- Email: [email protected]
Dynamics of an electron in a finite crystal with a superimposed electric field
lxxviii
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
Down to 30°K the particles of the dehydrated iron (UI) oxide-hydrate gel are superparamagnetic: the magnetic moment per gramme as a function of H and T fits a Langevin curve and the Mössbauer spectra in the region from room temperature down to 77°K, show only quadrupole splitting. The Langevin curve corresponds to a particle moment of 1.49 x 10 erg/Oe and a number of particles per gramme equal to 7. 4 x 10.18 This leads to an average of 1000 iron ions per particle and a particle size of about 30 A. -~
The magnetic moment per particle, calculated with Nedl’s IN theory for antiferromagnetic particles, is in good agreement with that obtained from the Langevin function, At temperature below 30°Kthe magnetization is less than expected from the Langevin curve, At liquid He temperature the Mössbauer spectra show hyperfine splitting. These facts point to a breakdown of the conditions for superparamagnetism, below 30°K.
15.
LOW FREQUENCY MAGNETIC RELAXATIONS IN MANGANESE FERROUS FERRITES AT LOW TEMPERATURES A. Broese van Groenou (Philips Research Laboratories N. V. Philips’ Gloeilampenfabrieken Eindhoven, Netherlands)
Permeability measurements on poiycrystalline Mn~Fe3_04 (x 1) and Mn~Zn~ Fe3~_~04 (x y <1) at temperatures below 100°K have shown that two relaxation phenomena occur for frequencies between 100 C/s and 100 kc/s. The temperature dependence of the relaxation time can be described by ~ = T0 exp (E/K T). For the high temperature relaxation E is about 0. 05 eV, in good agreement with results on the electrical conductivity by Miyata and Lotgering. The low temperature relaxation has a much lower activation energy. For y = 0 0. 02 eV is found, which value is reduced to 0. 007 eV for the samples containing Zn. <
+
DYNAMICS OF AN ELECTRON IN A FINITE CRYSTAL WITH A SUPERIMPOSED ELECTRIC FIELD ~i.D. Rees (Royal Radar Establishment Malvern, Worcs. England)
To describe bulk properties, the one electron Schr6dinger wave function for a crystal with a superimposed electric field can be formed from Bloch states with discrete k values. Auxiliary functions of continuous k are defined which satisfy equations similar tothose derived by previous authors for infinite crystals, but which are subject to additional constraints imposed by finite crystal size. The physical interpretation of these constrainst allows detailed comparison with earlier theories for infinite crystals and with the basic ideas of the Boltzmann transport equation. The Schr&linger wave functions depend explicitly on the length of the crystal but for a long enough crystal, perturbation effects and physical observables do not. The wave functions are therefore more complicated than necessary to describe perturbation effects, and perturbations are more simply described by a modified interaction representation. 16.
(Received 15 July 1966) 14.
Vol.4, No.11
ELASTIC CONSTANTS OF MgAg and MgCu2 SINGLE CRYSTALS C. H. Cheng (Metallurgical Laboratory Metal Products Department, The Dow Chemical Company Midland, Michigan)
The three independent elastic constants of MgAg and MgCu2 have been determined by the pulse-echo method from 80 to 500°K. The temperature coefficients of all the elastic constants are normal but smaller than the average of their constituent elements. The anisotropy factor is high for MgAg and low for MgCu2, as one would expect from their respective crystallographic configurations. The elastic behavior of MgCu2 was found to be similar to that of the diamond structure.
T
(Received 11 August 1966) (Revised 2 September 1966)
(Received 26 August 1966) 17.
