Theory of 47,49Ti and 17O Nuclear Quadrupole Interactions in TiO2

Sudha Srinivasa, N. Sahoob,c and T. P. Dasc *

a  Department of Physics, Central Michigan University, Mount Pleasant, MI, 48859, USA
b  Department of Radiation Oncology, The Albany Medical College, Albany, NY, 12208, USA
c  Department of Physics, State University of New York at Albany, Albany, NY, 12222, USA

*  Corresponding Author: FAX 1-(518)-442-5260

The Hartree-Fock Cluster procedure [1] has been used extensively by our research group at State University of New York at Albany for successful interpretation of nuclear quadrupole interactions in a number of ionic crystal systems [2] and high-Tc materials [3]. A crucial test of any theoretical procedure used for studying nuclear quadrupole interactions in ionic crystals is provided by the rare availability of the sign of the quadrupole coupling constant by experiment and the capability of the procedure to explain the sign. Such is the case for 17O in TiO2, measured by Nuclear Magnetic Resonance using Dynamic Nuclear Polarization Techniques [4].
The body-centered tetragonal rutile lattice structure and crystal parameters [5] have been used for TiO2. For our investigation of the 47,49Ti and 17O nuclear quadrupole interactions, we have used clusters centered respectively on Ti and O namely (TiO6)-8 and (OTi3)+10. The influence of the ions outside of the cluster is included by incorporating the potentials due to these ions, approximated as point charges in the potential experienced by the electrons in the cluster, about 700 point charges being used in the present investigation. The Gaussian basis sets used in our calculation are p-function augmented [6] (63311/5311/41) basis sets [7] for Ti4+ and a Watson sphere [8] optimized (8411/411) basis [9] for O2-. These basis functions were chosen carefully to incorporate polarization effects for Ti4+ ion and to incorporate the stability effects of the lattice in the basis sets for the highly diffuse O2- ions. The quadrupole moment used for 47Ti (I=7/2) and 49Ti (I=9/2) were 0.29 barns [10] and 0.24 barns [10] respectively and for 17Ti (I=5/2) the value Q=-0.02578 barns [11].

Table 1. Results for Nuclear Quadrupole Interaction Parameters for 47,49Ti and 17O in TiO2 from Present Work and Experiment. (a.   Ref. 4 and b.    Ref. 12)
 
Nucleus
 
Theory (This work)
   
Experiment
 
 
e2qQ (MHz)
h
Principal axis (Z)
e2qQ (MHz)
h
Principal axis (Z)
47Ti
-20.6
0.23
c axis
|16.14± 0.15|a

|16.8± 0.2|b

0.303± 0.008a

0.20b

c axisa

c axisb

47Ti
-17.1
0.23
c axis
|13.09± 0.11|a

|13.09± 0.2|b

0.303± 0.008a

0.20b

c axisa

c axisb

17O
+3.3
0.72
(011)
+1.497± 0.004a
0.868± 0.008 a
(011)

Our calculated values of the e2qQ and h for 47,49Ti and 17O are presented in Table 1 and compared with experiment [4,12]. The agreement with experiment for 47Ti and 49Ti is satisfactory for the asymmetry parameter and the principal axis direction for q and the magnitudes of e2qQ. The latter are within 20 percent of the experimental value. The signs of the experimental e2qQ are not available. For 17O, h is in reasonable agreement with experiment and the direction of the Z-principal axis for q also agrees with experiment. What is most important is the agreement between the available sign of e2qQ and our theoretical result. The magnitude of e2qQ is about twice as large as experiment. Possible sources for bridging this difference will be discussed, including the most likely source discussed in our paper on 17O nuclear quadrupole interaction in La2CuO4 at this Conference, namely the influence of the dipole moments [13] on the O2- ions outside of the cluster used for our electronic structure investigation. Comparison will be made with earlier band structure investigations using the LAPW Procedure [14].

[1] D. W. Michell et al., Phys, Rev. B48, 16449 (1993).
[2] M. Steiner et al., Phys. Rev. B50, 13555 (1994) and references therein.
[3] T. P. Das in "Electronic Properties of Solids using Cluster Methods" Ed. T. A. Kaplan and S. D. Mahanti, Plenum Press, New York (1995).
[4] Ch. Gabathuler, E. E. Hundt and E. Brun, "Magnetic Resonance and Related Phenomena, ed. V. Hovi, North Holland (1973).
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[7] D. Hood, R. M. Pitzer and H. F. Schaefer III, J. Chem. Phys. 71, 713 (1979).
[8] P. C. Kelires, K. C. Mishra and T. P. Das, Hyperfine Interactions 34, 289 (1987).
[9] R. Poirier, R. Kari and I. G. Csizmadia, "Hansbook of Gaussian Basis Sets", Elsevier (1985).
[10] P. Raghavan, "Atomic and Nuclear Data Tables" 42, 189 (1989).
[11] H. P. Schaefer III, R. A. Klemm and F. E. Harris, Phys. Rev. 181, 138 (1969).
[12] O. Kanet and H. Kolem, J. Phys. C21, 3909 (1988).
[13] R. R. Sharma and T. P. Das, J. Chem. Phys. 41, 3582 (1964).
[14] P. Blaha, D. J. Singh, P. I. Sorantin and Schwartz, Phys. Rev. B46, 1321 (1992).

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