ESR study of atomic hydrogen and tritium in solid T 2 and T 2 :H 2 matrices below 1K
S. Sheludiakov, J. Ahokas, J. Järvinen, O. Vainio, L. Lehtonen, D. Zvezdov, S. Vasiliev, D.M. Lee, V.V. Khmelenko
aa r X i v : . [ c ond - m a t . o t h e r] S e p ESR study of atomic hydrogen and tritium in solid T and T :H matrices below 1K S.Sheludiakov, J.Ahokas, J.Järvinen, O.Vainio, L.Lehtonen, D.Zvezdov,
1, 2
S.Vasiliev, ∗ D.M. Lee, and V.V. Khmelenko Department of Physics and Astronomy, University of Turku, 20014 Turku, Finland Kazan Federal University, 18 Kremlyovskaya St.,Kazan 42008, Republic of Tatarstan, Russian Federation Institute for Quantum Science and Engineering, Department of Physics and Astronomy,Texas A&M University, College Station, TX, 77843, USA (Dated: April 3, 2018)We report on the first ESR study of atomic hydrogen and tritium stabilized in a solid T and T :H matrices down to 70 mK. The concentrations of T atoms in pure T approached × cm − andrecord-high concentrations of H atoms ∼ × cm − were reached in T : H solid mixtures where afraction of T atoms became converted into H due to the isotopic exchange reaction T+H → TH+H.The maximum concentrations of unpaired T and H atoms was limited by their recombination whichbecomes enforced by efficient atomic diffusion due to a presence of a large number of vacanciesand phonons generated in the matrices by β -particles. Recombination also appeared in an explosivemanner both being stimulated and spontaneously in thick films where sample cooling was insufficient.We suggest that the main mechanism for H and T migration is physical diffusion related to tunnelingor hopping to vacant sites in contrast to isotopic chemical reactions which govern diffusion of H andD atoms created in H and D matrices by other methods. PACS numbers: choose
I. INTRODUCTION
The solid hydrogens are among the simplest quantumcrystals. Small masses and weak interactions result in adramatic influence of quantum effects on their properties.Light impurities of the atomic hydrogens introduced intosuch host matrices turned out to be mobile and able todiffuse by the repetition of quantum exchange reactions[1]. It might be expected that reducing the distance be-tween unpaired hydrogen atoms in the matrix by accumu-lating them to high concentrations may lead to a numberof fascinating phenomena related to quantum degeneracyor to emergence of a strong exchange interaction betweenelectron clouds and possible conductivity of the matrix.A number of methods are available for producingunpaired atoms inside the molecular hydrogen solids.Among them are condensing of rf-discharge productsonto liquid-helium cooled surfaces[2] or directly into su-perfluid helium[3, 4], γ -irradiation[5] or adding smallamounts of β − radioactive tritium into an initial gas mix-ture. The highest densities of H in H above 1 K havebeen obtained with the latter method, × cm − with a 2% T admixture [6], while densities approaching cm − were reached in pure tritium [7]. The methodwhere β -decay of tritium produces free radicals was pio-neered by Lambe [8] who studied radiation induced de-fects in solid T and by Sharnoff and Pound who studiedaccumulation and dynamic nuclear polarization of D insolid D [9]. First experiments below 1 K before ourwork were carried out by Webeler [10], who conducted acalorimetric study of H with a 0.02% tritium admixturein a range of 0.2-0.8 K. Both spontaneous and stimulatedheat spikes of the sample cell temperature were detected and attributed to collective recombination of H atoms inthe H matrix. Collins et al. [11] repeated Webeler’sexperiment using ESR as a detecting tool at a tempera-ture of 1.2 K and confirmed that the heat spikes are alsoaccompanied by abrupt en masse atomic recombination.Mapoles et al. [12] detected spectacular light emission intheir D-T (50% DT, 25% D and 25% T ) samples whichwas also assigned to explosive recombination of atoms.The atomic concentrations achieved in the experiments ofWebeler were estimated indirectly as × cm − , whilein following theoretical works, Zeleznik[13] and Rosen[14]hypothesized that they could be significantly increased ifthe storage temperature would be lowered. These theo-retical conclusions were supported by Collins et al. whoused X-band ESR for studying deuterium and tritiumatoms in solid D-T mixtures at temperatures 2.1-10 Kand found a strong dependence of the steady state con-centration of atoms on storage temperature [7].Another method for producing high concentrations ofH atoms was recently employed by Ahokas et al.[15],[16] who used a cryogenic rf discharge to dissociate H molecules in solid films in situ and reached H concentra-tions ≃ × cm − at 0.5 K. Later it was demon-strated that even higher concentrations of atomic hy-drogen can be produced in H :D mixtures where deu-terium atoms become converted into H in the courseof the isotopic exchange reactions D+H → HD+H andD+HD → D + H[17].Similar to the lighter counterparts, the isotopic ex-change reactions of hydrogen and deuterium with tritium(1) and (2) should proceed in T :H (D ) matrices.T + H → TH + H (1)T+TH → T + H (2)The rates of these reactions in the gas phase were cal-culated by Truhlar et al. [18] and later by Aratono etal. [19] who predicted an extremely high rate of the re-action (1) at low temperatures, k ex ∼ × − cm s − ,and a two order of magnitude smaller rate for the re-action (2). The only experimental observation of theisotopic exchange reactions (1) and (2) at low tempera-tures so far was done by Aratono et al. [20] who studiedthem in superfluid helium where they produced T atomsfrom He in situ by neutron bombardment. The authorswere unable to deduce the absolute reaction rates, butreported on the isotope effect when H is replaced with Din the reactions (1) and (2). For the reaction (1) it wasmeasured to be k ex H /k ex D ≈ , while for reaction (2) k ex TH /k ex TD < . . Reactions similar to (1) and (2) involv-ing deuterium and tritium atoms should proceed muchslower than those for hydrogen because of smaller zero-point energies of the reactants. This was also supportedby the only experimental study of D and T atoms in aD-T matrix carried out by Collins et al. [7] at T=2.1 Kwho reported on the abscence of T-to-D conversion intheir samples. The authors estimated the total atomicconcentrations to be ∼ cm − with a possible uncer-tainty ∼ k = 3(2) × − cm s − .The main purpose of these experiments was to examineopportunities for reaching the highest possible concentra-tions of atomic species using the β -decay of tritium. Weperformed the first quantitative ESR study of T and Hatoms stabilized in thin tritium films at temperaturesbelow 1 K down to 70 mK. The record-high concentra-tions of T atoms in pure T approaching × cm − and concentrations of H atoms of about × cm − in solid T : H were reached. It turned out that in thefilms thicker than 100 nm, maximum achievable densityof H and T was limited by a spontaneous and stimulatedexplosive recombination of atomic species. The explo-sion threshold density and periodicity turned out to bestrongly dependent on the storage temperature. Decreas-ing the film thickness below 100 nm allowed us to avoidexplosions, but the maximum density was also somewhatreduced due to less effective use of the electrons for dis-sociation of molecules. II. EXPERIMENTALA. Setup
The experiments were performed in the sample cell(SC) shown in Fig.1 with further details described in [21].The SC is located at the center of a 4.6 T superconduct-ing magnet and is attached to the mixing chamber of anOxford 2000 dilution refrigerator. The main investigationtools in our experiments are a 128 GHz ESR spectrometerand a quartz-crystal microbalance (QM) able to measurethe film thickness with a 0.2 monolayer accuracy. TheESR resonator (Q=5700 at 300 mK) has an open Fabry-Perot geomentry which made it possible to install beamlines for condensing films of hydrogen isotopes onto theQM and provide a flux of atomic hydrogen created ina specially constructed H-gas source. Three auxillary rfresonators for performing electron-nuclear double reso-nance (ENDOR) of H, D and T atoms are arranged nearthe QM. Only one of them, the H NMR coil, is shown inFig.1. A capillary for condensing the molecular hydrogencomes directly from the room temperature gas handlingsystem and it is kept above the tritium boiling temper-ature during condensing of the film by driving currentthrough electrical heaters. A special source of cold hy-drogen gas is arranged at the top of the sample cell bodyand connected to it via a stainless steel tubing system.The gas of H atoms is very useful for calibration of the ab-solute number of spins detected by our ESR spectrometeras well as for the accurate measurement of the magneticfield and the ESR line shifts [21]. The source can be alsoused for obtaining a flux of molecular hydrogen, whichwas not used in the present work.A Ru-oxide bolometer is arranged in close proximity tothe sample to measure the heat released during explosiverecombination. The bolometer was suspended on finesuperconducting wires which assure only a weak thermalcoupling to the sample cell body. The bolometer has anegligibly small heat capacity and even tiny amounts ofheat can quickly raise its temperature above the temper-ature of the sample cell.
