14440
J. Phys. Chem. B 2004, 108, 14440-14445
High-Temperature Diffusion of Lithium Adsorbed on Ru(001)† H. Lo1 ser,‡ D. Fick,‡,§ and H. J. Ja1 nsch*,‡ Philipps-UniVersita¨t, Fachbereich Physik und Zentrum fu¨r Materialwissenschaften, D35032 Marburg, Germany, and Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D14195 Berlin, Germany ReceiVed: January 11, 2004; In Final Form: May 20, 2004
Diffusion measurements on Li atoms adsorbed on a ruthenium single crystal were performed in the hightemperature regime, where desorption is an important path way in the atomic dynamics. Nuclear magnetic resonance (NMR) techniques were applied to highly nuclear spin-polarized 6Li atoms adsorbed on a Ru(001) surface. Pulsed radio frequency (rf) fields with spatial gradients were used to create magnetization patterns in the lithium adsorbate which decay by atomic tracer diffusion. In the temperature range of 1100-1200 K, the diffusion coefficients were on the order of 0.1 cm2/s. The temperature dependence could be described by D ) (10 ( 7 cm2/s) exp[-(0.46 ( 0.07 eV)/(kT)]. The very large prefactor can be explained by a mean jump length on the order of 200 Å. This means the adsorbate is in a gaslike state on the surface, where localization occurs at sites far apart from each other. In a spin-echo experiment at a surface temperature of 1150 K, the spin-spin relaxation time was determined to T2 ) 81 ( 8 ms.
1. Introduction The diffusion of atoms on surfaces occurs at any temperature but at vastly varying rates. Unquestionably, at low temperatures, jump diffusion between neighboring sites dominates, be it caused by thermal activation or by tunneling. The picture does change when the temperature increases. Multiple jump pathways occur or the adsorbate goes into a two-dimensional (2D) gaseous state with much-increased diffusion constants. In this state, collisions can occur, such as that in gas diffusion, but also more surfacetypical phenomena, such as localization at sites of higher binding energy or frictional damping, are observed. At high temperatures, the thermal desorption of adsorbates is often in competition with diffusion. This competition is what the word “high” means in the current context. This situation is typical for catalytic processes or chemical vapor deposition among others. Because of the obvious importance of diffusion, many methods have been devised to study microscopic as well as macroscopic diffusion.1-6 Most of the data in the literature stems from experiments at “modest” sample temperatures, although the high-temperature regime is very important. However, this regime is inaccessible for most techniques used in the field. (See discussion of experimental methods in several reviews.1,4,6) A particularly interesting example where the change in diffusion character is clearly observed is the one of CO on Pt(111). Tracer diffusion, measured microscopically at low temperature, shows small diffusion energies and a moderate prefactor7 that represents the terrace diffusion. Macroscopic measurements at moderate temperatures show a much increased diffusion energy that is typically identified with defect sites. At temperatures where desorption occurs, i.e., high temperatures, the observed diffusion constant is extremely large, such that it cannot be explained by †
Part of the special issue “Gerhard Ertl Festschrift”. * Author to whom correspondence should be addressed. E-mail address:
[email protected]. ‡ Philipps-Universita ¨ t. § Fritz-Haber-Institut der Max-Planck-Gesellschaft.
the extrapolation of the low-temperature data.8 Gas diffusion on the surface is used to explain the observations. Diffusion measurements at lower temperatures exist for lithium on Ru(001). Terrace diffusion was identified with a barrier of 0.18 eV, and an additional barrier of 0.46 eV was observed and tentatively assigned to step edge or other abundant defects.9-11 High-temperature data are lacking. The work presented here demonstrates a new method to measure, at high temperature, the macroscopic diffusion coefficient for lithium adsorbed on a Ru(001) single-crystal surface, using a nuclear magnetic resonance (NMR) experiment. NMR is a long established and very powerful technique. Its usability ranges from chemical structure analysis and imaging techniques to diffusion measurements in liquids or solids. Moreover, NMR is capable of measuring tracer diffusion coefficients from a microscopic scale to a macroscopic scale. On zeolites and powders, NMR it is widely used in surface science.12,13 However, conventional NMR measurements on single-crystal surfaces are hampered by the fact that ∼1018 equivalent nuclear spins are needed for a useful signal.14 A laboratory single-crystal surface typically has an area of 1 cm2 and only provides ∼1015 sites. However, in contrast to the bulk, the surface is accessible from the outside and, therefore, preparation and detection of the nuclear magnetization can be separate from the investigated surface. The use of this advantage on the one side, together with highly nuclear spin polarized adsorbates and single photon counting detection techniques on the other side, made the experiments described here possible. The sensitivity could be enhanced by at least 7 orders of magnitude.15-20 Overcoming the lack of sensitivity for single-crystal surfaces in this way ultimately allowed the utilization of standard NMR procedures to measure the diffusion of atoms across a hot single-crystal surface. 2. Experimental Setup All measurements are performed in an ultrahigh vacuum (UHV) chamber with a base pressure of 2 × 10-11 mbar. The chamber is equipped with a quadrupole mass spectrometer
10.1021/jp0498670 CCC: $27.50 © 2004 American Chemical Society Published on Web 07/14/2004
Diffusion of Lithium Adsorbed on Ru(001)
Figure 1. Schematic diagram of the experimental setup used.
