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Lindemann's criterion and the melting of solids at high pressures
vi
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
To discuss the Faraday and Voigt effects in the Eu chalcogenides we derive a general expression for the polarizability of a system in which the important electronic transitions are from localized to itinerant orbitals. This expression is applied to a model system in which the electronic transitions take place from a 4f orbital to a Sd t2g Wannier orbital centered at the same cell. We treat in detail the matrix elements of the electric dipole operator taking into account the many-body character of the intermediate state localized hole is included explicitly within a simple approximation. We present a numerical calculation of the frequency dependent Verdet constant and Voigt phase shift for the paramagnetic and ferromagnetic phases of EuSe.
electronic structure of the silver iodide polymorphs. The four phases which we have investigated are the a, J3 and y modifications and the high pressure polymorph having the NaC1 structure. The ionicity values obtained for these different phases agree well with the values of Phillips derived from the dielectric data and the cornputed bandstructures are in good agreement with independent pseudopotential calculations. Received 25 July 1975 Revised 31 October 1975 7.
A TIGHT-BINDING APPROACH TO THE ELECTRONIC STRUCTURE OF THE SILVER HALIDES I. SILVER CHLORIDE P.V. Smith, Department of Physics, University of New England, Armidale, N.S.W. 2350, Australia.
In this paper we present a modified version of the tight-binding method for determining the electronic structure of the silver halides. The main advantage of this approach is that it enables the bandstructure of these materials to be derived for all energies adjacent to the band gap. This is achieved by including an s function into the tight-binding basis set of atomic orbitals. In addition to the basic simplicity of the conventional tightbinding method this approach allows the ionicity of the potentials to be determined empirically by fitting the experimental band-gap and incorporates into the bandstructure calculation s p and s d interactions which may well be important. The validity of the approach is examined for the case of silver chloride and good agreement is obtained with previous calculations. Received 25 July 1975 Revised 31 October 1975 6.
A TIGHT-BINDING APPROACH TO THE ELECTRONIC STRUCTURE OF THE SILVER HALIDES II. THE SILVER IODIDE POLYMORPHS P.V. Smith, Department of Physics, University of New England, Armidale, N.S.W. 2351, Australia.
THERMAL EXPANSION OF CADMIUM FLUORIDE D. Shaharabany, M. Wolf and D. Gerlich, Department of Physics and Astronomy, TelAviv University, Ramat Aviv, Israel. The thermal expansion of CdF2 single crystal has
Received 30 December 1974 Revised 31 October 1975 5.
Vol. 18, No. 4
been measured over the temperature range 80 300°K. From the latter data, the thermal Gruneisen constant as a function of temperature has been evaluated, and compared with the elastic Gruneisen constant. The correlation between the two sets of data, and with possible lattice interactions is discussed. Received 19 June 1975 8.
FORCE FIELD OF FeS2 WITH PYRITE STRUCTURE AT ZERO WAVE VECTOR H. A. Lauwers and M.A. Herman, Laboratorium voor Anorganische Scheikunde, Rijksuniversitair Centrum Antwerpen, Goenenborgerlaan 171 2020 Antwerpen, Belgium.
Published experimental frequencies are used to calculate force field and effective charge of FeS2 with pyrite structure. The values obtained are discussed. Some preliminary calculations on MnS2 are reported. Received 21 July 1975 Revised 31 October 1975 9.
LINDEMANN’S CRITERION AND THE MELTING OF SOLIDS AT HIGH PRESSURES V.V. Palciauskas, Department of Geology, University of Illinois, Urbana, IL 61801, U.S.A.
The generalized Lindemann’s criterion is utilized to derive the variation of the melting temperature Tm with compression. The result incorporates the basic features of the lattice potential as well as the volume dependence of the frequency distribution through the first two moments of the mode Gruneisen parameter. This meltWe have applied the modified tight binding approach ing relation predicts that when Tm is plotted against the developed in the first paper of this series to calculate the volume of the melting solid, the fusion curves of solids
Vol. 18, No. 4
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
vii
bonded by Van der Waals forces are concave to the tem-
12.
perature axis and in accordance with the predictions of the Simon equation. On the other hand, the predicted melting curves of ionic compohnds, as the alkali-halides, are concave to the volume axis and exhibit a maxima at higher pressures. Since silicates generally possess an ionic contribution to the lattice energy, this melting relation should give a more accurate estimate of the high pressure melting temperature for these compounds than Simon’s and theoretically similar equations.
Neutron diffraction experiments have been carried out on a TbNi2 single crystal. Below the Curie temperature, 42 K, a magnetic contribution is observed only on
Received 21 April 1975 Revised 31 October 1975 10.
LOW-FREQUENCY ELECTRONIC RESISTIVITY OF CRYSTALS DUE TO THE SCATTERING FROM DIPOLES H.D. Dimitrov, International Centre for Theoretical Physics, Trieste, Italy.
