By Jean-Paul Poirier
New version of winning textbook on deep Earth for complex scholars in geophysics and mineralogy.
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Additional info for Introduction to the Physics of the Earths Interior
9 Vibrational spectrum (density of states) for periclase compared with the Debye spectrum (dashed curve). The frequencies of the modes, including the optical modes, are nearly all below the Debye frequency and both spectra converge at low frequencies (after O. L. Anderson, 1988). stishovite, corundum and periclase (Fig. 9), since only a small fraction of the phonon spectrum has frequencies higher than the Debye cut-off frequency. 8), whose thermoelastic properties are satisfactorily ac counted for by Debye’s theory (O.
E. thermal) energy of a solid. e. the expression of pressure P as a function of specific volume V and temperature T. 51) dV dV " We have thus expressed P in terms of known quantities and of the P:9 3 Lattice vibrations 46 variation of Debye’s temperature with volume. 3. The thermal pressure was then related to the increase in thermal energy by the thermodynamic Gru¨neisen parameter . Now we see that the thermal energy is the energy of the phonon gas and we have introduced a more physical definition of the Gru¨neisen parameter, expressing the volume dependence of the Debye frequency.
2) for calculating the longitudinal and transverse sound velocities v and v from single-crystal elastic constants. 1 The Brillouin zone is assumed to have the simple shape of a sphere with radius k given by: " 4 (2 ) k : 3 " V * The maximum radius k corresponds to a maximum cut-off frequency " , called Debye frequency: : k v . 5 Dispersion curve (a) and vibrational spectrum (b) in the case of the Debye approximation. The vibrational spectrum is the curve of the density of states g( ) vs frequency.
Introduction to the Physics of the Earths Interior by Jean-Paul Poirier