B. Procedure
The technique of condensing hydrogen onto a cold sur-face via the long and sufficiently cold capillary providesa rather efficient way of cleaning the condensed gas fromany other contaminants except hydrogen and its isotopes.Therefore, for the experiments described in this work, wehave not paid much attention to the chemical purity ofT gas, and utilized the most simple and cheap sourceavailable. The T gas we used was extracted from com-mercially available tritium vials produced for use as lu-minescent fishing floats. Each such 5 mm diameter and5 cm long vial contained about 5-10 µ moles of T , which H NMR coil(f=910MHz)Bolometer H↓ T :H
Quartzmicrobalance
Superfluidhelium in
H from RT H gassource to ESRspectrometer T :H from RT
ESRresonator LV
Figure 1. Sample cell schematic.The T and D NMR coils arenot shown in the figure was sufficient for several experiments described in thiswork. The purity of the gas extracted from the vials wasverified using a MKS-Granville-Phillips VQM 835 massspectrometer with the main concern being the amountof other hydrogen isotopes in it. It turned out that asthe main impurity, the gas in the vials typically con-tained about 15% of HT. It is known that the main im-purity in the T gas right after production should beDT( ∼ ), while significant HT contamination appearsduring storage[22]. We found that T gas quickly de-graded after extracting it from the glass vials. About20% of it became converted to HT and H after 3 monthsof storage. In order to minimize the HT content we usedonly fresh T gas for preparing our samples.The films of solid molecular tritium and hydrogen weredeposited by condensing a few µ mol of normal T orT :H mixtures onto the QM directly from a room tem-perature reservoir. A small amount of helium ( ∼ mmol)was condensed into the lower volume (LV in Fig.1) underthe quartz microbalance disk in order to have a saturatedhelium film there. The film flushes the lower surface ofthe QM and provides an efficient way to remove an excessof heat released during film deposition, recombination ofatoms and tritium β -decay. The SC temperature during sample deposition stayed between 1 and 1.5 K.Unpaired H and T atoms appeared in the solid films,and were detected by the ESR spectrometer immediatelyafter completing the deposition process. The atoms re-sult from the dissociation of molecules by the 5.7 keVelectrons of the T β -decay. We followed the kineticsof the growth of the atomic concentrations during thetime interval from several days up to two weeks, period-ically recording the ESR spectra and following the QMfrequency changes. The SC temperature was stabilizedto several different values below 1 K in order to studythe sample properties as a function of temperature. Itturned out that the presence of tritium introduces sub-stantial heating in the SC and limits minimum attainabletemperature to about 150 mK for the films with thick-ness about 300 nm. The sample cell temperature was alsoshortly raised by several tens of mK during the magneticfield sweeps due to eddy current heating. This was essen-tial for triggering the explosive recombination in some ofthe samples. After finishing the measurements for eachfilm, the sample cell and filling capillary were heated toa temperature above 30 K and pumped for several hoursin order to evacuate all hydrogen and clean all surfacesbefore creating a new sample. This cycle was repeatedseveral times for samples of different H :T compositionand thickness.For calibration purposes we utilized the ability to ac-cumulate the H gas in the main volume of the SC. Thisis normally done by: 1) condensing a certain amount ofmolecular hydrogen into the H gas source; 2) condens-ing small amounts of helium inside the upper volume ofthe SC and the source, sufficient to form a several nmthick superfluid He film ; 3) running the rf discharge inthe miniature rf coil inside the H gas source. The gasof atomic hydrogen is produced by dissociation by theelectrons of the discharge. The helium film covering thesurfaces prevents recombination of the atoms on the SCwalls. In the course of the experiments we found thatatomic hydrogen gas can be accumulated (with a sub-stantially smaller rate) also without running discharge,once a helium film is present in the SC. This effect wasonly observed in the experiments with tritium-hydrogenmixtures. It indicates that a fraction of the atoms result-ing from H dissociation in solid films by the electronsof the β -decay may be kicked out from the films into thebulk of the SC and get accumulated there. Unfortunatelywe were unable to observe gas lines of spin-polarizedtritium. This is caused by substantially larger adsorp-tion energy for T on helium surfaces and possibility thatatomic T may penetrate the helium film. Presence of ahelium film in the SC leads to an extra heat load causedby the film re-condensing from the upper parts of capil-laries. In order to avoid this disturbance and reach thelowest temperatures most of the experiments describedin this work were performed without helium film in theSC. C. Samples
The main emphasis of this work was placed on reachingthe highest-possible concentration of unpaired atoms inhydrogen solids using β -decay of tritium. Aiming on thatwe tried to find optimal values of two basic parameters ofthe films: the film thickness and T :H ratio. We stud-ied both pure tritium films and different mixtures of T and H . We expected that in the latter a significant frac-tion of T atoms will be converted to H by the chemicalexchange reactions (1) and (2). Varying the film thick-ness we tried to reach a trade-off between more efficientgeneration of unpaired atoms in thicker films and bettercooling expected for thinner samples. A summary of theproperties of 6 different samples studied in this work isgiven in Table I.A second goal of this work was to study in detail explo-sive recombination of H and T atoms previously observedin works of Webeler [10] and Collins et al. [11]. Varyingthe film parameters: thickness and isotope compositionas well as sample temperature, we tried to find the con-ditions for which this process can be suppressed.First a 1 µ m thick sample of para-H with a 1% tri-tium admixture was studied at T=150 mK. No signals ofatomic tritium were observed while the H concentrationsobtained in this sample levelled off at about 1 × cm − .We did not detect any signatures of explosive recombina-tion of atoms similar to what were reported in [10] and[11] for the bulk samples. This can be explained by alarger surface to volume ratio and much better cooling ofour hydrogen films compared to previous experiments. Inthe work [11] authors reported on suppression of eventsof spontaneous explosive recombination by providing bet-ter cooling to their samples after collecting bulk amountsof liquid helium in the sample cell. The films we stud-ied are rather thin compared to the penetration depth ofelectrons ( ∼ . µ m) released in β -decay of tritium [23]and only a fraction of their kinetic energy, h E k i = , i.e. without anyH added to it prior to condensing. A second sample wasa 250 nm pure tritium film, which we studied at the lowesttemperature of 160 mK, limited by the heat from tritiumdecay. In this sample we reached maximum atomic con-centrations approaching × cm − where most of theatoms were T, with the T:H ratio being about 6:1.The atomic concentrations in this sample were lim-ited by periodic collective recombination of atoms whichraised the SC temperature from 0.16K to about 0.25K.Similar heat spikes were also registered by the bolometer,which has a much faster response time. The spikes werefound to appear both while sweeping magnetic field andbetween the sweeps when the cell was gradually cooling s , nm Composition,% n × cm − H/(T+H)T H HT T H total observed expected1. 