Thermodynamics of mixing in diopside-jadeite, CaMgSi2O6-NaAlSi2O6, solid solution from staticlattice energy calculations

Static lattice energy calculations (SLEC), based on empirical interatomic potentials, have beenperformed for a set of 800 different structures in a 2 2 4 supercell of C2/c diopside with compositionsbetween diopside and jadeite, and with different states of order of the exchangeable Na/Ca and Mg/Al cations. Excess static energies of these structures have been cluster expanded in a basis set of 37 pair-interaction parameters. These parameters have been used to constrain Monte Carlo simulations of temperature-dependent properties in the range of 273?2,023 K and to calculate a temperature?composition phase diagram. The simulations predict the order?disorder transition in omphacite at1,150 20C in good agreement with the experimental data of Carpenter (Mineral Petrol 78:433?440, 1981). The stronger ordering of Mg/Al within the M1 site than of Ca/Na in the M2 site is attributed to the shorter M1?M1 nearest-neighbor distance, and, consequently, the stronger ordering force. The comparison of the simulated relationship between the order parameters corresponding to M1 and M2 sites with the X-ray refinement data on natural omphacites (Boffa Ballaran et al. in Am Mineral83:419?433, 1998) suggests that the cation ordering becomes kinetically ineffective at about 600C

Educational Policies Committee Minutes, March 3, 2011

Subcommittee Reports Curriculum Subcommittee Academic Standards Subcommittee General Education Subcommitte

Electron-phonon interactions in poly(para-phenylene) oligomers

The influence of molecular vibrations on the low-lying electronic levels of short oligomers of poly(para-phenylene) is studied. Within an interacting molecular orbital basis, the complete electron-phonon Hamiltonian is diagonalized numerically. Energy shifts and equilibrium phonon displacements are calculated for the totally symmetric vibrational modes. For the 1 1A+g - 1 1B-u transition, Huang-Rhys and Franck-Condon factors, as well as the change of equilibrium geometry, are computed. The importance of vibrations with a frequency of about 0.2 eV is confirmed. The intrinsic Stokes shift is found to be zero, in agreement with experimental data. © 1999 American Institute of Physics

1(1)B(u)(-)2 (1)A(g)(+) crossover in conjugated polymers: The phase diagram of the molecular-orbital model

Using the molecular-orbital model of conjugated polymers, a simple criterion for the relative ordering of 1 1Bu- and 21Ag+ states is provided. When the repeat unit electronic correlations increase, resulting in an increase in the triplet-singlet exchange energy, the 21Ag+ state is expected to lower relative to the 11Bu- state. This result is confirmed by density-matrix renormalization-group calculations. Close to the phase boundary there are finite-size corrections resulting in a 11Bu- and 21Ag+ crossover as a function of chain length. The nature of this crossover depends on the relative size of the excitons. A one-particle singlet excitation correlation function is shown to be a suitable means for evaluating particle-hole separations. It is further shown that the charge gap is a reliable means of determining the threshold of unbound states in the single-particle excitation channel. The biexciton triplet-triplet character of the 2Ag+ states is investigated. The triplet-triplet separation is measured via a two-particle triplet-triplet excitation correlation function. The triplet-triplet gap marks the threshold of unbound triplet-triplet states. © 1999 The American Physical Society

The low energy electronic structure of poly(p-phenylene vinylene)

A two state molecular orbital model of poly(p-phenylene vinylene) (PPV) is solved using the density matrix renormalisation group method. The energies and spatial correlation functions of the low lying states are calculated. A band of tightly bound 1Bu- excitons and a band of charge-transfer 1Ag+ excitons exist below the band gap. In the limit of infinite chains, the lowest lying 1Bu- exciton is at ca. 2.6 eV, while the lowest lying 1Ag+ exciton is at ca. 2.9 eV. The band threshold is at 3.2 eV. © 1999 El1sevier Science S.A. All rights reserved

Excitonic states of poly(para-phenylene)

Using a recently developed phenomenological Hamiltonian of poly(para-phenylene) and the density matrix renormalization group approach, we investigate the transition from bound to unbound states. Energies and exciton correlation functions of the lowest excited states are calculated. The lowest 1B1u- states situated below the charge gap are found to be bound excitons. The 21Ag+ state, being unbound, represents a band threshold; the exciton binding energy is found to be 0.74 eV