(QMS), a combined low-energy electron diffraction (LEED) and Auger electron spectrometer, an Ar+ sputter gun, and a gold evaporation source. A bakeable gas manifold that can be equipped with different gases provides the means for further surface treatment. The Ru(001) crystal itself is heated from the backside by electron bombardment. The temperature of the crystal is measured with a type C thermocouple spot-welded to the rear of the crystal. The temperature measurement was calibrated through the gold monolayer desorption peak from the clean Ru(001) surface.21,22 The UHV chamber is additionally connected to an atomic beam source producing highly nuclear spin-polarized 6Li (or 7Li). The exposure of the surface to the atomic beam can be turned on and off with a shutter. Atomic beam sources of the type used have been described in some detail recently;17,20 thus, only a brief description follows. An atomic beam is produced by lithium metal evaporated from an oven, then formed by a nozzle and an aperture system. The atomic beam is nuclear spin-polarized in a Stern-Gerlachtype setup and through adiabatic radio frequency (rf) transitions. Using the latter, the nuclear spin polarization can be switched on and off. The size of the nuclear spin polarization of P ≈ 0.6 must be compared with the thermal one of ∼10-6, with which NMR measurements are normally performed. The enormous increase enables the current experiments. An additional increase in NMR sensitivity is achieved through an unconventional signal detection scheme. Instead of measuring the total magnetization of the adsorbed nuclear spin ensemble using pickup coils, we measure the nuclear polarization of already thermally desorbed adsorbates within a beam-foil experiment23 (Figure 1). Therefore, such experiments are only feasible at elevated sample temperatures. In the present experiment, the sample temperatures must be chosen such that the mean residence time of the adsorbates on the surface is below the nuclear spin relaxation time of 0.8 s. This is the case above 1100 K. The concept of this photon-detected NMR has been described elsewhere in detail;17,20 therefore, we describe only the parts relevant in the current context. The desorption of a surface adsorbate can either occur in a neutral or ionic state. The distribution is governed by the SahaLangmuir equation: j+/j0 ) 0.5 exp(φ - I)/(kT), where j+ and j0 represent the ionic and atomic particle flux, respectively, I is the ionization potential of lithium (I ) 5.4 eV), and φ is the work function of the Ru(001) surface (φ ) 5.3 eV).24 Desorbing atoms and ions bear the same information.17 In the present experiment, only the nuclear spin polarization of the desorbed Li ions is detected through beam-foil spectroscopy. To do so, the desorbing ions are accelerated by 10 kV and in a separate chamber (1 m downstream) passed through a thin carbon foil (5 µg/cm2), to neutralize them (see Figure 1). Atoms leaving the carbon foil in the electronically excited 2P states decay through photon emission (D1 and D2 lines). During the lifetime of the 2P states (a few nanoseconds), the hyperfine interaction
J. Phys. Chem. B, Vol. 108, No. 38, 2004 14441
Figure 2. Amplitude of the spin-echo-signal at time 2τ normalized to the amplitude at 2τ ) 0. B0 denotes the strength of the magnetic field at the sample.