1000 1 99 - - 1.0 1.0 1.00 0.992. 250 85 - 15 15 2.5 18 0.14 0.083. 35 85 - 15 10 1.0 11 0.09 0.084. 80 81 4 14 4.2 4.5 8.7 0.53 0.115. 300 60 29 11 0.5 10.5 11 0.95 0.356. 250 4 95 1 - 2.5 2.5 1.00 0.96Table I. A summary table of the samples studied in this work.Film thickness is denoted as s . Expected values of H/(T+H)ratios were estimated from H and HT content. down. Collective recombination also resulted in a partialsublimation of tritium films detected by the QM. A frac-tion of evaporated tritium molecules re-condensed ontothe other surfaces of the SC including the spherical mir-ror.A different behaviour was observed in a substantiallythinner, 35 nm pure T film (sample 3). The accumu-lation of atoms in the film was not interrupted by theirexplosive recombination. Condensing a smaller amountof tritium also allowed us to store the sample at temper-ature of about 80 mK. However, the maximum densitiesof atoms in the thinner film were a factor of 2 lower thanthat in Sample 2.Three samples with different T :H content were stud-ied to examine the possibility of reaching the highest con-centrations of H atoms and possible observation of the ex-change reactions between two isotopes. Sample 4: 80 nmT :4%H , sample 5: T :30%H (300 nm) and sample 6:H :5%T (360 nm). Total density of atoms was a factorof 2 lower than in thick "pure" tritium sample, but inSample 5 we succeeded in reaching a record high densityof H atoms exceeding cm − . We observed no explo-sive atomic recombination in the samples of the T :H mixture films. All these samples featured a much smallerT:H ratio as compared to the initial content of T :H which we interpret in terms of the isotope exchange re-action. D. ESR and ENDOR spectra
ESR spectra were recorded by a cryogenic heterodynespectrometer which does not utilize field or frequencymodulation [24]. In this work we used the CW methodof operation, where the frequency of the excitation sourceis kept constant, while the magnetic field is swept acrossthe resonance. The ESR signal at the output of the de-tection system contains both components of the complexmagnetic susceptibility: absorption and dispersion as afunction of the magnetic field sweep. In all our spectrapresented below we will show absorption signals only.The ESR spectrum of atomic hydrogen and tritiumcontains a doublet of lines separated by a distance equal (cid:1) (cid:2) (cid:3) (cid:2) (cid:1) (cid:4) (cid:3) (cid:4) (cid:5) (cid:6) (cid:7) T (cid:9)(cid:10) (cid:11) (cid:12) T (cid:4) (cid:13) (cid:14) (cid:9)(cid:10)(cid:15) (cid:16)(cid:17) (cid:12) T n (cid:4) d (cid:16) d e .)01234 (cid:28)(cid:4)(cid:29)(cid:11)(cid:12)(cid:15)(cid:10)(cid:30)T(cid:31)(cid:10)(cid:12)(cid:9)(cid:17)T !(cid:12)(cid:12)(cid:14)Tn"e Figure 2. A panorama spectrum of T and H ESR lines ofsample 4 stored at 70 mK. Note the difference in T and H linepolarization. A broad line of unknown origin appears at theESR spectrum center to the hyperfine interaction. The hyperfine splitting be-tween the two lines is ≈ G for H and slightly larger ≈ G for T. A typical ESR spectrum which includes alllines of atomic hydrogen and tritium in T :H matricesis shown in Fig.2. The spectrum shown corresponds toSample 4, and is taken after the accumulation of atomicspecies has been saturated and a maximum density ofatomic species is reached. The T:H line ratio was dif-ferent for various samples. T lines in the samples 1 and6 were not detected at all, while H lines in the samples2 and 3 were substantially weaker than T lines. Eventhough the difference in the hyperfine constants looks rel-atively large, for the very high densities studied in thiswork the density dependent broadening was so large thatit was not always easy to resolve ESR line of H and Tfrom each other.At high densities of atoms studied in this work the ef-fects of dipole-dipole interaction between atoms start toplay important role and influence the shape and positionof ESR lines. It has been shown in our previous work [16]that the dipole-dipole interaction leads to a Lorentzianlineshape with the width linearly increasing as a func-tion of density. This dependence can be used for theabsolute determination of atomic density. A second im-portant consequence of high density fully polarized elec-tron spins is a macroscopic magnetization of the sample,which leads to shifts of the ESR lines. This effect dependson the geometry of the sample, and for thin films perpen-dicular to the main polarizing field the net dipolar fieldis opposite to the main polarizing field. This leads to thelinear density-dependent shift of the ESR lines towardsthe larger sweep fields, i.e. to the right in the spectra asthey are recorded by our technique. Having the possi-bility of using the H gas lines as absolute field markers,these shifts can be accurately measured and also providea measure of the absolute density of atoms in the films.For the high density samples and thick (>350 nm) filmsanother ESR line broadening effect caused by the radia- tion damping brings extra complications in the analysisof the ESR spectra. The effect of radiation damping isrelated to spontaneous and coherent emissions of energystored in the spin system into the resonant cavity at theelectron Larmor frequency [25]. It typically occurs in spinsystems strongly coupled to the microwave field of thecavity, when the relaxation time due to interaction of spinsystem with cavity field becomes comparable to the spin-spin relaxation time T , i.e. T ∼ T rad = (2 πM Qη ) − .Here M is the sample magnetization, Q is the res-onator quality factor and η is the resonator filling factor.In this case the effective relaxation time of the system /T ′ = /T + /T rad . This also results in an additionalline broadening proportional to the number of spins inthe sample. The radiation damping effect depends on thedetuning of the spectrometer frequency from the centerof the cavity resonance, and it is possible to reduce it toa negligible level by increasing the detuning to severalcavity resonance widths. This was verified for the thick-est films of the sample 1, where the effect was strongest.We observed a factor of 2 decrease in the ESR linewidthafter such detuning. For all other samples the radiationdamping effects were substantially weaker and added notmore than 20% to the actual linewidth, which was how-ever taken into account in the analysis.A typical dependence of the tritium ESR line shift andwidth on the total atomic density measured for the sam-ple 2 is presented in Fig.3. In the inset we show a realspectrum of the high field