Point-ion Calculations Research Articles

Electric field gradients from first-principles and point-ion calculations

Point-ion models have been extensively used to determine ``hole numbers'' at copper and oxygen sites in high-temperature superconducting cuprate compounds from measured nuclear quadrupole frequencies. The present study assesses the reliability of point-ion models to predict electric field gradients accurately and also the implicit assumption that the values can be calculated from the ``holes'' and not the total electronic structure. First-principles cluster calculations using basis sets centered on the nuclei have enabled the determination of the charge- and spin-density distribution in the ${\mathrm{CuO}}_{2}$ plane. The contributions to the electric field gradients and the magnetic hyperfine couplings are analyzed in detail. In particular they are partitioned into regions in an attempt to find a correlation with the most commonly used point-ion model, the Sternheimer equation, which depends on the two parameters R and $\ensuremath{\gamma}.$ Our most optimistic objective was to find expressions for these parameters, which would improve our understanding of them, but although estimates of the R parameter were encouraging, the method used to obtain the $\ensuremath{\gamma}$ parameter indicated that the two parameters may not be independent. The problem seems to stem from the covalently bonded nature of the ${\mathrm{CuO}}_{2}$ planes in these structures which severely questions using the Sternheimer equation for such crystals, since its derivation is heavily reliant on the application of perturbation theory to predominantly ionic structures. Furthermore, it is shown that the complementary contributions of electrons and holes in an isolated ion cannot be applied to estimates of electric field gradients at copper and oxygen nuclei in cuprates.

Cr3+ in pure and Mg-doped LiNbO3: analysis of the EPR and optical spectra

The electron paramagnetic resonance spectra of Cr3+ in LiNbO3 and heavily Mg-doped LiNbO3, have been measured and analysed according to the superposition model. The axial spectrum of Cr3+ in LiNbO3 is consistent with Nb substitution. On the other hand, the dominant isotropic spectrum found in Mg-doped LiNbO3 can be accounted for if an appropriate ( approximately=0.1 AA) relaxation of the Cr3+ along the c-axis is allowed. Moreover, a point-ion calculation shows that the axial shift of the impurity ion is also qualitatively consistent with recent observations of an enhanced pi -polarization character of the optical transitions in LiNbO3:Mg, Cr.

Extended-ion treatment of F centers in BaFCl and SrFCl

The extended-ion method has been applied to BaFCl and SrFCl in order to compute F center energies and spin-densities in these low-symmetry materials. When compared to point-ion calculations, the extended-ion method does not offer substantial improvement in computed optical transition energies. Each method consistently predicts deeper ground state energies for F-site than Cl-site F center electrons. The computed spin-density values using the extended-ion method are in much better agreement with experiment than are the values computed by the point-ion model. Several factors including the large ion-size and low symmetry of the crystal lead to the improved performance of the extended-ion method versus the point-ion method.

The calculation of dipole moments associated with defects in ionic crystals

Abstract Computer simulation methods have been used to calculate the dipole moments of first- second- and third-neighbour complexes of cation vacancies with the divalent impurity ions Mg2+, Ca2+, Sr2+, Ba2+, Mn2+, Cd2+ and Pb2+ in NaCl, KCl and KBr, and also for Zn2+, Mn2+, Cd2+, Sr2+ and Pb2+ in AgCl and AgBr. The results show, when the relaxation of the lattice ions is accounted for, that the effective dipole moment is significantly less than the value which would be given by a point-ion calculation for a perfect lattice. The decrease in dipole moment due to lattice relaxation is about 30% for the alkali halides and about 35% for the silver halides. For the nearest-neighbour and next-nearest-neighbour complexes a small decrease in the dipole moment is found as the radius of the impurity ion increases.

Electron-nuclear double resonance of theF+center inα-alumina

Electron paramagnetic resonance measurements of fast-neutron-irradiated $\ensuremath{\alpha}$-alumina show an intense 13-line spectrum which has been previously interpreted by La, Bartram, and Cox (LBC) as due to the ${F}^{+}$-center defect. Electron-nuclear double resonance (ENDOR) measurements on this center reveal superhyperfine (shf) interactions with neighboring A1 nuclei out to the sixth shell which support this ${F}^{+}$-center model. The original point-ion calculation of the shf constants performed by LBC is extended to include these more distant shells for comparison with the ENDOR measurements.

