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Proton spin diffusion in a nanodiamond
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 165301 (http://iopscience.iop.org/0953-8984/26/16/165301) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 163.118.172.206 This content was downloaded on 20/08/2014 at 16:44
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 165301 (5pp)
doi:10.1088/0953-8984/26/16/165301
Proton spin diffusion in a nanodiamond A M Panich Department of Physics, Ben-Gurion University of the Negev, PO Box 653, Be’er Sheva 8410501, Israel E-mail: [email protected] Received 8 August 2013, revised 17 September 2013 Accepted for publication 6 January 2014 Published 1 April 2014 Abstract
We report on a proton magnetic resonance study of a powder nanodiamond sample. We show that 1H spin–lattice relaxation in this compound is mainly driven by the interaction of nuclear spins with unpaired electron spins of paramagnetic defects. We measured the spin–lattice relaxation time T1 by means of a saturation comb pulse sequence followed by dipolar dephasing, and plotted T1 as a function of the dephasing time τd in different external magnetic fields. The received T1(τd) dependence provides a striking manifestation of the spin diffusion-assisted relaxation regime. The obtained experimental data allow us to estimate the spin diffusion coefficient and spin diffusion barrier radius. Keywords: spin diffusion, NMR, nanodiamond (Some figures may appear in colour only in the online journal)
1. Introduction
experimentally, such an effect in nanomaterials (in particular in nanodiamonds (NDs)) has not been studied yet. In the present paper, we report on a nuclear magnetic resonance (NMR) study of proton spin diffusion in a powder ND sample in the external magnetic fields 0.568 and 8.0196 T. ND particles with a diameter of ~4.5 nm have risen to the forefront of material research since they show great potential for a variety of applications [13–16]. It is now established [13–24] that the ND particle consists of a chemically inert and mechanically stable diamond core and a chemically active surface. The latter comprises a number of hydrocarbon and hydroxyl groups and adsorbed moisture [17–19, 21–26]. The compound is the electrical insulator. ND particles usually reveal ~ 6 × 1019 spin g-1 paramagnetic centers originating mainly from unpaired electrons of dangling bonds [17, 18, 20, 24]. They are mainly positioned closer to the surface rather than in the central part of the diamond core, and also on the surface itself [17, 18, 20, 24]. Measurements of 13C spin–lattice relaxation time show an anomalous reduction in T1 from several hours and even days in natural diamonds to hundreds of milliseconds in NDs, which is attributed to the interaction of nuclear spins with the aforementioned localized paramagnetic centers [17–24]. One can expect a similar interaction between 1H nuclei and uncoupled electrons of paramagnetic defects, which are positioned close to the ND surface and directly on the surface. In the present work, we report on the measurements of 1H spin–lattice relaxation time T1 in a dried ND sample by means of a saturation comb pulse sequence followed by dipolar dephasing.
To explain fast nuclear spin–lattice relaxation in solids, Bloembergen [1] suggested in 1949 that the spin magnetization in a rigid lattice could be spatially transferred by nuclear spin diffusion. This mechanism occurs through the mutual flips of neighboring nuclear spins due to interaction terms of Ii+I −j -type, and results in the magnetization transfer from the distant nuclear spins to the localized electron spins. Since 1949, a number of solid insulators and semiconductors have been studied to test the validity of nuclear spin–lattice relaxation mediated by spin diffusion (e.g., [2–7]). The latter is usually considered to be driven by the dipole–dipole interaction Hdip = ∑ Dij [ IizI jz − 14 ( Ii+I j− + Ii−I j+ )] , except in the case of thali, j
lium nuclei, for which the indirect nuclear exchange coupling Hexh = ∑ Jij [ IizI jz + 12 ( Ii+I −j + Ii−I j+ )] is the dominating linei, j broadening mechanism that mediates spin diffusion [8, 9]. Here, Dij and Jij are dipole–dipole and exchange interaction constants, respectively. Nowadays, spin diffusion in nanomaterials attracts considerable attention due to their increasing application in spintronics and quantum computing. Particularly, nanoscale diamonds are important physical systems for various nanotechnologies, as well as for quantum metrology, information processing and communications [10–12], in which relaxation processes play a significant role. However, since the relaxation that involves nuclear spin diffusion is notoriously difficult to pin down 0953-8984/14/165301+5$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
A M Panich
J. Phys.: Condens. Matter 26 (2014) 165301
The obtained plots of T1 as a function of the dephasing time τd in different external magnetic fields show that 1H spin–lattice relaxation is driven by the coupling of nuclear spins with localized electronic states, and reveal a striking manifestation of the spin diffusion-assisted relaxation regime. The latter is realized due to the dipole–dipole interaction among adjacent nuclear spins. The obtained experimental data allow us to estimate the spin diffusion coefficient and spin diffusion barrier radius.
