# Grain boundary effects in nanocrystalline diamond from LT transport measurements

Jirˇí J Mareš, Pavel Hubík, Jozef Krištofik, Miloš Nesládek

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Jirˇí J Mareš, Pavel Hubík, Jozef Krištofik, Miloš Nesládek. Grain boundary effects in nanocrystalline diamond from LT transport measurements. Physica Status Solidi A (applications and materials science), 2008, Special Issue: Hasselt Diamond Workshop 2008 – SBDD XIII September 2008, 205, pp.2163–2168. 10.1002/pssa.200879705 . cea-05457739v2

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# Grain boundary effects in nanocrystalline diamond

Jir'í J. Mareš ¹, ¹, Pavel Hubík ¹, Jozef Krištofik¹, and Miloš Nesládek¹, ²

¹ Institute of Physics ASCR, v.v.i., Cukrovarnická 10, 162 00 Prague 6, Czech Republic

² CEA-LIST (Recherche Technologique), CEA - Saclay, 911 91 Gif sur Yvette, France

* Corresponding author: e-mail semicon@fzu.cz, Phone: +420 220318412, Fax: +420 233343184

Thin films of heavily boron doped plasma-enhanced chemical vapour deposition grown nanocrystalline diamond were experimentally investigated by means of low temperature transport methods and noise analysis as well. The influence of grain boundaries on superconductivity and other related quantum phenomena observed in this system was treated using phenomenological model according to which the superconducting diamond grains in the film are interconnected by a single or a few weak links having a characteristic dimension in the nanometre range. Comparing then the experimental values of critical current and current-induced Josephson's noise in the superconductivity transition region with the figures predicted by our model, its relevance for the description of boron-doped nanocrystalline diamond has been proved.

**1 Introduction** Heavily boron-doped nanocrystallinediamond (B-NCD) is a material with promising applica-tions in various branches of science and technology, rang-ing from nanoengineering to electrochemistry and bioelec-tronics. Besides, this material reveals also a lot of proper-ties and effects interesting from the point of view of "pure"science, which can be only hardly observed in other mate-rials. Although this circumstance is mainly due to theuniqueness of diamond itself, it has been recently shown[1] that just the geometrical structure of nanocrystallineaggregates is of primary importance for the very existenceof some low-temperature effects observed in these systems.Therefore, before approaching this subject, the geometry ofB-NCD films should be mentioned first.

An important step prior to the growth of B-NCD filmsby plasma-enhanced chemical vapour deposition (PE-CVD) technique is a special treatment of the substrate theam of which is to prepare a sufficiently dense pattern ofnucleation centres there [2]. Without such patterns thediamond films do not grow at all or their growth is largelyirreproducible. It is thus necessary to submit the substrateto a controlled impact of diamond powder in an ultrasonicvibration table. For different settings of technologicalparameters (e.g. diamond powder grain size ranging~5-50 nm, intensity and duration of vibrations, hardnessof the substrate) such a treatment results either in a randomarray of indentations or in a random coverage of substrateby diamond nanocrystals "sticking" on the surface. Typicaldensities of indentations or nanocrystals are as high as~10¹⁵ m². As the indentations are exact imprints of dia-mond facets in e.g. glass, during the initial phase of thePE-CVD growth the shape-related part of Gibbs's energyis minimized there and, consequently, the nucleation rate isenhanced appreciably. Of course, the enhancement of nu-cleation rate due to the presence of diamond nanoparticleson the substrate, e.g. synthetic detonation nanodiamond oftypical size 5 nm, should be even more effective (seeFig. 1). The final result of both these treatments is, how-ever, essentially the same; the positions and orientations ofnucleation centres on the substrate are quite random.Therefore, also the matching of the lattices of the neigh-bouring diamond crystals in ready-made polycrystallinefilm cannot be perfect in principle. On purely geometricalgrounds the satisfactory matching of neighbouring grainscan be achieved only in a limited number of small spotswhile the rest of the space between grains is filled withnon-diamond disordered phase of rather a complicated na-ture containing an appreciable amount of graphite [3].

