By Jean-Paul Poirier
Enlarged and entirely up-to-date, this re-creation takes under consideration the massive experimental and theoretical growth lately made within the box. creation to the Physics of the Earth's inside describes the constitution, composition and temperature of the deep Earth. The publication experiences the basics of continuum mechanics and thermodynamics of solids, and offers the idea of lattice vibration in solids. It introduces some of the equations of country and discusses melting legislation and shipping homes. the amount closes with a dialogue of present seismological, thermal and compositional types of the Earth. approximately 250 new references were extra
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Extra resources for Introduction to the Physics of the Earth's Interior, Second Edition
2 The reasoning would, of course, be the same for transverse waves. Indeed, there are three dispersion curves, one for the P-waves and one for each polarization of the S-waves. 14), we see that the relevant elastic modulus is proportional to the 32 3 Lattice vibrations second derivative of the potential energy with respect to strain. Therefore, the elastic constants, introduced as phenomenological material constants in the thermodynamic approach, can be physically interpreted in terms of interatomic potentials.
We will now show that the two deﬁnitions are equivalent and that : . 53) with respect to T and obtain: dP dT dE " : " V dT : "C V 4 4 4 now, by deﬁnition of the coeﬃcient of thermal expansion have: : 1 *V V *T :9 . e. macroscopic one: and a microscopic one: . Now, " there are many more ways of deﬁning a Gru¨neisen parameter or ‘‘gamma’’ and we will review here those that are the more important and currently encountered in the literature (see Stacey, 1977b). 56) If all the s have the same volume dependence and there is only one G Debye cut-oﬀ frequency, all the mode gammas are equal to the Debye gamma deﬁned above.
Indeed, there are three dispersion curves, one for the P-waves and one for each polarization of the S-waves. 14), we see that the relevant elastic modulus is proportional to the 32 3 Lattice vibrations second derivative of the potential energy with respect to strain. Therefore, the elastic constants, introduced as phenomenological material constants in the thermodynamic approach, can be physically interpreted in terms of interatomic potentials. As an example, let us calculate the value of the bulk modulus K at 0 K (no thermal energy), for a simple ionic crystal like NaCl (Kittel, 1967).
Introduction to the Physics of the Earth's Interior, Second Edition by Jean-Paul Poirier