Normalized amplitude
1.0
2. Experimental The specimen used in this study is a commercial detonation ND powder, which was carefully purified to remove nondiamond carbon and possible metal and metal oxide impurities and to extract the species consisting of ND particles as described elsewhere [17, 26]. To remove moisture adsorbed on the ND surface, the sample was pumped out down to 10– 4 Torr at room temperature and sealed into a glass NMR tube. 1 H NMR measurements of a powder ND sample were carried out at room temperature (T = 295 K) using a Tecmag pulse solid state NMR spectrometer, a Varian electromagnet and an Oxford superconducting magnet. The measurements were made in the external magnetic fields B0 = 0.568 T and 8.0196 T, corresponding to 1H resonance frequencies 24.20 MHz and 341.41 MHz, respectively. The spectra were measured using solid echo pulse sequence (π / 2)0° − τd − (π / 2)90°, a technique that refocuses homonuclear dipole–dipole couplings (here, subscripts denote the phases of pulses). Herewith we measured the spectra and line width for different pulse spacings τd. 1H spin–lattice relaxation time T1 was measured by means of a saturation comb pulse sequence (π / 2 pulse train) followed by dipolar dephasing. The latter was performed using а solid echo sequence with spacing τd between pulses instead of the commonly used π / 2 reading pulse. Thus, the pulse sequence used in our experiments was [(π / 2) − ts − (π / 2) − ts − … (π / 2)]n − τ − (π / 2)0° − τd – (π / 2)90°. The separation between the pulses in the saturation comb sequence ts was chosen as 720 μs. The spin–lattice relaxation time T1 was measured with a variable delay τ between the comb and echo sequences. T1 was determined from magnetization recovery as a function of τ, which is well described by a single exponential. Each particular measurement was done at a fixed τd. Herewith we carried out a number of experiments with various τd and plotted T1 as a function of τd in order to obtain T1(τd) dependence. The duration of the π/2 pulse was 1.8 μs at 24.20 MHz and 1.5 μs at 341.41 MHz. Room temperature election paramagnetic resonance (EPR) measurements were made using a Bruker EMX-220 digital X-band (9.4 GHz) spectrometer and reveal the density of paramagnetic defects (dangling bonds) NS = 6.3 × 1019 spin g-1, which was determined precisely by recording of the spectra of the ND sample and 1.1 × 10–3M TEMPOL solution in ethanol as a standard [27].
0.8
1
H
0.6 0.4 0.2 0.0 -100
-50
0
50
100
Frequency, kHz Figure 1. 1H NMR spectrum of nanodiamond received at τd = 8 μs.
20 18
∆ν, kHz
16 1
H
14 12 10 8 6 0
100
200
300
400
τd, µs
500
600
700
Figure 2. Dependence of the 1H NMR line width on pulse spacing τd for the nanodiamond sample.
[17–19, 21–24]. The characteristic static 1H spectrum of the evacuated ND sample is shown in figure 1. It is a symmetric broad line with the line width Δν = 20 kHz, which reflects strong dipole–dipole interactions among the 1H spins, indicating a significant proton density on the surface. It was shown [19, 21–24] that the hydrogen atoms on the ND surface are irregularly positioned, presumably forming more hydrogenated spots of limited sizes alternating with less hydrogenated or nearly non-hydrogenated zones. The line width of the 1H spectra measured in our experiment was found to be dependent on the spacing τd between the echo pulses and to decrease with increasing τd (figure 2). This indicates that the spectrum can be described as a superposition of a variety of components showing different widths and spin– spin relaxation times T2. For the long τd, the components with short T2 are dephased and are not registered in the experiment. Herewith, the contribution to the magnetic resonance signal for the members of the long T2 ensembles is quite small, and the measurement of such a signal requires many more signal accumulations compared to those of short T2 ensembles. For example, the measurement with short τd = 8 μs was done with 16 scans, while that for long τd = 720 μs required between
3. Results of the experiments and discussion The ND surface is known to be partially terminated by hydrogen atoms forming hydrocarbon and hydroxyl groups 2
A M Panich
J. Phys.: Condens. Matter 26 (2014) 165301
Our measurements allow us to determine the spin diffusion coefficient D, which is expressed as [29]:
100 1
80
H NMR
T1, ms
341.41 MHz
20
24.20 MHz 0
0
50
100
150
τd, µs
200
250
r2 × ( S2 )1/2 . 30
(1)
Here, S2 is the second moment of the spectrum calculated to be 240 kHz2, and r is the distance between the neighboring spins. The latter can be taken as the sum of the van der Waals radii of hydrogen, rw = 1.2 Å, i.e. r = 2.4 Å. Herewith we receive D = 2.97 × 10 –13 cm2 s-1. Another approach [3, 4] allows determination of the spin diffusion coefficient using the spin–spin relaxation time T2:
60 40
D=
300
D=
r2 . 30T2
(2)
Using r = 2.4 Å and T2 = 55 ms measured for our system, one can calculate D = 3.5 × 10 –13 cm2 s-1, which is ~15% larger than the value determined above. The quenching of spin diffusion is normally introduced by defining a radius b0 about each paramagnetic center, called the spin diffusion barrier radius, inside of which D = 0 and outside of which D has a finite value. This radius b0 is defined as the distance from the paramagnetic center at which the change of Bp, the magnetic field of the paramagnetic ion, is of the order of the local field Bl produced by nuclei at the sites of other nuclei. It can also been introduced as the distance from the magnetic ion, for which the difference in Zeeman frequencies of the neighboring nuclei (located along the radius) is of the order of the width of the NMR line. For the nuclei located in a sphere of such a radius, the flip–flop transitions and corresponding diffusion are strongly hindered. EPR measurements show that there are around 12 paramagnetic centers (i.e., dangling bonds) in each ND particle [24, 30–32]. Their specific location over the ND particle is unknown. Their density is suggested to increase from the core center towards the ND surface, although the surface dangling bonds are partially terminated by hydrogen [17, 18, 20, 24]. For dipole–dipole coupling among electron and nuclear spins, the diffusion barrier is derived by the expression [2–4]
Figure 3. Dependence of 1H spin–lattice relaxation time T1 on the spacing between pulses of solid echo τd at the resonance frequencies 341.41 (filled red circles) and 24.20 MHz (open blue circles).
