Growth morphology of zinc tris(thiourea) sulphate crystals

The growth morphology of crystals of zinc tris(thiourea) sulphate (ZTS) is investigated experimentally, and computed using the Hartman-Perdok approach. Attachment energies of the observed habit faces are calculated for determining their relative morphological importance. A computer code is developed for carrying out these calculations. A special procedure is adopted for computing the cohesive energy of a slice of the structure parallel to any rational crystallographic plane. For estimating the cohesive energies, formal charges on the experimentally determined atomic positions in the molecules of ZTS are calculated by ab initio molecular-orbital computations, with wave functions obtained by the Hartree-Fock procedure. Fairly good agreement with the observed crystal morphology is obtained for a model of growth mechanism in which ZTS is assumed to exist in solution sa szinc tris(thiourea) ions and sulphate ions.     

Fine structure in the low temperature luminescence of Zn2SiO4:Mn and Mg4Ta2O9:Mn

The luminescence of powder samples of the well-known green-emitting Zn₂SiO₄:Mn and the red-emitting Mg₄Ta₂O₉:Mn phosphor shows a considerable fine structure at 4° K in appropriately prepared samples containing a sufficiently low Mn concentration. For (Zn_1-xMn_x)₂SiO₄ (0.0005?x?0.05) two sharp lines were found which are interpreted as due to zero phonon transitions between the ⁴T₁ and ⁶A₁ levels of Mn²⁺ ions on the two crystallographically different zinc sites. The remaining structure is ascribed to vibronic sidebands. The decay times of the luminescence bands associated with the two sites differ; they are 12 and 15 ms for the high and low energy bands respectively. The experimental results of Vlam are confirmed by our data. In addition some (Zn_1-yBe_y)₂SiO₄:Mn (0.025? y ?1) samples were investigated. In Mg₄Ta₂O₉:Mn two zero phonon lines could be identified, indicating that in this material Mn²⁺ is distributed over two inequivalent Mg sites. Most of the phonon replicas were found at intervals of 15 meV. Raman scattering experiments showed that this energy corresponds to one of the lattice vibrations. The decay time of this luminescence band is 1.0 ms.     

Optimal appointment scheduling in continuous time: The lag order approximation method

We study appointment scheduling problems in continuous time. A finite number of clients are scheduled such that a function of the waiting time of clients, the idle time of the server, and the lateness of the schedule is minimized. The optimal schedule is notoriously hard to derive within reasonable computation times. Therefore, we develop the lag order approximation method, that sets the client’s optimal appointment time based on only a part of his predecessors. We show that a lag order of two, i.e., taking two predecessors into account, results in nearly optimal schedules within reasonable computation times. We illustrate our approximation method with an appointment scheduling problem in a CT-scan area.