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Calculation of electrostatic fields in ionic crystals based upon the ewald method
viii
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
suggesting that the number of carriers is constant. On the other hand, the mobility is activated, with activation energy EH = 0.40eV at small x and increasing to 0.52 eV at x = 0.25. The results for the mobility preexponential are consistent with the adiabatic theory of small polaron behavior. A puzzling feature of the Seebeck data as a function of x is that, for low x, the data fit the well-known Heikes formula, without a degeneracy factor of 2 for spin. Nevertheless, these data are interpreted to show that the proportion of mobile carriers decreases as x increases, presumably because of the presence of short-range ordered configurations which immobilize some carriers.
7cm2. While the photoexcited electron escape 3 x 1O~ cross-section is about 10_20 cm2. The potential of a neutral Cr acceptor is of the delta function type with weak coulombic tails. The maximum radius of the Bohr orbit of an electron in the ground state is 4 atomic units. Received 1 September 1976 Revised 3 February 1977 7.
OPTICAL ABSORPTION OF MgO: Fe K.W. Blazey, IBM Zurich Research Laboratory, 8803 RUschlikon-ZH, Switzerland.
The optical absorption spectra of as-grown, oxidized and reduced MgO: Fe crystals at low temperatures are reported. It is found that reduction at 1500°Cconverts 2” revealing optical more of the Fe and non-cubic sites, spectrathan due99% to Fe2~ in iron bothto cubic Oxidation, however, converts only 60—70% of the iron to Fe3” and no clear Fe3~crystal-field spectrum is observed. A cubic Fe2~band at 4.9 eV exhibits a progression of 13 vibronic sidebands typical of a Jahn— Teller distortion.
THE INTERACTION BETWEEN NONPARALLEL {lo2} CRYSTALLOGRAPHIC SHEAR PLANES IN SLIGHTLY REDUCED TUNGSTEN TRIOXIDES E. Iguchi, Departement of Metallurgical Engineering, Faculty of Engineering, Yokohama National University Ohoka,
Received 30 September 1976 Revised 1 December 1976 5.
Vol. 22, No.3
Minami-ku, Yokohama 233, Japan. The displacements of non-parallel {102} CS planes in slightly reduced W0 3 observed by electron microscopy were quantified with the theory of elasticity for an isotropic continum. By this calculation, the magnitude of the force between cations in CS planes was estimated. It was found the principle force an attractive onethat between cations in the involved CS planewas which was calculated to be 1.2 x 1013 (dyne cm2) = 7.8 (eV A3). Using this value, the magnitude of the strain energy was also evaluated, and was found to be larger in value than the energy associated with the dissociation of oxygen atoms from W0 3 lattice. This suggests that the strain energy plays a dominant role in the behaviour of CS planes. ~
Received 28 June 1976 6.
PHOTOELECTRONIC INVESTIGATIONS OF SEMI-INSULATING p-TYPE GaAs: Cr CONTAINING NEUTRAL CHROMIUM ACCEPTORS W. Plesiewics, Instytut Fizyki PAN, 02.668 Warszawa, Poland.
A photoelectronic analysis of p-type GaAs: Cr, i.e. measurements of thermally stimulated currents and the dependences of photoconductivity and photo-Hall effect on photon energy, temperature and light intensity, have enabled trap locations and densities as well as properties of neutral chromium acceptors to be determined. Hole traps proved to be located at 0.15 and 0.23 eV above the valence band, and 5their densities 3 and x 1016 cm3 have been estimated to be 10~~ cm is related to the presence respectively. Their occurrence of copper in the samples investigated. Neutral chromium acceptors are located at 0.77 eV above the valence band and are at a constant distance from the conduction band. Their photoexcited electron escape cross-section is
Received 28 October 1976 Revised 28 January 1977 8.
CALCULATION OF ELECTROSTATIC FIELDS IN IONIC CRYSTALS BASED UPON THE EWALD METHOD J.W. Weenk and H.A. Harwig, Inorganic Chemistry Department, State University Utrecht, Croesestraat 77A, Utrecht, The Netherlands.
Formulas for the electrostatic potential, field strength and field gradient due to monopoles, diopoles and quadrupoles are given, based upon the Ewald summation method.inA the convenient choice isofdemonthe convergence parameter Ewald method strated in some actual calculations. A method to calculate self-consistent electrostatic fields due to self-induced dipoles is evaluated. Monopole and self-consistent fields are calculated in Pb 2O3, I3.Mn203, FeTiO3, MnF3 and Pb3O4. The influence of the anion parameter on the
Vol. 22, No. 3
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
electrostatic field is investigated for idealized CdCl2 and TiO2. Results of Madelung and induced dipole polariz. ation energy for a series of arbitrary compounds are given. The effect of spontaneous polarization in polar crystals is discussed. Received 1 September 1976 Revised 3 February 1977 9.