12 000 and 16 000 scans to achieve a satisfactory signal-tonoise ratio. Interestingly, the spin–lattice relaxation time T1 also appeared to be dependent on τd (figure 3), exhibiting an increase in T1 with increasing τd. This effect indicates a manifestation of the relaxation mechanism mediated by spin diffusion. Indeed, the probability of the mutual spin flips decreases as the dipole–dipole coupling among nuclear spins decreases. In a dipolar-coupled spin system, short T2 components result from the strong dipole–dipole coupling among nuclear spins, which in turn causes mutual spin flips resulting in spin diffusion. Elongation of the pulse spacing τd yields dephasing of the short T2 components with stronger dipole–dipole interaction, leaving to dominate those with longer T2 and, respectively, with weaker dipole–dipole coupling. The latter yields slower spin diffusion and thus slower relaxation via paramagnetic centers. To approve the above suggestion on the spin diffusionmediated relaxation mechanism, we carried out T1 measurements in two external magnetic fields, B0 = 8.0196 and 0.568 T (figure 3). One can find from figure 3 that T1 increases with the increasing magnetic field. Among the relaxation mechanisms relevant to the compound under study, a characteristic feature of the Raman process is independence of the relaxation time on the applied magnetic field, while a direct relaxation process usually predicts very long relaxation times (T1> 10 4 s) and yields a reduction in T1 with the increasing magnetic field as T1 ~ B0−2 [28]. Analogous T1 ~ B0−2 dependence [28] is characteristic of the contribution of chemical shielding anisotropy. The only mechanism that causes an increase in T1 with the increased magnetic field is the heat contact with the lattice via localized electronic states (e.g., paramagnetic centers). This mechanism yields either T1 ~ B02 or T1 ~ B01/2 in the cases of rapid spin diffusion and diffusion-limited relaxation, respectively [4]. Such an effect is observed in our measurements of T1 (figure 3), supporting the domination of the aforementioned relaxation mechanism via localized electronic states and the assistance of spin diffusion.
⎡ ⎛ γ ⎞ ℏγ B0 ⎤1/3 b0 = ⎢ ⎜ S ⎟ × S ⎥ × r . ⎢⎣ ⎝ γI ⎠ 2kBT ⎥⎦
(3)
Here γs and γI are the electron and nuclear gyromagnetic ratios, T is temperature and ћ and kB are the Planck and Boltzmann constants, respectively. At room temperature, this yields b0 = 0.3 nm at B0 = 8.0196 T and b0 = 0.124 nm for B0 = 0.568 T. Both of these values are less than the ND particle size (~4.5 nm). The irregular location of hydrogen atoms on the ND surface causes alternation of the proton density. The larger the proton density, the stronger the dipole–dipole interaction between nuclei, and the faster the spin diffusion. Therefore the spin diffusion-assisted relaxation of the densely located 1 H nuclei is more effective, and their T1 is shorter in comparison to that of the more diluted protons. This is observed in our experiment, providing a striking manifestation of the spin diffusion-mediated relaxation regime. 3
A M Panich
J. Phys.: Condens. Matter 26 (2014) 165301
Our experiment yields tb = 39.2 ms for B0 = 8.0196 T and tb = 12.0 ms for B0 = 0.568 T. Thus the experimental ratio tb (341.41 MHz) / tb (24.14 MHz) = 3.3, which devi2 ates some what from (341.41 / 24.14) 3 = 5.8 expected from equations (3) and (4). Next, as mentioned above, in the case of diffusion-limited relaxation T1~ B01/2 [3, 4]. In our experiment, the square root of the resonance frequency ratio 1 (341.4 MHz / 24.14 MHz) 2 = 3.76, while the average ratio T1(341.4 MHz) / T1(24.14 MHz) = 2.404, which is of the same order of magnitude but smaller than the theoretical value. The obtained deviations are evidently due to the limitation of the theory [2–4] based on the model of the finite potential well for the D(r) function; i.e. D = 0 for r < b0 and D = const = D for r > b0 . However, as shown by Atsarkin and Demidov [6, 33], nuclear spin diffusion may be effective even in strong local fields of the paramagnetic centers; i.e., inside a sphere of the commonly derived diffusion barrier radius b0. The matter is that this field is not static, thus its spectral component at the frequency, equal to the difference in the resonance frequencies of two neighboring nuclei, may induce joint flips of these nuclei. Next, the diffusion barrier was shown to be highly anisotropic, reflecting anisotropy of the electron–nuclear interaction. In particular, near the magic angle of θ = 54 ° 44 ′, the local electron field on the nucleus vanishes, removing the obstacles for spin diffusion [33]. Thus, the obtained deviations between theory and experiment likely indicate the limitation of equations (3) and (4) used in our estimations.
