Dynamic nuclear polarization and relaxation of H and D atoms in solid mixtures of hydrogen isotopes
S. Sheludiakov, J. Ahokas, J. Järvinen, O. Vainio, L. Lehtonen, S. Vasiliev, D.M. Lee, V.V. Khmelenko
aa r X i v : . [ phy s i c s . a t m - c l u s ] S e p Noname manuscript No. (will be inserted by the editor)
Dynamic nuclear polarization and relaxation of H and Datoms in solid mixtures of hydrogen isotopes
S. Sheludiakov , J. Ahokas , J. J¨arvinen ,O. Vainio , L. Lehtonen , S. Vasiliev ,D.M. Lee and V.V. Khmelenko October 3, 2016
Abstract
We report on a study of Dynamic Nuclear Polarization and elec-tron and nuclear spin relaxation of atomic hydrogen and deuterium in solidmolecular matrices of H , D , and HD mixtures. The electron and nuclear spinrelaxation times ( T e and T N ) were measured within the temperature range0.15-2.5 K in a magnetic field of 4.6 T, conditions which ensure a high polar-ization of electron spins. We found that T e is nearly temperature independentin this temperature range, while T N decreased by 2 orders of magnitude. Suchstrong temperature dependence is typical for the nuclear Orbach mechanism ofrelaxation via the electron spins. We found that the nuclear spins of H atomsin solid D and D :HD can be efficiently polarized by the Overhauser effect.Pumping the forbidden transitions of H atoms also leads to DNP, with the ef-ficiency strongly dependent on the concentration of D atoms. This behaviourindicates the Cross effect mechanism of the DNP and nuclear relaxation, whichturns out to be well resolved in the conditions of our experiments. EfficientDNP of H atoms was also observed when pumping the middle D line locatedin center of the ESR spectrum. This phenomenon can be explained in terms ofclusters or pairs of H atoms with strong exchange interaction. These clustershave partially allowed transitions in the center of the ESR spectrum and DNPmay be created via the resolved Cross effect. Hydrogen atoms in a matrix of molecular hydrogen at high enough concen-trations may lead to a number of fascinating quantum phenomena. Quantumcorrelations between atoms may lead to a BEC-like behavior of H atoms or to Wihuri Physical Laboratory, Department of Physics and Astronomy, University of Turku,20014 Turku, Finland Institute for Quantum Science and Engineering, Department of Physics and Astronomy,Texas A&M University, College Station, TX, 77843, USAPlease give a shorter version with: \authorrunning and \titlerunning prior to \maketitle a transition to the conducting state of a normally insulating H matrix. Such ametal-insulator transition occurs in semiconductors, e.g. P-doped silicon at acritical concentration of [P]=3 × cm − . Similar effects for H atoms may beexpected at much higher concentrations because of the smaller size of H atomscompared to phosphorus donors. In our recent study of Dynamic Nuclear Po-larization (DNP) of H atoms in solid D with a small admixture of H and HD[1] we observed effects, which may indicate the possible onset of the insulator-to-metal transition. We found that pumping exactly in the center of the ESRspectrum, where no DNP effects are expected for isolated atoms, leads to aneffective polarization of the nuclear spins of H atoms. This resembles the well-known Overhauser effect in metals where nuclear spins become polarized afterESR pumping at the Larmor frequency of conduction electrons. The nuclearspins relax through the hyperfine coupling to the conduction electrons andthe spin polarization emerges due to a difference in the rates of the flip-flopand flip-flip cross-relaxation [2]. Similar effects were also recently observed ininsulating glassy solids doped by radicals [3] and Si:P where ESR pumping ofthe exchange-coupled donor line led to polarizing Si nuclei [4].In this work we deal with three main methods for polarizing nuclear spinsdynamically, i.e excluding a brute force technique: the Overhauser effect (OE),the Solid effect (SE) and the Cross effect (CE). In all these methods the al-lowed or forbidden transitions are induced by applied rf power, which leadsto a change of the populations of the electron and nuclear spin states. As aresult, the electron spin polarization is effectively transferred to the nuclei, andtherefore the DNP is most effective at low temperatures and high magneticfields, when high degree of electron spin polarization is obtained in equilib-rium. The Solid effect relies on saturating the forbidden transitions followedby the thermal relaxation of electron spins, and