Investigation of defects in dielectric crystals using magnetic resonance techniques

An ENDOR spectrometer has been designed and constructed which is capable of operating at 9000 Mc/s or 23,000 Mc/s. Simple 115 kc/s field modulation detection is used and the nuclear resonance power is frequency modulated. Nuclear transitions ere detected as a change in the dispersive component of the E.P.R. signal. Apart from conventional cryogenics allowing the use of temperature down to that of pumped helium a second system allows X-irradiation of the sample at similar temperatures while actually in the X or K band microwave cavity.
Detailed E.P.R. and ENDOR measurements have been made of 169Tm2+ ions and hydrogen atoms in CaF2.
Tm2+ ions on interstitial sites with eightfold cubic co-ordination are produced by X-irradiation of CaF2:Tm3+ at room temperature. The E.P.R. spectrum observed at 20°K has two lines, showing poorly resolved fluorine structure, about 30 G wide whose positions are described by
ℋ = g8H.S + AI.S
with S = 1⁄2, I = 1⁄2, g = 3.452 ± 0.003 and |A| = (368 ± 2) × 10−4 cm.−1
The ground configuration of Tm2+ is 4f13, 2F. The spin orbit coupling splits the ground term by 7⁄2 ζ into J = 7⁄2 and J = 5⁄2 with J = 7⁄2 lowest. ζ = 2513 cm.−1 in CaF2. The cubic field splits J = 7⁄2 into two doublets, Γ6, Γ7, and a quartet, Γ8, with Γ7 lowest. J = 5⁄2 is split into a doublet, Γ7′, and a quartet Γ8′. Kiss (1962) has measured directly by optical fluorescence the energies of Γ8, Γ7′ and Γ8′. Second order crystal field effects admix to the Γ7 groundstate an amplitude α = 0.0487 of the Γ7′ doublet. The g value calculated for this groundstate is 0.022 greater than the experimental value because of covalency. The values are reconciled by introducing an orbital reduction fadtor k = 0.991 ± 0.001.
The experimental hyperfine parameter is corrected for the core polarisation contribution, estimated at + 13.7 Mc/s, and for the orbital reduction factor, leading to an estimate of the hyperfine parameter of a free Tm2+ ion of 382.4 Mc/s. Comparison with Ritter's (1962) atomic beam measurements on the Tm atom indicates a value of 〈r−3〉 for Tm2+ greater by 2% then for the atom. This is consistent with Judd and Lindgren's (1961) calculations of 10.51 a.u. for Tm0 and 10.95 a.u. for Tm3+.
Thulium ENDOR measurements give a much more precise value for the hyperfine parameter of 1101.376 ± 0.004 Mc/s. An apparent nuclear g value for 169Tm is derived of 0.756 ± 0.005 (n.m.). A correction of −0.288 due to second order perturbation via the magnetic field and hyperfine interaction is calculated from Kiss' results for the positions of excited states. The resulting nuclear moment μn = −0.234 ± 0.003 n.m. is close to Ritter's atomic beam value of −0.229 ± 0.003 n.m.
Fluorine ENDOR of CaF2:Tm2+ was used to measure the hyperfine interaction with fluorine shells l, 2, 3 and 4. Only the first shell differs significantly from a classical magnetic point dipolar interaction. The first shell parameters are As 2.584 ± 0.01 Mc/s and Ap = 12.283 ± 0.01 Mc/s, both with the same sign. The classical point dipolar interaction is +9.809 Mc/s, indicating the choice of positive sign for Ap and a contribution due to bonding of 2.474 Mc/s. This is contrary to Watson and Freeman (1961) who predict a polarisation spin density et the extremity of a rare earth ion which is antiparallel to that of the 4f electrons.
The measured first shell parameters are adequate to explain the EPR line structure as a superposition of forbidden transitions in which first shell fluorine nuclei are flipped.
The thulium arid fluorine ENDOR linewidths behave as if inhomogeneously broadened and those for fluorine ENDOR agree with van Vleck's (1948) calculations for N.M.R. in CaF2.
The bonding of the Tm2+ ion to its ligands is described in terms of the molecular orbital picture. The Tm2+ ground state is expressed in terms of single f electron functions. These are augmented by combinations of ligand orbitals transforming according to the same representations of the cubic group. For Tm2+ both π and σ bonding occurs. Using the independent bonding model, the one-electron hyperfine operator is applied to that part of the molecular orbital centred on one ligand to give expressions for the isotropic and anisotropic hyperfine interactions. These are functions of the π, σ and s bonding parameters: fπ, fσ, fs and (fσfπ)1⁄2. The experimental results do not give sufficient information to determine the bonding parameters separately.
X-irradiation at room temperature of hydrogenated CaF2 produces interstitial hydrogen atoms (Hall and Schumacher 1962). X-irradiation below 100°K is found to produce hydrogen atoms on substitutional fluorine sites whose E.P.R. spectrum shows a resolved interaction with the six nearest fluorine nuclei. This is described by
ℋF = Σn=16 [S . AnF . InF − gF8nH.InF]
where AnF is axial. The solution of this Hamiltonian and derivation of the E.P.R. parameters are discussed.
At 145°K the hydrogen atoms move irreversibly to interstitial sites with perfect eightfold co-ordination.
Similar results are found for SrF2:H but BaF2:H gives rise only to a very weak substitutional spectrum.
All the hydrogen spectra in alkaline earth fluorides have g values greater than that of free hydrogen and it is suggested that this is due to charge transfer being important. The proton hyperfine interactions are all larger by up to 40 Mc/S than that for free hydrogen (1420 Mc/s) but this is only about 10% of the increase calculated if the fluorine hyperfine interaction is assigned only to overlap effects. Charge transfer is again suggested to account for the small size of the increases.
Fluorine ENDOR measurements on substitutional hydrogen in CaF2 give spectra in principal crystal directions which cannot readily be interpreted. Angular plots were made in (110) and (111) planes to enable the ENDOR lines to be identified. It emerges that the third and fourth shell fluorines have values of Ap equal to twice the classical point dipolar values and values of As of 1.371 ± 0.01 Mc/s and 0.806 ± 0.02 Mc/s respectively. This is explained as a transferred interaction via first shell fluorine 2pσ orbitals for the fourth shell and via nearest neighbour Ca2+ ions for the third shell. The second shell fluorines have Ap equal to 0.09 Mc/s less than the classical point dipolar value end As equals −0.020 ± 0.01 Mc/s. Overlap with excited π states on the first shell fluorines, admixed by spin-orbit coupling, is proposed to account for the effective negative bonding contribution.
ENDOR lines due to first shell fluorines confirm the E.P.R. parameters. Small shifts due to the proton and splitting due to indirect nuclear-nuclear interaction are observed and agree well with calculation.