The effect of granularity of highly doped NCD may beclearly demonstrated by a typical low-temperature phenomenon, superconducting (SC) transition. The sharpness ofthe SC transition observed in various equally boron-dopeddiamond systems is, namely, different for systems havingdifferent grain size. If we specify the relative width oftheSC transition as a ratio δT/T<sub>c</sub> where δT is the differencebetween the on-set and the off-set transition temperaturesand T<sub>c</sub> is the off-set transition temperature (see Fig. 2), weobtain the following figures. For materials having grainsize from the ~100 nm range, i.e. for really nano-crystalline materials this ratio δT/T<sub>c</sub> ≈ 0.3-0.4 [4-6]whereas for films composed of crystals larger than ~10 µmand for epitaxial single crystal layers this ratio attains anappreciable smaller value, δT/T<sub>c</sub> ≈ 0.1 [7-9].

This illustrative example shows without ambiguity thatthe grain boundaries really do influence the low tempera-ture phenomena in highly B-doped diamond films but priordetailed analysis of such influence it is necessary to sum-marize our knowledge concerning these phenomena per se.

**2 Mott's metal at low temperatures** Numerousexperimental observations lead to consensus that the transition of heavily B-doped diamond into superconductingstate can take place just only if the system becomes socalled Mott's metal. In order to ensure the metallic behavior of typically insulating system as genuine diamond un-doubtedly is, it is necessary to increase the shallow impurity doping concentration above a certain critical value NCgiven by a semi-empirical relation N<sub>C</sub><sup>1/3</sup>aB ≈ 1/2(2π)<sup>1/3</sup> [10], where aB is impurity Bohr's radius (for boron in aB ≈ 3.1 × 10<sup>-10</sup> m, N<sub>C</sub> ≈ 6.7 × 10<sup>26</sup> m<sup>-3</sup>). Therefore, at me-tal-insulator transition, where the boron concentration justexceeds

<figure><img src="image_2.png" /><figcaption>**Figure 1** Two modes of the nanodiamond nucleation; (a) from indentations due to ultrasonic treatment by diamond powder and (b) from the seeding particles of detonation nanodiamond.</figcaption></figure>
the critical value N<sub>c</sub>, the Fermi level originally pinned by boron impurities in the gap at about E<sub>B</sub> ~ 0.37 eV above the top of valence band has to be shifted to the top of the valence band. The relation between such a shift and required acceptor concentration NC is given by a standard formula [11, 12]

$$E_B = [3(2\pi)^2/4]^{2/3} (\hbar^2 N_c^{2/3}/2m) . \quad (1)$$

Putting there m ≈ m<sub>e</sub>, we obtain immediately another estimate for N<sub>c</sub> ≈ 1.03 × 10<sup>27</sup> m<sup>-3</sup> which is close (notice the ~20% uncertainty in effective mass of holes and permittivity!) to the value given by Mott's semi-empirical formulation above. The agreement between these two independent estimates strongly supports the view that there must exist an enhancement of density of states near the top of the valence band, which is quite sufficient for pinning of the Fermi level there, ensuring thus the metallic behaviour of the system.

There are, however, substantial differences between regular metals and Mott's metal realized by heavily doped B-NCD system. Common metals have, namely, the regular crystal lattice, whereas the boron sublattice in B-NCD which is responsible for the metallic character of this material is quite random (cf. e.g. impressive STM images in [13]). Notice that such a type of disorder is a matter of special importance because the absence of translational invariance of electron-phonon interaction between holes and localized impurity-induced phonons makes the generation of superconducting translational-symmetric state extended over the whole volume, by localized phonons, unlikely. Also the transport properties of disordered Mott's metal differ from those of regular metal. In normal metal, at temperatures low in comparison with Debye's temperature, the electric conductivity is controlled by inelastic interaction of charge carriers with the lattice vibrations (Bloch-Grüneisen's mechanism) and by direct inelastic collisions between electrons or holes (Barber's mechanism) [14]. Such behaviour is, however, characterized by monotonic decrease of resistivity with decreasing temperature, in contrast with behaviour observed in B-NCD. This witnesses the fact that besides the above mentioned two mechanisms another mechanism has to operate there simultaneously which is not directly linked with inelastic scattering and which plays a decisive role at low temperatures.

Figure 2 Dependence of resistance R of B-NCD sample on temperature T in Kelvin range. Hatched area shows a region of transition between normal and superconducting behaviour.