line with all three components:T and H lines from the atoms in the film, and the H gasline from the atoms in the bulk of the SC. In this samplethe lines from the atoms in the solid are of comparableamplitude and poorly resolved from each other because oftheir rather large width. The H gas line is very narrowand easily distinguishable in the spectrum. We fittedsuch lineshapes with three Lorentzian functions, whichare also presented in the inset of the Fig.3.For the measurement of the absolute density of atomsin thin solid films we used known dependence of the ESRline width and shift on density [16]. This dependence wasverified during several experimental runs with respect tothe calorimetric method of measurement of the absolutenumber of hydrogen atoms. The calorimetric methodis based on the measurement of the energy released instimulated by ESR recombination of the atoms of theH gas versus the reduction of their ESR signal. Thismethod agreed to within 20% accuracy with calibrationsbased on the linewidth and shift measurements, and weconsider 20% as an upper limit estimate of the error indensity determination in this work.A broad, ∼ G wide, line of an unknown nature wasobserved at the center of the ESR spectrum for all sam-ples studied in this work (Fig.2). The line width and areaincreased during storage and saturated after one week ofmeasurements. The line remained in the spectrum afterthe SC cleaning procedure when we raised the SC tem- (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:5)(cid:2)(cid:7)(cid:4) (cid:8) (cid:2) (cid:9) (cid:10) d (cid:12) (cid:2) (cid:3) (cid:4) (cid:5) d (cid:13) (cid:9)(cid:3) d (cid:3) (cid:2) (cid:14)(cid:15) (cid:16) (cid:13) (cid:17) d (cid:18) (cid:5) (cid:2) (cid:7) (cid:4) d (cid:20) w (1G(G1)()10( B(cid:15)(cid:9)(cid:28)(cid:10)(cid:9)(cid:4)(cid:17)(cid:13)(cid:4)(cid:2)(cid:15)(cid:9)d(cid:29)dG( Gc (cid:28)(cid:31) l0 ( )r1 1 3r1 G( G)r1 G1 G3r1 %d∆ (cid:9)w'(cid:2)(cid:10)(cid:16)(cid:3)d(cid:18)(cid:12)(cid:10)(cid:10)(cid:14)d (cid:20)w(1( ()1 ( )1 1( Figure 3. The ESR line width and shift from the H-gas phaseline as a function of the atomic concentration. Inset: a typicalspectrum of the H and T low field lines fitted by 3 lorentziancurves. The concentration-dependent (dipolar) shift from theH-gas line (H ↓ ) is labeled as ∆ B(n) in the inset. peratures above ≃ K and cooled back to 1 K. Sincethe solid molecular film has been completely removed af-ter such cleaning, it seems that the central line originatesfrom some atoms or free radicals in the metallic mirrorsof the Fabry-Perot resonator. We have not observed thisline after warming up to room temperature and startingnew experimental run. A large area of the central linealso implies a large number of the free radicals whichproduce it, about same as the number of unpaired atomsin our molecular films. A strong broad signal seen atthe center of the spectrum in Fig.2 is reminiscent of thecentral peak seen in the semiconductor Si:P at high phos-phorus concentration and was taken to be attributed tothe formation of the donor pairs coupled by the strongexchange interaction [26]. The work is continuing in anattempt to fully understand this important observation.A weak line of trapped electrons similar to that foundfor other hydrogen matrices [27] was observed in thick T and T :H samples but it was absent in the films thinnerthan 100 nm (samples 3 and 4). In our ESR spectra wehave not observed any signatures of ions or other speciestrapped in hydrogen films. The most stable of ions H + and H +3 (T + and T +3 ) have a zero electron spin and cannotbe detected by ESR. The yield of other ions, such asH +2 (T +2 ) and H − (T − ) is expected to be 4 orders ofmagnitude smaller than for unpaired atoms[28] and liesbelow our sensitivity threshold.In addition to the conventional ESR diagnostics we im-plemented measurements of the Electron-Nuclear DoubleResonance (ENDOR) on our samples. The method isbased on detecting the frequency of the NMR transitionby its influence on the amplitude of the ESR lines. TheENDOR measurement was typically done by sweepingthe magnetic field to the center of the ESR line, andthen applying the rf excitation to one of the miniaturecoils located near the sample on the QM electrode. Thenthe frequency of the rf source was swept slowly near the expected NMR transition of H or T atoms. The NMRfrequencies can be determined as ω NMR ≃ π A γB (3)where A is the hyperfine constant of H (1417.3 MHz)or T (1512.6 MHz), γ is the proton or triton gyromag-netic ratio and B is the local magnetic field felt by atoms.A change of the ESR signal was observed when the fre-quency of the rf source matched the NMR transition.Typical ENDOR spectra recorded by this method arepresented in Figs.8 and 10. III. EXPERIMENTAL RESULTSA. Pure tritium samples
In our "pure" tritium samples we have not added anyextra hydrogen to the tritium gas which we extractedfrom the vials. Since the analysis showed a 15% HT im-purity, we assume that all our “pure” tritium films con-tained about 15% of HT. This is the smallest hydrogenimpurity which could be realized in experiments with tri-tium, but it is still rather large to assure abscence of Hatoms in the samples. Our study includes two pure tri-tium samples, 2 and 3 (Tab.I) with thickness of 250 and35 nm respectively.Accumulation of T atoms due to energetic electronsfrom T-decay in sample 2 recorded at 160 mK is shownin Figs. 4 and 5. Tritium ESR lines appeared almostimmediately after film deposition with a width of ∼ × and a substantiallylarger change at around sec on the time scale of Fig.4. These changes in the ESR and QM signals were ac-companied by spikes in the SC temperature up to ∼ ≈ . × cm − to ≈ . × cm − . Occasionally the explosions were triggered by theSC overheating during sweeps of magnetic field betweenESR lines. The T:H ratio did not change after the explo-sions.Accumulation of the atomic densities in the muchthinner (35 nm) Sample 3 followed monotonically in-creasing function which saturated at a total density of ≈ . × cm − and remained stable at temperaturesdown to 70 mK for the observation time of several days.No explosive recombination events were seen for Sample (cid:1) (cid:2) (cid:3) R (cid:5)(cid:6) (cid:7) (cid:8) R (cid:9) (cid:10) (cid:8)(cid:9) (cid:11) R s (cid:9) (cid:14) ( (cid:22) (cid:23) R (cid:24)(cid:10) (cid:8) (cid:25)(cid:14) (cid:8) (cid:7) (cid:26) (cid:27) R s (cid:28) (cid:29) ( M f"86 M c2f"86 M f f f Figure 4. Accumulation of atomic concentration in the sample2 (circles), and QM response on explosive recombination ofatoms in sample 2. (cid:1) (cid:2)(cid:3) (cid:4)(cid:5) (cid:3) (cid:6) (cid:7) (cid:8) (cid:6)(cid:9) (cid:2)(cid:3) n (cid:11) m n (cid:4) (cid:16) m T ( ( T(cid:11)64 ( ((cid:11)64 ( s(cid:11)64 ( )(cid:11)64 ( ( (cid:22)(cid:9)(cid:16)(cid:5)n(cid:11)n64 ( n(cid:24) (cid:3) n (cid:11) m (cid:4) (cid:16) m T (cid:28) (cid:1) (cid:29) n (cid:22) n × (cid:30) Figure 5. Time evolution of the total T and H atomic concen-tration in sample 2 stored at 160 mK . The explosive recom-bination events presented here appear spontaneously. Inset:the sample cell temperature spike during one of such events.
