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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 2376-2387 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The unitary irreducible representations of the central extension of the Poincaré group in 1+1 dimensions are constructed by an application of the Kirillov theory. These are then lifted to projective unitary irreducible representations of the Poincaré group. The 1+1 Galilean group is treated separately in an appendix. © 1996 American Institute of Physics.
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 875-890 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using the Mackey theory of induced representations, the unitary irreducible representations of the proper Galilean group in 2+1 space–time dimensions are constructed. All representations, both true as well as the projective ones, are found. The concomitant representations of the Lie algebra are given. © 1995 American Institute of Physics.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 169 (1995), S. 385-395 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The problem of constructing the central extensions, by the circle group, of the group of Galilean transformations in two spatial dimensions; as well as that of its universal covering group, is solved. Also solved is the problem of the central extension of the corresponding Lie algebra. We find that the Lie algebra has a three parameter family of central extensions, as does the simply-connected group corresponding to the Lie algebra. The Galilean group itself has a two parameter family of central extensions. A corollary of our result is the impossibility of the appearance of non-integer-valued angular momentum for systems possessing Galilean invariance.
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  • 4
    ISSN: 1573-4889
    Keywords: oxidation ; copper ; Li-doped copper ; Cr-doped copper ; short-circuiting ; Mott's parabola ; Wagner's parabola
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The influence of shorting circuitry attachment between metal-oxide and oxideoxygen interfaces on the oxidation kinetics of copper, lithium-doped copper (Li: 400 ppm), and chromium-doped copper (Cr: 12 ppm) have been studied in dry air $$(P_{O_2 } = 21.27kPa)$$ in the temperature range of 523–1073 K. Oxide film or scale growth under short-circuiting as well as under normal oxidation conditions conforms to the parabolic rate law. The oxidation kinetics under short-circuiting resulted in decreased rates for Cu and Li-doped Cu up to a temperature of 773 K, while Cr-doped Cu exhibited an enhancement in rate compared to its normal oxidation in the same temperature range. However, above 873 K, all three systems under shorting circuitry attachment exhibited enhanced rates compared to their normal oxidation rates in conformity to the existing theoretical model. Use of additional resistances in series in the outer short-circuit Pt path have clearly established that below 773 K Mott's fieldinduced migration plays the most important role, while at elevated temperatures Wagner's electrochemical potential-gradient factor acts as the main driving force in the scale-growth process. The results have been interpreted on the basis of average defect concentration, the electrochemical potential gradient, electrical field gradient, and transport coefficient in the Cu2O layer.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Oxidation of metals 49 (1998), S. 261-295 
    ISSN: 1573-4889
    Keywords: COPPER ; OXIDATION KINETICS ; STATIC CHARGE ; MOTT'S PARABOLIC FILM GROWTH ; WAGNER'S PARABOLIC SCALE GROWTH ; SELF-DIFFUSIVITY