between the nuclear spin and its newly formed electron shell transfers part of the nuclear polarization to the shell. The circular polarization of the fluorescence light emitted in the direction of the nuclear spin turns out to be directly proportional to the nuclear polarization of the ions passing the carbon foil.20,23 A low noise detection of the circular polarization of the photons with single photon counting enables the determination of the nuclear spin polarization. Such beam-foil experiments can also be used for a time-resolved measurement (determination of the T1 times) of the polarization of the desorbing ions.17 One can count the photons emitted in the direction of the magnetic field or perpendicular to it and thereby choose to measure either the longitudinal or the transversal nuclear polarization of the ions (see Figure 1). Using this setup, Fourier transform nuclear magnetic resonance (FT-NMR) measurements on the Li atoms adsorbed on single-crystal surfaces are feasible. A prerequisite in NMR measurements is the knowledge of the nuclear spin relaxation times T1 and T2.25-27 The spin-lattice relaxation time T1 denotes the time required by a spin ensemble to thermally equilibrate with its surrounding, whereas the spin-spin relaxation time T2 describes the time during which a spin ensemble dephases incoherently, such that the total transversal magnetization is lost. In a previous experiment, a T1 value of 760 ms has been obtained at T ) 1160 K for 6Li adsorbed on Ru(001).10 The long T1 time is the reason the rare lithium isotope 6Li was chosen for the current experiments. Spin-echo experiments are performed to determine the T2 time.25-27 In such an experiment, a π/2-pulse is applied to generate transverse magnetization. After a waiting time τ, a π-pulse is applied and the echo observed at 2τ. In practice, the experiment is analyzed in the frequency rather than in the time domain. Figure 2 displays the normalized echo signals, as a function of 2τ. A fit to the data with exp(-2τ/T2) yields T2 ) 81 ( 8 ms. This value is considerably higher than that reported from our group previously (T2 ) 17 ( 4 ms).20 Meanwhile, it could be shown, however, that magnetic field fluctuations of 10 µT at a frequency of ∼250 Hz could cause the short T2 times.28 A possible source for such a disturbance was observed in the sample heating system (an electron beam heater with a regulated tungsten emission filament). The use of an rf power source at 7.2 MHz (100 times the Larmor frequency of 6Li) to heat the tungsten filament cured the problem, i.e., eliminated the disturbance and increased the time T2. The surface coverage at high temperature is estimated from the product of the mean residence time τres and the atomic flux. The latter is known from thermal desorption experiments (temperature-programmed desorption, TPD) to be 0.0067 ML/s. τres at high temperatures is measured by interrupting the atomic beam with a fast chopper and analyzing the time dependence
14442 J. Phys. Chem. B, Vol. 108, No. 38, 2004
Lo¨ser et al. constant magnetization (polarization) of the 6Li adsorbates over the surface. Despite the 2D nature of the problem, it is displayed only in one dimension along the x-axis, along which, in the next step, the gradient of the rf pulse ∂B1/∂x is applied. This creates a sinusoidal magnetization pattern of the z-component Mz(x) along the x-axis, with a period of k/(2π), which is dependent linearly on the product of pulse length τ and the strength of the gradient ∂B1/∂x and the gyromagnetic ratio γ:
k)γ
Figure 3. Sketch of the different steps in the diffusion measurement experiment. The time arrow is depicted on the left-hand side, and the right-hand shows the corresponding spatial evolution of the local amplitude of the z-magnetization, which is shown as a function of the surface coordinate x. The dashed line depicts the amplitude of the magnetic field B1 of the rf pulse.
of the desorption signal.17 We observe an Arrhenius-type behavior of τres(T) ) τ0 exp(-EDes/(kT)), where EDes ) 3.4 ( 0.1 eV and τ0 ) 0.64 × 10-16(0.7.36 At 1150 K, this results in a surface coverage of 0.3 × 10-3. 3. Diffusion Measurement Diffusion measurements often rely on the observation of the decay of chemical potential differences on a surface. One concept that is closely related to ours involves producing a periodic concentration pattern (i.e., a one-dimensional grid) and monitoring its decay. This is utilized in second harmonic generation (SHG) diffusion measurements, for example.29,30 In NMR, it is possible to produce and observe spatial patterns of magnetization, e.g., all magnetic resonance imaging (MRI) procedures rely on this.31 The concept is to create a spatial pattern with an initial rf pulse and read the amplitude of the pattern using a second pulse after an appropriate waiting period. The amplitude of the pattern decays