PHONON BROADENING OF IMPURITY SPECTRAL LINES: III. DIAGRAM TECHNIQUE

1966 ◽  
Vol 44 (1) ◽  
pp. 109-138 ◽  
Author(s):  
Robert Barrie ◽  
R. G. Rystephanick
Keyword(s):  
Shape Function ◽  
Particle Temperature ◽  
Spectral Lines ◽  
Diagram Technique ◽  
Temperature Dependent ◽  
Impurity Potential ◽  
Method Of Calculation ◽  
Double Time ◽  
Particle Propagator ◽  
Temperature Green’S Function

The theory of the phonon broadening of optical absorption lines associated with impurities in semiconductors is discussed, using the diagram technique for the evaluation of an appropriate two-particle temperature Green's function. The single-particle propagator for an electron moving in the impurity potential and simultaneously in interaction with the phonons is calculated and used. The interaction with the phonons is treated as weak. The line-shape function is found, and a comparison is made between this method of calculation and a previous one based on the decoupling of an infinite hierarchy of equations for double-time temperature-dependent Green's functions.

scholarly journals Collision Strengths and Line Strengths for Transitions from the ls23ℓ, Levels to the ls2ℓ'3ℓ" Levels in Li-Like Ions

1984 ◽  
Vol 86 ◽  
pp. 110-113
Author(s):  
D.H. Sampson ◽  
S.J. Goett ◽  
G.V. Petrou ◽  
R.E.H. Clark
Keyword(s):  
Line Strength ◽  
Numerical Results ◽  
Spectral Lines ◽  
Atomic Data ◽  
Alternative Mechanism ◽  
Plasma Diagnostic ◽  
Exchange Method ◽  
Method Of Calculation ◽  
Configuration Mixing ◽  
Line Strengths

It is well known that radiation from the levels of the ls2ℓ2ℓ' and ls2ℓ3ℓ' configurations of Li-like ions form satellites of spectral lines from He-like ions that are of high interest for plasma diagnostic purposes. Recently Sampson et al (1984) have made calculations of the collision strengths for innershell excitation to these upper levels from the ls22s and ls22p levels for a large number of Li-like ions using a Coulomb-Born-exchange method. Here we consider the alternative mechanism for populating the ls2ℓ3ℓ' levels by collisional excitation from the ls23s, ls23p and ls23d levels. Although the poDulations of the ls23ℓ levels are lower than those of the ls22ℓ levels, this is at least partially compensated for by the fact that the collision strengths for the ls23ℓ − ls2ℓ'3ℓ" transitions are considerably larger on the average than those for the ls22ℓ − ls2ℓ'3ℓ" transitions. The method of calculation is the same as that used by Sampson et al (1984), where all possible configuration mixing, parentage mixing and intermediate coupling type mixing among the states in a complex (the states having the same n values, parity and J values) was included. Also the present application is sufficiently simple that after summation over J values for the initial level the results for the collision strength Ω can be expressed in a simple manner in terms of the Z scaled hydrogenic collision strengths Z2ΩH and analogous to Eqs (8)-(15) of Sampson et al (1984). The appropriate formulae and the numerical results for both excitation to upper fine structure levels and to upper energy terms for 19 Li-like ions have been submitted for publication to Atomic Data and Nuclear Data Tables. Here we give only the pertinent formula and sample numerical results for transitions between energy terms in Li-like iron. This formula iswhere due to configuration mixing neither ℓ need equal ℓ" nor ℓa need equal ℓ'. The recommended values for σ and σe are zero for transitions involving ls−2s and are −0.5 and 0.3, respectively, for transitions involving ls−2p. Numerical values for the coefficients A and Ae for Li-like iron are given in Tables I-III. Values for Z2ΩH and for impact electron energies up to 15 times threshold are given in Golden et al (1981) and Clark et al (1982) and are repeated in Table IV for convenience. Finally we note that the line strengths S for transitions involving ls−2p are obtained by multiplying the corresponding value for A(ls−2p) by the scaled hydrogenic line strength 1.665 and dividing by (Z-σ)2.