therefore requires much higherexcitation power. The Cross effect and thermal mixing are the three-spin phe-nomena. They require two electron spins being coupled together by the dipolarinteraction and a nuclear spin having hyperfine or dipolar coupling to one ofthe electron spins. The Cross effect may be realized when the ESR frequenciesof two electrons ω e and ω e differ by the Larmor frequency ω N of a nucleuscoupled to one of them [5], so that: ω e = ω e + ω N (1)In this case saturating first electron transition at ω e leads to emergence ofstrong oscillating internal fields, and hence to an increase of the photon densityat this frequency. This stimulates simultaneous flips of the second electron andnuclear spin, resulting in DNP. Here, unlike the Overhauser and Solid effects,pumping and cross-relaxation occur at the same frequency. Although the Crosseffect is a well established method, it has been exclusively observed for inho-mogeneously broadened ESR lines having a breadth greater than the nuclearLarmor frequency [6]. In this situation it cannot be resolved from the Solideffect, and the analysis of the DNP dynamics becomes rather complicated.Polarizing nuclear spins by the Solid effect requires much larger oscillatingfields than in the case of the Overhauser effect. Saturating a flip-flop forbidden itle Suppressed Due to Excessive Length 3 HD,D from RTH from RT H gassourceto ESRspectrometerHD,D H HNMRQM
Fig. 1
The sample cell schematic. Here QM is the quartz crystal microbalance, HNMR isthe helical resonator used for running discharge in the sample cell. transition requires mm-wave fields of the order of (
A/B ) − larger than for theallowed transition, where A is the hyperfine constant (507 G for H) and B is magnetic field. The flip-flip transition is completely forbidden for the freeatoms but becomes allowed in solids by the factor ( B dip /B ) where B dip is thedipolar term of the electron-nuclear interaction. The probability of polarizingnuclear spins by the well-resolved Cross effect for the case when requirement(1) is fulfilled can be substantially larger than that for the Solid effect becausethe allowed ESR transition is saturated in this case [7].In order to create large enough nuclear polarization by means of DNP,two main requirements should be fulfilled. The electron polarization shouldbe close to unity and the nuclear relaxation time should be longer than therelaxation time through the forbidden transitions. These conditions are ful-filled in high magnetic fields (above 1 T) and low temperatures (below 1 K). Acomprehensive study of the spin-lattice relaxation in Si:P, a system similar toH in H , was carried out in works of Feher [8] and Honig [9] while a thoroughtheoretical analysis of the mechanisms of electronic and nuclear relaxation ispresented in the book of Abragam and Goldman [10].In this work we will focus on clarification of mechanisms responsible forthe formation of DNP of hydrogen atoms recently observed by our group ina D :H matrix [1]. We present a detailed study of the spin-lattice relaxationand extended our experiments on DNP of H and D atoms to several othermatrices, including p-H , o-D , HD and D :2%HD mixtures. The measure-ments are performed at the conditions of high magnetic field B =4.6 T and lowtemperatures T ∼
100 mK where electron spins are fully polarized, while theH nuclear spin polarization is relatively low p = ( n a − n b ) / ( n a + n b ) ∼ Please give a shorter version with: \authorrunning and \titlerunning prior to \maketitle
We observed a much faster relaxation of the H nuclear spins in a solidD matrix compared to other hydrogen matrices, H and HD. It turned outthat the nuclear relaxation times below about 0.7 K for all cases were almosttemperature independent. At higher temperatures we observed a strong tem-perature dependence, which may be explained by the nuclear Orbach process.We found that nuclear polarization of H can be created in D , HD and D :HDmatrices by pumping forbidden transitions of H atoms and the center of theESR spectrum which match the position of D lines in our magnetic field. Anextensive study of H and D DNP in different hydrogen matrices makes itpossible for us to conclude that the presence of unpaired D atoms becomesessential for effective polarization and cross-relaxation of H nuclear spins. Awell resolved Cross effect between H and D atoms is suggested as a possibleexplanation of such behaviour. The experiments were conducted in the experimental cell shown in Fig.1. Thecell