(a)
[Mz-M(t)]/Mz
1
H 341.41 MHz tb = 39.2 ms
0.1
0.01
0
100
200
300
t, ms 1
(b)
[Mz-M(t)]/Mz
1
H 24.2 MHz tb = 12.0 ms
0.1
0.01
4. Summary 0
20
40
60
80
100
Summarizing, we measured 1H nuclear spin–lattice relaxation in a dried nanodiamond sample and showed that it is mainly driven by the interaction of nuclear spins with unpaired electron spins of paramagnetic defects. The experimental data provide a striking manifestation of the spin diffusion-assisted relaxation regime and allow us to estimate the spin diffusion coefficient and spin diffusion barrier radius.
t, ms Figure 4. Semi-logarithmic plots of the 1H magnetization recoveries
at the resonance frequencies (a) 341.41 MHz and (b) 24.20 MHz.
Let us now discuss the magnetization recovery plots, ln(( Mz − M ( t )) / Mz ) (here, Mz is the equilibrium magnetization), measured in two applied magnetic fields (figure 4). According to the theory of spin diffusion-assisted relaxation, this process comprises two regimes. Since the magnetization is initially saturated and there is no gradient of magnetization density, at the beginning of the relaxation process spin diffusion is not of importance, and direct relaxation dominates. The direct relaxation is valid until the time
Acknowledgments The author thanks A I Shames for the EPR measurements and the Israeli Ministry of Science & Technology for support of this work under grant No 3-9754.
b02 (4) , D where b0 is the spin diffusion barrier radius and time tb is required to transport the value of M over the distance b0. Then the relaxation curve proceeds asymptotically to the region where spin diffusion dominates and results in equilibrium spin magnetization. These two regimes are clearly seen in figure 4. 3 1 They meet at the time tb = C 2 D− 2 , [2] corresponding to a dis1 tance b0 = ( C / D ) 4 from the localized electron spin (here, C is the constant). It can be seen from figure 4 that the values of tb measured in different magnetic fields are different and that tb increases with the increasing magnetic field, according to the theory (equations (3) and (4)).
References
tb =
[1] Bloembergen N 1949 On the interaction of nuclear spins in a crystalline lattice Physica 15 386–426 [2] Blumberg W E 1960 Nuclear spin–lattice relaxation caused by paramagnetic impurities Phys. Rev. 119 79–84 [3] Khutsishvili G R 1966 Spin diffusion Sov. Phys.—Usp. 8 743–69 Khutsishvili G R 1965 Usp. Fiz. Nauk 87 211–54 [4] Khutsishvili G R 1969 Spin diffusion and nuclear magnetic relaxation in crystal with paramagnetic impurity Sov. Phys. Usp. 11 802–15 Khutsishvili G R 1968 Usp. Fiz. Nauk 96 441–66 [5] Tse D and Lowe I J 1968 Nuclear spin–lattice relaxation in CaF2 crystals via paramagnetic centers Phys. Rev. 166 292–302 4
A M Panich
J. Phys.: Condens. Matter 26 (2014) 165301
[21] Shenderova O, Panich A M, Moseenkov S, Hens S C, Kuznetsov V L and Vieth H-M 2011 Hydroxylated detonation nanodiamond: FTIR, XPS and NMR studies. J. Phys. Chem. C 115 19005–11 [22] Panich A M, Vieth H M and Shenderova O 2012 Nuclear magnetic resonance study of hydroxylated detonation nanodiamond Fullerenes, Nanotubes Carbon Nanostruct. 20 579–86 [23] Panich A M, Altman A, Shames A I, Osipov V Yu, Alexenskiy A E and Vul’ A Ya 2011 Proton magnetic resonance study of diamond nanoparticles decorated by transition metal ions. J. Phys. D: Appl. Phys. 44 125303 [24] Panich A M 2012 Nuclear magnetic resonance studies of nanodiamonds Crit. Rev. Solid State Mater. Sci. 37 276–303 [25] Dubois M, Guerin K, Petit E, Batisse N, Hamwi A, Komatsu N, Giraudet J, Pirotte P and Masin F 2009 Solid-state NMR study of nanodiamonds produced by the detonation technique J. Phys. Chem. C 113 10371–8 [26] Panich A M, Shames A I, Sergeev N A, Olszewski M, McDonough J K, Mochalin V N and Gogotsi Y 2013 Nanodiamond graphitization: a magnetic resonance study J. Phys.: Condens. Matter 25 245303 [27] Shames A I et al 2002 Defects and impurities in nanodiamonds: EPR, NMR and TEM study J. Phys. Chem. Solids 63 1993–2001 [28] Abragam A 1961 The Principles of Nuclear Magnetism (Oxford: Clarendon) [29] Goldman M 1970 Spin Temperature and Nuclear Magnetic Resonance in Solids (Oxford: Clarendon) chapter 3 [30] Shames A I, Panich A M, Kempiński W, Baidakova M V, Osipov V Yu Enoki T and Vul’ A Ya 2005 Magnetic resonance study of nanodiamonds. Synthesis, Properties and Applications of Ultrananocrystalline Diamond ed D M Gruen et al (NATO Science Series II vol 192) (Berlin: Springer) pp 271–82 [31] Osipov V Yu, Shames A I, Enoki T, Takai K, Baidakova M V and Vul’ A Ya 2007 Paramagnetic defects and exchange coupled spins in pristine ultrananocrystalline diamonds Diamond Relat. Mater. 16 2035–8 [32] Shames A I et al 2007 Defects localization and nature in bulk and thin film ultrananocrystalline diamond Diamond Relat. Mater. 16 1806–12 [33] Atsarkin V A 1980 Dynamical Nuclear Polarization in Solid Insulators (Moscow: Nauka)