Simulation and Experimental Studies of Particles Interaction with Plasma Jet in Vacuum Plasma Spraying Processes

2000 ◽  
Author(s):  
A. Ilyuschenko ◽  
V. Okovity ◽  
S. Kundas ◽  
V. Gurevich
Keyword(s):  
Particle Temperature ◽  
Experimental Studies ◽  
Al2o3 Particle ◽  
Temperature Dependent ◽  
Vacuum Plasma Spraying ◽  
Program Complex ◽  
Real Process ◽  
Process Error ◽  
Temperature Dependent Properties ◽  
Intensity Radiation

Abstract Mathematical and computer models of movement and heating of particles in low pressure conditions are developed. The mathematical models are based on the molecular-kinetics theory of gases. A program complex for computer realization of models is developed. It contains a built-in data base of temperature dependent properties of substances, system of processing and graphic visualization of simulation results. For verification of the developed models, computer simulation and experimental measurements of Al2O3 particle temperature and velocity are conducted. These materials were sprayed with Plasma-Technik equipment at pressure 60 mBar in argon. Particle velocity was measured with a special optical device, particle temperature was defined by intensity radiation method. It was established that the developed models are adequate to real process (error of 5-8 %) and may be used for study and improvement of VPS processes.

scholarly journals CHANGES IN FERROELECTRIC PROPERTIES OF MASD ALUM ALONG WITH TEMPERATURE BY USING PLCM MODEL

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Anubhuti Mamgain ◽  
Trilok Chandra Upadhyay
Keyword(s):  
Ferroelectric Properties ◽  
Function Technique ◽  
Temperature Dependent ◽  
Spin Lattice ◽  
Coupled Mode ◽  
Dielectric Constant And Loss ◽  
Double Time ◽  
Anharmonic Interactions ◽  
Theoretical Results ◽  
Good Agreement

With addition of third-and fourth-order phonon anharmonic interactions, and extra spin-lattice interaction term into pseudospin-lattice coupled mode (PLCM) model, MASD alum has been studied. Employing double time temperature dependent Green′s function technique expressions for shift and width of response function, normal mode frequency, dielectric constant and loss stangent have been derived for MASD alum. Numerical calculation has been done. Theoretical results have been compared with experimental results of Pepinsky et al. [16]. A good agreement has been found.

ON THE TEMPERATURE DEPENDENCE OF THE SHAPE OF PARAMAGNETIC RESONANCE LINES

1960 ◽  
Vol 38 (9) ◽  
pp. 1168-1186 ◽  
Author(s):  
Malcolm McMillan ◽  
W. Opechowski
Keyword(s):  
Thermal Expansion ◽  
General Theory ◽  
Temperature Dependence ◽  
Shape Function ◽  
Temperature Dependent ◽  
Paramagnetic Resonance ◽  
Effective Spin ◽  
Spin Lattice ◽  
Second Moments ◽  
Line Shape Function

A theory of the temperature dependence of the shape of paramagnetic resonance lines is developed for temperatures sufficiently low to make the effects of the spin–lattice interaction and thermal expansion negligible. General expressions for the first and second moments of the line shape function as functions of the temperature are obtained, and the approximations used are discussed in detail. These expressions are applied to the case of effective spin [Formula: see text] and 1. As an illustration of the general theory numerical results are given for the paramagnetic resonance lines of nickel fluosilicate. In this case the moments become strongly temperature dependent below 10 °K.

scholarly journals Dephasing of Local Vibrations in a Planar Lattice of Adsorbed Molecules

1998 ◽  
Vol 05 (05) ◽  
pp. 965-970 ◽  
Author(s):  
V. M. Rozenbaum ◽  
I. V. Kuzmenko
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Temperature Limit ◽  
Spectral Lines ◽  
Planar Lattice ◽  
Adsorbed Molecules ◽  
Resonance Modes ◽  
Anharmonic Coupling ◽  
Line Positions ◽  
Temperature Green’S Function