is anchored to the mixing chamber of the Oxford 2000 dilution refrigeratorand is located at the center of a 4.6 T superconducting magnet. The maindiagnostic tools in our experiments are a 128 GHz ESR spectrometer and aquartz-crystal microbalance used for measuring the thickness of the hydrogenfilms [11]. The films of solid hydrogen isotopes are deposited directly from theroom temperature gas handling system onto the top electrode of the quartz-crystal microbalance which also plays a role as the bottom mirror of the Fabry-Perot ESR resonator. The temperature of the quartz surface is kept below 1K in the deposition process, which allows growing smooth and homogeneousfilms [11].Prior to depositing the samples, a small amount of He was condensed intothe volume below the QM in order to have a saturated film which flushesthe substrate and helps to provide a proper cooling to the samples. After thehydrogen films are deposited, a rf discharge is started in the sample cell usinga helical resonator (HNMR) and the accumulation of unpaired atoms begins.The films we studied were ∼
250 nm thick, which is ∼ . ∼
100 eV) generated during discharge. Thedischarge was turned off after running it for ∼ ∼ × cm − while the H:D ratio varied fromsample to sample. The maximum D concentration reached in HD films was ∼ × cm − . In these samples the D atom concentrations decayed with acharacteristic time of ∼ itle Suppressed Due to Excessive Length 5 (cid:1)− (cid:1) (cid:2) (cid:3) (cid:4) α − (cid:6)(cid:7)(cid:8)(cid:9) (cid:10)(cid:11) (cid:5)(cid:6)(cid:7)(cid:8) (cid:12)R5E(cid:12)R52sR52rsR5ER5ESs c (cid:21) (cid:22) (cid:1) (cid:23) (cid:24) (cid:25) (cid:26) (cid:27) (cid:28)(cid:29) (cid:25)(cid:30) (cid:1) (cid:31) (cid:27) (cid:29)(cid:28) !" α (cid:1) ! − f (cid:7)(cid:9)(cid:6) f (cid:8)(cid:9)(cid:6) z (cid:9)0(cid:8) z (cid:10)0(cid:7) z (cid:11)0(cid:6) f (cid:7)(cid:9)(cid:5) f (cid:8)(cid:9)(cid:5) (cid:23)− f (cid:27)(cid:25) (cid:1) (cid:26) (cid:29) '(cid:1) (cid:28)(cid:29) (cid:25)(cid:30) (− b5sr b5sp b5st b5o b5oE b5oS b5oR Fig. 2 a) Energy levels and ESR transitions for atomic H an D in magnetic field B=4.6 T, b)ESR spectrum of H and D, the H forbidden transitions are shown dotted, c) Nuclear polar-ization of H atoms as a function of the ESR pumping position. The equilibrium polarizationis subtracted for convenience. The solid line is drawn as a guide for the eye. characteristics of the trapped atoms. This was especially useful for findingexact location of forbidden transitions of H atoms.
Relaxation measurements . In order to clarify the influence of the environmenton the efficiency of DNP and relaxation of impurity atoms, the measurementswere performed with several distinct hydrogen matrices: para-H , ortho-D ,HD and D :2%HD mixtures. We studied both relaxation behavior as a functionof temperature and the DNP effects by pumping allowed and forbidden ESRtransitions. In all matrices except pure D , concentrations of D atoms weremuch smaller than H due to the fast conversion of D atoms to H caused by theisotopic exchange reactions D+H → HD+H and D+HD → D +H. In pure HDmatrices the signal of D disappeared within about ∼ sample where a large fraction of D atoms remained unconverted intoH. The electron spin-lattice relaxation times were measured by a saturation-recovery method: first we saturated the ESR line using mm-wave power of ≈ µ W and then measured the line recovery after the ESR excitation wasdecreased by 30 dB to a low enough level to neglect saturation effects. The
Please give a shorter version with: \authorrunning and \titlerunning prior to \maketitle T e times for both H and D were ∼ ∼ matrix compared to para-H and to therelaxation rate of D in the same D sample. These results are summarized inFig.4.The measurements of the cross-relaxation were done using OverhauserDNP, by saturating the allowed b − c or a − d ESR transitions. The rateof the DNP growth is determined by the cross-relaxation, which was moni-tored as the evolution of the ESR lines as a function of the pumping time. Thecross-relaxation through the flip-flop transition for H atoms turned out to bemost efficient in the D sample, T ca =10 s, which is significantly smaller thanfor H in H : T ca ∼ s. The most peculiar behavior was observed in HD wherethe cross-relaxation times were dependent on the age of the sample: they wereshorter right after stopping discharge in the sample cell and increased uponsample storage. The cross-relaxation time through the flip-flip transition, T