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The born model and the effects of hydrostatic and non-hydrostatic stresses on rubidium halide structural phase transitions
Solid State Communications, Vol. 25, pp. iii—vi, 1978.
Pergamon Press.
Printed in Great Britain
Abstracts of Articles to be Published in The Journal of Physics and Chemistry of Solids ‘J Phys. Chem. Solids (to be published)’ should be cited in references to material quoted from this section prior to the publication of the relevant article. 1.
THE BORN MODEL AND THE EFFECTS OF HYDROSTATIC AND NON-HYDROSTATIC STRESSES ON RUBIDIUM HALIDE
2.
STRUCTURAL PHASE TRANSITIONS R.J. Wallat, Department of Physics and Materials Research Laboratory; and i. Holder, Department of Geology and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, illinois 61801, U.S.A. An analytic Born model, with the same set of repulsive parameters for both phases in each salt, has been used to calculate the properties of the NaCl—CaC1 structural phase transformation in three rubidium halides. The treatment required a careful evaluation of the three repulsive parameters by comparison with equilibrium conditions in both phases and measured bulk moduli, and involved a self consistent analysis which takes into account the experimental uncertainties in reported values of CsC1-phase lattice parameters. Calculated values for the equilibrium transition pressure, lattice parameters, and lattice energies are in satisfactory agreement with reported experimental results. The model has also been used to calculate the lattice energy continuously from the NaCl to the CsCl phases, as a function of both hydrostatic and non-hydrostatic stresses. These calculations give a semiquantitative estimate of an energy barrier between the two stable structures, which is consistent with reported measurements of elastic constant and hysteresis effects near the transition pressure. The calculated effects of a uniaxial stress are found to be as much as three times larger than those of a hydrostatic stress, and the effects of the uniaxial stress on the barrier height are found to be approximately the same as the effects on the equilibrium energy differences. Measurements of the effect of this uniaxial stress on the forward transition pressure of RbI were carried out, and the measured variations were found to be in excellent agreement with the calculated change in equilibrium transition pressure as expected from the energy barrier calculations, Received 13 June 1977 Revised 14 December 1977
OPTICAL ABSORPTION DUE TO TRANSITIONS BETWEEN BANDS AND LOCAL LEVELS IN CdCr2 Se4
D.M. Eagles, Laboratoire de Magnétisme, CNRS, 92190 Meudon-Bellevue, France. The theory of optical absorption due to transitions between a valence band and a hydrogen-like local level associated with a conduction band is modified to permit an arbitrary power-law dependence of energy on the magnitude of the wave-vector of carriers in the valence band. The observed absorption for photon energies below 1.6 eV in the ferromagnetic semiconductor CdCr2 Se4 is discussed in terms of a combination of two types of terms. The first type of absorption is due to transitions to a local level from a band with two branches, in each of which there is an energy region with a width of 0.28 eV or more beginning 0.10 to 0.16 eV from the band edge, in which the energy measured from some origin near but not necessarily equal to the bandedge is approximately proportional to (wave-vector) [1, 3]. The second type of absorption has a dependence on photon energy hw of the form (hw E3 )2, where E3 is a threshold energy probably connected with indirect transitions between bands as suggested by Sakai, Sugano and Okabe. After constraints on parameters appearing in the theory are imposed by use of results of these authors and of Shepherd, it is found that curves of Harbeke and Lehmann on optical absorption in CdCr2 Se4 at 4.2, 78, 130 and 298 K in the photonenergy range 1.14 to 1.42 eV can be fitted to a mean accuracy of 3%, using an average of 3.75 adjustable parameters for each curve. The strength of the indirect band-to-band absorption does not have the temperature dependence expected for phonon-assisted indirect band-to-band transitions, but can be described by a term independent of temperature plus another term proportional to the square of the deviation of the magnetization from saturation. The fitting of the absorption curves requires that the ratio ofthe widths of the two branches of the bands varies from about 1.6 at low temperatures to 1.35 at 298 K, and that the total width of the bands involved is less than 1 eV. Received 18 October 1977 —
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Pergamon Press.