<figure><img src="image_3.png" /><figcaption></figcaption></figure>

**3 Fundamental scaling parameters** In such a situation where the processes taking place between two subsequent inelastic collisions become significant, a parameter characterizing the intrinsic spatial extent of coherence of electron (hole) wave function starts to play an extraordinary role. This quantity called coherence length measures in fact the remaining disturbing influence of environment on the phase of the moving electron. The phase-breaking due to the omnipresent electric fluctuations, such as equilibrium thermal radiation (optical phonons) and random field generated by other electrons, can be described by the famous Aharonov-Bohm's quantum relation for phase shift over the path C [15], namely

$$\delta\varphi = (e/\hbar) \int_c (\partial t/ \partial x) \psi \, dx, \quad (2)$$

where ψ = ψ(x, t) is the time dependent electric potential inside the material. Assuming, in accordance with experiments, that the potential fluctuations are confined only to the kT-band, relation (2) can be used for a closed test path C rewritten in the form

$$\delta\varphi \approx (e\psi/\hbar v_F) \times (\xi b), \quad (3)$$

where v<sub>F</sub> is the Fermi velocity, ξ the coherence length (i.e. the external measure of the kernel of the wave function) and β the ratio between the coherence length and the actual length of the test path C. Finally, making somewhat arbitrary but physically reasonable assumption that the phase change of δφ ≈ 1 makes a wave function completely incoherent, we obtain for fundamental length scale represented by the coherent length a simple formula

$$\xi = \hbar v_F / \beta \, \text{kT}. \quad (4)$$

Of course, the value of the dimensionless parameter β depends to some extent on the convention. For example, for the square test path β = 4, for the circular path β = π and for the double circular loop corresponding to Cooper's pair, β should be equal to 2π. Notice that relation (4) involves also a time scaling parameter τ = ħ/kT (coherence time) having the following very obvious physical meaning: on the grounds of quantum uncertainty relation, for time periods ≤ħ/kT, the influence of environment is insufficient to destroy the coherence of electron (hole) wave function. Therefore, all the processes having duration shorter than this limit must be essentially non-dissipative and reversible in thermodynamic sense [16]. Such a regime known in the literature as Ornstein's diffusion regime gives a room for plenty of effects involving e.g. ballistic electron transport, weak localization and superconductivity. In contrast, for an single process having duration appreciable longer than ħ/kT the interaction with environment becomes essential, as a rule, the process is irreversible and dissipative. Such a situation corresponds to so-called Einstein's diffusion regime. As the distinguishing between reversible (non-dissipative) and irreversible (dissipative, entropy producing) processes is crucial for their correct interpretation, it is evident that the evaluation of coherence length and coherence time is of primary importance.

**4 Ballistic transport and inter-grain matching** Let us evaluate first the coherence length and the coherence time intrinsic at helium temperature to the hole wavefunction in B-NCD. Putting β = 4 and v<sub>F</sub> ≈ 5 × 10<sup>5</sup> m/s, we obtain from formula (4) at T ≈ 4.2 K the following estimates: ξ ≈ 2.3 × 10<sup>-7</sup> m and τ ≈ 1.8 × 10<sup>-12</sup> s. It is apparent at first glance that the extent of coherent wave function is comparable with the typical dimension of diamond grains in B-NCD film which is d ≈ 200 nm. We can thus imagine that the interior of every grain is filled with
the coherentwave function which can be transferred to the neighbour-ing grain only via a small spot where, as has been men-tioned above, the lattice mismatch of both grains is mini-mal. As the dissipation due to the carriers which are pre-vailingly in Ornstein's diffusion regime is negligible, thelow temperature inter-grain resistance has to be controlledmainly by a resistance value of such a spot. The corre-sponding figure may be determined using modified 3D Sharvin's formula [17]

