ALBERT

Description: The tables and graphs result from evaluation of Model 1 (see Veröffentlichungen des Zentralinstituts für Physik der Erde, Nr. 41, Potsdam 1976). They help to approximate values of the hydrostatic pressure P, the bulk modulus and its pressure derivative and the seismic parameter of a sample at any volume contraction x in the range between 0.5 and 1 if these quantities referred to the initial state (P = 0) are known. The considered functions are tabulated for a set of grid points of the rectangle 0.5 ≤ x ≤ 1, 2.1 ≤ ϰ_1 ≤ 10, where ϰ_1 is the initial value of the pressure derivative of the bulk modulus. The lattice pitchs are 0.01 in x and 0.1 in ϰ_1. The inverse problem can also be solved approximately with the aid of the tables and, above all, the plots presented here by using the "method of corresponding curves".

Description: Summary 1. Preface 2. Theoretical excursus 3. Some remarks on Model 1 4. Instructions for using tables and plots 5. References 6. Tables and figures

Description: Evaluation of numerous data from different methods of measurement and theories applied in high-pressure physics shows that the strain energy of a monophase system, which represents the low- or a high-pressure phase of a hydrostatically compressed substance mostly relevant to planetary physics, approximates to a term proportional to the square of an auxiliary function of the volumetric contraction, the bulk modulus and its successive partial derivatives with respect to pressure at the initial state of the thermodynamical system. From this it follows that new-defined polynomial equations in the initial values of the bulk modulus and its pressure derivatives must be satisfied, which is checked for many elements, halides, oxides, minerals, and rocks. Using a suitably chosen auxiliary function, the strain energy, pressure, bulk modulus and its first pressure derivative at any equilibrium state of the monophase system are represented by approximation functions of the volumetric contraction as well as the initial values of the bulk modulus and its derivatives. The information content of these functional relations called Model N if they include derivatives of the bulk modulus only up to the order N surpasses, already in the cases N = 1 end N = 2, that of other relations hitherto used for interpreting the compressional behaviour of different substances. Model 1 is discussed on the base of more than 70 substances with various compressional properties, among them stishovite and solid hydrogene, proved to be suitable, in particular, for the physics of the interiors of the Earth and of terrestrial planets. Considering the reliability of the data material available, Model 1 is pointed out to predict experimental values from the tested substances for volumetric contractions down to about 0.5 with a relative error between 1 % and 5 %. Model 2, extending the information volume of Model 1, turns out to be appropriate for volumetric contractions less than 0.5 as is the case in the interiors of the Jovian planets. For practical use of both models tables and graphs of sensitivities and errors of significant quantities are presented. In case data from shock-wave experiments on rocks and minerals are available, Model 1 is used for identification of crystal structures of high-pressure phases. As a result, for the majority of high-pressure phases the compressional behaviour differs from that of the corresponding oxide mixtures. For some substances new conclusions on their crystal structures can be drawn.

Description: 1. Introduction 2. Basic relations 3. Approximations for the equation of state 4. The conditions of the auxiliary variable 5. Development of Model 1 and Model 2 6. Practical analysis of the models 6. 1. Preliminaries 6.2. The parameters "0 and "1 6.3. Intercomparison of different forms of the equation of state 6.4. The parameter n2 6.5. Problems of accuracy 6.6. Discussion of [x,P]-data of elements 6.7. Discussion of [x,P]-data of halides 6.8. Discussion of [x,P]-data of oxides, minerals, and rocks 6.9. On the "interpolating equations of state" 7. Conclusion 8. Tables and Figures References