Thomson scattering from analytical plasmas

Electrons play an essential role in energy transfer and many other processes within analytical plasmas, so a complete characterization of any plasma requires spatially and temporally resolved data for the electron number density and temperature, as well as the electron energy distribution function. Thomson scattering provides a reliable non-intrusive means of determining inherently radially resolved absolute values for these fundamental parameters, without the assumptions about cylindrical symmetry or thermodynamic conditions in the plasma that are required by many other techniques. However, because of the relatively complex and expensive instrumentation required to perform successful Thomson scattering measurements, this method has not been widely applied in the field of analytical chemistry. The goal of this review was to clarify the history and theory of Thomson scattering, discuss the instrumental details that must be considered in a Thomson scattering experiment, and summarize the results of studies in which the technique has been applied to the characterization of analytical plasmas, in order to demonstrate the power of Thomson scattering as a tool for plasma characterization.     

Thomson scattering from an ICP

Fundamental parameters related to laser light scattering by electrons in the ICP are explained and calculated. The theory concerning how electrons in the plasma scatter incident laser light and how the scattered-light spectra are related to electron-density fluctuations is briefly described. Special problems and detailed experimental considerations for Thomson scattering from an ICP are discussed.     

Thomson-resonant interference effects in elastic x-ray scattering near the Cl K edge of HCl

We experimentally observed interference effects in elastic x-ray scattering from gas-phase HCl in the vicinity of the Cl K edge. Comparison to theory identifies these effects as interference effects between non-resonant elastic Thomson scattering and resonant Raman scattering. The results indicate the non-resonant Thomson and resonant Raman contributions are of comparable strength. The measurements also exhibit strong polarization dependence, allowing an easy identification of the resonant and non-resonant contributions.     

Comparison of active and passive spectroscopic methods to investigate atmospheric inductively coupled plasmas

A comparison of Thomson and Rayleigh scattering, diode laser absorption and line emission measurements is performed on a 100 MHz atmospheric argon-flowing inductively coupled plasma. The parameters, which are measured in two or more ways, are the electron density, the electron temperature and the heavy particle temperature. The optimized diagnostics show the same behavior for the electron density and temperature. Nevertheless, the Thomson scattering diagnostic is the best at retrieving the radial profile. The heavy particle temperature, as measured by using both Rayleigh scattering and diode laser absorption, is identical within the estimated errors. The technique of measuring the temperature during power interruption, with both Thomson scattering and emission spectroscopy, shows that the electron and heavy particle temperatures are not equal during the period of power interruption.     

Small-angle neutron scattering from two-phase polymeric systems

A small-angle neutron scattering method is presented for the determination of single-chain scattering functions in heterogeneous two-phase polymeric materials such as incompatible polymer blends and microphase-separated diblock copolymers. Development of the method makes use of both the discrete and continuum approaches to scattering theory. In this fashion it is shown that extraction of the single-chain scattering function requires only two experimental observations, regardless of the compressibility of the system. These experiments consist of small-angle neutron scattering profiles from two samples: an unlabeled two-phase material and a similar two-phase material in which a portion of the molecules in one phase have been replaced by molecules which are contrast labeled by isotopic deuterium substitution. Anticipated difficulties associated with actual application of the procedure and requirements of the necessary experimental samples are discussed.     

Effect of birefringence on the scattering of light. II. Oriented polymers

It has been considered for some time that the presence of birefringence in an oriented polymer must affect the light-scattering behavior. Previous analyses of this phenomenon are restricted to single-particle scattering. A more complete theory of the effect of birefringence on the scattering of light from correlated systems is presented. The measured scattering intensity is shown to be dependent upon the optical properties of the sample as well as the experimental technique and conditions.     

Study of early laser-induced plasma dynamics: Transient electron density gradients via Thomson scattering and Stark Broadening,and the implications on laser-induced breakdown spectroscopy measurements

