Oct 30, 2010 - Springer Science+Business Media B.V. 2010. Abstract We ... properties of VOx-NTs may be controlled by electron or hole doping [1]. VOx-.
Hyperfine Interact (2010) 198:31–34 DOI 10.1007/s10751-010-0187-2
51 V
nuclear magnetic resonance study of vanadium oxide nanotubes
A. M. Panich · Ch. E. Lee
Published online: 30 October 2010 © Springer Science+Business Media B.V. 2010
Abstract We report on a 51 V NMR study of vanadium oxide - decylamine nanotubes. 51 V NMR spectra show three lines resulting from a diamagnetic V5+ and two paramagnetic V4+ ions, respectively.The V4+ /V5+ ratio is estimated to be ∼0.47. 51 V spin-lattice relaxation comprises both magnetic and quadrupolar contributions. Keywords Nanotube · Vanadium oxide · NMR Among tubular nanostructures, vanadium oxide nanotubes (VOx -NTs) are of special interest since they are exceptionally rich in both structural diversity and electronic properties. Their structure is composed of scrolled V7 O16 layers, between which alkylamine molecules (acting as the structure-directing agents) are embedded. The properties of VOx -NTs may be controlled by electron or hole doping [1]. VOx NTs with 1.0< x 1/2, such as 51 V (I = 7/2), the energy level spacings in magnetic field are rendered unequal by quadrupole interaction. The nuclear spin-lattice relaxation process involves the transitions with m = 1 and m = 2, and, in general, is described by 2I relaxation times [4], yielding a multi-exponential expression for the magnetization recovery M (t) =1− Ai exp (−λi W t) M∞ i
(1)
where M(t) is the nuclear magnetization at the recovery time t, M∞ is the magnetization after long recovery time, Ai are the pre-exponential factors and λi are the eigenvalues of the relaxation rate equations. Both Ai and λi are determined by the quantities W1 and W2 which are a measure of the transition probabilities for m = 1 and m = 2, respectively. Analytical expressions were derived for the case W1 = W2 only, separately for the cases of pure magnetic and pure quadrupole mechanisms of the spin-lattice relaxation. In both these cases, the magnetization recovery for the spin I = 7/2 is described by a superposition of four exponents, with Ai = 1.527, 0.903, 0.335 and 0.041 and λi = 0.476, 1.333, 2.381 and 3.81 for the quadrupole mechanism of the spin-lattice relaxation [5] and Ai = 0.012, 0.068, 0.206 and 0.714, and λi = 2,
nuclear magnetic resonance study of vanadium oxide nanotubes
Fig. 2 Temperature dependence of 51 V spin-lattice relaxation rates R1 and times T1 (inset) in vanadium oxide nanotubes for two spectral components
33 12
450
low frequency line 51
400
10
V in VOxNTs
T1, ms
51 V
R1, ms -1
350
high frequency line
300
8 6 high frequency line 4 2
250
50
low frequency line
100 150 200 250 300
T, K
200 150 100 4
6
8
1000/T, K
10
12
14
-1
12, 30 and 56 for the magnetic relaxation mechanism [6, 7]. Our attempt to fit the experimental magnetization recovery using the four-exponential curves with the aforementioned values of Ai and λi did not result in a good fit. The main reason is that in the case in question both quadrupole and magnetic mechanisms of the spinlattice relaxation are present, and likely W1 = W2 . Therefore one can expect that the magnetization recovery is described by a superposition of seven exponentials, for which the pre-exponential factors Ai and the eigenvalues λi are unknown, and the estimation of the individual values of T1 ’s is hardly possible. In such a case, a very good and widely used in physics model is a stretched-exponential function α t M (t) = 1 − exp − M∞ T1
(2)
with the parameter α varying in the range of 0 < α < 1 [8]. Indeed, we found that Eq. 2 yields a good fit of the M(t) recovery. The temperature dependence of the spin-lattice relaxation rate R1 is plotted in Fig. 2. The quadrupolar contribution to the spin-lattice relaxation in the case in question results from modulation of the quadrupolar interaction by lattice vibrations and mainly comes from the two-phonon Raman process, yielding temperature dependence of the spin-lattice relaxation rate R1Q ∼ T 7 and R1Q ∼ T 2 a − Tb2 (here a>>b) for low (T< TD ) and high (T> TD ) temperatures, respectively [9] (here TD is the Debye temperature). Therefore a decrease in R1 on cooling, observed in our experiment in the low temperature range (Fig. 2), is attributed to the quadrupolar contribution to the relaxation. Magnetic contribution to the relaxation rate isRm 1 ∼ τe , where ω is the nuclear magnetic resonance frequency and τ is the electron 0 e 1+ω2 τ 2 0 e
correlation time. Since τe varies in the range of 10−9 –10−12 s, usually ω0 τe
