spectrometry caused by matrices with low second ionization potentials—identification of the secondary factor

Plasma-related matrix effects induced by a comprehensive list of matrix elements (a total of fifty-one matrices) in inductively coupled plasma-atomic emission spectrometry were investigated and used to confirm that matrix effects caused by elements with a low second ionization potential are more severe than those from matrix elements having a low first ionization potential. Although the matrix effect is correlated unambiguously with the second ionization potential of a matrix, the correlation is not monotonic, which suggests that at least one other factor is operative. Through study of a large pool of matrix elements, it becomes possible to identify another critical parameter that defines the magnitude of the matrix effect; namely the presence of low-lying energy levels in the doubly charged matrix ion. Penning ionization by Ar excited states is proposed as the dominant mechanism for both analyte ionization/excitation and matrix effects; matrices with a low second ionization potential can effectively quench the population of Ar excited states through successive Penning ionization followed by ion-electron recombination and lead to more severe matrix effects.     

Matrix elements of multi-electron operator in restricted Hartree-Fock theory

A theorem has been established for the matrix elements of a general t-electron operator between N-dimensional determinantal wave functions arising in the solution of the atomic and molecular multi-electron problem by the restricted Hartree-Fock (RHF) method (1 ≤ t ≤ N). The required matrix elements of this operator are sums of matrix elements over t-dimensional basic determinantal wave functions. The final results are especially useful in the determination of multi-electron properties for atoms and molecules when the Hylleraas approach in RHF theory is employed.     

Calculation of the Stark effect of neon I usingjl coupled wave functions

A method to calculate the Stark shifts and splittings in noble gases is described and results for neon I are presented. The energy values in a static homogeneous electric field are found by diagonalizing the energy matrix numerically. This matrix consists of the energy values of the free atom taken from experiment and of off-diagonal matrix elements of the electric field operator. The latter are computed using wave functions consisting of a radial function of the excited electron found by numerical integration, and of a two-particle (core+electron) spin-orbital part represented by rigorousjl coupling. As an example, the splitting of the levels 6s to 6p is shown and is explained in terms of atomic level positions, the relative size of matrix elements and of selection rules. A nomenclature for the high field Stark effect is developed in accord with group theory.     

Direct determination of trace rare earth elements in ancient porcelain samples with slurry sampling electrothermal vaporization inductively coupled plasma mass spectrometry

A method for the direct determination of trace rare earth elements in ancient porcelain samples by slurry sampling fluorinating electrothermal vaporization inductively coupled plasma mass spectrometry was developed with the use of polytetrafluoroethylene as fluorinating reagent. It was found that Si, as a main matrix element in ancient porcelain sample, could be mostly removed at the ashing temperature of 1200 °C without considerable losses of the analytes. However, the chemical composition of ancient porcelain sample is very complicated, which makes the influences resulting from other matrix elements not be ignored. Therefore, the matrix effect of ancient porcelain sample was also investigated, and it was found that the matrix effect is obvious when the matrix concentration was larger than 0.8 g l^− 1. The study results of particle size effect indicated that when the sample particle size was less than 0.057 mm, the particle size effect is negligible. Under the optimized operation conditions, the detection limits for rare earth elements by fluorinating electrothermal vaporization inductively coupled plasma mass spectrometry were 0.7 ng g^− 1 (Eu)–33.3 ng g^− 1(Nd) with the precisions of 4.1% (Yb)–10% (La) (c = 1 μg l^− 1, n = 9). The proposed method was used to directly determine the trace rare earth elements in ancient porcelain samples produced in different dynasty (Sui, Ming and Qing), and the analytical results are satisfactory.     

Eigenvalue independent partitioning and direct minimization in self-consistent field theory

It is pointed out that the matrix elements of a partitioning operator, f, introduced previously for constructing effective hamiltonians, provide natural sets of unconstrained and non-redundant variables in which to formulate self-consistent field theory. The elements of f are complementary to corresponding elements of the density matrix, the relation being essentially that between covariant and contravariant vectors. Some consequences for direct minimization SCF techniques are considered.     