Optical properties of theF+center in crystallineAl2O3

Ultraviolet optical absorption, emission, and excitation spectra are presented for 14-MeV neutron-irradiated high-purity crystalline ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$. Low-temperature polarized excitation spectra for the 3.8-eV luminescence correlated well with polarized absorption at 4.8 eV (both polarizations) and 5.4 eV ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$). These optical properties compare favorably with those predicted using wave functions from an earlier pointion calculation for the ${\mathrm{F}}^{+}$ center by La, Bartram, and Cox. The 4.8- and 5.4-eV absorption bands are assigned to the $1A\ensuremath{\rightarrow}1B$ and $1A\ensuremath{\rightarrow}2A$ transitions, respectively, of the ${F}^{+}$ center and the 3.8-eV luminescence is assigned to the $1B\ensuremath{\rightarrow}1A$ transition. The $1A\ensuremath{\rightarrow}2B$ transition could not be conclusively identified, but preliminary evidence suggests it occurs near 6.3 eV. Similar absorption and emission bands are observed following energetic-proton and ${\mathrm{Al}}^{+}$ bombardment. Other uv optical properties are presented, including the quantum efficiency, lifetime, and temperature dependence of the emission.

STUDY OF F CENTRES IN QUADRATIC AND ORTHOROMBIC CRYSTALS

We present point-ion calculations of the electronic structure of F centres in BaClF, SrClF and BaC12. The relative positions of the singlet and doublet absorption bands of the F centres at Fand C1sites have been determined in BaClF and SrCIF. In BaC12, calculations of energy levels suggest the existence of only the F centres which are surrounded with four Ba++ ions.

A theoretical study of F centres in BaClF and SrClF

We present point-ion calculations of the electronic structure of F centres in BaClF and SrClF. The relative positions of the singlet and doublet absorption bands of the F centres at F − and Cl − sites suggest a new assignment of the bands to the F centre sites. The F(F −) has the singlet below the doublet, the F(Cl −) the reverse order. Comparison of calculated spin resonance parameters with experiment supports this suggestion.

F and perturbed F(F*) centres in strontium chloride

Point-ion and ion-size calculations on F centres and F* centres (F centres perturbed by an alkaline impurity) in SrCl2 are described. The point-ion calculation for the F centre gives a transition energy of 2.11 eV (experiment 2.13 eV) and a hyperfine interaction with the hearest 35Cl nuclei of 45.7 MHz (experiment 23.8 MHz). Ion-size calculations lead to an improved value for the hyperfine interaction. A model of the F* centre with an interstitial alkali ion in a second-neighbour position and associated distortions explains the observed optical absorption spectra.

The F centre in potassium magnesium fluoride

Calculations of the electronic structure of the F centre in KMgF3 are reported and their results compared with experiment. The hyperfine interaction of the ground state with the nearest F- ion is predicted to be 70 G, in good agreement with the experimental result of 60 G. The energy for optical absorption to the Eu excited state is given by a point-ion calculation as 4.4 eV, compared with the observed 4.6 eV. The predicted spin-orbit splitting of the excited state is 57 cm-1, close to the experimental value of 60 cm-1.

The F centre in magnesium fluoride

Point-ion calculations with ion-size corrections of the electronic structure of the F centre in MgF2 predict a transition energy close to the experimental value of 4.8 eV. The hyperfine interactions with the first six shells of fluoride ions are well represented by the variational wavefunction orthogonalized to orthonormal core orbitals.

The F+ center in reactor-irradiated aluminum oxide

A point-ion calculation has been performed for the F + center in α-Al 2O 3 (one electron in an O 2− vacancy). Optical transitions are predicted at 2·26, 3·39 and 5·15 eV. Contact hyperfine interactions with the two nearest pairs of Al 3+ ions are calculated to be 151 and 39 G. Single crystals of α-Al 2O 3 were reactor-irradiated up to doses of 10 20 fast neutrons per cm 2, and studied by electron spin resonance (ESR). A broad ESR spectrum with 13 resolved components at g=2·0029±0·0005 was interpreted as the interaction of an unpaired electron with two pairs of Al 3+ nuclei with hyperfine constants of 49·2 and 13·5 G. These values are in the same ratio as the values calculated for the F + center, to which this ESR spectrum is attributed. The discrepancy of a factor of three is typical of point-ion calculations. The optical absorption spectrum for heavily-irradiated samples is not available for comparison with calculated transition energies.