through diffusion because atoms with opposing polarization interdiffuse and thereby reduce the total local magnetization. This can be done with a homogeneous concentration, i.e., without chemical potential differences. Therefore, the method measures the tracer diffusion. Three-dimensional versions of this method are described in detail in various monographs.31-33 Suitable magnetization grids can be produced with a combination of an rf pulse and a spatial gradient in the static magnetic field. An alternative method (and applied here) involves the use of an rf field with a spatial gradient in the rf amplitude. Relaxation reduces the amplitude of the magnetization pattern. However, this can be taken into account and means essentially that the entire procedure must be fast enough. To measure the diffusion coefficient, the surface is dosed with a beam of polarized 6Li atoms for a short period of time, resulting in a coverage of ∼0.3 × 10-3 ML. This adsorbate coverage is low enough to render adsorbate adsorbate interactions negligible. The concept of the experimental procedure is shown, from above to below, in Figure 3. We start with a
( )
∂B1 τ ∂x
(1)
(In the ideal situation, Mz is not dependent on the y-coordinate.) Inserting typical experimental values (τ ) 1.33 ms, ∂B1/∂x ) 1 mT/cm) and using γ(6Li) ) 2π × 6.27 kHz/mT, one obtains k ) 2π × 8.3/cm ≈ 50/cm. Thus, the spatial period length is slightly more than 1 mm. During the waiting time t, this pattern fades through the diffusion of the adsorbates (and relaxation). For Gaussian diffusion, which we assume here, a δ-function-like probability to find an adsorbate at a certain position (e.g., r ) 0) spreads with increasing time t, according to exp(-r2/(4Dt)), washing out the sinusoidal pattern Mz(x). To be able to eliminate effects due to the quadrupole interaction of 6Li, the waiting time t is chosen in multiples of the quadrupole interaction time of 1.33 ms. (For details, see the Appendix.) After the waiting time t, which is always much smaller than the T1 and T2 times, a socalled “readout pulse” is applied, which is, again, an rf pulse of duration τ, but now with an inverse sign: -∂B1/∂x. It transforms the sinusoidal pattern back to a spatially constant magnetization Mz(t + 2τ), generally of reduced size. This can now be detected through the beam-foil technique previously described. The decrease of the magnetization from its original value is due to the diffusion of the adsorbates over the surface, destroying the phase information stored in the magnetization grid. After the first gradient pulse, the average magnetization Mz over the surface is essentially zero (see Figure 3). This is observed in the data displayed in Figure 4, where Mz quickly decreases from a finite value to zero, after the first gradient pulse has started. The application of the inverse subsequent “readout pulse” restores Mz partially. In the upper part of Figure 4, the readout pulse is much too long, so that the signal appears similar to an echo. In the lower part of the figure, the second pulse has optimal length and the signal is regained. Introducing a waiting time t between the pulses allows for further diffusion and, thus, stronger reduction in Mz. This waiting-time-dependent signal reduction is the actual signal to be analyzed to obtain the diffusion constant. Under the conditions of the present experiments (times T1 and T2 much longer than t and τ) and with a proper choice of t and τ, to eliminate the effects from the quadrupole interaction of 6Li, the magnetization averaged over the surface after this pulse sequence is given by
[ ( ) ( )] ∂B1 τ ∂x
Mz(2τ + t) ) A(t,τ) exp -D γ
2
τ ) 3 A*(t,τ) exp(-Dtk2)) (2) t-
(For details, see the Appendix.) The decay in the magnetization is a direct function of the diffusion constant D, the nuclear gyromagnetic ratio γ, and experimentally controlled parameters, such as the strength of the gradient ∂B1/∂x, the duration of the rf pulse τ, and the waiting time t. The known effects of
Diffusion of Lithium Adsorbed on Ru(001)
J. Phys. Chem. B, Vol. 108, No. 38, 2004 14443
Figure 6. Temperature dependence of the diffusion constant. All available measurements are plotted; some are repeated at the same temperature. The data points are fitted with an Arrhenius law.
Figure 4. Mz measurements with a positive gradient ∂B1/∂x pulse (denoted by “+”) immediately followed by a negative gradient -∂B1/ ∂x pulse (denoted by “-”). One can see that the total z-magnetization is destroyed quickly after the start of the first pulse. In the upper panel, the second pulse is much longer than the first one; therefore, the magnetization is restored and destroyed again. In the lower panel, the second pulse stops at the maximum of the reconstruction. The z-magnetization is partially restored and then remains constant, because the measuring time is much smaller than T1.