Nuclear coordinate dependence of electronic matrix elements for radiationless transitions

The nuclear coordinate dependence of the electronic matrix elements for radiationless transitions (in the weak coupling limit) is investigated by the use of a Q-centroid approximation. This approach bears a similarity to the familiar r-centroid method in diatomic spectroscopy, but has a wholy different physical character. Because the Q-centroid for electronic relaxation is obtained as an average with density of states weighted Franck—Condon factors, it is not restricted to geometries near the equilibrium position of the initial electronic state as it is in the case of radiative transitions (in the weak coupling limit). For totally symmetric vibrations, it is shown that the Q-centroids for poor accepting modes are in the vicinity of the equilibrium positions for this vibration, while those for good accepting modes tend towards the surface crossing along those vibrational modes. Thus, in the case of dominant accepting modes, the electronic matrix element reflects a Teller surface crossing mechanism for electronic relaxation, even though the density of states weighted Franck—Condon factors reflect a tunnelling mechanism. For non-totally symmetric vibrations, Q-centroids may be large or small independent of their accepting mode capabilities. Thus, coupling mechanisms, which are “forbidden” at the equilibrium geometry in aromatic hydrocarbons, may become allowed and even dominant because of very distorted Q-centroid configurations. This leads to another possible reason for the absence of observation of a vibration that is clearly assignable as a promoting mode in the single vibronic level fluorescence studies of benzene-like molecules. The results underscore previous warnings as to the enormous errors incurred by using the Condon approximation for the nuclear coordinate dependent energy denominators that appear in the electronic matrix elements.     

Adjustment of numerical models for gamma-ray spectra of samples when subtracting spectra of matrix elements in neutron activation analysis

Approaches to adjustment of numerical models for gamma-ray spectra of matrix elements are considered. These approaches are aimed at (1) the elimination of the substrate effect in the preparation of the initial spectra of individual elements, (2) the energy calibration of spectra, (3) the improvement of agreement between model and actually observed spectra using the comparison test for peak amplitudes of matrix elements, and (4) special processing of the spectra obtained after the subtraction of matrix elements in the test samples. The adjustment allows the contribution of matrix elements to be more precisely subtracted from the spectra of the samples under study. Thus, additional analytical lines are obtained for some elements, and detection limits are lowered for the majority of lines produced by the standard method of spectrum processing. This extends the potential of neutron activation analysis in solving scientific and practical problems.     

Angular dependence of inductive effect and cis—trans influence in coordination compounds

Within the framework of the perturbation theory the implication of excited antibonding states in chemical bonding through the replacement of the AX bond by a more covalent AL bond in octahedra AX^″±₆ is shown to bring about greater weakening of the AX_tr bond in compounds of transition elements and of the AX_cis bond in compounds of non-transition elements. Weakening of AX_i bonds is proportional to non-diagonal matrix elements a_cis and a_tr between the respective localized orbitals. On the basis of these calculations the angular dependence of the inductive effect is also determined for compounds with multiple and donor—acceptor bonds. The predominant direction of the inductive effect in mutual influence of ligands depends on the nature of the atom A. The role of nonvalent interactions for determining the relative strength of bonds is considered. Theoretical conclusions are in agreement with the experimental data.     

Calculations of Jahn-Teller coupling constants in the weak-field basis via the angular overlap model: a simple operator equivalent technique

Within the framework of the angular overlap model the matrix elements of the linear Jahn-Teller operator may easily be calculated in the weak-field basis in terms of simple operator equivalents. The method is applied to the calculation of the 〈M_J|?V/?Q|M_j〉 matrix elements for the |LSJMj〉 ground states of t^x species (x = 1) ? 13) in )^* symmetry.     

Analytic quantum mechanics of the morse oscillator

The approximate eigenfunctions of the Morse oscillator, expressed in terms of Laguerre polynomials, are shown to form an approximately orthogonal basis. Analytic expressions for the matrix elements of common operators are obtained within this representation. With such matrix elements in closed form, the Morse oscillator becomes, as the harmonic oscillator has been, a practical building block in molecular theory.     