The screened potential of an electrical dipole impurity in crystalline solids is obtained in the Debye Huckel approximation. In the one-band effective-mass approximation and second Born approximation of the scattering, we calculate low-frequency transport relaxation time of current-carriers, electrical conductivity and the electronic part of permittivity of crystals when the scattering mechanism is connected with the randomly distributed screened dipole centres. It is shown that in some cases the scattering from dipole impurity centres may be essential and even more effective than the other scattering mechanisms. Received 4March 1975 11.
METHYL ROTATION IN NMP TCNQ M.A. Butler and F. Wudl, Bell Laboratories, Murray Hill, NJ 07974, U.S.A.
Comparisons of continuous wave NMR in NMP— TCNQ and the analog in which the methyl group is deuterated are used to show that methyl reorientation occurs in NMP TCNQ at all temperatures (7~>1 .5°K). Methyl reorientation is suggested to contribute to the nuclear spin-lattice relaxation, and its effects on the specific heat are discussed. Received 9 September 1975
POLARIZED NEUTRON STUDY OF TbNi2 D. Givord, F. Givord and D. Gignoux, Laboratoire de Magnétisme, C.N.R.S. Grenoble, France, and W.C. Koehier and R.M. Moon, Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, U.S.A.
nuclear scattering peaks. Therefore, the terbium atoms form a ferromagnetic structure. Polarized neutron measurements performed in the paramagnetic state, in an applied magnetic field of 57 kOe, reveal a nonuniform polarization of the conduction band. Within the experimental accuracy, no 3d magnetic moment is observed on nickel atoms. This result is consistent with the assumption of rare earth magnetic ordering occurring through the polarization of conduction electrons. Received 6 October 1975 13.
ON THE INFLUENCE OF MULTIPLE REFLECTIONS ON THE ELECTROREFLECTANCE SPECTRUM OF THE GROUNDEXCITON LINE OF GaSe A. Balzarotti, Istituto di Fisica, Università di Roma, Rome, Italy and Istituto di Fisica, Università dell’Aquila, L’Aquila, Italy; and P. Picozzi, Istituto di Fisica, Università dell’Aquila, L’Aquila, Italy.
The electroreflectance spectrum of GaSe near its fundamental (2 eV) edge is reported and shown to be sensitive to multiple light reflections, which give rise to structures previously ascribed to extrinsic states. Electroabsorption is less sensitive to multiple reflection and therefore better suited to quantitative comparison with theory. Received 19 May 1975 Revised 14 November 1975
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
To discuss the Faraday and Voigt effects in the Eu chalcogenides we derive a general expression for the polarizability of a system in which the important electronic transitions are from localized to itinerant orbitals. This expression is applied to a model system in which the electronic transitions take place from a 4f orbital to a Sd t2g Wannier orbital centered at the same cell. We treat in detail the matrix elements of the electric dipole operator taking into account the many-body character of the intermediate state localized hole is included explicitly within a simple approximation. We present a numerical calculation of the frequency dependent Verdet constant and Voigt phase shift for the paramagnetic and ferromagnetic phases of EuSe.
electronic structure of the silver iodide polymorphs. The four phases which we have investigated are the a, J3 and y modifications and the high pressure polymorph having the NaC1 structure. The ionicity values obtained for these different phases agree well with the values of Phillips derived from the dielectric data and the cornputed bandstructures are in good agreement with independent pseudopotential calculations. Received 25 July 1975 Revised 31 October 1975 7.
A TIGHT-BINDING APPROACH TO THE ELECTRONIC STRUCTURE OF THE SILVER HALIDES I. SILVER CHLORIDE P.V. Smith, Department of Physics, University of New England, Armidale, N.S.W. 2350, Australia.
In this paper we present a modified version of the tight-binding method for determining the electronic structure of the silver halides. The main advantage of this approach is that it enables the bandstructure of these materials to be derived for all energies adjacent to the band gap. This is achieved by including an s function into the tight-binding basis set of atomic orbitals. In addition to the basic simplicity of the conventional tightbinding method this approach allows the ionicity of the potentials to be determined empirically by fitting the experimental band-gap and incorporates into the bandstructure calculation s p and s d interactions which may well be important. The validity of the approach is examined for the case of silver chloride and good agreement is obtained with previous calculations. Received 25 July 1975 Revised 31 October 1975 6.
A TIGHT-BINDING APPROACH TO THE ELECTRONIC STRUCTURE OF THE SILVER HALIDES II. THE SILVER IODIDE POLYMORPHS P.V. Smith, Department of Physics, University of New England, Armidale, N.S.W. 2351, Australia.
THERMAL EXPANSION OF CADMIUM FLUORIDE D. Shaharabany, M. Wolf and D. Gerlich, Department of Physics and Astronomy, TelAviv University, Ramat Aviv, Israel. The thermal expansion of CdF2 single crystal has
Received 30 December 1974 Revised 31 October 1975 5.