Figure 5. Magnetization, as function of the waiting time t, measured for two different gradient amplitudes at 1150 K and at an external magnetic field of B0 ) 10 mT. The gradient pulses had a duration of τ ) 1.33 ms.
relaxation are small but correctly taken into account in the fitting of the data below. Figure 5 displays the results of a diffusion measurement, using the method previously described. At a sample temperature of T ) 1150 K and a magnetic field strength of 10 mT, the average magnetization Mz is shown as a function of the waiting time t. The gradient pulses have a duration of τ ) 1.33 ms. Two sets of data are shown, giving the results of measurements using two rf-gradient amplitudes differing by a factor of ∼2. As expected from eq 2, Mz decreases much faster if the rf gradient is higher. A fit to both data sets yields diffusion constants D, which agree well within their error bars. This shows, on one hand, the consistency of the measurements and, on the other hand, the applicability of the theoretical treatment, in particular the handling of the influence of the quadrupole interaction (see Appendix). Combining the two results of the data in Figure 5 yields a diffusion constant of D ) 0.092 ( 0.005 cm2/s. This value is surprisingly and extraordinarily large. In a thermally activated
next-neighbor-hopping diffusion process, one expects a D value of no more than ∼10-3 cm2, even at very high temperatures,1 in contrast to the current observation. To investigate this surprising result further, the temperature dependence of D has been investigated. In the current experiment, only the limited range of 1100-1200 K is accessible. The results are shown in Figure 6. At lower temperatures, the flux of desorbing ions becomes too small to measure data with reasonable error bars, and at >1200 K, the mean residence time is already close to the duration of the rf-pulse sequence, thereby spoiling the timing of the experiment. Nevertheless, even the limited data in Figure 6 bear amazing results, which will be discussed in the upcoming section. 4. Discussion From the conditions under which the experiment could be successfully performed, we may already identify a large mean jump length 〈λ〉 as the origin of the large diffusion coefficient found here. Atoms undergo a random walk in a diffusion process. The root-mean-square (rms) distance covered by diffusion is defined as xDt ) xN〈λ〉, with N being the number of jumps. The total length of the path covered is L ) N〈λ〉, which must be smaller than the thermal velocity of the atom times the total time of the diffusion process: N〈λ〉e Vtht. At 1150 K, the thermal velocity is ∼1700 m/s. At a waiting time of t ) 10 ms, the amplitude of the magnetization is reduced to ∼1/10 (Figure 5). Therefore, L ) N〈λ〉 e Vtht ) 17 m, and, from eq 2, it follows that ln 1/10 ) -Dtk2, or Dt ) 2.3/k2. From the previous chapter, we use a value of k ≈ 50/cm. From both conditions, one obtains a lower limit for the mean jump length:
〈λ〉 )
N〈λ〉2 Dt ) g 50 Å L N〈λ〉
(3)
This is certainly an order of magnitude greater than the lower limit for 〈λ〉, but it shows that, without a doubt, a mean jump length far above the next-neighbor distance (∼3 Å) must be expected under the current conditions. The estimate is a lower limit, because L may be considerably less than Vtht if localization occurs with some waiting between the jumps. Experimental evidence in general and a treatment with Langevin dynamics demonstrate that tracer diffusion coefficients obey an Arrhenius law, as long as the condition Ediff/(kT) g 4 is fulfilled:4
(
D ) D0 exp -
)
Ediff kT
(4)
D0 may have a complicated dependence on friction coeffi-
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Lo¨ser et al.
cients, barrier forms, etc. However, notwithstanding, it can be interpreted in terms of a typical frequency ν0 (often denoted as the “attempt frequency”) and the square of the mean jump length:
1 D0 ) 〈λ〉2ν0 4
(5)
A fit of an Arrhenius law to the data of Figure 6 yields Ediff ) 0.46 ( 0.07 eV and D0 ) 10 ( 7 cm2/s. For T e 1200 K, for which data was taken, one finds Ediff/(kT) > 4.45, which means that we are just still within the range where an Arrhenius law may be applicable. Adopting a “standard” attempt frequency of ν0 ) 1013/s, one obtains, with eq 5 from the value of D0 found in the fit, a mean free jump length of 〈λ〉 ) 200 ( 61 Å, which agrees well with the qualitative arguments presented previously. For the discussion below, it is worthwhile to mention that the value of 〈λ〉 deduced from D0 agrees within the error bars with the terrace width of 245 Å obtained from the miscut (error estimate) of (0.5° of the Ru(001) surface. The actual miscut may be smaller, giving a nominally larger terrace width; however, the high-temperature treatment of the crystal most likely induces additional steps at random orientations. Given that the surface atoms form an adsorbate 2D gas, one should