ELECTROSTATIC LATTICE ENERGIES OF SOME ABX3 POLYTYPES WITH CLOSE— PACKED AX3 LAYERS. J.W. Weenk and H.A. Harwig, Inorganic Chemistry Department, State University Utrecht, Croesestraat 77A, Utrecht, The Netherlands.
Electrostatic lattice energies (Madelung and polarization energies) for five ideal ABX3 structure types with close-packed AX3 layers (X = F, Cl, Br, I, 0, 5) are calculated. Stability regions for the ideal structure types are indicated as function of the anion radius and the anion polarizabiity. The effect on the electrostatic lattice energy due to trigonal deformations of the AX3 layers in the 2L and 3L stacked structuresis discussed for the anions F and Cl. Received 28 October 1976 Revised 28 January 1977 10.
DIFFERENTIAL THERMAL ANALYSIS AT HIGH PRESSURES VII: PHASE BEHAVIOUR OF SOLID METHANOL UP TO 3 kbar A. WUrflinger and R. Landau, Institute of Physical Chemistry, University of Bochum, GFR.
The phase behaviour of solid methanol was invistigated from 196°Cto the melting temperature and up —
ix
to 3 kbar, using a low-temperature high-pressure data apparatus, The melting temperature rises from 98°Cat 1 atm to 64°Cat 2775 bar. Solid methanol exhibits a transition at atmospheric pressure at approximately 115°C;the transition has a strong tendency to superheat and to occur at 110°C.The transition temperature rises from approximately 115°Cat 1 atm to 81°Cat 2725 bar. Small impurities of waver induce a —
—
—
—-
—
—
“second transition” at 117.3°Cthat must be attributed to the waver—methanol eutecic. Volume changes accompanying the Clapeyron phase transition have been calcualted using the Clausius equation. —
Received 2 August 1976 Revised 28 January 1977 11.
THE PHONON CONTRIBUTIONS TO THE GIBBS FREE ENERGY OF y ~3Cul M.B. Haxton, Department of Physics, Indiana University, Blooington IN47401, U.S.A.; and Institute of Theoretical Science and Department of Physics, University of Oregon Eugene, OR 97403, U.S.A.
Equations are derived for the phonon contributions to the Gibbs free energy and entropy in terms of the phonon energy states. The energy states are determined from phonon dispersion relations, as calculated by the author in previous papers, for the ~ and jl phases of Cul. The resulting Gibbs free energies and entropies for each phase are plotted as a function of temperature and compared in the region of the y to jl phase transition. It is found that the phonon contributions are not important factors in the phase transition. Comments are made on other factors which are felt to be important in the phase transition. Received 25 October 1975 Revised 28 January 1977
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
suggesting that the number of carriers is constant. On the other hand, the mobility is activated, with activation energy EH = 0.40eV at small x and increasing to 0.52 eV at x = 0.25. The results for the mobility preexponential are consistent with the adiabatic theory of small polaron behavior. A puzzling feature of the Seebeck data as a function of x is that, for low x, the data fit the well-known Heikes formula, without a degeneracy factor of 2 for spin. Nevertheless, these data are interpreted to show that the proportion of mobile carriers decreases as x increases, presumably because of the presence of short-range ordered configurations which immobilize some carriers.
7cm2. While the photoexcited electron escape 3 x 1O~ cross-section is about 10_20 cm2. The potential of a neutral Cr acceptor is of the delta function type with weak coulombic tails. The maximum radius of the Bohr orbit of an electron in the ground state is 4 atomic units. Received 1 September 1976 Revised 3 February 1977 7.
OPTICAL ABSORPTION OF MgO: Fe K.W. Blazey, IBM Zurich Research Laboratory, 8803 RUschlikon-ZH, Switzerland.
The optical absorption spectra of as-grown, oxidized and reduced MgO: Fe crystals at low temperatures are reported. It is found that reduction at 1500°Cconverts 2” revealing optical more of the Fe and non-cubic sites, spectrathan due99% to Fe2~ in iron bothto cubic Oxidation, however, converts only 60—70% of the iron to Fe3” and no clear Fe3~crystal-field spectrum is observed. A cubic Fe2~band at 4.9 eV exhibits a progression of 13 vibronic sidebands typical of a Jahn— Teller distortion.
THE INTERACTION BETWEEN NONPARALLEL {lo2} CRYSTALLOGRAPHIC SHEAR PLANES IN SLIGHTLY REDUCED TUNGSTEN TRIOXIDES E. Iguchi, Departement of Metallurgical Engineering, Faculty of Engineering, Yokohama National University Ohoka,
Received 30 September 1976 Revised 1 December 1976 5.
Vol. 22, No.3
Minami-ku, Yokohama 233, Japan. The displacements of non-parallel {102} CS planes in slightly reduced W0 3 observed by electron microscopy were quantified with the theory of elasticity for an isotropic continum. By this calculation, the magnitude of the force between cations in CS planes was estimated. It was found the principle force an attractive onethat between cations in the involved CS planewas which was calculated to be 1.2 x 1013 (dyne cm2) = 7.8 (eV A3). Using this value, the magnitude of the strain energy was also evaluated, and was found to be larger in value than the energy associated with the dissociation of oxygen atoms from W0 3 lattice. This suggests that the strain energy plays a dominant role in the behaviour of CS planes. ~
Received 28 June 1976 6.