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The kinetics of copper oxidation under theinfluence of an externally-supplied static charge ofeither kind at one of the reaction interfaces of agrowing oxide film on its subsequent thickening weredetermined in the temperature range of 523-1173 K andoxygen-pressure range of 5.06-50.66 kPa. The kineticsconformed to the parabolic rate law under all conditionsof experimentation. In the temperature range of 523-723 K, charge supply of either kind ateither of the oxide interfaces, reduced the ratescompared to normal oxidation. The reduction in rates ismore pronounced with (-)ve charge supply. In thistemperature range, Mott's in situ electrical-potentialgradient across the oxide film is identified as thepredominant driving force for migration of copper ionsduring the subsequent film-thickening process. On the other hand, in the temperature range of 873-973K, a charge supply of either kind enhanced the ratescompared to normal oxidation, where Wagner'selectrochemical-potential gradient acts as the maindriving force for ion diffusion. However, at 1073 K and1173 K, the rates were found to decrease slightlycompared to normal oxidation. The oxygen-pressuredependencies of rate constants at 623 K exhibitedrelations of the type kP ∝P O2 1/4 for normal and kp ∝P O2 1/8 (approximately) for oxidation witheither (+)ve or (-)ve charge supply at the oxide/oxygeninterface. However, at 873 K the oxygen-pressuredependencies of rate constants conform to kP ∝P O2 1/6 for normal as well as for oxidationwith either (+)ve or (-)ve charge supply at theoxide/oxygen interface. The estimated activationenergies are 54 kJ/mol and 160 kJ/mol in Mott's and Wagner's parabolic ranges,respectively. It is established that migration of Cu+ions through the growing film is the rate-limiting stepunder all conditions of experimentation. This study has clearly demonstrated that changes inoxidation rates can be brought about by disturbing theinterfacial defect equilibria with anexternally-supplied static charge when no net currentflows through the oxide film. The estimated self-diffusivityvalues of Cu+ ions in the growingCu2O at 873 K are also reported.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Oxidation of metals 49 (1998), S. 431-453 
    ISSN: 1573-4889
    Keywords: LEAD-IODIDE FILM ; DOPING EFFECT ; SHORT-CIRCUIT ; MOTT'S ELECTRICAL FIELD ; SCHOTTKY-WAGNER DISORDER ; HOLE MIGRATION ; ION TRANSPORT
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The influence of Ag as a lower-valent dopant onthe kinetics of lead iodination under normal andshort-circuit conditions in iodine pressures of 0.615 to6.578 kPa in the temperature range of 423 to 523 K was investigated. Like pure Pb, Ag-doped Pbalso follows the parabolic law of film growth. Theisothermal parabolic rate constants are found todecrease in the presence of the dopant. The iodinevapor-pressure dependence of isothermal parabolic rateconstants was observed to be kP ∝p I2 1/2 . Results for normal iodination areexplained in terms of migration of electron holes underthe influence of Cabrera-Mott's electrical field across the film. Theactivation energy for normal iodination of Ag-doped Pbis estimated to be 84 kJ•mol-1 comparedto that of 64 kJ•mol-1 for pure lead. Therate of iodide-film growth has been found to decrease further undershort-circuit mode of experiments. Such observationshave been explained with the concept of ion migration asthe ratelimiting step for the film-growth process. The iodine pressure dependence of the rateconstants under short-circuit conditions is observed tobe kP ∝ p I2 1/3 associatedwith an activation energy value of 66kJ•mol-1. Unlike pure lead, introduction of additional resistances in series to theshort-circuit Pt path during iodination of Ag-doped Pbcaused an increase in the rates with gradual increasedvalue of resistances. Kinetics results are explained by considering the prevalence ofSchottky-Wagner type of point defects in lead iodide.The driving forces for migration of the defect speciesthrough the growing pure PbI2 films andAg-doped PbI2 are confirmed to be Wagner's electrochemical potentialgradient and Cabrera-Mott's electrical field,respectively. The iodide films were characterized bySEM, EDS, EPMA, AES, and XRD analyses to substantiatethe kinetic results.