$$R_N = (\hbar/e^2) (2\pi/k_F b)^2, (5)$$

where k<sub>F</sub> is the absolute value of the wave vector at the Fermi level and b<sup>2</sup> the effective cross-section of the saidspot. Of course, the electric current can in principle flowfrom one grain to another also directly through the graph-ite-like phase filling up the space between the diamondgrains. Taking into consideration, however, the fact thatthe carriers have to suffer at such a discontinuity enormousinelastic scattering, such a transport path can be efficientonly at sufficiently high temperatures where the coherence-length becomes very small and the ballistic transportceases. It can be further shown by a somewhat idealizedgeometrical consideration that the quantity R<sub>N</sub> is simply re-lated to the experimentally observed resistance (per square)of the film as a whole, only provided that the transport re-gime is ballistic. Indeed, assuming that the film consists ofα regular square arrays of constrictions (every one ofwhich has a resistance ~R<sub>N</sub>) stacked one onto another, theresulting resistance (per square) R of such a system shouldbe R ≈ R<sub>N</sub>/α. As the film resistance (per square) measuredat ~1.7 K is ~200 Ω, thickness of the layer ~400 nm andgrain size d ≈ 200 nm (i.e. α ≈ 2), we immediately obtainfor inter-grain resistance an estimate R<sub>N</sub> ≈ 4 × 10<sup>-2</sup> Ω. Tak-ing then into account that k<sub>F</sub> ≈ 4.3 × 10<sup>-9</sup> m<sup>-1</sup> (as above,vF ≈ 5 × 10<sup>5</sup> m/s, m ≈ m<sub>e</sub>), and substituting the values of k<sub>F</sub> and R<sub>N</sub> into Sharvin's formula (5), we obtain an estimatefor external measure of the spot matching neighbouringgrains, namely, b ≈ 5 nm.

**5 Weak localization and superconductivity**

Our recent low temperature transport experiments have provedunambiguously that the existence of temporarily stable in-terference patterns in highly doped nanocrystalline dia-mond films is a matter of fact [5, 18]. Such patterns, alter-natively called weakly localized orbits, represent physicalentities enabling a unified approach to the understanding ofmajority of non-dissipative processes in these materials. Itshould be noticed first that the effect of weakly localizedorbit on electric transport is somewhat ambiguous. In case,namely, where the electron or hole is captured by weakly localized orbit these charge carriers cannot contribute tothe current and the resistance of the system thus increases. For example, such an increase of resistance with decreas-ing temperature is systematically observed in B-NCD justabove the SC transition [5]. On the other side, at suffi-ciently low temperatures the weakly localized orbit repre-sents a fully coherent state occupying an almost macro-scopic region (see Fig. 3). The scattering of a carrier into such a state and the subsequent scattering out of this stateat another place, departed say by ξ, may be treated as a combination of two spatially confined dissipative eventsand non-dissipative transfer of a carrier over the relativelylarge distance ξ. The idea just described served as a basisfor a model of unconventional superconductivity in B-NCD alternative to BCS theory. Accordingly, the holes onweakly localized orbits may be coupled by spin-spin in-teraction into the Boson-like pairs which can be furtherchained till the collective non-dissipative wave functionoccupying the whole volume of the sample arises [5]. Sucha scenario accounting for the genesis of superconductivestate in disordered B-NCD simultaneously gives the fol-lowing simple formula for critical temperature

<figure><img src="image_4.png" /><figcaption>**Figure 3** Illustration of ambiguous role of weakly localized orbit (with the coherence length ξ): entity immobilizing free charge carriers vs. entity enabling non-dissipative charge transport over macroscopic distances.</figcaption></figure>

$$kT_c = \mu_0\mu_s^2/\lambda b^3, (6)$$

where λ is a dimensionless constant ~1, b the effective in-ter-atomic distance in diamond lattice and k, μ<sub>0</sub>, and μB areBoltzmann's constant, permeability of vacuum and Bohr'smagneton, respectively. Formula (6) provides a reasonableestimate for actually observed transition temperature T<sub>c</sub>(e.g. for λ = 1, b = 1.54 × 10<sup>-10</sup> m, T<sub>c</sub> = 2.14 K). Besides, italso predicts the dependence of T<sub>c</sub> on the deformation ofthe diamond lattice which has been observed only recently. Formula (6) may be quite formally also rewritten in termsof "superconducting gap" Δ(0), using Cooper's relation inthe form kT<sub>c</sub> ≈ Δ(0)/2λ, which is more useful in sometypes of considerations.

It should be noticed here that the superconductive net-work in B-NCD is not very dense. Taking for granted thefact that the superconductivity is due to the Bose condensa-tion of paired holes on weakly localized orbits, their num-ber, n<sub>s</sub>, required for the creation of the dense Bose conden-sate sufficient for the superconductive transition is givenby a formula [19]

$$kT_c = (\pi\hbar^2/m) [n_s/2\zeta(3/2)]^{2/3}, (7)$$

where ζ(3/2) ≈ 2.6124 is Riemann's zeta function. Puttinginto relation (7) an experimentally observed value for T<sub>c</sub> ≈ 1.67 K, we immediately obtain that n<sub>s</sub> ≈ 7.8 × 10<sup>22</sup> m<sup>-3</sup>.In other words, the ratio between the number of normalholes and the number of holes belonging to the supercon-ducting state in the vicinity of transition temperature is asmall as ~10<sup>-4</sup>.