[6] Atsarkin V A and Demidov V V 1980 Nuclear magnetic relaxation and spin diffusion in the local fields of paramagnetic centers Sov. Phys.—JETP 52 726–32 Atsarkin V A and Demidov V V 1980 Zh. Eksp. Teor. Fiz. 79 1438–50 [7] Zhang W and Cory D G 1998 First direct measurement of the spin diffusion rate in a homogenous solid Phys. Rev. Lett. 80 1324–27 [8] Panich A M, Teske C L and Bensch W 2006 Nuclear spin diffusion in the semiconductor TlTaS3 Phys. Rev. B 73 115209 [9] Panich A M 2004 Nuclear exchange coupling and electronic structure of low-dimensional semiconductors Appl. Magn. Reson. 27 29–39 [10] Barnard A S, Sternberg M 2007 Mapping the location and configuration of nitrogen in diamond nanoparticles Nanotechnology 18 025702 [11] Wolters J, Schell A W, Kewes G, Nüsse N, Schoengen M, Döscher H, Hannappel Th, Löchel B, Barth M and Benson O 2010 Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity Appl. Phys. Lett. 97 141108 [12] Doherty M W, Manson N B, Delaney P, Jelezko F, Wrachtrupe J and Hollenberg L C L 2013 The nitrogenvacancy colour centre in diamond Phys. Rep. 528 1–45 [13] Schrand A M, Ciftan Hens S A and Shenderova O A 2009 Nanodiamond particles: properties and perspectives for bioapplications Crit. Rev. Solid State Mater. Sci. 34 18–74 [14] Dolmatov V Yu 2007 Detonation-synthesis nanodiamonds: synthesis, structure, properties and applications Russ. Chem. Rev. 76 339–60 [15] Barnard A S 2009 Diamond standard in diagnostics: nanodiamond biolabels make their mark Analyst 134 1751–64 [16] Osawa E 2008 Monodisperse single nanodiamond particulates Pure Appl. Chem. 80 1365–79 [17] Panich A M, Shames A I, Vieth H-M, Ōsawa E, Takahashi M and Vul’ A Ya 2006 Nuclear magnetic resonance study of ultrananocrystalline diamonds Eur. Phys. J. B 52 397–402 [18] Panich A M 2007 Solid state nuclear magnetic resonance studies of nanocarbons Diamond Relat. Mater. 16 2044–9 [19] Panich A M, Shames A I, Zousman B and Levinson O 2012 Magnetic resonance study of nanodiamonds prepared by laser-assisted technique Diamond Relat. Mater. 23 150–3 [20] Panich A M, Vieth H M, Shames A I, Froumin N, Ōsawa E and Yao A 2010 Structure and bonding in fluorinated nanodiamond. J. Phys. Chem. C 114 774–82
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Proton spin diffusion in a nanodiamond
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 165301 (http://iopscience.iop.org/0953-8984/26/16/165301) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 163.118.172.206 This content was downloaded on 20/08/2014 at 16:44
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 165301 (5pp)
doi:10.1088/0953-8984/26/16/165301
Proton spin diffusion in a nanodiamond A M Panich Department of Physics, Ben-Gurion University of the Negev, PO Box 653, Be’er Sheva 8410501, Israel E-mail: [email protected] Received 8 August 2013, revised 17 September 2013 Accepted for publication 6 January 2014 Published 1 April 2014 Abstract
We report on a proton magnetic resonance study of a powder nanodiamond sample. We show that 1H spin–lattice relaxation in this compound is mainly driven by the interaction of nuclear spins with unpaired electron spins of paramagnetic defects. We measured the spin–lattice relaxation time T1 by means of a saturation comb pulse sequence followed by dipolar dephasing, and plotted T1 as a function of the dephasing time τd in different external magnetic fields. The received T1(τd) dependence provides a striking manifestation of the spin diffusion-assisted relaxation regime. The obtained experimental data allow us to estimate the spin diffusion coefficient and spin diffusion barrier radius. Keywords: spin diffusion, NMR, nanodiamond (Some figures may appear in colour only in the online journal)
1. Introduction
experimentally, such an effect in nanomaterials (in particular in nanodiamonds (NDs)) has not been studied yet. In the present paper, we report on a nuclear magnetic resonance (NMR) study of proton spin diffusion in a powder ND sample in the external magnetic fields 0.568 and 8.0196 T. ND particles with a diameter of ~4.5 nm have risen to the forefront of material research since they show great potential for a variety of applications [13–16]. It is now established [13–24] that the ND particle consists of a chemically inert and mechanically stable diamond core and a chemically active surface. The latter comprises a number of hydrocarbon and hydroxyl groups and adsorbed moisture [17–19, 21–26]. The compound is the electrical insulator. ND particles usually reveal ~ 6 × 1019 spin g-1 paramagnetic centers originating mainly from unpaired electrons of dangling bonds [17, 18, 20, 24]. They are mainly positioned closer to the surface rather than in the central part of the diamond core, and also on the surface itself [17, 18, 20, 24]. Measurements of 13C spin–lattice relaxation time show an anomalous reduction in T1 from several hours and even days in natural diamonds to hundreds of milliseconds in NDs, which is attributed to the interaction of nuclear spins with the aforementioned localized paramagnetic centers [17–24]. One can expect a similar interaction between 1H nuclei and uncoupled electrons of paramagnetic defects, which are positioned close to the ND surface and directly on the surface. In the present work, we report on the measurements of 1H spin–lattice relaxation time T1 in a dried ND sample by means of a saturation comb pulse sequence followed by dipolar dephasing.