3. Smaller concentrations in the thinner film can be ex-plained by less efficient accumulation of atoms becausethe high-energy electrons escape from the film carryingsubstantial part of their energy, which is not used fordissociation.Signals of atomic hydrogen behaved similarly to thoseof T in both samples, but the total area of H ESR lineswas 6 to 10 times smaller than that for the T lines. Thisroughly corresponds to the T:H atomic ratio in the gasmixture prior to condensing and did not change duringthe course of measurement. This means that the major-ity of H atoms in these samples were created by directdissociation of HT molecules while the isotopic exchangereaction T+HT → T +H is quite inefficient and does notlead to significant T-H conversion.A zero-concentration or matrix width of ≈ G for Hand T lines in pure normal T can be found as an off-set on the vertical axis of the width vs. density plot(see Fig.3). This value is substantially larger than that (cid:1) (cid:2) (cid:3) (cid:4) (cid:5) (cid:6) (cid:5) x (cid:8) (cid:9)(cid:10) (cid:8)(cid:11) (cid:10) (cid:12) (cid:13) (cid:2) (cid:12)(cid:4) (cid:9)(cid:10) x e (cid:8) (cid:5) t (cid:23)(cid:11)(cid:5)(cid:24)(cid:11)(cid:13)(cid:2)(cid:12)(cid:6)(cid:13)(cid:11)xe(cid:25)t0 9 T K 6 80 (cid:28) (cid:11) (cid:3) x (cid:29) T (cid:30) (cid:10) x (cid:29) x (cid:8) (cid:5) (cid:23)xe(cid:25)t 9)pp4)p88)p90 0)p 8 Figure 6. Maximum concentrations of unpaired atoms ob-tained in our work and in previous works using tritium disin-tegration. Present work (sample 2) T in T (black diamonds),T in T [7] (open squares), D, T in D-T matrix (50% DT,25% D and 25% T ) [7] (open circles) Inset: Dependence ofatomic concentration on storage temperature (sample 2) blackdiamonds and dependence of average period of explosive re-combination events on storage temperature: open diamonds.The inset data was measured in sample 2 in n-H (1.1 G). The line broadening due to ortho-T molecules should rapidly vanish due to the fast ortho-para conversion which is catalysed by high concentra-tion of atoms. The conversion should proceed for themolecules in the closest neighbourhood of T and H atomswith a time constant of about 10 s and to be of order of ≃ s for the whole sample [29]. We suggest that themain contribution to the matrix width of H and T inour T samples comes from a large HT impurity. A HTmolecule is composed of distinguishable atoms and themagnetic moments of a proton and triton may contributeto the line broadening. The matrix width for unpairedatoms in HD, 2.8 G is known to be larger than that inn-H (1.1 G) and o-D (1.3 G). Taking into account thatthe deuteron magnetic moment is about 3.5 times smallerthan that of T, one may expect a nearly 2 time larger ma-trix width in pure HT than in HD and some fraction ofthat in our samples.Recombination explosions of unpaired atoms werestudied at different temperatures: 300, 750 mK and 1 K.(see Fig.6). Increasing the temperature slowed downgrowth of density as the recombination rate increased.The heat spikes were observed at all three temperatures,but the time intervals between the spikes greatly in-creased and changed from about × s at 160 and300 mK to × s at 1K. This trend agrees with the re-sults obtained previously by Collins et al.[7, 11]who ob-served the heat spikes in their bulk H +2% T samples at1.2 K and reported on their absence at 2 K. Storing thesample at higher temperatures also resulted in smalleratomic concentrations reached. Similar results were alsofound by Collins et al.[7] who reported on gradual de-crease of atomic concentrations while raising the storagetemperature from 2.1 to 10 K. (cid:1) (cid:2) (cid:3) (cid:2) (cid:4) (cid:5) (cid:6) (cid:5) (cid:7) l (cid:6) (cid:5) (cid:4) (cid:9) (cid:5) (cid:7) (cid:10) (cid:6) (cid:11) (cid:7) (cid:5) l u (cid:13) ( T58T51T518 (cid:19)(cid:20)(cid:4)(cid:5)u(cid:21)(T sT 4T 1T (cid:24)T (cid:19) (cid:5) (cid:4) (cid:9) (cid:5) (cid:7) (cid:10) (cid:6) (cid:11) (cid:7) (cid:5) u (cid:13) ( T548T58T588T51 (cid:19)(cid:20)(cid:4)(cid:5)u(cid:21)(i85s8 i858 i8578 i1
Figure 7. Bolometer response on the explosive recombinationof atoms in sample 2. The bolometer temperature jump dueto thermal explosion is zoomed in the inset
We studied the onset of thermal explosions using a Ru-oxide bolometer which was arranged in the upper vol-ume of the SC near the QM surface with the samples.The bolometer temperature was somewhat higher thanthe SC temperature due to heating by excitation duringmeasurement and noise pick-up (Fig.7). The bolometertemperature increased significantly during explosive re-combination from 0.4 K to almost 0.65 K which is muchhigher than the cell temperature at the same time. Thereare two possible ways of heating the bolometer: conden-sation of hot tritium and hydrogen molecules onto it or bymeans of radiation similar to that observed by Mapoleset al.[12]. The bolometer temperature after each eventof explosive recombination recovered to slightly higherreading which brings evidence of re-condensing T ontoit.Although the thermal response of the bolometer to theheat spikes is substantially faster than that of the samplecell, neither of them is fast enough to follow the actualtime evolution of the recombination explosions. Fromthe bolometer response we can conclude that the explo-sion event develops in the time scale faster than ∼ ≤ P ≃ mW pulse. Then, calculating the totalenergy released by such pulse we evaluated the numberof recombined atoms which would produce such energy (cid:1)A(cid:3)0spiatA(cid:10)(cid:11)(cid:12) (cid:1) (cid:2) (cid:3)(cid:4)(cid:5)(cid:2)(cid:6)(cid:7)(cid:8)(cid:7) (cid:10)(cid:11)(cid:12) (cid:13) (cid:14) (cid:15) A (cid:16) (cid:17) (cid:18)(cid:19) (cid:20) (cid:21) A (cid:20) (cid:22) (cid:23) (cid:21)(cid:17)(cid:24) (cid:25)(cid:26) (cid:27) A H (cid:20) (cid:29) (cid:30) i (cid:25)(cid:19) (cid:17)(cid:24) (cid:16) z nniltnitnidtaailt (cid:1)(cid:9)(cid:1) (cid:2) AH(cid:10)(cid:11)(cid:12)z