Analysis of Cadmium and Cadmium Oxide by Inductively Coupled Plasma Atomic Emission Spectrometry

A procedure of the multielement analysis of cadmium and cadmium oxide by inductively coupled plasma atomic emission spectrometry is proposed. The effect of the concentration of the matrix component on the analytical signals of impurity elements is studied and the analytical lines of the analytes are chosen. For the chosen concentration of the matrix component, the optimum conditions of analysis are selected, i.e., power delivered to the plasma and the flow rate of sputtering argon gas. The accuracy of the developed procedure, ensuring the determination of up to 41 impurity elements with limits of detection in the range from n × 10^–7 to n × 10^–4 wt %, is estimated.     

Calculation of electro-optical parameters: A new approach

A new approach has been suggested for the calculation of electro-optical parameters from the data on infrared band intensities employing the first order approximation. The off-diagonal elements in the matrix of dipole moment derivatives are considered in terms of the diagonal elements and the ratios of the L-matrix elements.     

Theory of the implementation of the fundamental parameter method for the X-ray fluorescence determination of low-atomic-number elements

The theory of X-ray fluorescence generation in elements with a low atomic number Z is extended to the case of host matrices with high Z. The total contribution of the selective excitation effects is estimated with regard to the cascade K-L transitions. The influence of the elemental composition of the matrix and the excitation conditions on the X-ray fluorescence intensity of the elements in study is assessed. The accuracy of the model of X-ray fluorescence generation in the low-atomic-number elements is confirmed by the agreement of the experimental and calculated intensities of carbon in various carbon-containing compounds.     

Decoherence in an anharmonic oscillator coupled to a thermal environment: a semiclassical forward-backward approach

The decoherence of an anharmonic oscillator in a thermal harmonic bath is examined via a semiclassical approach. A computational strategy is presented and exploited to calculate the time dependence of the purity and the decay of individual matrix elements in the energy representation for a variety of initial states. The time dependence of the decoherence is found to depend on the temperature of the bath, the coupling strength, the initial state of the oscillator, and the choice of quantity measuring the decoherence. Recurrences in the purity and in the off-diagonal matrix elements are observed, as well as the collapse of these matrix elements to the diagonal, providing evidence for the retention of quantum coherence for time scales longer than that indicated by the purity. The results are used to analyze the utility of the Caldeira-Leggett and Redfield models of decoherence and to assess the dependence of dephasing rates on the degree of structure in phase space. In several cases we find that the dephasing dynamics can be described as an initial Zeno-effect regime, followed by a Caldeira-Leggett region, followed by recurrences.     

Problem of the Account of Matrix Effect in Electron Probe Microanalysis of Rock-Forming Minerals

Four methods of correction and three methods of calculation of absorption coefficients are tested in electron probe microanalysis of rock-forming minerals. Experimental data by Pouchou and Pichoir, Sewell–Love–Scott, and Armstrong are attracted in tests. It is shown that the correction factor can be calculated with the error no more than 1 rel. % if a short-wave line (matrix effect is determined mainly by the effect of atomic number) is used as an analytical line or the analytical line belongs to the absorption K-edge of elements present in the sample. In the presence of binary matrix effect, when the analytical line absorbs in the K–L₁ region, the situation is more complex and additional studies are required.     

Error matrices in gas-electron diffraction: II. Influence of weight matrix

The properties of three different forms of error matrices in electron diffraction are investigated, assuming the presence of stationary, Gaussian, Markovian noise in the primary data. The error matrices studied are M_x^p based on the optimum weight matrix P the bona fide error matrix M_x^w based on the nonoptimum weight matrix W, and the false error matrix M_x^o commonly calculated by diffractionists using the formula for the optimum error matrix while incorporating a nonoptimum weighting. Simple formulae relating the elements of the various matrices are derived in the case where W is the best diagonal weight matrix and where geometric constraints are not imposed on parameters. The influence of geometric constraints is tested. Calculations indicate that diagonal weight matrices in ordinary circumstances give results imperceptibly inferior to the results obtained with the best nondiagonal weight matrices. Elements of M_x^w closely approach those of M_x^p whereas elements of the false error matrix, taken alone, may be very misleading.     

