Cluster Models of Doped Ionic Crystal Scintillators. Quantum Calculations
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ABSTRACT We have performed quantum electronic ab initio calculations of clusters of alkali halides, both pure and doped. In order to estimate the pure crystal energy gap and the dopant excitation, we have considered a central cation and four shells of ions surrounding it. We have studied KC1, Nal, NaCl and KI, both pure and with a Tl+ ion replacing the central alkali cation. Encouraging results are presented for absorption and emission.
INTRODUCTION The electronic properties of ground and excited states of doped crystals allow us to study the spectroscopy of luminescent materials [1]. The most direct way of calculating these states is to model the pure crystal as a molecular cluster, substitute one ion for the activator, and recalculate the ground and excited states of the modified cluster. We thus get information on the crystal's energy gap and the position of the impurity level, as well as on the Stokes shift. According to Franck-Condon principle, absorption is calculated from the electronic ground state minimum, while emission starts at the electronic excited state minimum. The first part of the calculation involves modeling the pure crystal as a cluster [2-6], in order to estimate the energy gap between the filled valence band and the empty conduction band. We have used ab initio programs at the SCF level, with an additional singles-only configuration interaction (CIS) to calculate the energy difference between the ground state and the excited state [7]. The nuclear configuration in these computations was the one obtained using the experimental crystal lattice constants [8]. All the crystals in the present paper refer to alkali halides with fcc structure. We have also used faster semiempirical programs such as extended Hlickel with CIS [9]. The second part of the calculation models the doped crystal as a cluster [5, 6] with a Tl+ ion at the center, replacing the corresponding alkali halide cation. Both for the electronic ground and first excited states, we vary the nuclear configurations in the cluster, thus finding the region around the minima for the two states. The energy minimum search is constrained to radial variations around the activator ion, i.e. all the ions in a shell are displaced simultaneously. For the cluster models we have studied, we have found it necessary to move the first, second, and (for most cases) third shells. In this doped case, ASCF calculations were performed to estimate the absorption and emission energy difference. This implies that, instead of one CIS, we do two SCF calculations per energy surface minimum. For absorption we consider the difference between the SCF ground state minimum energy and 373 Mat. Res. SOc. Symp. Proc. Vol. 348. 01994 Materials Research Society
the SCF excited state energy corresponding to the same nuclear geometry. Emission occurs from the relaxed configuration corresponding to the minimum of the excited state energy surface. Our estimate of the Stokes energy shift corresponds, of course, to the difference between these two energy differences. In the sec
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