Optical absorption of Ag− centres in KCl:: line shape calculation
Introduction
Experimental evidence for the existence of negative heavy metal ion Ag− in additively or electrolytically coloured alkali halides has been reported in the 1970s [1], [2], [3]. This ion forms anionic centres with the electronic configuration ns2 (n=5) in the ground state and an (a1g t1u) configuration in the first state. This means that the ground state is an one and there are five excited states, namely .
The properties of isoelectronic cationic s2-type centres are well known [4], [5], [6]. These centres show three or four absorption bands in alkali halides crystals, called A, B, C and D in the order of increasing energy, and mainly two emission bands, A and C. The absorption spectrum of Ag− centres agrees with general optical features of Tl+-type ions in alkali halides.
At first, only one Ag− absorption band, namely the C band, was found [1], [2] but measurements of excitation spectrum of the A emission of KCl : Ag− [3] show two very weak bands at 401.5 and 381.5 nm, which were interpreted as A and B bands. Later, Kleemannn [7] discovered the A and B bands in heavily doped crystals, in agreement with the peak positions found in the excitation spectrum. A distinct doublet structure appeared in the A band, in contrast to the symmetrical shape of the excitation band.
Kojima et al. [3] estimated the coupling constants from moments of the A and C absorption bands and from data of emission, without taking into account the spin–orbit interaction. The last concentration was small, in order to obtain the intensity of the C absorption band less than 20 cm−1. Their model, based on the Toyozawa and Inoue [8] and Cho's calculation [9] omitted the coupling of the state with other states and treated the vibronic interactions with the states by perturbation methods.
Later, Nasu and Kojima [10] used the independent ordering approximation in performing a quantum mechanical calculation of the line shape for A1g→T1g transition. They showed that for large coupling constants it is possible to neglect the time dependence of the phonon correlation function and the semiclassical adiabatic approximation is recovered.
Kamishina et al. [11] reformulated the problem of calculating the line shape for optical absorption. They diagonalized directly the complete Hamiltonian matrix. Integration over the interaction mode coordinates was carried out numerically using Gaussian quadrature formulae. The method gave excellent agreement between theoretical and experimental data on absorption of KCl : Ga+ [12], KBr : Sn2+ [13] and KBr : Pb2+ [14].
In this paper we present experimental data on the absorption bands A–C in KCl : Ag− crystals and we report the first theoretical calculation of the line shape of the absorption spectra at various temperature. We compare our calculated line shapes at various temperatures with the experimental results on absorption spectra of Ag− ions in KCl crystals. We prove that the theoretical method developed to explain the optical absorption of ns2 cations gives excellent results also for the ns2-type anions.
Section snippets
Experimental procedure
Single crystals of KCl : Ag+ were grown from reagent grade powders Merck by the Kyropoulos method. The melt was doped with 10−2 and 10−3 mol% of AgCl. The last concentration was small in order to keep the intense C band absorption in the measurable range. The conversion from Ag+ to Ag− centres was performed by electrolytical colouring at 450°C and 250–450 V/cm, as described in Ref. [15]. The formation of the silver colloids was avoided by rapid quenching of the samples.
The optical absorption
Results and discussion
The absorption spectra for the C band at various temperatures are plotted in Fig. 1 and for the A and B bands in Fig. 2a (80 K), Fig. 2b (160 K) and c (300 K). The A and B bands of Ag− centres are found in thick sample, containing ∼1017 Ag− ions/cm3. The different ordinate scales in Fig. 1, Fig. 2 elucidates the small oscillator strength of the A and B bands. The peak positions of the A, B and C bands are in agreement with those previously reported [3], [7]. The distinct doublet structure of the A
Line shape calculation
The matrix representative of the Hamiltonian for the (a1g t1u) configuration of the s2 ion in Oh symmetry is a 12×12 matrix which includes the spin-orbit coupling and the linear electron–lattice interaction. The basis functions are the wave functions and . The diagonalization of this matrix gives the eigenvalues and the eigenvectors.
The linear term in the electron–lattice interaction is
The coupling constants, which described the
Conclusions
The method developed for the line shape calculation of Tl+-like ions in alkali halides [11] has been applied for the first time to Ag− ions in KCl crystals. Optical absorption line shapes at different temperatures are calculated and compared with those obtained experimentally. The coupling constant sets that determine the absorption A, B and C bands are obtained from the fitting of the calculated lineshapes with those measured. The calculated line shapes reproduce the main features of the
Acknowledgements
We would like to express our sincere thanks to Professor Dr. V. Topa for his encouragement and helpful support of this work.
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