Sudha Srinivas^a, N. Sahoo^b,c and T. P. Das^{c *}

^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-T_c 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 O^2-. 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 O^2- 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 O^2- 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).
[5] M. G. Blanchin, E. Vicario and R. A. Ploc, J. Appl. Cryt. 10, 228 (1977).
[6] S. Huzinaga, "Gaussian Basis Sets for Molecular Orbital Calculations", Elsevier (1986).
[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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