To explain fast nuclear spin–lattice relaxation in solids, Bloembergen [1] suggested in 1949 that the spin magnetization in a rigid lattice could be spatially transferred by nuclear spin diffusion. This mechanism occurs through the mutual flips of neighboring nuclear spins due to interaction terms of Ii+I −j -type, and results in the magnetization transfer from the distant nuclear spins to the localized electron spins. Since 1949, a number of solid insulators and semiconductors have been studied to test the validity of nuclear spin–lattice relaxation mediated by spin diffusion (e.g., [2–7]). The latter is usually considered to be driven by the dipole–dipole interaction Hdip = ∑ Dij [ IizI jz − 14 ( Ii+I j− + Ii−I j+ )] , except in the case of thali, j
lium nuclei, for which the indirect nuclear exchange coupling Hexh = ∑ Jij [ IizI jz + 12 ( Ii+I −j + Ii−I j+ )] is the dominating linei, j broadening mechanism that mediates spin diffusion [8, 9]. Here, Dij and Jij are dipole–dipole and exchange interaction constants, respectively. Nowadays, spin diffusion in nanomaterials attracts considerable attention due to their increasing application in spintronics and quantum computing. Particularly, nanoscale diamonds are important physical systems for various nanotechnologies, as well as for quantum metrology, information processing and communications [10–12], in which relaxation processes play a significant role. However, since the relaxation that involves nuclear spin diffusion is notoriously difficult to pin down 0953-8984/14/165301+5$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
A M Panich
J. Phys.: Condens. Matter 26 (2014) 165301
The obtained plots of T1 as a function of the dephasing time τd in different external magnetic fields show that 1H spin–lattice relaxation is driven by the coupling of nuclear spins with localized electronic states, and reveal a striking manifestation of the spin diffusion-assisted relaxation regime. The latter is realized due to the dipole–dipole interaction among adjacent nuclear spins. The obtained experimental data allow us to estimate the spin diffusion coefficient and spin diffusion barrier radius.
Normalized amplitude
1.0
2. Experimental The specimen used in this study is a commercial detonation ND powder, which was carefully purified to remove nondiamond carbon and possible metal and metal oxide impurities and to extract the species consisting of ND particles as described elsewhere [17, 26]. To remove moisture adsorbed on the ND surface, the sample was pumped out down to 10– 4 Torr at room temperature and sealed into a glass NMR tube. 1 H NMR measurements of a powder ND sample were carried out at room temperature (T = 295 K) using a Tecmag pulse solid state NMR spectrometer, a Varian electromagnet and an Oxford superconducting magnet. The measurements were made in the external magnetic fields B0 = 0.568 T and 8.0196 T, corresponding to 1H resonance frequencies 24.20 MHz and 341.41 MHz, respectively. The spectra were measured using solid echo pulse sequence (π / 2)0° − τd − (π / 2)90°, a technique that refocuses homonuclear dipole–dipole couplings (here, subscripts denote the phases of pulses). Herewith we measured the spectra and line width for different pulse spacings τd. 1H spin–lattice relaxation time T1 was measured by means of a saturation comb pulse sequence (π / 2 pulse train) followed by dipolar dephasing. The latter was performed using а solid echo sequence with spacing τd between pulses instead of the commonly used π / 2 reading pulse. Thus, the pulse sequence used in our experiments was [(π / 2) − ts − (π / 2) − ts − … (π / 2)]n − τ − (π / 2)0° − τd – (π / 2)90°. The separation between the pulses in the saturation comb sequence ts was chosen as 720 μs. The spin–lattice relaxation time T1 was measured with a variable delay τ between the comb and echo sequences. T1 was determined from magnetization recovery as a function of τ, which is well described by a single exponential. Each particular measurement was done at a fixed τd. Herewith we carried out a number of experiments with various τd and plotted T1 as a function of τd in order to obtain T1(τd) dependence. The duration of the π/2 pulse was 1.8 μs at 24.20 MHz and 1.5 μs at 341.41 MHz. Room temperature election paramagnetic resonance (EPR) measurements were made using a Bruker EMX-220 digital X-band (9.4 GHz) spectrometer and reveal the density of paramagnetic defects (dangling bonds) NS = 6.3 × 1019 spin g-1, which was determined precisely by recording of the spectra of the ND sample and 1.1 × 10–3M TEMPOL solution in ethanol as a standard [27].
0.8
1
H
0.6 0.4 0.2 0.0 -100
-50
0
50
100
Frequency, kHz Figure 1. 1H NMR spectrum of nanodiamond received at τd = 8 μs.