Figure 8. ENDOR of atomic tritium in a T matrix. Thecalculated transition frequency for atoms in the gas phase isdenoted as f bursts as 1.0 × . This number matches well the de-crease in atom number 9.0 × measured by our ESRtechnique. A good agreement between these two num-bers also proves good accuracy of our calibration of theabsolute density as a function the ESR line width andarea.Accumulation of unpaired atoms in solid T can bedescribed by a simple model based on a second-order dif-ferential equation (4) d [ T ] dt = 2 F [T ] − K rT [T] , (4)where [T] and [T ] are the concentrations of tritiumatoms and molecules, F is the production rate (dissoci-ation probability per second) of T-atom pairs and K rT is the temperature dependent recombination constant.Both production rate and temperature dependent recom-bination can be extracted by fitting the density growthrate, d [ T ] dt , with a square function and keeping F and K rT as fitting parameters. Using the value of F extractedfrom the fit to the data of Sample 2 we estimated thateach electron released after β -decay of T creates ∼
50 un-paired H or T atoms. This result is in a fair agreementwith that of Collins at al. [7] who found that the pro-duction effciency at 2.1 K is about 70 atoms per disinte-gration event [7]. However this value is larger than thatreported by Sharnoff and Pound: 22 unpaired atoms intheir D samples [9].Measuring the spectra of electron-nuclear double reso-nance (ENDOR) in “pure” T samples we found a cleartransition at ≈ and D ma-trices. We carefully checked the frequency range a fewMHz above the free atom value, but no other transitionswere detected there. This result agrees with the previ-ous results by Lambe [8] and Sharnoff and Pound [9] butcontradicts to the data of Collins et al. [7] who reported (cid:1) ×(cid:3)(cid:1)(cid:3) (cid:4) (cid:5)(cid:6) (cid:7)(cid:8) (cid:6) (cid:9) (cid:10) (cid:11) (cid:9)(cid:12) (cid:5)(cid:6) T (cid:14) T (cid:7) (cid:19) m26()3m (cid:3)(cid:12)(cid:19)(cid:8)Ta(cid:26)im 2-8(cid:14)3m s-8(cid:14)3m Figure 9. Time evolution of H and T concentrations in thesample 4 stored at 80 mK a large positive increase of the hyperfine constant for Tatoms in a T matrix. B. Tritium:hydrogen mixtures
We studied three T :H mixture samples (Samples4,5,6). The maximum concentration of atomic hydro-gen was achieved in the Sample 5: . × cm − .However only modest concentrations, ∼ × and ≃ . × cm − were achieved in the 4th and 6th sam-ples (Tab.I). The T:H ratios in all three samples weremuch smaller than one would expect from the ratio ofT:H atoms in the gas mixture used for preparing thesamples. This gives evidence of a fast T-to-H conversiondue to the isotopic exchange reaction (1).The kinetics of the isotopic exchange reactions (1) and(2) was studied in the 80 nm T :H sample 4. The timeevolution of H and T concentrations in this sample isshown in Fig.9. The H and T lines appeared few minutesafter deposition and had equal amplitudes. A nearly 1-to-1 ratio of their areas remained for the whole measure-ment and can be explained by the very fast reaction (1).A weak increase of the H:T ratio after t=80000 s whilethe total [H]+[T] concentrations remained conserved canbe explained by the contribution from the reaction (2).Based on that we concluded that the reaction (2) indeedproceeds much slower and we can neglect its contributionto the [H] growth for our estimate of the rate of the fasterexchange reaction (1).The evolution of T and H atomic concentrations canbe expressed by the differential equations: d [ T ] dt = 2 F ([ T ]+ 12 [ HT ]) − K ex [ T ][ H ] − K rT [ T ] − K rT H [ T ][ H ] (5) d [ H ] dt = 2 F ([ H ]+ 12 [ HT ])+ K ex [ T ][ H ] − K rH [ H ] − K rT H [ T ][ H ] (6) where K ex is a second-order rate constant of the ex-change reaction (1) and K r are the recombination rateconstants. The production of H atoms includes twoterms: dissociation of H and HT molecules by β -particles and the isotopic exchange reaction (1). If weconsider the initial part of the measurement immedi-ately after the deposition of the film, the concentrationsof atoms are close to zero and we have only the firstterms in equations, e.g. production due to the dissoci-ation. Due to the much larger concentration of T inthe sample, we should observe a proportionally largerrate of the atomic [T] growth with respect to [H]. Asone can see from Fig.9, both [T](t) and [H](t) curvesstart with the same slope and the densities of T and Hare equal to each other during the whole measurement.This implies that the exchange term in equations growsfaster than we can observe with our ESR technique, andthe exchange reaction (1) occurs on the time scale τ ex <100 sec, a typical time interval between sweeps of ESRlines. Having [H]=[T] in the course of measurement al-lows us to fit the rate of the H atom growth, d [ H ] dt witha parabolic function, f ( x ) = k + k ex x − k r x , where x ≡ [ T ] , [ H ] , k = 2 F ([ H ] + [ HT ]) is a constant repre-senting the rate of production, k r = K rT H + K rH is theeffective recombination constant, k ex = K ex [ H ] . Fromthe data of Fig.9 we extracted the values for K ex and k r × − cm s − and 10(5) × − cm s − , respec-tively. The relatively large error in these rate constantsis caused by a large uncertainty in the concentration ofH in our mixtures. Such uncertainty appears due tothe small amount of tritium gas we worked with ( ∼ µ mol) which created difficulties in preparing T :H mix-tures with a small admixtures of H . The exchange re-action rate found here is smaller than that calculatedby Aratono [19] ( × − cm s − ), while the recombi-nation rate agrees with that found in pure T samples.The recombination constant of tritium atoms obtainedby Collins et al. [7] is K = 1 × − cm s at 2.1 K.Estimating the rate of the slower exchange reaction(2) requires a more sophisticated analysis because thedifferential equations (5) and (6) will contain more terms.Also a longer measurement might be required. IV. DISCUSSION