To further develop laser-induced breakdown spectroscopy (LIBS) as an analytical technique, it is necessary to better understand the fundamental processes and mechanisms taking place during the plasma evolution. This paper addresses the very early plasma dynamics (first 100 ns) using direct plasma imaging, light scattering, and transmission measurements from a synchronized 532-nm probe laser pulse. During the first 50 ns following breakdown, significant Thomson scattering was observed while the probe laser interacted with the laser-induced plasma. The Thomson scattering was observed to peak 15–25 ns following plasma initiation and then decay rapidly, thereby revealing the highly transient nature of the free electron density and plasma equilibrium immediately following breakdown. Such an intense free electron density gradient is suggestive of a non-equilibrium, free electron wave generated by the initial breakdown and growth processes. Additional probe beam transmission measurements and electron density measurements via Stark broadening of the 500.1-nm nitrogen ion line corroborate the Thomson scattering observations. In concert, the data support the finding of a highly transient plasma that deviates from local thermodynamic equilibrium (LTE) conditions during the first tens of nanoseconds of plasma lifetime. The implications of this early plasma transient behavior are discussed in the context of plasma–analyte interactions and the role on LIBS measurements.     

Quantitative determination of large structures by small-angle light scattering

A new small-angle light scattering camera has been developed. In contrast to conventional detection the present system is based on a recently developed two-dimensional charge-coupled-device chip made by Thomson (France). The advantage of this chip is its excellent linear response and very low dark signal even at room temperature. The best linearity was obtained by leading each pixel signal through the same amplifying system. The optical system covered a diffraction angular region from about 1° to 15° (q = 0.2–2.6 μm⁻¹). The camera was calibrated with grids and pinholes and was tested with polymer latex particles in solution and with spherulites from polymer films. Received: 06 December 1999 Accepted: 04 February 2000     

Collisionally damped ion motion in ICR spectrometry

A Schrödinger equation equivalent to the Langevin equation of ion motion in ICR cells is presented. A wave function for the scattering states has been found as the solution to the equation of ion motion under the influence of electric and magnetic fields perturbed by a scattering potential. Applying the minimized wave packet as a wave function describing coherent states, the scattering amplitudes are determined explicitly. The connection between the collision cross section and the scattering amplitudes is found by making use of the incoming and outgoing particle flux density. The collision cross section found in this way is converted from quantum theory to classical physics. The collision cross section, which plays an essential role in the determination of rate constants can be determined by the aid of ICR experimental data if the contribution of an alternating electric field is taken into account.     

Interpretation of the hydrogen anomaly in neutron and electron compton scattering

In Compton scattering with neutrons in the energy range 20–120 eV, it has been observed that the relative H/M cross sections in a variety of H‐containing materials are 20–40% lower than expected from the composition ratio H/M (M being a heavier element in the same compound). The same phenomenon has also been observed in Compton scattering with electrons of 2 and 20 keV energy. There is, at present, no consensus about the reason for these anomalies. In this theory, they are explained as a result of interference when the scattering particle interacts with more than one hydrogen nucleus. The coherence volume of the actual setup, which limits the number of interfering particles, is therefore an important parameter. It is shown here that the large zero‐point motion of the hydrogen nuclei leads to reductions in the scattering intensity from interfering pairs. Coherence is preserved over the sub‐fs scattering times relevant for this process, even in the condensed systems studied. It is gradually lost when the scattering time is increased, which happens when the neutron energy is reduced (as reflected in lower anomalies for smaller scattering angles). Explicit expressions for the decoherence effect are presented and compared with experimental observation for a selection of observed H‐ and D‐containing systems. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Scattering of Xe from graphite

Recently a series of experimental measurements for the scattering of Xe atoms from graphite has been reported for both energy-resolved spectra and angular distributions. This system is of fundamental interest because the projectile Xe atoms are considerably more massive than the carbon atoms making up the graphite surface. These measurements were initially analyzed using the hard cubes model and molecular dynamics simulations, and both treatments indicated that the scattering process was a single collision in which the incoming Xe atom interacted strongly with a large number of carbon atoms in the outermost graphite layer. In this work we analyze the data using a single scattering theory that has been shown to explain a number of other experiments on molecular beam scattering from surfaces. These calculations confirm that the scattering process is a single collision with an effective surface mass that is substantially larger than that of the basic graphite ring.     

New method to measure the K-shell absorption jump factor in some rare-earth elements

The Compton scattering of 59.54 keV gamma rays by an Al scatterer has been used as a primer source at scattering angles from 48 to 118° by using a Si(Li) detector, and this primer gamma ray has been send to absorbers including Gd, Tb, Dy, Ho and Er. A new method has been developed to determine the K-shell absorption jump factor of elements and compounds. This method is based on simultaneous measurement of fluorescence radiation and scattered radiation, thus avoiding the problems with measuring the source strength and source-to-detector solid angle. In this method, the jump factor is effected from the scattering angle. Evident energies near to K-absorption edges of each lanthanide element have been determined for chosen angles, after the incident photon energy (59.5 keV) is exposed to Compton scattering from Al (secondary source). The experimental absorption jump factors are compared with the theoretical estimates and literature experimental values.     