We investigate anharmonically coupled high- and low-frequency excitations in a planar lattice of adsorbed molecules interacting with phonons of a crystal. Dephasing of high-frequency local vibrations by low-frequency resonance modes is described in terms of the temperature Green's function. The equations obtained are solved, first, with a small ratio of the anharmonic-coupling coefficient for high- and low-frequency modes to the resonance width, and second, in the low-temperature limit. High-frequency spectral-line positions and widths depend on dispersion laws and resonance-mode lifetimes. It is shown that lateral interactions of low-frequency modes of adsorbed molecules can lead to a significant narrowing of high-frequency spectral lines, which is consistent with experimental data.

scholarly journals Dynamics of hindered CF3-rotor in 2,5-bis (trifl uoromethyl )-nitroben zene radical -anion in anhydro us DMF. A temperature - activation theory of reversible HFS transformations of EPR spectrum

2016 ◽  
Vol 11 (3) ◽  
pp. 31-38
Author(s):  
E. A. Polenov ◽  
P. V. Melnikov
Keyword(s):  
Radical Anion ◽  
Spectral Lines ◽  
Ortho Position ◽  
Temperature Dependent ◽  
Epr Spectrum ◽  
Hindered Rotation ◽  
Activation Theory ◽  
Temperature Activation ◽  
Range Splitting ◽  
Reconstruction Model

The temperature dependence of EPR spectrum of 2,5-bis(trifluoromethyl)nitrobenzene radical anion in anhydrous DMF was investigated. Internal dynamics of hindered rotation of the CF3-group in ortho-position to NO2-group causes HFS modulation. The spectrum changes are reversible and temperature-dependent. An original temperature-activation representation of complex spectral density was proposed instead of the traditional spectral-kinetics representation to explain the observed transformation. The change resulted in a new convenient phenomenological reconstruction model, which allowed simulating the spectra in the whole temperature range. Splitting constants and contributions to the spectral widths of the spectral lines were found. The activation energy of the CF3-group hindered rotation is significant and amounts to 37 kJ/mol.

scholarly journals Theoretical Study of Ferroelectric Triglycine Sulphate (TGS) Crystal in External Electric Fields

2013 ◽  
Vol 11 ◽  
pp. 54-65 ◽  
Author(s):  
Trilok Chandra Upadhyay ◽  
Ashish Nautiyal
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Temperature Dependent ◽  
Triglycine Sulphate ◽  
Acoustical Properties ◽  
Coupled Mode ◽  
Electric Field Dependence ◽  
Crystal Electric Field ◽  
Double Time ◽  
Good Agreement

A modified two sub-lattice pseudospin-lattice coupled mode model of Mitsui et al [Phys. Rev., 111 (1958) 1259] by adding third, fourth order phonon anharmonic interaction and external electric field terms has been applied to ferroelectric triglycine sulphate crystal. Electric field dependence of ferroelectric, dielectric and acoustical properties has been studied. With the help of double time temperature dependent Green’s function method, expressions for shift, width, soft mode frequency, dielectric constant, loss tangent and acoustic attenuation have been derived. Numerically calculations have been made and results have been compared with experimental data reported by Bye et al [Ferroelectrics 4 (1974) 243] and Shreekumar et al [Ferroelectrics 160 (1994) 23] for TGS crystal and a good agreement has been observed.

scholarly journals CHANGES IN FERROELECTRIC PROPERTIES OF MASD ALUM ALONG WITH TEMPERATURE BY USING PLCM MODEL

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Anubhuti Mamgain ◽  
Trilok Chandra Upadhyay
Keyword(s):  
Ferroelectric Properties ◽  
Function Technique ◽  
Temperature Dependent ◽  
Spin Lattice ◽  
Coupled Mode ◽  
Dielectric Constant And Loss ◽  
Double Time ◽  
Anharmonic Interactions ◽  
Theoretical Results ◽  
Good Agreement

With addition of third-and fourth-order phonon anharmonic interactions, and extra spin-lattice interaction term into pseudospin-lattice coupled mode (PLCM) model, MASD alum has been studied. Employing double time temperature dependent Green′s function technique expressions for shift and width of response function, normal mode frequency, dielectric constant and loss stangent have been derived for MASD alum. Numerical calculation has been done. Theoretical results have been compared with experimental results of Pepinsky et al. [16]. A good agreement has been found.

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