Excess entropy and thermal behavior of Cu- and Ti-doped bioactive glasses

Bioactive glasses belong to the ceramic family. They are good materials for implantation due to their excellent capacities to create an intimate bond with bones. Copper is known for its anti-inflammatory, antibacterial, and antifungal properties. Titanium is biocompatible and resistant to corrosion. These chemical elements can be introduced in bioactive glasses to provide a wide variety of uses and to enhance the physiological properties of implanted biomaterials. In this work, bioactive glasses doped with different contents of copper and titanium were synthesized by the melting method. The purpose is to study the effect of doping metal element on the thermal characteristics (T _g, T _c, and T _f). The results revealed that the increase of the content of copper and titanium in the glass matrix decreases the melting temperature and induces an increase of the thermal stability. The excess entropies of pure and doped glasses were calculated. Obtained results highlighted the decrease of the excess entropy with the increase of metal elements contents.     

Time-resolved measurements of individual ion cloud signals to investigate space-charge effects in plasma mass spectrometry

A new approach to directly monitor space charge induced effects due to high concentrations of efficiently ionized elements in inductively coupled plasma mass spectrometry (ICP-MS) is described. The broadening of ion clouds produced from individual, monodisperse drops of sample is measured by using time-resolved ICP-MS. The extent of broadening due to high concentrations of Pb in the sample is related inversely to the analyte mass. For the lightest analyte investigated, Li⁺, the relative width of the time-resolved analyte peak increases and then shows a dip in the center as the Pb concentration is increased to 500 and then 1500 µg/mL. The initial results of experiments that investigated chemical matrix effects as a function of concomitant species concentration, analyte mass, and sampling location in ICP-MS are consistent with space-charge effects.     

A multivariate study of the acid effect and the selection of internal standards for inductively coupled plasma mass spectrometry

The effects of nitric acid concentration and liquid flow rate on the signals obtained with an inductively coupled plasma mass spectrometer, operated with a microconcentric nebulizer (MCN-100), have been studied by the use of partial least squares regression. Thirteen elements, covering the mass range 51–238, were studied. The nitric acid concentration was varied in the range 0.14–2.8 mol l⁻¹ and the acid effect was found to vary significantly between the elements — depending mainly on the value of the first ionisation potential of the element. The effect of the liquid flow rate was studied within the range 34.5–172.5 μl min⁻¹ and it was only significant (P=0.05) for ¹⁰⁷Ag and ¹⁰⁹Ag. It is possible to compensate completely for the acid matrix effect by the use of a proper internal standard. The use of multivariate analysis methods, e.g. partial least squares regression is recommended in order to choose the most suitable internal standards.     

Verbundverfahren zur Multielement-Spurenbestimmung in hochreinem Chrom nach Spuren—Matrix-Trennung

(Simultaneous determination of trace elements in high-purity chromium by inductively-coupled plasma/atomic emission spectrometry after matrix separation.) The production of high-purity metals requires routine determinations of elements in the ng g^?1 range. Procedures based on wet chemical separation of matrix and trace elements followed by inductively-coupled plasma/atomic emission spectrometry are suitable. The separation of 19 trace metals (Be, Bi, Ca, Cd, Co, Cu, Fe, La, Mg, Mn, Nb, Ni, Pb, Ta, Ti, Th, U, Zn and Zr) from high-purity chromium powder is described. The powder is dissolved in hydrochloric acid and oxidized with perchloric acid or alkaline hydrogen peroxide, and the trace elements are precipitated at pH 11–13 and collected on cellulose loaded with indium hydroxide or on cellulose-Hyphan. The detection limits of the total procedure vary from 10 ng g^?1 for cadmium to 600 ng g^?1 for zinc.