CRYSTALLINE FIELD AT THE RARE EARTH ION IN DYSPROSIUM AND SAMARIUM GALLIUM GARNETS M. Veyssie and B. Dreyfus
From the study of the optical absorption spectra, the authors have determined the main crystalline field coefficients for the dysprosium and samarium gallium garnets. For Dy GaG, they tentatively evaluated the nine parameters in
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
Down to 30°K the particles of the dehydrated iron (UI) oxide-hydrate gel are superparamagnetic: the magnetic moment per gramme as a function of H and T fits a Langevin curve and the Mössbauer spectra in the region from room temperature down to 77°K, show only quadrupole splitting. The Langevin curve corresponds to a particle moment of 1.49 x 10 erg/Oe and a number of particles per gramme equal to 7. 4 x 10.18 This leads to an average of 1000 iron ions per particle and a particle size of about 30 A. -~
The magnetic moment per particle, calculated with Nedl’s IN theory for antiferromagnetic particles, is in good agreement with that obtained from the Langevin function, At temperature below 30°Kthe magnetization is less than expected from the Langevin curve, At liquid He temperature the Mössbauer spectra show hyperfine splitting. These facts point to a breakdown of the conditions for superparamagnetism, below 30°K.
15.
LOW FREQUENCY MAGNETIC RELAXATIONS IN MANGANESE FERROUS FERRITES AT LOW TEMPERATURES A. Broese van Groenou (Philips Research Laboratories N. V. Philips’ Gloeilampenfabrieken Eindhoven, Netherlands)
Permeability measurements on poiycrystalline Mn~Fe3_04 (x 1) and Mn~Zn~ Fe3~_~04 (x y <1) at temperatures below 100°K have shown that two relaxation phenomena occur for frequencies between 100 C/s and 100 kc/s. The temperature dependence of the relaxation time can be described by ~ = T0 exp (E/K T). For the high temperature relaxation E is about 0. 05 eV, in good agreement with results on the electrical conductivity by Miyata and Lotgering. The low temperature relaxation has a much lower activation energy. For y = 0 0. 02 eV is found, which value is reduced to 0. 007 eV for the samples containing Zn. <
+
DYNAMICS OF AN ELECTRON IN A FINITE CRYSTAL WITH A SUPERIMPOSED ELECTRIC FIELD ~i.D. Rees (Royal Radar Establishment Malvern, Worcs. England)
To describe bulk properties, the one electron Schr6dinger wave function for a crystal with a superimposed electric field can be formed from Bloch states with discrete k values. Auxiliary functions of continuous k are defined which satisfy equations similar tothose derived by previous authors for infinite crystals, but which are subject to additional constraints imposed by finite crystal size. The physical interpretation of these constrainst allows detailed comparison with earlier theories for infinite crystals and with the basic ideas of the Boltzmann transport equation. The Schr&linger wave functions depend explicitly on the length of the crystal but for a long enough crystal, perturbation effects and physical observables do not. The wave functions are therefore more complicated than necessary to describe perturbation effects, and perturbations are more simply described by a modified interaction representation. 16.
(Received 15 July 1966) 14.
Vol.4, No.11
ELASTIC CONSTANTS OF MgAg and MgCu2 SINGLE CRYSTALS C. H. Cheng (Metallurgical Laboratory Metal Products Department, The Dow Chemical Company Midland, Michigan)
The three independent elastic constants of MgAg and MgCu2 have been determined by the pulse-echo method from 80 to 500°K. The temperature coefficients of all the elastic constants are normal but smaller than the average of their constituent elements. The anisotropy factor is high for MgAg and low for MgCu2, as one would expect from their respective crystallographic configurations. The elastic behavior of MgCu2 was found to be similar to that of the diamond structure.
T
(Received 11 August 1966) (Revised 2 September 1966)
(Received 26 August 1966) 17.
CRYSTALLINE FIELD AT THE RARE EARTH ION IN DYSPROSIUM AND SAMARIUM GALLIUM GARNETS M. Veyssie and B. Dreyfus
From the study of the optical absorption spectra, the authors have determined the main crystalline field coefficients for the dysprosium and samarium gallium garnets. For Dy GaG, they tentatively evaluated the nine parameters in