Wave Functions for theFCenter in Sodium Azide

Wave functions have been calculated for the $F$ center in sodium azide (Na${\mathrm{N}}_{3}$) in both the high-temperature (rhombohedral) and low-temperature (monoclinic) phases, by the point-ion method. The point symmetry at the anion site is ${D}_{3d}$ in the rhombohedral phase and ${C}_{2h}$ in the monoclinic phase. A predicted ${A}_{1}^{+}\ensuremath{\rightarrow}{E}^{\ensuremath{-}}$ optical transition at 2.06 eV in ${D}_{3d}$ symmetry corresponds to two transitions, ${A}^{+}\ensuremath{\rightarrow}{A}^{\ensuremath{-}}$ at 1.82 eV and ${A}^{+}\ensuremath{\rightarrow}{B}^{\ensuremath{-}}$ at 1.96 eV, in ${C}_{2h}$ symmetry. The latter transitions are too close to resolve, and correlate well with the observed $F$ band at 1.70 eV. An ${A}_{1}^{+}\ensuremath{\rightarrow}{A}_{2}^{\ensuremath{-}}$ infrared transition at 0.82 eV in ${D}_{3d}$ symmetry, which corresponds to an ${A}^{+}\ensuremath{\rightarrow}{B}^{\ensuremath{-}}$ transition at 0.94 eV in ${C}_{2h}$ symmetry, is polarized parallel to the hexagonal $c$ axis, and could not be observed with the crystal orientations used in prior measurements. The calculated isotropic hyperfine interactions are larger by a factor of three than those inferred from ESR spectra, a common defect of point-ion calculations. However, it is shown that, as a consequence of wave-function anisotropy, the hyperfine constants remain nearly equal in spite of monoclinic distortion, thus explaining the resolved 19-line hyperfine pattern even in the monoclinic phase.

Theory of F centres in alkaline earth fluorides

The point symmetry of the anion site in alkaline earth fluorides is T3d and the F centre (an electron in an anion vacancy) in these crystals lacks inversion symmetry. Point ion calculations have been performed for the F centre in alkaline earth fluorides with trial functions of sufficient flexibility to incorporate the anisotropy of the potential. The predicted strong admixture of s and f orbitals in the ground Gamma 1 state yields calculated fluorine hyperfine interactions in substantial agreement with results of Endor measurements. An even stronger admixture of p and d orbitals in the first excited state leads to a linear Stark effect and the magnitude of this effect has been calculated for the F band. Experimental investigation of the Stark effect of the F band in SrF2 provides an upper bound to the linear Stark splitting which is consistent with the predicted value. The quadratic Stark effect is discussed.

Absorption in the vacuum ultraviolet of alkaline earth fluorides containing hydrogen

The measured peak positions of electronic absorption bands of substitutional H- ions in alkaline earth fluorides are compared with the results of a point-ion calculation.

Hyperfine interactions of F centres in alkaline earth fluorides

The hyperfine interactions of the F centre electron (an electron trapped at an anion vacancy) with the four nearest fluorine shells have been measured by the endor method in CaF 2 , SrF 2 and BaF 2 . The third shell fluorines are divided into two separate groups, labelled 3 a and 3 b , which are characterized by the presence and absence of a cation between the F centre and the fluorine. The hyperfine interaction with 3 a fluorines shows the unusual feature of increasing form CaF 2 to BaF 2 ; all other shells show a decrease. In the case of the F centre with the magnetic Ba nuclei in the nearest Ba shell has also been measured by the endor method. The hyperfine constants of the F centre in CaF 2 , SrF 2 and BaF 2 have been calculated and are compared with experiment. The theoretical wavefunctions used are the sum of a spherically symmetric part and anisotropic parts. The wavefunctions are orthogonalized to the other occupied orbitals in the crystal. The isotropic parts are taken from Bennett & Lidiard's point-ion calculation and give reasonable agreement with experiment. The anisotropic terms are needed because the F centre has only tetrahedral symmetry. The admixture of these terms is calculated by perturbation theory using the point ion model and anisotropic function from a continuum calculation. It is possible to get reasonable agreement with the anisotropy in the hyperfine constants found experimentally. The discrepancies are analysed as a preliminary to more sophisticated colour centre calculations.