Printed in Great Britain
Abstracts of Articles to be Published in The Journal of Physics and Chemistry of Solids ‘J Phys. Chem. Solids (to be published)’ should be cited in references to material quoted from this section prior to the publication of the relevant article. 1.
THE BORN MODEL AND THE EFFECTS OF HYDROSTATIC AND NON-HYDROSTATIC STRESSES ON RUBIDIUM HALIDE
2.
STRUCTURAL PHASE TRANSITIONS R.J. Wallat, Department of Physics and Materials Research Laboratory; and i. Holder, Department of Geology and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, illinois 61801, U.S.A. An analytic Born model, with the same set of repulsive parameters for both phases in each salt, has been used to calculate the properties of the NaCl—CaC1 structural phase transformation in three rubidium halides. The treatment required a careful evaluation of the three repulsive parameters by comparison with equilibrium conditions in both phases and measured bulk moduli, and involved a self consistent analysis which takes into account the experimental uncertainties in reported values of CsC1-phase lattice parameters. Calculated values for the equilibrium transition pressure, lattice parameters, and lattice energies are in satisfactory agreement with reported experimental results. The model has also been used to calculate the lattice energy continuously from the NaCl to the CsCl phases, as a function of both hydrostatic and non-hydrostatic stresses. These calculations give a semiquantitative estimate of an energy barrier between the two stable structures, which is consistent with reported measurements of elastic constant and hysteresis effects near the transition pressure. The calculated effects of a uniaxial stress are found to be as much as three times larger than those of a hydrostatic stress, and the effects of the uniaxial stress on the barrier height are found to be approximately the same as the effects on the equilibrium energy differences. Measurements of the effect of this uniaxial stress on the forward transition pressure of RbI were carried out, and the measured variations were found to be in excellent agreement with the calculated change in equilibrium transition pressure as expected from the energy barrier calculations, Received 13 June 1977 Revised 14 December 1977
OPTICAL ABSORPTION DUE TO TRANSITIONS BETWEEN BANDS AND LOCAL LEVELS IN CdCr2 Se4
D.M. Eagles, Laboratoire de Magnétisme, CNRS, 92190 Meudon-Bellevue, France. The theory of optical absorption due to transitions between a valence band and a hydrogen-like local level associated with a conduction band is modified to permit an arbitrary power-law dependence of energy on the magnitude of the wave-vector of carriers in the valence band. The observed absorption for photon energies below 1.6 eV in the ferromagnetic semiconductor CdCr2 Se4 is discussed in terms of a combination of two types of terms. The first type of absorption is due to transitions to a local level from a band with two branches, in each of which there is an energy region with a width of 0.28 eV or more beginning 0.10 to 0.16 eV from the band edge, in which the energy measured from some origin near but not necessarily equal to the bandedge is approximately proportional to (wave-vector) [1, 3]. The second type of absorption has a dependence on photon energy hw of the form (hw E3 )2, where E3 is a threshold energy probably connected with indirect transitions between bands as suggested by Sakai, Sugano and Okabe. After constraints on parameters appearing in the theory are imposed by use of results of these authors and of Shepherd, it is found that curves of Harbeke and Lehmann on optical absorption in CdCr2 Se4 at 4.2, 78, 130 and 298 K in the photonenergy range 1.14 to 1.42 eV can be fitted to a mean accuracy of 3%, using an average of 3.75 adjustable parameters for each curve. The strength of the indirect band-to-band absorption does not have the temperature dependence expected for phonon-assisted indirect band-to-band transitions, but can be described by a term independent of temperature plus another term proportional to the square of the deviation of the magnetization from saturation. The fitting of the absorption curves requires that the ratio ofthe widths of the two branches of the bands varies from about 1.6 at low temperatures to 1.35 at 298 K, and that the total width of the bands involved is less than 1 eV. Received 18 October 1977 —
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