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Title: The role of lattice vibrations in the zero field splitting of Gd³⁺ in an ethylsulphate host lattice
Author: Kelly, Martin
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1993
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The crystal field theory of S-state ions is characterized by the need to use high order perturbation theory in order to gat non-zero contributions to the zero field splitting. As a consequence, the splitting is usually a delicate balance between several competing mechanisms. A typical example is the splitting of the *S?/2 ground state of Gd3* ions in lanthanum ethylsulphate (GdES), and over the years a great deal of effort has been expanded in trying to get agreement with experimental data. The result of these efforts is a theoretical splitting which is around 20% greater than the experimental splittings. In addition, they suggest that the splitting is Independent of temperature, yet it is well known that the splitting exhibits a particularly interesting temperature dependence. The reason for this is that the existing mechanisms are calculated on the assumption that the lattice is stationary, and of course this is unrealistic, even at absolute zero. In this thesis, our intention is to investigate the effect of inserting lattice vibrations into the GdES crystal lattice. In particular, we examine how much one of the most important inter-site mechanisms is changed under these circumstances. To do this we use a many-electron theory, due to Stevens, which allows affective crystal field operators (and in particular spin correlated crystal field operators) to be calculated in a simple way. Although this theory was originally developed for use in a stationary lattice, the modifications required to incorporate lattice vibrations are comparatively straightforward. The method has the drawback that it leads to a complicated formalism, and so we are forced to make certain approximations in order to make the problem tractable. Within the framework of these approximations we find that the introduction of lattice vibrations causes a negative temperature dependent contribution to be added to the inter-site mechanism. The new contribution is of the right sign and order of magnitude to improve agreement with experiment, but the actual temperature dependence is Incorrect in the low temperature limit. We also examine soma of the other mechanisms which could lead to an improvement in the theoretical temperature dependence, in particular those related to the thermal expansion of the lattice.
Supervisor: Not available Sponsor: Science and Engineering Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QC Physics ; QD Chemistry