CI calculations of electron and x-ray scattering cross sections of non-linear molecules: H2O and NH3

Differential cross sections for high-energy electron and X-ray scattering on H₂O and NH₃ molecules have been calculated in the first Born approximation using approximate Hartree—Fock and configuration-interaction wavefunctions. For non-linear molecules, the first theoretical inelastic and total cross sections with explicit inclusion of electron correlation are presented. A comparison between the theoretical and experimental scattering functions is made. Apart from minor discrepancies which can be due to deficiencies in the theoretical as well as the experimental procedures, agreement between theory and experiment is satisfactory.     

High resolution Dopplerimetry of correlated angular and quantum state-resolved CO(2) scattering dynamics at the gas-liquid interface

Full three dimensional (3D) translational distributions for quantum state-resolved scattering dynamics at the gas-liquid interface are presented for experimental and theoretical studies of CO(2) + perfluorinated surfaces. Experimentally, high resolution absorption profiles are measured as a function of incident (θ(inc)) and scattering (θ(scat)) angles for CO(2) that has been scattered from a 300 K perfluorinated polyether surface (PFPE) with an incident energy of E(inc) = 10.6(8) kcal mol(-1). Line shape analysis of the absorption profiles reveals non-equilibrium dynamics that are characterized by trapping-desorption (TD) and impulsive scattering (IS) components, with each channel simply characterized by an effective "temperature" that compares very well with previous results from rotational state analysis [Perkins and Nesbitt, J. Phys. Chem. A, 2008, 112, 9324]. From a theoretical perspective, molecular dynamics (MD) simulations of CO(2) + fluorinated self-assembled monolayer surface (F-SAMs) yield translational probability distributions that are also compared with experimental results. Trajectories are parsed by θ(scat) and J, with the results rigorously corrected by flux-to-density transformation and providing comparisons in near quantitative agreement with experiment. 3D flux and velocity distributions obtained from MD simulations are also presented to illustrate the role of in- and out-of-plane scattering.     

Prediction of thermodynamic derivative properties of natural condensate gases at high pressure by Monte Carlo simulation

We have employed Monte Carlo simulation in the isobaric–isothermal ensemble to determine thermodynamic derivative properties of naturally occurring hydrocarbon gas mixtures. Thermal expansivity, isothermal compressibility, heat capacity and Joule–Thomson coefficient have been obtained from a fluctuation method detailed in our previous work [Phys. Chem. Chem. Phys. 3 (2001) 4333]. We have investigated two natural gases using an original method to model hydrocarbon distribution in a representative way with a limited number of linear, branched and cyclic hydrocarbon molecules. The composition used in Monte Carlo simulations was represented by 500 molecules of 20 different types with up to 35 carbon atoms. The two condensate gases are composed of rigid and flexible molecules for which intermolecular potentials have been used without fitting any parameters. Predictions are in good agreement with respect to available molar volumes at high pressure. Joule–Thomson coefficients and the other thermodynamic derivative properties have been then predicted at pressures up to 110 MPa at reservoir temperature, showing a consistent behaviour compared with light hydrocarbon gases. Inversion pressure of the Joule–Thomson effect is obtained within 1.2% compared to experimental value from volumetric measurements.     

Invalidity of deriving interparticle distance in clay-water systems using the experimental structure factor maximum obtained by small-angle scattering

Small-angle X-ray scattering (SAXS) has been widely used to investigate the organization of clay colloids in response to the particle concentration and ionic strength of the suspending medium. In such investigations, measuring the interparticle distance and/or spacing is usually attempted. In random or short-range ordered clay-water systems, the interparticle distances are often derived from the experimental structure factor maximum; however, the validity of such practice has never been theoretically or experimentally evaluated. The experimental structure factors of several clay-water systems with and without polyphosphate treatment to block the edge charges of clay particles were obtained from SAXS data in order to understand the physical meaning of this property. The results show that the polyphosphate treatment eliminated the experimental structure factor maximum and that the particle concentration effects were correlated with the depression on the curve in a random clay-water system (e.g., illite and laponite). For clay particles with greater anisotropy (i.e., montmorillonite), polyphosphate treatment enhanced the ordering of clay layers at high particle concentrations forming long-range ordered crystals showing Bragg reflections. In this ordered system, distinctive and symmetrical peaks representing the interparticle spacing were obtained by using a Fourier transform of the scattering curves. Thus, we conclude that the experimental structure factor maximum is induced by the edge-face oriented interactions, which may not be in direct contact as in a house-of-cards structure, and the position of the maximum should not be interpreted as an averaged interparticle distance in a clay-water system unless particles orient along the same direction.     