db ,was found to be about 10 s for H in D but was too long to measure in othersamples. We did not observe any dependence of the cross-relaxation times ontemperature. Dynamic nuclear polarization . DNP for H and D atoms was performed bystopping magnetic field sweep at the value corresponding to a certain allowedor forbidden transition, and maximum excitation power of ≈ µ W was turnedon for 0.5-1 hour. This power was sufficient for partial saturation of the al-lowed ESR transitions. On the other hand, forbidden transitions were veryfar from saturation. The lines of atoms in the matrices containing deuteriumwere broadened by a mixture of homogeneous and inhomogeneous broadeningeffects. Therefore, in order to saturate the whole line, the frequency of theexcitation source was modulated with a deviation of several MHz. The linesof H in H were homogeneously broadened, and no modulation was needed tosaturate the whole line by staying at its peak.The only way to create DNP in the para-H samples was the Overhausereffect by saturating the b − c transition. We achieved H polarization p =0.8by pumping the high field line for ≈ by pumping at the positions of any other transitions of H orD. The situation was completely different for H atoms in matrices containingdeuterium. Efficient DNP was observed by pumping all allowed and forbiddentransitions of H and allowed transitions of D atoms. The effect did not work theother way round: by pumping allowed transitions of H we did not observe anyDNP effects on D. The most efficient way to create DNP of H was to pump its b − c transition. The b -state atoms were rapidly transferred into the a -state, andpolarizations close to p ∼ . p = − . itle Suppressed Due to Excessive Length 7 ( (cid:2)1(cid:4) (cid:5) (cid:2)1(cid:6) (cid:7) (cid:8) (cid:9) (cid:2) (cid:10) (cid:11) (cid:12)(cid:2) (cid:13)(cid:11) (cid:8)(cid:14) (cid:15)6(cid:15)80 (cid:15)80ε(cid:15)803(cid:15)8048 (cid:15)48 (cid:15)68 8 68 48 180218041806 ( (cid:24)1(cid:25) (cid:15)48(cid:15)68 8 68 48 (cid:5) - (cid:28)(cid:8) (cid:9) (cid:2) (cid:10) (cid:11) (cid:12)(cid:2) (cid:13)(cid:11) (cid:8)(cid:14) ( (cid:29)1(cid:30) (cid:5) (cid:31)1 !(cid:2)"(cid:14) (cid:15)48(cid:15)68 8 68 48 Fig. 3
The patterns of H atom DNP after ESR pumping near the lines of atomic deuteriumin solid D (open circles). The pumping times near D α − ζ , D β − ǫ and D γ − δ transitions were1 . we performed OE DNP for D atoms. The DNP effect was also observed inthis case, but its efficiency was substantially smaller than that for H atoms. Inaddition we found that pumping the D lines leads to effective polarization of Hatoms. This was not surprising for the first and third lines, since they coincidewith the locations of the H forbidden transitions, and the SE was expected towork for creating DNP of H. A completely unexpected observation was thatpumping the middle line of D also leads to a negative polarization of H. Wenote that there are no either allowed or forbidden transitions for unpaired Hatoms at this location.Next we performed the measurement of the H DNP enhancement as afunction of the pumping positions at the locations of all three lines of atomicdeuterium for the D sample. In our previous work the H DNP transitionnear D α − ζ was very broad and appeared saturated [1]. Now we reduced thepumping time and width in order to reveal the lineshapes in more detail.The results are presented in Fig.2 c and 3. As was described earlier, pumpingD α − ζ line and D β − ǫ leads to a large negative polarization of H nuclear spins,while pumping D γ − δ creates a clear positive polarization. The H polarizationenhancement coincides well with the shapes of the D ESR transitions (Fig.3).The H DNP transition near D γ − δ appears to be slightly shifted towards theH b − d transition.A similar behavior was observed for DNP in HD samples where the effectswere somewhat weaker. The strength of these effects were also dependent onthe age of the sample; they slowly disappeared with the characteristic timeof 3-4 days. We also tried DNP with D atoms in D samples. The only wayof polarizing D spins was the Overhauser effect when the allowed transitionswere pumped. No polarization enhancement appeared after pumping forbiddentransitions of D atoms. Please give a shorter version with: \authorrunning and \titlerunning prior to \maketitle