Vol. 18, No. 4
been measured over the temperature range 80 300°K. From the latter data, the thermal Gruneisen constant as a function of temperature has been evaluated, and compared with the elastic Gruneisen constant. The correlation between the two sets of data, and with possible lattice interactions is discussed. Received 19 June 1975 8.
FORCE FIELD OF FeS2 WITH PYRITE STRUCTURE AT ZERO WAVE VECTOR H. A. Lauwers and M.A. Herman, Laboratorium voor Anorganische Scheikunde, Rijksuniversitair Centrum Antwerpen, Goenenborgerlaan 171 2020 Antwerpen, Belgium.
Published experimental frequencies are used to calculate force field and effective charge of FeS2 with pyrite structure. The values obtained are discussed. Some preliminary calculations on MnS2 are reported. Received 21 July 1975 Revised 31 October 1975 9.
LINDEMANN’S CRITERION AND THE MELTING OF SOLIDS AT HIGH PRESSURES V.V. Palciauskas, Department of Geology, University of Illinois, Urbana, IL 61801, U.S.A.
The generalized Lindemann’s criterion is utilized to derive the variation of the melting temperature Tm with compression. The result incorporates the basic features of the lattice potential as well as the volume dependence of the frequency distribution through the first two moments of the mode Gruneisen parameter. This meltWe have applied the modified tight binding approach ing relation predicts that when Tm is plotted against the developed in the first paper of this series to calculate the volume of the melting solid, the fusion curves of solids
Vol. 18, No. 4
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
vii
bonded by Van der Waals forces are concave to the tem-
12.
perature axis and in accordance with the predictions of the Simon equation. On the other hand, the predicted melting curves of ionic compohnds, as the alkali-halides, are concave to the volume axis and exhibit a maxima at higher pressures. Since silicates generally possess an ionic contribution to the lattice energy, this melting relation should give a more accurate estimate of the high pressure melting temperature for these compounds than Simon’s and theoretically similar equations.
Neutron diffraction experiments have been carried out on a TbNi2 single crystal. Below the Curie temperature, 42 K, a magnetic contribution is observed only on
Received 21 April 1975 Revised 31 October 1975 10.
LOW-FREQUENCY ELECTRONIC RESISTIVITY OF CRYSTALS DUE TO THE SCATTERING FROM DIPOLES H.D. Dimitrov, International Centre for Theoretical Physics, Trieste, Italy.
The screened potential of an electrical dipole impurity in crystalline solids is obtained in the Debye Huckel approximation. In the one-band effective-mass approximation and second Born approximation of the scattering, we calculate low-frequency transport relaxation time of current-carriers, electrical conductivity and the electronic part of permittivity of crystals when the scattering mechanism is connected with the randomly distributed screened dipole centres. It is shown that in some cases the scattering from dipole impurity centres may be essential and even more effective than the other scattering mechanisms. Received 4March 1975 11.
METHYL ROTATION IN NMP TCNQ M.A. Butler and F. Wudl, Bell Laboratories, Murray Hill, NJ 07974, U.S.A.
Comparisons of continuous wave NMR in NMP— TCNQ and the analog in which the methyl group is deuterated are used to show that methyl reorientation occurs in NMP TCNQ at all temperatures (7~>1 .5°K). Methyl reorientation is suggested to contribute to the nuclear spin-lattice relaxation, and its effects on the specific heat are discussed. Received 9 September 1975
POLARIZED NEUTRON STUDY OF TbNi2 D. Givord, F. Givord and D. Gignoux, Laboratoire de Magnétisme, C.N.R.S. Grenoble, France, and W.C. Koehier and R.M. Moon, Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, U.S.A.
nuclear scattering peaks. Therefore, the terbium atoms form a ferromagnetic structure. Polarized neutron measurements performed in the paramagnetic state, in an applied magnetic field of 57 kOe, reveal a nonuniform polarization of the conduction band. Within the experimental accuracy, no 3d magnetic moment is observed on nickel atoms. This result is consistent with the assumption of rare earth magnetic ordering occurring through the polarization of conduction electrons. Received 6 October 1975 13.
ON THE INFLUENCE OF MULTIPLE REFLECTIONS ON THE ELECTROREFLECTANCE SPECTRUM OF THE GROUNDEXCITON LINE OF GaSe A. Balzarotti, Istituto di Fisica, Università di Roma, Rome, Italy and Istituto di Fisica, Università dell’Aquila, L’Aquila, Italy; and P. Picozzi, Istituto di Fisica, Università dell’Aquila, L’Aquila, Italy.
The electroreflectance spectrum of GaSe near its fundamental (2 eV) edge is reported and shown to be sensitive to multiple light reflections, which give rise to structures previously ascribed to extrinsic states. Electroabsorption is less sensitive to multiple reflection and therefore better suited to quantitative comparison with theory. Received 19 May 1975 Revised 14 November 1975