estimate the gas collision mean free path (lg ≈ 1/x2nσ) at the low but nonzero surface coverage. In two dimensions, the gas kinetic “cross section” σ is 3 or 5 Å long. The density of a full ML is n0 ) 1.6 × 1019/m2. At an experimental coverage of 0.3 × 10-3 ML, one obtains lg ≈ 2900 Å, which is far greater than the estimates of 〈λ〉. Lithium diffusion on Ru(001) was measured at much lower temperatures, using β-NMR techniques.9-11 Those analyses showed the existence of at least two diffusion barriers, with heights of 0.45 and 0.176 eV. They were tentatively identified with a diffusion process over steps and across terraces, respectively. Because the first one agrees almost perfectly with that observed here, it is tempting to identify the diffusion energy in the present experiment with the diffusion barrier that occurs at steps. This sounds reasonable, because steps usually present an additional barrier for atoms, with a size of a few tenths of an electron volt.5,6 On the other hand, for temperatures >1100 K, diffusion across terraces is far from the Arrhenius law regime (Ediff/(kT) < 1.8) and probably more or less ballistic with a very large mean free path. Therefore, the observed mean free path is not determined by the properties of the terrace binding sites but rather by collision or localization centers (i.e., defects, among which steps are the most abundant ones). This is why the terrace diffusion barrier is not visible in the present experiment and why the observed mean jump length 〈λ〉 is approximately equal to the average terrace width. The latter fact, of course, could be fortuitous. Considering all the observations together, a rather concise picture emerges. At elevated temperatures, the adsorbed Li atom moves ballistically across the surface terraces until it reaches a defect, most probably a step site. The very large prefactor of the diffusion coefficient stems from the large mean jump length necessary to overcome a terrace in a ballistic flight from step to step. 5. Conclusions Very high diffusion coefficients of lithium on Ru(001) have been observed for surface temperatures of >1100 K. These hightemperature measurements fall into a diffusion regimesnamely, large diffusion coefficients (D) and large length scaleswhere
few measurements exist, as observed in recent reviews.4,6 The present experiments, the first of its type in the surface sciences, show that NMR techniques are able to open a new window in the studies of macroscopic diffusion on surfaces. Using a magnetization grid, the tracer diffusion can be studied under homogeneous conditions. The very low coverage used avoids the mutual interaction of the adsorbates. Nevertheless, the method is applicable also for investigations of homogeneous diffusion at higher coverage. Because of the detection technique used, the present experiment is limited to high sample temperatures. However, one may consider that β-NMR techniques10,11 or the newly established Xe-NMR procedure34 may extend the experimental applicability of the work presented. Acknowledgment. Support of the “Deutsche Forschungsgemeinschaft” (DFG), under Contract No. JA 2195, is kindly acknowledged. We thank the target laboratory of the MaxPlanck Institut fu¨r Kernphysik, Heidelberg, which has provided the carbon foils used for the beam-foil experiments over the years. Appendix. Magnetic Rotating Frame Diffusion Measurement with Spin ) 1 Nuclei The derivation of the formula describing a diffusion experiment with a magnetic grid for a spin ) 1/2 nucleus can be found in refs 31-33. The time dependence of the magnetization after rf pulses of a duration τ and waiting time t between the pulses is given by
[ (
) ( )][ ( )] [ ]
∂B1(x) τ ∂x
Mz(2τ + t) ) M0 exp -D γ
exp
-t T2
2
τ 1 1 + × 3 2 2 -(2τ + t) exp (A-1) T1 t-
where all symbols have the meaning of the main text. As one can see, the magnetization is dependent on three factors: the magnetization loss due to diffusion (given by the diffusion constant D), the loss during the waiting time t due to spinspin relaxation of the transversal components (described by T2), and finally the loss due to the spin-lattice relaxation of the spin ensemble during the entire experiment (described by T1). In our case, the T2 and T1 relaxation times are much longer than 2τ + t or t alone. Therefore, the relaxation terms do not contribute much. Changing to an I ) 1 nucleus, such as 6Li, creates a new problem, because of its quadrupole moment of Q(6Li) ) -0.81 mb.35 The resulting quadrupole frequency ωQ is given by the quadrupole moment and the electric field gradient (EFG) VZZ at the nucleus:25
ωQ )
eQVZZ 4pI(2I - 1)
(A-2)
From other experiments,20,28 it is known that the Li nuclei experience an average EFG of VZZ ) - 5.0(2) × 1015 V/cm2. From the line width of the satellite lines of a 7Li (I ) 3/2) NMR spectrum on the Ru(001) single crystal and their relative amplitudes, we can deduce that the EFG inhomogeneity is
