Electronic structure of defects in crystals

We have made a study of some properties of the F-centre in the alkaline earth fluorides CaF2, SrF2 and BaF2, and in the alkaline earth oxides CaO, SrO and BaO. Investigation by Zeeman spectroscopy of the electronic states which give rise to the broad F-band is not practicable, and so we have used the technique of optical Faraday rotation. We have been able to locate the F-band in these materials, and to measure the spin-orbit splitting in the unrelaxed 2p-like excited state of the F-centre in each case.
F-centres have been prepared in alkaline earth fluorides by additive coloration. In our experience, the production of F-centres in this way is always accompanied by the formation of aggregate trapped-electron centres. In the samples used, the F-band typically constitutes 60 per cent of the overlying band in SrF2 and BaF2, and rather less of the α-band in CaF2. The relative concentration of F-centres is sensitive to details of the coloration technique and to subsequent crystal handling.
The esr (electron spin resonance) spectrum of the F-centre in SrF2 is reported. It consists of a seven-line isotropic hyperfine structure characteristic of interaction with six equivalent fluorines. The parameters of the esr spectrum are
g = 1.986 &pm; 0.001 , A = 120 &pm; 6 Kc/s
Values for the F-centre spin-orbit splitting have been obtained from Faraday rotation patterns by the method of moments analysis developed by Henry, Schnatterly and Slichter (1965). For this purpose, an accurate knowledge of the F-band optical density is required. Due to the absorption of F-aggregate centres this cannot be obtained in additively coloured crystals. It is found that trapped electron centres are produced by X-irradiation at 77°K of undoped SrF2 and BaF2 crystals, and of hydrogen doped CaF2, SrF2 and BaF2 crystals, and the spin-orbit splitting is determined for these centres. Paramagnetic resonance experiments show (Bessent, Hayes, Hodby and Smith, 1968} that the trapped electron centres are 'perturbed F-centres' closely related to the normal F-centers found in additively coloured crystals.
In SrF2 and BaF2, 77°K X-irradiation of undoped and hydrogen doped crystals gives similar results. Perturbed F-centres are seen optically, by esr, and by Faraday rotation in both cases; the main effect of hydrogen doping is to increase the F-centre production rate by a factor of three. The case of CaF2 less straightforward. F-centres cannot be produced in undoped crystals in sufficient numbers for detection by esr or Faraday rotation, and X-irradiation of hydrogen-doped crystals produces strongly perturbed F-centres, whose F-band is severely broadened and shifted as compared with normal F-centres. The resistance to coloration by X-rays of undoped CaF2 is attributed to the slow formation of vacancy-interstitial anion pairs by X-irradiation.
Results of thermal annealing experiments are presented; it is found, that no irradiation-produced F-centres are stable at room temperature.
We have carried out a theoretical calculation of the spin-orbit splitting of the unrelaxed first excited state of the F-centre. The calculation is along the lines of that of Smith (1965) for the F-centre in NaCl, but is algebraically more involved since the F-centre in alkaline earth fluorides is at a point of tetrahedral (Td) symmetry in the crystal. An envelope F-centre wavefunction developed by Bennett and Lidiard (1965) on a point-ion model is used. The main contribution to th F-centre spin-orbit splitting is found to come from the overlap of the F-centre wavefunction to ions of the nearest neighbour cation shell.
For comparison with theory, it is assumed that the spin-orbit splitting for the irradiation-induced trapped electron centres is not appreciably different from that for normal F-centres. We obtain good agreement between theory and experiment.
F-centres have been introduced into Ca0 arid Sr0 by neutron irradiation, and into Ba0 by proton irradiation. We have located the F-band peak in these crystals by the Faraday rotation technique. By making careful measurements on samples of optical density less than two, and using the method of moments analysis, we have again derived values of the spin-orbit splitting in the unrelaxed excited state of the F-centre in these materials. We have also made a simple calculation of the splitting, similar to that for fluorides, but using an F-centre envelope wavefunction derived by Bartram, Swenberg and La (1967), with a hydrogenic form for the radial wavefunction. The theoretical and experimental values are in reasonable agreement. Within the approximations of the method the calculation provides a test of the wavefunctions used; it is concluded that Bartram's F-centre wavefunction is adequate in Ca0, but over-compact in Sr0 and Ba0.