The author wishes to thank'the staff of the MRL Xerox Z5 computer for their aid during the computing of the I iH and He systems. He also thanks Dr. Donald Reynolds for the hospitality shown the author as a visitor at the aerospace research laboratories where the H4 calculation was performed.Finally, hethanks Dr. R. ¹ Euwemafor aseries of conversations relating tothe theory of local orbitals.The theory of the thermal resistivity of dielectric crystals at ordinary and high temperatures in terms of anharmonic three-phonon interactions is reformulated. The resistivity is similar in form to that obtained by Leibfried and Schlomann, but larger by a factor of 6.8. The theory is then extended to crystals where the unit cell contains many atoms. To include all three-phonon interactions one sums over all harmonics of the reciprocal-lattice vectors in an extended-zone representation. This sum increases the scattering rate. However, the matrix elements of the three-phonon processes are reduced in the case of large unit cells, because coherence is lost in the Fourier transform of the different bonds in each cell. A simplified model is chosen, and in this case the latter effect cancels the former, so that the anharmonie relaxation rate is substantially independent of the number of atoms per unit cell. However, the zone boundaries affect the phonon dispersion curves and reduce the group velocity of most modes; Using a model proposed by Slack, in which only the acoustic phonons of the fundamental zone contribute to the conductivity, and invoking the independence of the relaxation time with cell size here derived, the conductivity varies as the inverse cube root of the number of atoms per cell. The conductivity varies inversely with temperature, even if the phonon mean free path is shorter than the cell dimensions, because the major contribution to the anharmonic interaction comes from the highest harmonics of the fundamental reciprocal-lattice vectors.

Simple perturbation theory predicts that the lattice thermal conductivity should be inversely proportional to the absolute temperature. It is shown that the lattice thermal conductivity of minerals should not depart markedly from that variation, even when the average phonon mean free path is comparable to the lattice spacing.

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Theory predicts and measurements confirm that anharmonic properties such as the lattice thermal resistivity, the Grüneisen parameter, and the coefficient of thermal expansion generally decrease as a function of increasing density upon compression of solids. The Debye‐Grüneisen continuum model further predicts a discontinuous decrease of anharmonic properties during a phase transition with a density increase, in contradiction with available experimental data on alkali halides. We present results calculated from a model based on interatomic potentials. This model correctly predicts an increase in anharmonic properties for simple compounds transforming from a six‐ to an eight‐coordinated structure. These results stress the importance of interatomic spacing as well as density in determining changes in thermodynamic properties due to polymorphism. The change in crystal structure across a phase transition also affects the thermal conductivity via Brillouin zone summations over the interacting phonon modes. We have used in the calculations either the bulk sound speed, or the Debye average velocity calculated from the longitudinal and transverse velocities (in both cases, theoretically derived from the interatomic potentials). We have found that the pressure dependence of thermal conductivity determined from the bulk sound speed agrees much better with experimental data for each phase than that determined from the average velocity. Apparently, shear modes contribute less to the change of thermal conductivity with compression than has been thought.

Surface-ship and satellite derived data have been compiled in new free-air gravity anomaly, bathymetry and geoid anomaly maps of the Pacific Ocean basin and its margin. The maps are based on smoothed values of the gravity anomaly, bathymetry and geoid interpolated on to a 90 x 90 km grid.Each smoothed value was obtained by Gaussian filtering measurements along individual ship and subsatellite tracks. The resulting maps resolve features in the gravity, bathymetry and geoid with wavelengths that range from a few hundred to a few thousand kilometres. The smoothed values of bathymetry and geoid anomaly have been corrected for age. The resulting maps show the Pacific ocean basin is associated with a number of ENE-WSW-trending geoid anomaly highs with amplitudes of about k 5 m and wavelengths of about 3000 km. The most prominent of these highs correlate with the Magellan seamounts-Marshall Gilbert Islands-Magellan rise and the Hess rise-Hawaiian ridge regions. The correlation between geoid anomaly and bathymetry cannot be explained by models of static compensation, but is consistent with a model in which the geoid anomaly and bathymetry are supported by some form of dynamic compensation. We suggest that the dynamic compensation, which characterizes oceanic lithosphere older than 80 Myr, is the result of mantle convection on scales that are smaller than the lithospheric plates themselves.