Partition coefficients of Hf, Zr, and REE between olivine, orthopyroxene, clinopyroxene, plagioclase, garnet, amphibole, ilmenite, phlogopite, and liquid are presented. Samples consist of megacrysts in kimberlite, phenocrysts in alkaline basalts, tholeiitic basalts and andesitic to dacitic rocks, and synthetic garnet and clinopyroxene in Hawaiian tholeiites. The Hf‐Lu and Zr‐Lu elemental fractionations are as large as the Lu‐Sm or Lu‐Nd fractionation. The Hf and Zr partition coefficients between mafic phenocrysts and liquids are smaller than the Lu partition coefficients, but are similar to the Nd or Sm partition coefficients. The Hf and Zr partition coefficients between ilmenite, phlogopite, and liquid are larger than the Lu partition coefficients for these minerals and their corresponding liquids. The Hf‐Zr elemental fractionation does not occur except for extreme fractionation involving Zr‐minerals and extremely low fo2. These data have an important bearing on chronological and petrogenetic tracer studies involving the Lu‐Hf isotopic system.

We examine the interplay of surface and volume effects in systems undergoing heat flow. In particular, we compute the thermal conductivity in the Fermi-Pasta-Ulam beta model as a function of temperature and lattice size, and scaling arguments are used to provide analytic guidance. From this we show that boundary temperature jumps can be quantitatively understood, and that they play an important role in determining the dynamics of the system, relating soliton dynamics, kinetic theory, and Fourier transport.

No abstract

Abstract.We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier's law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed.

No abstract