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All riehts reservPrlNo part of this publication may be reproduced in any form without written permission from the publisher PREFACE TO THE AMERICAN EDITIONWe started our work on theoretical methods in the phys ics of high pressures (in connection with geophysical applications) in 1956, and we immediately encountered many problems. Naturally, we searched the published Iiterature for solutions to these problems but whenever we failed to find a solution or when the solution did not satisfy us, we attempted to solve the problern ourselves. We realized that other investigators working in the physics of high pressures would probably encounter the same problems and doubts. Therefore, we decided to write this book in order to save our colleagues time and effort. Apart from the descriptions of experimental methods, the book deals only with those problems which we encountered in our own work.Allproblems in high-pressure physics have, at present, only approximate solutions, which are very rough. Therefore, it is not surprising that different investigators approach the same problems in different ways. Our approach does not prejudge the issue and we are fully aware that there are other points of view. Our aim was always to solve a glven problern on a physical basis. For example, the concept of the Grüneisenparameter needs further development but it is based on reliable physical ideas. On the other hand, Simon's equation for the melting curve has, in our opinion, no clear physical basis and is purely empirical. Equations of this type are useful in systematic presentation of the experimental material but they are unsuitable for any major extrapolation.A couple of years have passed since the manuscript of this book was sent to press. Since then, additional experimental data have become available. A high proportion of these data can be analyzed by the methods described in the present book. However, their incorporation would not improve the book very greatly. One of the most pressing needs in high-pressure physics is to improve the accuracy of the measurements. When this barrier is surmounted, we shall then see which methods for the analysis of the experimental data should be refined and which should be replaced.We are pleased to hear that our book will be published in the home country of P. W. Bridgman, and we are grateful to Plenum Publishing Corporation for arranging the translation. Moscow, November 1969 V V. N. Zharkov V. A. Kalinin PREFACEThe theoretical methods used in the high-pressure physics of solids are the subject of the present book. The development of these methods has been stimulated primarily by geophysics problems to which such methods have been applied in the first instance. Special attention is paid in the book to the equation of state, i.e., to the dependence of the pressure P on the volume V and the temperature T.The equation of state is the basic relationship in high-pressure physics. It contains valuable information on the properties of a medium and it allows us to carry out transformations from one thermod...

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In most of these papers, the authors constructed models of the Martian interior using a chemical model suggested by W ä nke and Dreibus (the DW model; see W ä nke, 1981 ; Dreibus and W ä nke, 1989; W ä nke and Dreibus, 1994). Abstract -We present the results of extensive numerical modeling of the Martian interior. Yoder et al. in 2003 reported a mean moment of inertia of Mars that was somewhat smaller than the previously used value and the Love number k 2 obtained from observations of solar tides on Mars. These values of k 2 and the mean moment of inertia impose a strong new constraint on the model of the planet. The models of the Martian interior are elastic, while k 2 contains both elastic and inelastic components. We thoroughly examined the problem of partitioning the Love number k 2 into elastic and inelastic components. The information necessary to construct models of the planet (observation data, choice of a chemical model, and the cosmogonic aspect of the problem) are discussed in the introduction. The model of the planet comprises four submodels-a model of the outer porous layer, a model of the consolidated crust, a model of the silicate mantle, and a core model. We estimated the possible content of hydrogen in the core of Mars. The following parameters were varied while constructing the models: the ferric number of the mantle (Fe#) and the sulfur and hydrogen content in the core. We used experimental data concerning the pressure and temperature dependence of elastic properties of minerals and the information about the behavior of Fe ( γ -Fe ), FeS, FeH, and their mixtures at high P and T . The model density, pressure, temperature, and compressional and shear velocities are given as functions of the planetary radius. The trial model M13 has the following parameters: Fe# = 0.20; 14 wt % of sulfur in the core; 50 mol % of hydrogen in the core; the core mass is 20.9 wt %; the core radius is 1699 km; the pressure at the mantle-core boundary is 20.4 GPa; the crust thickness is 50 km; Fe is 25.6 wt %; the Fe/Si weight ratio is 1.58, and there is no perovskite layer. The model gives a radius of the Martian core within 1600-1820 km while ≥ 30 mol % of hydrogen is incorporated into the core. When the inelasticity of the Martian interior is taken into account, the Love number k 2 increases by several thousandths; therefore, the model radius of the planetary core increases as well. The prognostic value of the Chandler period of Mars is 199.5 days, including one day due to inelasticity. Finally, we calculated parameters of the equilibrium figure of Mars for the M13 model: = 1.82 × 10 -3 , = -7.79 × 10 -6 , = 1/242.3 (the dynamical flattening of the core-mantle boundary). J 2 0 J 4 0 e c-m D 344 SOLAR SYSTEM RESEARCH Vol. 39 No. 5 2005 ZHARKOV, GUDKOVA

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