The crystals doped with Ce³⁺ are utilized as various optical materials such as solid-state lasers, scintillators, and phosphors. Since the 4f-5d transition energy of Ce³⁺ in crystals strongly depends on the coordination environment, it is important to understand the relationship between the energy levels and the coordination environment for theoretical design of novel optical materials. For this purpose, garnet solid solutions are useful as host crystals since the physical properties can be modified by forming variety of solid-solutions through cation substitution. For example it is known that the 4f-5d transition energy of Ce³⁺ in Y(Al_1-xGa_x)₅O₁₂ increases monotonically as x increases [1].

In this work, in order to investigate the relationship between the 4f-5d transition energy and the coordination environment of Ce³⁺ in Y(Al_1-xGa_x)₅O₁₂, first-principles calculations were performed using the relativistic DV-Xα molecular orbital method [2]. At first YO₈ clusters with D₂ symmetry were constructed based on the crystal structure of Y(Al_1-xGa_x)₅O₁₂ [3,4]. Then Ce was substituted for Y and the Ce-O bond lengths were adjusted based on the Shannon’s crystal radii [5] so as to consider the lattice relaxation effect [6]. In order to produce the effective Madelung potential, point charges were located at the atomic sites outside the cluster. As the exchange-correlation potential, the VWN potential [7] with the relativistic correction [8] was adopted. The 4f-5d transition energy was calculated using the Slater’s transition state method [9].

The calculated results showed that the variations of the average energy and the crystal field splitting of 5d levels of Ce³⁺ depending on x can be understood by the variations of the bond lengths, they are not monotonic. Although the 4f-5d transition energy is basically determined by these factors, interestingly the resultant theoretical 4f-5d transition energy showed monotonic variation. As a result the experimentally observed increasing tendency of the 4f-5d transition energy for increasing x was well reproduced.

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[3] A. Nakatsuka, A. Yoshiasa, and S. Takeno, Acta Crystallogr., B51, 737 (1995).

[4] A. Nakatsuka, A. Yoshiasa, and T. Yamanaka, Acta Crystallogr., B55, 266 (1999).

[5] R.D. Shannon, Acta Crystallogr., A32, 751 (1976).

[6] S. Watanabe, T. Ishii, K. Fujimura, and K. Ogasawara, J. Solid State Chem., 179, 2438 (2006).

[7] S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980).

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[9] J. C. Slater, Quantum Theory of Molecules and Solids (McGraw-Hill, New York, 1974), Vol. 4.