On the structure of glassy polymers. IV. Small-angle x-ray scattering from rigid polyvinyl chloride

The small-angle x-ray scattering (SAXS) from quenched and annealed rigid polyvinyl chloride (PVC) has been measured using a Bonse–Hart system. After correcting for absorption, background, and beam divergence, the scattering has been placed on an absolute basis using a standard silica suspension as a reference. The scattering from annealed (6 days at 75°C) and unannealed PVC was identical within experimental error, varying with scattering angle in a manner similar to the SAXS from other amorphous polymers. The intensity decreases rapidly with increasing scattering angle over the ranges from 20 sec to 20 min. Beyond 20 min the intensity is fairly constant, decreasing only slightly with increasing angle. At the largest angles of measurement (in the range of 120 min), the measured intensity is close to the value calculated for thermal density fluctuations frozen-in at the glass transition. The angular variation of intensity is well described by the scattering from heterogeneities of various sizes and concentrations superimposed on the scattering from thermal density fluctuations. These heterogeneities range in radius from 50 to 4500 Å and, assuming the crystalline excess density, the total concentration of heterogeneities is less than 0.5%. The mean-square fluctuation in density, determined from the measured intensity invariant, is also consistent with such a distribution of heterogeneities. The present SAXS results on rigid PVC are inconsistent with the presence of nodular features as representative of the bulk polymer. Rather, it is suggested that they are associated with surface effects. It is further suggested that previously indicated volume fractions of crystallinity in rigid PVC (generally in the range of 5–12%) are incorrect, and that the model of a three-dimensional network of crystallites used to explain the rheological behavior of this material should be re-examined.     

Monte-Carlo simulation of microwave noise in n-type InSb

Numerical Monte Carlo calculations of the electron noise temperature dependence on the electric field strength in n-type InSb are presented. It is established that hot electron noise temperature in strongly compensated InSb increases with the increase of electron density due to more intensive electron–electron scattering stimulating delocalization of electrons from the bottom of the conduction band. For low electron density, when the electron–electron scattering is negligibly small, the electron noise temperature is found to become close to the lattice temperature in a wide range of electric field strength in which the electron gas cooling effect takes place. Satisfactory agreement between calculations of the electron noise temperature and available experimental data has been obtained.     

Estimation of morphological characteristics of single particles from light scattering data in flow cytometry

Numerical methods for solving the reverse problem of light scattering for single particles and a variety of experimental results have been reviewed. In particular, the two-dimensional Mie scattering method for the estimation of sizes and refractive indices of single particles has been developed. The method of triple two-dimensional Mie scattering has been elaborated, which extends the range of particle sizes with correct solutions of the reverse light scattering problem. The flying light scattering indicatrix method, which allows the estimation of the parameters of spherical particles, is presented. The results of the use of a flow cytometer of standard design for the anaysis of milk microflora and for an AIDS immunoassay by latex agglutination are given. The design of a scanning flow cytometer is considered. The results of measuring the light scattering from polystyrene latex particles are given.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1181–1190, July, 1994.The author is grateful to A. K. Petrov and M. A. Kamkhe for supporting the work on cytometry, E. G. Saprykin for useful discussion and comments, G. Alm (Swedish Agricultural Univ.) for initiating the interest to immunological studies, and A. V. Chernyshev, T. S. Mashnin, V. I. Prots, and A. A. Doroshkin for cooperation.     

Orientational disorder and diffuse scattering inβ-nitrogen

The scattering density distribution in β-N₂ at 1.2 kbar has been determined by neutron scattering methods. Diffuse scattering has been observed as a function of pressure. Calculations of the diffuse scattering on the assumption of randomly oriented N₂ molecules are in poor agreement with the experimental observation.