We studied several samples of atomic tritium and hy-drogen stabilized in matrices of T and T :H . The max-imum concentrations of H and T atoms were limited bytheir recombination. Recombination of atomic hydrogenin solid hydrogen matrices at low temperatures proceedsin two steps: a diffusion stage when atoms approach eachother by the distance of a lattice constant followed byrapid recombination into molecules. Kumada[30] showedthat diffusion of hydrogen atoms at temperatures ≃ K0 (cid:1) i(cid:3)(cid:4)i(cid:1) ) (cid:1)i(cid:3)(cid:4)i(cid:6) ) (cid:1)i(cid:3)(cid:4)i(cid:7) ) (cid:8) (cid:9) (cid:10) i (cid:11) (cid:12) (cid:13) (cid:14)(cid:3)(cid:15) (cid:16)(cid:17) (cid:18) i a (cid:11) d (cid:16) d m (cid:22)(d)((d)(d0(d6 (cid:1) (cid:2) (cid:3)(cid:1) (cid:4)(cid:5)(cid:6) ia(cid:26)(cid:1)(cid:27)m(cid:22).dM (cid:22).d6 (cid:22).d4 (cid:22).d0 Figure 10. ENDORs of H atoms in matrices of hydrogenisotopes. The calculated transition frequency for H atoms inthe gas phase is denoted as f proceeds in a series of exchange tunneling reactionsH+H → H + H (7)Similar exchange reaction also governs diffusion of atomicdeuterium in solid D , and is also expected in tritium.However its rate should be much smaller than those forhydrogen and deuterium due to a larger mass and smallerzero-point energies of the reactants. The rate of the gasphase reaction (7) at 4.2 K, k ∼ − cm s − , was cal-culated by Takayanagi et al.[31] and is in a fair agree-ment with the recombination rates of H atoms in solidH . The measured recombination rates for D atoms inD are about 2 orders of magnitude smaller than thosefor hydrogen[32]. Based on that, we may expect that therecombination rates of T atoms in pure T at the sametemperatures should be at least 1-2 orders of magnitudesmaller than those for D in D .The reaction (7) and its isotopic analogs have a largeactivation barrier, E a ≃ K, and proceed at low tem-peratures by tunneling. Any impurity or crystal defectcan perturb the periodic potential of the matrix and cre-ate an energy level mismatch for a tunneling event. Themismatch can be compensated by phonons. Ahokas etal.[16] reported enhancement of recombination rate dur-ing recombination of gas-phase H atoms at the surface oftheir H samples. The recombination rates of T atomsin our samples, k ∼ − − − cm s − , are muchlarger than what could be expected from the rates of theisotopic exchange reaction T+T → T + T which shouldhave a rate at least 3 orders of magnitude smaller thanthe value we obtained. This is an upper limit estimatefor this exchange reaction in the abscence of any limit-ing factors such as energy level mismatch due to crystaldefects. An alternative way can be a physical diffusionof T atoms related to formation of vacancies. Gaines etal. [33] estimated the activation energy for physical dif-fusion of T in T as 411 K which is about 2 times largerthan that for H in H (195 K)[34]. Based on that, onemay expect a cross-over temperature from quantum dif- fusion to Arrhenius-like behavior to be about 2 timeslarger for tritium than that for hydrogen: about 9 Kagainst 4.5 K. The pre-exponential factors for these pro-cesses were found to differ only by a factor of 6 [33], [34]which does not influence the result.Much higher concentrations of T atoms in “pure” T Sample 2 compared to T samples with H admixtures(4,5,6) leads us to expect a faster recombination of Hatoms compared to T. Analysing the differential equa-tions for the evolution of [H] and [T] concentrations inthe T sample 3 and T : H sample 6 we obtained a 3times larger recombination rate for H atoms in the lattersample. β -decay of tritium results in the formation of a largenumber of non-equlibrium vacancies and phonons whichmay lead to a significant enhancement of physical diffu-sion. Ebner and Sung [35] considered two cases of dif-fusion through vacancies in H : tunneling and hoppingto the empty sites. Pure tunneling of a T or H atom ina T matrix should be suppressed due to a large num-ber of lattice defects but it can be enforced by phononsgenerated by tritium decay. The phonons may not onlyhelp to compensate for the energy level mismatch butalso help atoms to hop over the barrier and stimulatephysical diffusion followed by recombination. Due to thevery large energy released in the tritium decay the realtemperature of phonons may be much higher than thetypical storage temperatures ∼ mK used in our ex-periments. Recombination of atoms brings extra heating,which leads to enhancement of diffusion and recombina-tion rate at higher densities of atoms. Such positive feed-back in the system finally leads to a thermal explosionof atoms which occurs at a certain critical density. Athigh enough concentration of atoms even a small increaseof temperature may cause an instantaneous increase ofnumber of phonons and provoke a so-called stimulatedexplosion.The fact that only a fraction of atoms in the film re-combines during explosions may probably be explainedby better stability of atoms more close to the film sub-strate due to better cooling whereas the atoms closer tothe top of the films recombine preferentially. This alsoexplains the absence of thermal explosions in thin filmsand their suppression after adding helium to the samplecell which provides better cooling to the upper surface ofthe film.We tried to estimate possible overheating of the tritiumfilm during a recombination explosion using a simple heatbalance model. We assume that the heat released in a re-combination event is conducted by the phonons from theT film to the quartz microbalance and further down intothe SC lower volume, where part of the recombinationenergy is removed by sublimation of tritium molecules.From the frequency change of our QM we know that ≈ film becomes sublimated after typical explosiverecombination when the density of atoms is decreased by1 × cm − (see Fig.5) corresponding to recombina-tion of ∼ atoms. Taking the sublimation heat ofsolid T , H=1400 J/mol[22], we evaluate that about 1/3of energy released in recombination of atoms is removedfrom the sample by the sublimated molecules. The rest ofthe energy is conducted into the lower volume of the SCand passes through several boundaries between solid hy-drogen and gold electrode, gold-quartz and finally gold-helium interfaces. It turns out that the boundary ther-mal resistance between gold electrode and T film be-comes the bottleneck for cooling the sample. The bound-ary thermal resistances for gold-quartz and solid T -goldinterfaces were calculated using the acoustic mismatchmodel, which agreed with a factor of 2 with experimen-tal values [36]. The temperatures for all layers of themicrobalance: both gold electrodes and the quartz wereestimated by a simple model, similar to the estimate byWyatt[37] using the equations: ˙ q = G ij A ( T nh − T nc ) Here G ij is the thermal boundary conductance be-tween interfaces i and j (e.g. solid hydrogen and gold), A is the QM surface area (1 cm ), n =4 for the solid-solidinterfaces and n =5 for the interfaces between liquid he-lium and solids. T h and T c are the temperatures of thehotter and colder layers respectively. For the estimate ofthe heat power ˙ q we need to know the time duration ofthe recombination explosion event. From our bolometerresponse we obtain the value of τ rec . m s, while thelight flashes observed by Mapoles et. al.[12] indicate thatit can be shorter than 1 m s. Using the heat conductancemodel above for the duration of the recombination ex-plosion of 1 m s we evaluate overheating of the tritiumfilm to ∼