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  • 7
    ISSN: 1573-4889
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Oxidation of metals 43 (1995), S. 185-215 
    ISSN: 1573-4889
    Keywords: copper ; oxidation ; direct current ; uninterrupted mode ; interrupted mode
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Oxidation kinetics of copper in the temperature range of 973–1173 K atP O 2=21.27 kPa exhibit enhancement and deceleration in the rates with changing polarity compared to normal oxidation under interrupted mode of directcurrent application. These conditions are achieved by connecting the oxidizing copper covered with an initially formed thin oxide film to the positive and negative terminal of a dc source, respectively. However, the influence of direction of the current is found to be opposite under uninterrupted mode of impressed current flow in the same temperature range. The effect of short-circuiting the metal to the outer oxide/air interface on the reaction kinetics is also reported. The rate of oxide-scale growth under normal condition, and two different modes of current applications as well as with shorting circuitry attachment conform to the parabolic growth law. The results pertaining to the two different modes of impressed current have been discussed considering both the phenomena of electrolysis of the oxide electrolyte and the polarization at the two phase boundaries. The enhancement and the reduction in rates under uninterrupted impressed current conditions are explained on the basis of increased and decreased average defect concentrations, respectively, within the oxide layer. The acceleration and deceleration in the rates under interrupted mode of current flow have been explained in the light of sustenance of a steeper and flatter electrochemical-potential gradient of defects, respectively, across the growing-oxide layer. The possible different responses of the metal/oxide and oxide/air interfaces to the impressed current brought into play by two different modes of current application, have enabled to display a better insight on the mechanistic aspects of scale growth under the influence of an externally applied current.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Oxidation of metals 46 (1996), S. 399-422 
    ISSN: 1573-4889
    Keywords: tarnishing of lead ; lead-iodide film ; Wagner's parabolic law ; hole transport ; ion transport ; shorting-circuitry attachment
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The tarnishing rate of Pb with iodine vapor in the temperature and pressure ranges of 423–523 K and 0.615–6.578 kPa, respectively, have been studied. The film-growth kinetics follow the parabolic law. The iodine-vapor-pressure dependence of the isothermal parabolic rate constant has been observed to be kP∝p I2 1/2 which is explained on the basis of the migration of electron holes across the film as the rate-limiting step. The activation energy value for iodination of Pb under normal conditions in an iodine pressure of 0.615 kPa is estimated to be 64 kJ·mol−1. In contrast, the rate of iodide-film growth has been found to increase considerably under a short-circuit mode of experiments. Such observations have been explained with the help of ion migration as the rate-limiting step for the film-growth process. The iodine-pressure dependence of the rate constant under short-circuit conditions is found to be kP∝p I2 1/3 associated with an activation energy of 51 kJ·mol−1. Results of the present study have been explained assuming Schottky-Wagner-type point defects in the lead-iodide film, where an equivalent number of vacancies in the cationic and anionic sublattices are present, and taking into account Wagner's electrochemical potential gradient as the main driving force for the film-growth process. The kinetics results have been substantiated through characterization of iodide films by SEM, EDS, EPMA, and XRD analyses.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Oxidation of metals 47 (1997), S. 295-315 
    ISSN: 1573-4889
    Keywords: lead-iodide film ; Wagner's parabolic law ; doping effect ; hole migration ; shortcircuit effect ; ion transport ; Schottky-Wagner defects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The effect of a higher-valent dopant like Sb on the iodination rate of lead under normal and short-circuit conditions in iodine pressure of 0.615–6.578 kPa and in the temperature range of 423–523 K has been investigated. Like pure Pb, Sb-doped Pb also follows the parabolic law of film growth. The isothermal parabolic rate constants are found to be enhanced due to the presence of Sb. The iodine-vapor-pressure dependence of the isothermal parabolic rate constant has been observed to be kp∝pI 2 1/2 . This has been explained on the consideration of electron-hole migration across the film as the rate-limiting step. The activation energy for iodination of Sb-doped Pb under normal condition is estimated to be 64 kJ · mol−1 in an iodine pressure of 0.615 kPa. The rate of iodide-film growth has been found to increase considerably under a short-circuit mode of experiments. Such observations have been explained with the concept of ion migration as the rate-limiting step for the film-growth process. The iodine pressure dependence of rate constants under short-circuit conditions is observed to be kp∝I 2 1/3 , associated with an activation energy value of 51 kJ mol−1. The effect of putting additional resistances in series to the short-circuit Pt path during iodination of Sb-doped Pb is found to be similar to that observed for pure Pb. Results of the present study have been explained considering the prevalence of Schottky-Wagner type of point defects in the lead-iodide film. Wagner's electrochemical potential gradient has been confirmed to be the main driving force for the film-growth process. Iodide films have been characterized by SEM, EDS, EPMA, XRD, and AES analyses to substantiate the kinetics results.
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