PHOTOELECTRONIC INVESTIGATIONS OF SEMI-INSULATING p-TYPE GaAs: Cr CONTAINING NEUTRAL CHROMIUM ACCEPTORS W. Plesiewics, Instytut Fizyki PAN, 02.668 Warszawa, Poland.
A photoelectronic analysis of p-type GaAs: Cr, i.e. measurements of thermally stimulated currents and the dependences of photoconductivity and photo-Hall effect on photon energy, temperature and light intensity, have enabled trap locations and densities as well as properties of neutral chromium acceptors to be determined. Hole traps proved to be located at 0.15 and 0.23 eV above the valence band, and 5their densities 3 and x 1016 cm3 have been estimated to be 10~~ cm is related to the presence respectively. Their occurrence of copper in the samples investigated. Neutral chromium acceptors are located at 0.77 eV above the valence band and are at a constant distance from the conduction band. Their photoexcited electron escape cross-section is
Received 28 October 1976 Revised 28 January 1977 8.
CALCULATION OF ELECTROSTATIC FIELDS IN IONIC CRYSTALS BASED UPON THE EWALD METHOD J.W. Weenk and H.A. Harwig, Inorganic Chemistry Department, State University Utrecht, Croesestraat 77A, Utrecht, The Netherlands.
Formulas for the electrostatic potential, field strength and field gradient due to monopoles, diopoles and quadrupoles are given, based upon the Ewald summation method.inA the convenient choice isofdemonthe convergence parameter Ewald method strated in some actual calculations. A method to calculate self-consistent electrostatic fields due to self-induced dipoles is evaluated. Monopole and self-consistent fields are calculated in Pb 2O3, I3.Mn203, FeTiO3, MnF3 and Pb3O4. The influence of the anion parameter on the
Vol. 22, No. 3
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
electrostatic field is investigated for idealized CdCl2 and TiO2. Results of Madelung and induced dipole polariz. ation energy for a series of arbitrary compounds are given. The effect of spontaneous polarization in polar crystals is discussed. Received 1 September 1976 Revised 3 February 1977 9.
ELECTROSTATIC LATTICE ENERGIES OF SOME ABX3 POLYTYPES WITH CLOSE— PACKED AX3 LAYERS. J.W. Weenk and H.A. Harwig, Inorganic Chemistry Department, State University Utrecht, Croesestraat 77A, Utrecht, The Netherlands.
Electrostatic lattice energies (Madelung and polarization energies) for five ideal ABX3 structure types with close-packed AX3 layers (X = F, Cl, Br, I, 0, 5) are calculated. Stability regions for the ideal structure types are indicated as function of the anion radius and the anion polarizabiity. The effect on the electrostatic lattice energy due to trigonal deformations of the AX3 layers in the 2L and 3L stacked structuresis discussed for the anions F and Cl. Received 28 October 1976 Revised 28 January 1977 10.
DIFFERENTIAL THERMAL ANALYSIS AT HIGH PRESSURES VII: PHASE BEHAVIOUR OF SOLID METHANOL UP TO 3 kbar A. WUrflinger and R. Landau, Institute of Physical Chemistry, University of Bochum, GFR.
The phase behaviour of solid methanol was invistigated from 196°Cto the melting temperature and up —
ix
to 3 kbar, using a low-temperature high-pressure data apparatus, The melting temperature rises from 98°Cat 1 atm to 64°Cat 2775 bar. Solid methanol exhibits a transition at atmospheric pressure at approximately 115°C;the transition has a strong tendency to superheat and to occur at 110°C.The transition temperature rises from approximately 115°Cat 1 atm to 81°Cat 2725 bar. Small impurities of waver induce a —
—
—
—-
—
—
“second transition” at 117.3°Cthat must be attributed to the waver—methanol eutecic. Volume changes accompanying the Clapeyron phase transition have been calcualted using the Clausius equation. —
Received 2 August 1976 Revised 28 January 1977 11.
THE PHONON CONTRIBUTIONS TO THE GIBBS FREE ENERGY OF y ~3Cul M.B. Haxton, Department of Physics, Indiana University, Blooington IN47401, U.S.A.; and Institute of Theoretical Science and Department of Physics, University of Oregon Eugene, OR 97403, U.S.A.
Equations are derived for the phonon contributions to the Gibbs free energy and entropy in terms of the phonon energy states. The energy states are determined from phonon dispersion relations, as calculated by the author in previous papers, for the ~ and jl phases of Cul. The resulting Gibbs free energies and entropies for each phase are plotted as a function of temperature and compared in the region of the y to jl phase transition. It is found that the phonon contributions are not important factors in the phase transition. Comments are made on other factors which are felt to be important in the phase transition. Received 25 October 1975 Revised 28 January 1977