20 18
∆ν, kHz
16 1
H
14 12 10 8 6 0
100
200
300
400
τd, µs
500
600
700
Figure 2. Dependence of the 1H NMR line width on pulse spacing τd for the nanodiamond sample.
[17–19, 21–24]. The characteristic static 1H spectrum of the evacuated ND sample is shown in figure 1. It is a symmetric broad line with the line width Δν = 20 kHz, which reflects strong dipole–dipole interactions among the 1H spins, indicating a significant proton density on the surface. It was shown [19, 21–24] that the hydrogen atoms on the ND surface are irregularly positioned, presumably forming more hydrogenated spots of limited sizes alternating with less hydrogenated or nearly non-hydrogenated zones. The line width of the 1H spectra measured in our experiment was found to be dependent on the spacing τd between the echo pulses and to decrease with increasing τd (figure 2). This indicates that the spectrum can be described as a superposition of a variety of components showing different widths and spin– spin relaxation times T2. For the long τd, the components with short T2 are dephased and are not registered in the experiment. Herewith, the contribution to the magnetic resonance signal for the members of the long T2 ensembles is quite small, and the measurement of such a signal requires many more signal accumulations compared to those of short T2 ensembles. For example, the measurement with short τd = 8 μs was done with 16 scans, while that for long τd = 720 μs required between
3. Results of the experiments and discussion The ND surface is known to be partially terminated by hydrogen atoms forming hydrocarbon and hydroxyl groups 2
A M Panich
J. Phys.: Condens. Matter 26 (2014) 165301
Our measurements allow us to determine the spin diffusion coefficient D, which is expressed as [29]:
100 1
80
H NMR
T1, ms
341.41 MHz
20
24.20 MHz 0
0
50
100
150
τd, µs
200
250
r2 × ( S2 )1/2 . 30
(1)
Here, S2 is the second moment of the spectrum calculated to be 240 kHz2, and r is the distance between the neighboring spins. The latter can be taken as the sum of the van der Waals radii of hydrogen, rw = 1.2 Å, i.e. r = 2.4 Å. Herewith we receive D = 2.97 × 10 –13 cm2 s-1. Another approach [3, 4] allows determination of the spin diffusion coefficient using the spin–spin relaxation time T2:
60 40
D=
300
D=
r2 . 30T2
(2)
Using r = 2.4 Å and T2 = 55 ms measured for our system, one can calculate D = 3.5 × 10 –13 cm2 s-1, which is ~15% larger than the value determined above. The quenching of spin diffusion is normally introduced by defining a radius b0 about each paramagnetic center, called the spin diffusion barrier radius, inside of which D = 0 and outside of which D has a finite value. This radius b0 is defined as the distance from the paramagnetic center at which the change of Bp, the magnetic field of the paramagnetic ion, is of the order of the local field Bl produced by nuclei at the sites of other nuclei. It can also been introduced as the distance from the magnetic ion, for which the difference in Zeeman frequencies of the neighboring nuclei (located along the radius) is of the order of the width of the NMR line. For the nuclei located in a sphere of such a radius, the flip–flop transitions and corresponding diffusion are strongly hindered. EPR measurements show that there are around 12 paramagnetic centers (i.e., dangling bonds) in each ND particle [24, 30–32]. Their specific location over the ND particle is unknown. Their density is suggested to increase from the core center towards the ND surface, although the surface dangling bonds are partially terminated by hydrogen [17, 18, 20, 24]. For dipole–dipole coupling among electron and nuclear spins, the diffusion barrier is derived by the expression [2–4]
Figure 3. Dependence of 1H spin–lattice relaxation time T1 on the spacing between pulses of solid echo τd at the resonance frequencies 341.41 (filled red circles) and 24.20 MHz (open blue circles).
12 000 and 16 000 scans to achieve a satisfactory signal-tonoise ratio. Interestingly, the spin–lattice relaxation time T1 also appeared to be dependent on τd (figure 3), exhibiting an increase in T1 with increasing τd. This effect indicates a manifestation of the relaxation mechanism mediated by spin diffusion. Indeed, the probability of the mutual spin flips decreases as the dipole–dipole coupling among nuclear spins decreases. In a dipolar-coupled spin system, short T2 components result from the strong dipole–dipole coupling among nuclear spins, which in turn causes mutual spin flips resulting in spin diffusion. Elongation of the pulse spacing τd yields dephasing of the short T2 components with stronger dipole–dipole interaction, leaving to dominate those with longer T2 and, respectively, with weaker dipole–dipole coupling. The latter yields slower spin diffusion and thus slower relaxation via paramagnetic centers. To approve the above suggestion on the spin diffusionmediated relaxation mechanism, we carried out T1 measurements in two external magnetic fields, B0 = 8.0196 and 0.568 T (figure 3). One can find from figure 3 that T1 increases with the increasing magnetic field. Among the relaxation mechanisms relevant to the compound under study, a characteristic feature of the Raman process is independence of the relaxation time on the applied magnetic field, while a direct relaxation process usually predicts very long relaxation times (T1> 10 4 s) and yields a reduction in T1 with the increasing magnetic field as T1 ~ B0−2 [28]. Analogous T1 ~ B0−2 dependence [28] is characteristic of the contribution of chemical shielding anisotropy. The only mechanism that causes an increase in T1 with the increased magnetic field is the heat contact with the lattice via localized electronic states (e.g., paramagnetic centers). This mechanism yields either T1 ~ B02 or T1 ~ B01/2 in the cases of rapid spin diffusion and diffusion-limited relaxation, respectively [4]. Such an effect is observed in our measurements of T1 (figure 3), supporting the domination of the aforementioned relaxation mechanism via localized electronic states and the assistance of spin diffusion.