16 K, and ∼
12 K if the explosion occurs during10 m s. Both temperatures are high enough to evaporatesolid tritium, and for substantial enhancement of the rateof the physical diffusion of T atoms.Analysis of our data from ENDOR measurements al-lows making certain conclusions about the structure ofthe tritium films we studied. The lattice structure isestimated from the influence of the host molecules onthe electron clouds of unpaired atoms. Depending on alattice site either a long-range attractive van-der-Waalsinteraction or a short-range Pauli repulsion prevails. Anegative change of the hyperfine constant corresponds tothe substitutional lattice sites where the attractive van-der-Waals contribution takes over. In this work we ob-served a single ENDOR transition for T atoms in solidT corresponding to a ≈ − . MHz shift of the hyper-fine constant with respect to the free atom transition.We have also performed ENDOR measurements for Hatoms in a T matrix. We present it in Fig.10 togetherwith the spectra in the matrices of H and D for thesake of comparison. The change of the hyperfine con-stant of H atoms stabilized in a T matrix was found to be -3.17 MHz which is about 0.1 MHz larger compared tothat of H atoms in the matrices of other hydrogen iso-topes. Tritium molecules have the lowest zero-point en-ergy among the hydrogens and so the lattice constant forsolid T is the smallest as compared to the other isotopes.The H atoms placed in more quantum matrices of lighterhydrogens are pushed further away by the molecules andthe hyperfine constant is closer to that of free atoms.This also explains why the shift of the ENDOR transi-tion of H in T is larger than in H . Observation of asingle ENDOR transition in all four cases indicates thatthe impurity atoms occupy the same substitutional sitein the lattice, and the lattice type is most likely the samefor all matrices. V. CONCLUSIONS
In conclusion, we reported on the first ESR study ofT and H atoms stabilized in “pure” T and T : H ma-trices at temperatures down to 70 mK. The concentra-tions of T atoms approaching × cm − were reachedin pure T films. The record-high concentrations of Hatoms ∼ × cm − were reached in T :H solid mix-tures. It turned out that the isotopic exchange reactionT+H → HT+H proceeds with a much higher efficiencycompared to reaction T+HT → T +H and results in aspectacular T-to-H conversion in T :H mixtures. Theaccumulation of H and T atoms was limited by their re-combination which also occurred in an explosive mannerdepending on the storage conditions. We suggest thatthe main mechanism for H and T migration in solid T is physical diffusion related to tunneling or hopping tovacant sites in the lattice in contrast to isotopic chem-ical reactions which govern diffusion of H and D atomscreated in H and D matrices by other methods.We acknowledge funding from the Wihuri Foundationand the Academy of Finland grants No. 258074, 260531and 268745. This work is also supported by NSF grantNo DMR 1209255. S.S. thanks UTUGS for support. ∗ servas@utu.fi[1] T. Kumada, M. Sakakibara, T. Nagasaka, H. Fukuta,J. Kumagai, and T. Miyazaki, J. Chem. Phys. , 1109(2002).[2] A. V. Ivliev, A. S. Iskovskikh, A. Y. Katunin, I. I. Luka-shevich, V. V. Sklyarevskii, V. V. Suraev, V. V. Filippov,N. I. Filippov, and V. A. Shevtsov, JETP Lett. , 379(1983).[3] E. B. Gordon, A. A. Pel’menev, O. F. Pugachev, andV. V. Khmelenko, JETP Lett. , 282 (1983).[4] S. I. Kiselev, V. V. Khmelenko, and D. M. Lee, Phys.Rev. Lett. , 175301 (2002).[5] T. Miyazaki, K. P. Lee, K. Fueki, and A. Takeuchi, J.Phys. Chem. , 4959 (1984). [6] G. W. Collins, J. L. Maienschein, E. R. Mapoles, R. T.Tsugawa, E. M. Fearon, P. C. Souers, J. R. Gaines, andP. A. Fedders, Phys. Rev. B , 12620 (1993).[7] G. W. Collins, P. C. Souers, J. L. Maienschein, E. R.Mapoles, and J. R. Gaines, Phys. Rev. B , 549 (1992).[8] J. Lambe, Phys. Rev. , 1208 (1960).[9] M. Sharnoff and R. V. Pound, Phys. Rev. , 1003(1963).[10] R. W. H. Webeler, The Journal of Chemical Physics ,2253 (1976).[11] G. W. Collins, E. M. Fearon, J. L. Maienschein, E. R.Mapoles, R. T. Tsugawa, P. C. Souers, and J. R. Gaines,Phys. Rev. Lett. , 444 (1990).[12] E. R. Mapoles, F. Magnotta, G. W. Collins, and P. C.Souers, Phys. Rev. B , 11653 (1990).[13] F. J. Zeleznik, The Journal of Chemical Physics , 4492(1976).[14] G. Rosen, The Journal of Chemical Physics , 1735(1976).[15] J. Ahokas, O. Vainio, J. Järvinen, V. V. Khmelenko,D. M. Lee, and S. Vasiliev, Phys. Rev. B , 220505(2009).[16] J. Ahokas, O. Vainio, S. Novotny, J. Järvinen, V. V.Khmelenko, D. M. Lee, and S. Vasiliev, Phys. Rev. B , 104516 (2010).[17] S. Sheludiakov, J. Ahokas, J. Järvinen, D. Zvezdov,O. Vainio, L. Lehtonen, S. Vasiliev, S. Mao, V. V. Khme-lenko, and D. M. Lee, Phys. Rev. Lett. , 265303(2014).[18] D. G. Truhlar, R. S. Grev, and B. C. Garrett, The Jour-nal of Physical Chemistry , 3415 (1983).[19] Y. Aratono, T. Matsumoto, T. Takayanagi, T. Kumada,K. Komaguchi, , and T. Miyazaki, The Journal of Phys-ical Chemistry A , 1968 (2000).[20] Y. Aratono, T. Matsumoto, T. Takayanagi, T. Kumada,K. Komaguchi, , and T. Miyazaki, The Journal of Phys-ical Chemistry A , 1501 (1998). [21] S. Sheludiakov, J. Ahokas, O. Vainio, J. Järvinen,D. Zvezdov, S. Vasiliev, V. V. Khmelenko, S. Mao, andD. M. Lee, Rev. Sci. Instrum. , 053902 (2014).[22] P. Souers, Hydrogen Properties for Fusion Energy (Uni-versity of California Press, 1986).[23] J. Schou and H. Sørensen, Journal of Applied Physics ,816 (1978).[24] S. Vasilyev, J. Jarvinen, E. Tjukanoff, A. Kharitonov,and S. Jaakkola, Rev. Sci. Instrum. , 94 (2004).[25] N. Bloembergen and R. V. Pound, Phys. Rev. , 8(1954).[26] C. P. Slichter, Phys. Rev. , 479 (1955).[27] S. Sheludiakov, J. Ahokas, J. Järvinen, O. Vainio,L. Lehtonen, D. Zvezdov, V. Khmelenko, D. M. Lee, andS. Vasiliev, Journal of Low Temperature Physics ,120 (2015).[28] T. Miyazaki, in Atom Tunneling Phenomena in Physics,Chemistry and Biology , edited by T. Miyazaki (SpringerBerlin Heidelberg, 2004), vol. 36 of
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