Magnetic relaxation at low temperatures is stimulated by the lattice phonons,and its rate depends on the number of phonons which are in resonance, or”on speaking terms” with the transitions between the energy levels in the spinsystem. The electron spins at helium temperatures relax through the directprocess which corresponds to the emission or absorption of a single resonantphonon [8,10]. The relaxation appears either as a spontaneous process at thelowest temperatures when its rate is temperature independent or acquires alinear dependence at higher temperatures which comes from the shape of thephonon spectrum. The electron spin-lattice relaxation times were measuredpreviously in several experiments. It turned out that the relaxation times mea-sured at 0.3 T [14,15,16], 0.86 T [17], 4.6 T [18] and the present work agree witheach other within 1-2 orders of magnitude. Based on the assumption that theelectron-spin relaxation at helium temperatures and below proceeds via the di-rect process, a strong, T e ∼ B , dependence is expected [9,10]. Although, thedecrease of the relaxation time in higher fields is basically seen in the previousresults, it is difficult to figure out the actual dependence due to the relativelylarge scatter of the data in the works cited above. However, the weak temper-ature dependence reported there and observed in our work provides evidencefor the direct process as the main relaxation mechanism of electron spins.The direct process for the nuclear spins at the same temperatures is a factorof ( ω e /ω N ) less efficient than for the case of the electron spins. This shouldlead to a factor of ∼ longer relaxation times for the nuclear spins comparedto electronic relaxation. As a result, the nuclear relaxation is driven by thenuclear Orbach process. In this process the phonons of the lattice stimulatetransitions to the upper electronic states followed by the relaxation via theforbidden transitions. The rate of this process is defined by the rate of theforbidden relaxation multiplied by the Boltzmann factor to take into accountlower population of the upper states in equilibrium:1 T N = ( 1 T ca + 1 T bd ) × exp ( − µ B Bk B T ) (2)The electron Zeeman energy in the exponent provides a very strong temper-ature dependence, especially at low temperatures and strong magnetic fields,which is easily observed in our experiments.In order to check the contribution of the nuclear Orbach process we plottedthe relaxation rates in Arrhenius coordinates (Fig.4). The data points for H:D ,H:D :2%HD and D:D at temperatures > E a ≃ E Zeeman =6.3 K. At lower temperatures,the data tend to deviate from these exponential functions, and have weakertemperature dependence. This may indicate a possible contribution from otherrelaxation mechanisms, e.g. the direct process.Comparing the nuclear relaxation and DNP efficiency for H atoms in dif-ferent matrices we note a general feature observed in this work: the efficiency itle Suppressed Due to Excessive Length 9 (cid:1)K(cid:1)(cid:3)(cid:3)K(cid:3) s (cid:1)K(cid:1) s (cid:1)K(cid:3) s Ksg(cid:1)(cid:3) (cid:1)K(cid:3) s (cid:6) (cid:7)(cid:8) − (cid:1) (cid:2) (cid:3) (cid:1) (cid:4) (cid:11)m(cid:11)t(cid:11) (cid:11)s(cid:11)r (cid:16)(cid:17)(cid:18)(cid:19)(cid:20)(cid:21)(cid:19)D(cid:23)(cid:19)(cid:24)(cid:25)(cid:19)(cid:20)(cid:26)(cid:23)(cid:27)(cid:20)(cid:19)1D (cid:1)(cid:2)(cid:3) D−(cid:29) Ir Fig. 4
Relaxation rates plotted in Arrhenius coordinates for
T > , H:D :2%HD and D:D ( E a ≃ andH in HD of these processes is greatly enhanced by the presence of D atoms in the samematrix . Thus the nuclear relaxation rate of H in D is two orders of magnitudefaster than in pure H . At the same time, we observed that the forbiddencross-relaxation rate is also faster by two orders of magnitude for the formercase. These two observations are in a fair agreement with the nuclear Orbachprocess, when the relaxation rates are related by equation (2). We believe thatsuch influence of D atoms on the DNP and relaxation is caused by the coinci-dence of allowed ESR transitions energies for D with the forbidden transitionsfor H atoms. This match of energies ensures an easy exchange between theH and D electron Zeeman systems [7], and stimulates cross-relaxation of Hatoms. Similar behavior was observed in hydrated copper salts where the nu-clear spin-lattice relaxation accelerated upon matching the condition for theCross effect (1) [19]. In our case a simultaneous flip of the electron and nuclearspin of an H atom may be accompanied by a D atom electron spin flip. Thismay proceed adiabatically for both forbidden transitions of H atoms becauseboth of them have significant overlap