⎡ ⎛ γ ⎞ ℏγ B0 ⎤1/3 b0 = ⎢ ⎜ S ⎟ × S ⎥ × r . ⎢⎣ ⎝ γI ⎠ 2kBT ⎥⎦
(3)
Here γs and γI are the electron and nuclear gyromagnetic ratios, T is temperature and ћ and kB are the Planck and Boltzmann constants, respectively. At room temperature, this yields b0 = 0.3 nm at B0 = 8.0196 T and b0 = 0.124 nm for B0 = 0.568 T. Both of these values are less than the ND particle size (~4.5 nm). The irregular location of hydrogen atoms on the ND surface causes alternation of the proton density. The larger the proton density, the stronger the dipole–dipole interaction between nuclei, and the faster the spin diffusion. Therefore the spin diffusion-assisted relaxation of the densely located 1 H nuclei is more effective, and their T1 is shorter in comparison to that of the more diluted protons. This is observed in our experiment, providing a striking manifestation of the spin diffusion-mediated relaxation regime. 3
A M Panich
J. Phys.: Condens. Matter 26 (2014) 165301
Our experiment yields tb = 39.2 ms for B0 = 8.0196 T and tb = 12.0 ms for B0 = 0.568 T. Thus the experimental ratio tb (341.41 MHz) / tb (24.14 MHz) = 3.3, which devi2 ates some what from (341.41 / 24.14) 3 = 5.8 expected from equations (3) and (4). Next, as mentioned above, in the case of diffusion-limited relaxation T1~ B01/2 [3, 4]. In our experiment, the square root of the resonance frequency ratio 1 (341.4 MHz / 24.14 MHz) 2 = 3.76, while the average ratio T1(341.4 MHz) / T1(24.14 MHz) = 2.404, which is of the same order of magnitude but smaller than the theoretical value. The obtained deviations are evidently due to the limitation of the theory [2–4] based on the model of the finite potential well for the D(r) function; i.e. D = 0 for r < b0 and D = const = D for r > b0 . However, as shown by Atsarkin and Demidov [6, 33], nuclear spin diffusion may be effective even in strong local fields of the paramagnetic centers; i.e., inside a sphere of the commonly derived diffusion barrier radius b0. The matter is that this field is not static, thus its spectral component at the frequency, equal to the difference in the resonance frequencies of two neighboring nuclei, may induce joint flips of these nuclei. Next, the diffusion barrier was shown to be highly anisotropic, reflecting anisotropy of the electron–nuclear interaction. In particular, near the magic angle of θ = 54 ° 44 ′, the local electron field on the nucleus vanishes, removing the obstacles for spin diffusion [33]. Thus, the obtained deviations between theory and experiment likely indicate the limitation of equations (3) and (4) used in our estimations.
(a)
[Mz-M(t)]/Mz
1
H 341.41 MHz tb = 39.2 ms
0.1
0.01
0
100
200
300
t, ms 1
(b)
[Mz-M(t)]/Mz
1
H 24.2 MHz tb = 12.0 ms
0.1
0.01
4. Summary 0
20
40
60
80
100
Summarizing, we measured 1H nuclear spin–lattice relaxation in a dried nanodiamond sample and showed that it is mainly driven by the interaction of nuclear spins with unpaired electron spins of paramagnetic defects. The experimental data provide a striking manifestation of the spin diffusion-assisted relaxation regime and allow us to estimate the spin diffusion coefficient and spin diffusion barrier radius.
t, ms Figure 4. Semi-logarithmic plots of the 1H magnetization recoveries
at the resonance frequencies (a) 341.41 MHz and (b) 24.20 MHz.
Let us now discuss the magnetization recovery plots, ln(( Mz − M ( t )) / Mz ) (here, Mz is the equilibrium magnetization), measured in two applied magnetic fields (figure 4). According to the theory of spin diffusion-assisted relaxation, this process comprises two regimes. Since the magnetization is initially saturated and there is no gradient of magnetization density, at the beginning of the relaxation process spin diffusion is not of importance, and direct relaxation dominates. The direct relaxation is valid until the time
Acknowledgments The author thanks A I Shames for the EPR measurements and the Israeli Ministry of Science & Technology for support of this work under grant No 3-9754.
b02 (4) , D where b0 is the spin diffusion barrier radius and time tb is required to transport the value of M over the distance b0. Then the relaxation curve proceeds asymptotically to the region where spin diffusion dominates and results in equilibrium spin magnetization. These two regimes are clearly seen in figure 4. 3 1 They meet at the time tb = C 2 D− 2 , [2] corresponding to a dis1 tance b0 = ( C / D ) 4 from the localized electron spin (here, C is the constant). It can be seen from figure 4 that the values of tb measured in different magnetic fields are different and that tb increases with the increasing magnetic field, according to the theory (equations (3) and (4)).
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J. Phys.: Condens. Matter 26 (2014) 165301
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