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Vibronic spectra of V 2+ and Cr 3+ impurities in MgO have been used to determine the pressure dependences of the energies of MgO phonons at several critical points of the Brillouin zone to more than 100 kbar at 90 and 295 K. From these data, approximate densities of states for MgO at 100 and 500 kbar and vibrational partition functions were constructed, and contributions to the constant-volume .heat capacity, entropy, internal and free energies, and the Debye temperature were calculated. Argon Was successfully used as a nearly hydrostatic pressure medium for the measurements at 90 K to 102 kbar. INTRODUCTIONOxides are important constituents of the earth's mantle; however, the significance of any particular oxide can be assessed only if the thermodynamics of the oxide and the species with which it equilibrates can be determined. Few precise thermodynamic measurements are possible under mantle conditions; thus, most properties of mantle constituents are estimated by more or less crude extrapolations of static data obtained at other temperatures and pressures. Ideally, these extrapolations are based on microscopic models of the energetics of the solid; however, for the oxides and many similar solids, no satisfactory few-parameter model of structures or dynamics exists, even at atmospheric pressure. At best, density dependences of vibrational energies have been determined for a few modes at the center of the Brillouin zone by Raman and infrared spectroscopy, but this solution also fails for alkaline earth oxides. These materials have no Raman and only one infrared active mode; the pressure dependence of one mode, even if it were known, hardly provides a basis for extrapolating lattice dynamics to high pressures and temperatures. This paper describes an alternative approach for determining pressure dependences of the vibrational spectra of oxide crystals under high pressures. The basis of this approach is that vibrational modes of a crystal may modulate electronic spectra of impurity ions. In favorable cases, e.g., V 2+ for Mg 2+ or Cr 3+ for Mg 2+ or AI 3+, impurities substitute, but only slightly perturb, the vibrations of surrounding ions, and much of the phonon density of states of the host lattice can be observed in vibronic spectra, even at very high pressures. This method is illustrated in this report for V 2+ and Cr 3+ in MgO.Although many minerals can be studied by this method, MgO was chosen for several reasons. MgO has simple cubic symmetry, and the density of vibrational states at 1 bar is well-known from inelastic neutron scattering and lattice dynamic calculations [Peckham, 1967;. MgO undergoes no known phase transitions. The pressure dependences of several macroscopic properties of MgO have been determined, including Hugoniot and isothermal p-V equations of state, dielectric constants, and elastic constams. Furthermore, optical spectra of several transitions of impurity ions in MgO have been studied at 1 bar [Sturge, 1963;Castelli and Forster, 1975].
Vibronic spectra of V 2+ and Cr 3+ impurities in MgO have been used to determine the pressure dependences of the energies of MgO phonons at several critical points of the Brillouin zone to more than 100 kbar at 90 and 295 K. From these data, approximate densities of states for MgO at 100 and 500 kbar and vibrational partition functions were constructed, and contributions to the constant-volume .heat capacity, entropy, internal and free energies, and the Debye temperature were calculated. Argon Was successfully used as a nearly hydrostatic pressure medium for the measurements at 90 K to 102 kbar. INTRODUCTIONOxides are important constituents of the earth's mantle; however, the significance of any particular oxide can be assessed only if the thermodynamics of the oxide and the species with which it equilibrates can be determined. Few precise thermodynamic measurements are possible under mantle conditions; thus, most properties of mantle constituents are estimated by more or less crude extrapolations of static data obtained at other temperatures and pressures. Ideally, these extrapolations are based on microscopic models of the energetics of the solid; however, for the oxides and many similar solids, no satisfactory few-parameter model of structures or dynamics exists, even at atmospheric pressure. At best, density dependences of vibrational energies have been determined for a few modes at the center of the Brillouin zone by Raman and infrared spectroscopy, but this solution also fails for alkaline earth oxides. These materials have no Raman and only one infrared active mode; the pressure dependence of one mode, even if it were known, hardly provides a basis for extrapolating lattice dynamics to high pressures and temperatures. This paper describes an alternative approach for determining pressure dependences of the vibrational spectra of oxide crystals under high pressures. The basis of this approach is that vibrational modes of a crystal may modulate electronic spectra of impurity ions. In favorable cases, e.g., V 2+ for Mg 2+ or Cr 3+ for Mg 2+ or AI 3+, impurities substitute, but only slightly perturb, the vibrations of surrounding ions, and much of the phonon density of states of the host lattice can be observed in vibronic spectra, even at very high pressures. This method is illustrated in this report for V 2+ and Cr 3+ in MgO.Although many minerals can be studied by this method, MgO was chosen for several reasons. MgO has simple cubic symmetry, and the density of vibrational states at 1 bar is well-known from inelastic neutron scattering and lattice dynamic calculations [Peckham, 1967;. MgO undergoes no known phase transitions. The pressure dependences of several macroscopic properties of MgO have been determined, including Hugoniot and isothermal p-V equations of state, dielectric constants, and elastic constams. Furthermore, optical spectra of several transitions of impurity ions in MgO have been studied at 1 bar [Sturge, 1963;Castelli and Forster, 1975].
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