with the deuterium lines. However thiseffect is expected to be weaker for b − d cross-relaxation because the probabilityof this flip-flip transition is much smaller than that for the a − c transition.The explanation of the D atom influence is also supported by our observa-tion that the rate of the Overhauser DNP and nuclear relaxation of H in HD isdecreased slowly upon storage of the sample. This is caused by the decrease ofthe D atom density due to the reaction of isotopic exchange [13]. Although theESR signal of D atoms vanishes in noise after 3-4 hours, substantial amounts ofthem are still present in the matrix, continuously decaying in time and leadingto the slow decrease of the cross-relaxation rates observed in our experiments.In Fig.3 we presented the H DNP enhancement data together with the ESRspectra of D and calculated positions of the H forbidden transitions. The dataand the ESR lines are scaled to the same amplitude for a better comparison.This picture demonstrates how closely the D lines match the locations of theH forbidden transitions in our field. One can see that the centers of the fitsto the data are slightly shifted towards the forbidden transitions, where the \authorrunning and \titlerunning prior to \maketitle largest overlap for these transitions occurs. The formation of H DNP afterpumping D α − ζ and D γ − δ lines may be caused by two competing effects: bythe well-resolved Solid or Cross effects. The Solid effect is a two-spin effect andinvolves only an electron and a nuclear spin stimulated by a single rf photon.It does not involve any other atoms, and is not dependent on the D density.In contrast, in the Cross effect the allowed D-atom transition is saturated atthe same time. Tilting the dipolar moments of D atoms leads to emergenceof the oscillating magnetic fields at the exactly same frequency as requiredto stimulate the H forbidden transition. The density of resonant rf photons isstrongly increased, which leads to an enhancement of the forbidden transitionsof H. The efficiency of the CE is proportional to the D density, as is observed inour experiments. This provides evidence that the well-resolved Cross effect isthe main DNP mechanism in the samples with mixed H and D atoms. To ourknowledge, in all previous experiments with the Cross effect this phenomenonwas studied when the allowed and forbidden transitions were not resolved, andall three DNP mechanisms OE, SE and CE occurred simultaneously. In theexperiments of this work, we are able to resolve these effects, and observed theCross effect to be well resolved from other DNP mechanisms.However the Cross effect cannot be used to explain the DNP of H atomsafter pumping the center of the ESR spectrum (middle D-line, see Fig. 3).There are no allowed or forbidden transitions for unpaired H atoms in thisregion of magnetic field. In our previous work [1] we suggested that the DNPobserved after pumping the center of the ESR spectra is related to the for-mation of radical pairs or clusters of H or H and D atoms which have strongexchange interaction between their electrons. As is known for metals, the ex-change effects lead to the averaging of the hyperfine interaction and makeallowed electron spin transitions exactly at the center of the ESR spectrum,as would be the case for a free electron spin. Overhauser DNP in metals is per-formed by pumping these transitions, and leads to the negative polarizationof nuclei. A weak and broad ESR line from clusters and pairs of atoms is alsoobserved for P donors in silicon [20] at sufficiently high density of donors,but still in the dielectric state. In our case the ESR signal from the pairs istoo weak to be seen directly in the ESR spectrum. But the presence of Datoms via the resolved Cross effect allows their indirect detection via the DNPcreated by pumping the center of the ESR spectrum. As in the case of metals,negative polarization is obtained because the flip-flop transition probability isusually higher than the flip-flip probability. We believe that further studies ofthe DNP phenomena in high density samples of H and D atoms stabilized insolid molecular matrices will provide more evidence for these intriguing effects.
Acknowledgements
We acknowledge the funding from the Wihuri Foundation and theAcademy of Finland grants No. 258074, 260531 and 268745. This work is also supported byNSF grant No DMR 1209255. S.S. thanks UTUGS for support.itle Suppressed Due to Excessive Length 11
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