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Dislocation etching of cesium iodide crystals
Vol. 4, No. 12
ABSTRACTS OF PAPERS TO APPEAR IN J. PBYS. CHEM. SOLIDS
The thermal conductivity of alpha plutonium was determined at 80, 195 and 300’ K. The measurements gave values at room temperature of about 0.865 watt/cm - OK which decreased with decreasing temperature to about 0.030 at 80’K. 14..
QUANTUMTHEORY OF DYNAMIC MAGNETORESISTANCE Charles C. Chen and Shigeji Fujita
The connmcteddiagram expansion method is applied in the evaluation of the dynamic conductivity of an electron-impurity system subjected to a constant magnetic field B. This method treats the two cases, B 4 0 fid B = 0, on the same footing such that the differences appear at the final stage of calculation. A clear physical picture is sustained throughout because no extraneous arguments about the splitting of a density operator into diagonal and non-diagonal parts in free-electron states, which appeared in most of the past literatures, are used. A transport equation in the limits of low impurity density n, and small coupling )i is given explicitly. This equation is meant to describe the dynamic conductivity at an arbitrary frequency u)of an applying field and at an arbitrary magnitude of B. It reduces to the transport equation of Argyres in the limit of zero frequency and to that of YamadaRon in the limit of zero field. The conductivity in the limits of large w, large B, small n, and small 1, is calculated explicitly. The limiting forms of the new expressions are in agreement with the result of Titeica (2 = 0, w = 0) and with that of Yamada -Ron (B = 0, u:t 0). The expression explicitly indicates that the dynamical response can be no more interpreted in terms of scattering cross section. The conductivity of an electronphonon system is discussed briefly. 15.
CONNECTED- DIAGRAM‘EXPANSION OF TRANSPORT COEFFICIENTSI. ELECTRON-IMPURITY Shigeji Fujita
A connected-diagram expansion method is applied in the evaluation of the correlation function formulas for transport coefficient of an electron-impurity system. This method does not utilize any special representation and is applicable whether the system is subjected to a time-dependent or time-independent electric field and whether or not it is subjected to a constant magnetic field. The connection between the correlation function formula and the generalized transport equation of Kohn and Luttinger is clarified. The first density correction the conventional formula for the static conductivity of a weak-
1XXXV
coupling system is explicityly formulated in integrals with the assumption of a more realistic distribution of impurities than the usually assumed uniform distribution. The expansion in powers of the impurity density, whose validity may be questioned in the light of recent controversies over the virial expansion of transport coefficients of a classical gas, does not seem to lead to difficulties for weak, short-range impurity potentials. The cases of dynamic conductivity and magnetoresistance are discussed in terms of generalized transport equations. 16.
ELECTRIC CHARGE ON DISLOCATION ARRAYS IN SODIUMCHLORIDE R. J. Schwensfeir, Jr. and C. Elbaum (Brown University, Providence, R.I.)
The electric charge on dislocation arrays was studied as a function of temperature by observing the displacement of pure tilt low angle grain boundaries in sodium chloride bicrystals maintained in an electric field. The sign of the charge was determined unambiguously by direct observation of the boundary displacement relative to the polarity of the electric field; the existence of an isoelectric point was confirmed. No measurable boundary displacement is found below a certain (threshold) value of electric field which; depends on temperature. For larger fields boundary migration is observed to occur with no delay in time and at a uniform rate which increases monotonically with increasing field. The method used permits the determination of the driving force on the boundary and of the migration velocity as two independent quantities; from the temperature dependence of the boundary mobility thus determined an activation energy for the process was obtained. (Revised 3 August 1966) 17.
DISLOCATIONETCIIING OF CESIUM IODIDE CRYSTALS. R. Thyagarajan and A. A. Urusovskaya
In the dislocation etching of CsI crystals there is anoptimal concentration of inhibitor ions to produce well faceted and contrasted etch pits. Etching characteristics reveal that the fall in the tangential velocity of dissolution occurs due to the selective absorption of Cu+ ions at the kink sites, thus lowering the kink motion. The role of various inhibitor ions forming strong complexes or simple compounds with the anionic constituent of the crystal, in the etching behaviour, shows neither valency nor size to be a determining factor in the selective etching
ABSTRACTS OF PAPERS TO APPEAR IN J. PBYS. CHEM. SOLIDS
The thermal conductivity of alpha plutonium was determined at 80, 195 and 300’ K. The measurements gave values at room temperature of about 0.865 watt/cm - OK which decreased with decreasing temperature to about 0.030 at 80’K. 14..
QUANTUMTHEORY OF DYNAMIC MAGNETORESISTANCE Charles C. Chen and Shigeji Fujita
The connmcteddiagram expansion method is applied in the evaluation of the dynamic conductivity of an electron-impurity system subjected to a constant magnetic field B. This method treats the two cases, B 4 0 fid B = 0, on the same footing such that the differences appear at the final stage of calculation. A clear physical picture is sustained throughout because no extraneous arguments about the splitting of a density operator into diagonal and non-diagonal parts in free-electron states, which appeared in most of the past literatures, are used. A transport equation in the limits of low impurity density n, and small coupling )i is given explicitly. This equation is meant to describe the dynamic conductivity at an arbitrary frequency u)of an applying field and at an arbitrary magnitude of B. It reduces to the transport equation of Argyres in the limit of zero frequency and to that of YamadaRon in the limit of zero field. The conductivity in the limits of large w, large B, small n, and small 1, is calculated explicitly. The limiting forms of the new expressions are in agreement with the result of Titeica (2 = 0, w = 0) and with that of Yamada -Ron (B = 0, u:t 0). The expression explicitly indicates that the dynamical response can be no more interpreted in terms of scattering cross section. The conductivity of an electronphonon system is discussed briefly. 15.
CONNECTED- DIAGRAM‘EXPANSION OF TRANSPORT COEFFICIENTSI. ELECTRON-IMPURITY Shigeji Fujita
A connected-diagram expansion method is applied in the evaluation of the correlation function formulas for transport coefficient of an electron-impurity system. This method does not utilize any special representation and is applicable whether the system is subjected to a time-dependent or time-independent electric field and whether or not it is subjected to a constant magnetic field. The connection between the correlation function formula and the generalized transport equation of Kohn and Luttinger is clarified. The first density correction the conventional formula for the static conductivity of a weak-
1XXXV
coupling system is explicityly formulated in integrals with the assumption of a more realistic distribution of impurities than the usually assumed uniform distribution. The expansion in powers of the impurity density, whose validity may be questioned in the light of recent controversies over the virial expansion of transport coefficients of a classical gas, does not seem to lead to difficulties for weak, short-range impurity potentials. The cases of dynamic conductivity and magnetoresistance are discussed in terms of generalized transport equations. 16.
ELECTRIC CHARGE ON DISLOCATION ARRAYS IN SODIUMCHLORIDE R. J. Schwensfeir, Jr. and C. Elbaum (Brown University, Providence, R.I.)
The electric charge on dislocation arrays was studied as a function of temperature by observing the displacement of pure tilt low angle grain boundaries in sodium chloride bicrystals maintained in an electric field. The sign of the charge was determined unambiguously by direct observation of the boundary displacement relative to the polarity of the electric field; the existence of an isoelectric point was confirmed. No measurable boundary displacement is found below a certain (threshold) value of electric field which; depends on temperature. For larger fields boundary migration is observed to occur with no delay in time and at a uniform rate which increases monotonically with increasing field. The method used permits the determination of the driving force on the boundary and of the migration velocity as two independent quantities; from the temperature dependence of the boundary mobility thus determined an activation energy for the process was obtained. (Revised 3 August 1966) 17.
DISLOCATIONETCIIING OF CESIUM IODIDE CRYSTALS. R. Thyagarajan and A. A. Urusovskaya
In the dislocation etching of CsI crystals there is anoptimal concentration of inhibitor ions to produce well faceted and contrasted etch pits. Etching characteristics reveal that the fall in the tangential velocity of dissolution occurs due to the selective absorption of Cu+ ions at the kink sites, thus lowering the kink motion. The role of various inhibitor ions forming strong complexes or simple compounds with the anionic constituent of the crystal, in the etching behaviour, shows neither valency nor size to be a determining factor in the selective etching