**6 Weak link**

Central concept of superconductivity ininhomogeneous systems is so called weak link [20]. This isa region inserted between two lumps of superconductorwhere the order parameter is reduced appreciably, however,without ceasing. The weak link has not the properties of aregular superconductor, nevertheless, it is simultaneouslyassumed to be able to carry supercurrent. The most fre-quent model of the weak link is a resistively shunted junc-tion. The total current flowing through the weak link isplit there into a supercurrent component flowing directlythrough the junction and a normal current flowing throughthe shunt resistance. As the amplitude of the supercurrenthas its upper limit given by a value of the critical current, I<sub>c</sub>, the weak link inserted into the superconducting systembrings about the so-called resistive behaviour. Under thisname one understands the finite sharpness of supercon-ducting transition and the appearance of ohmic resistancein this region. Another extremely important consequenceof insertion of the weak link into the
superconducting cir-cuit is an appearance of Josephson's supercurrents. It is rather fundamental quantum feature of supercurrent that itis, in a contrast to normal current, driven not by the voltagebut by the phase difference. As, on the basis of quite gen-eral quantum-mechanical considerations [21], the observedrate of change of the electron (hole) phase difference be-tween two distinct points in the superconductor is directlyproportional to the difference of electrochemical potentialsat these points, the following relations between the voltagedrop and the supercurrent may be deduced. For zero volt-age drop (e.g. in the absence of weak link) the phase dif-ference will be constant giving rise to a constant d.c. su-percurrent. Alternatively, at a finite constant voltage dropmaintained on the weak link by some external mean thephase difference will continually grow. In such a case,however, because of the 2π periodicity of the phase also anoscillating supercurrent reflecting this periodicity shouldappear there [22]. The frequency f of this co called Joseph-son's a.c. supercurrent is given by a fairly simple formula

$f = eV/\pi h, (8)$

where on the right side besides universal constants there isonly a voltage drop V across the weak link. As has alreadybeen mentioned above (see Fig. 2), the well pronouncedresistive behavior is the characteristic feature of the nano-crystalline form of heavily boron-doped diamond. There-fore, because of lack of another plausible explanation ofthis very fact the existence of the weak links and conse-quently, the manifestations of Josephson's effects have tobe expected there. Moreover, in this connection, it seemsto us that the identification of the above discussed spotsmatching the neighboring grains with weak links is quite anatural and physically reasonable assumption.

**7 Current-induced Josephson's noise** In order toprove the above assumed existence of a.c. Josephson's ef-fect in B-NCD also experimentally, an arrangement ex-ploiting the superconducting circuit with intrinsic weaklinks as a voltage-to-frequency convertor, has been used. Asquare sample of B-NCD film provided in its corners withTi/Au contacts, in which the transition into superconduct-ing state was already established, was placed in a screenedcavity in a helium cryostat and connected as shown in theinset of Fig. 4. The exciting current was supplied to twoneighbouring contacts on the sample by a floating sourcerealized by a galvanic cell with potentiometer. The r.f. sig-nal was then collected from the two other voltage probes ofthe sample and analysed by a high-quality band-pass filterfollowed by a low-noise amplifier and an oscilloscope. Thehome-made band-pass filter tuneable in a vicinity of10 MHz (±0.5 MHz) was realized by a normal capacitorwith build-in toroidal coil winded on a Teflon core. In spiteof that the whole circuitry was carefully screened andgrounded at one point only, an appreciable backgroundnoise signal, likely due to heavy electromagnetic pollutionpresent in the vicinity of our laboratory, was observed. Inorder to identify unambiguously Josephson's component ofthe noise, the superconducting properties of the samplewere changed by the application of magnetic field with theB-vector perpendicular to the B-NCD film and other auxiliary tests (e.g. switching-off the current source with simul-taneous shortening of the potentiometer) were performed.

<figure><img src="image_5.png" /><figcaption>**Figure 4** Noise voltage signal measured at frequency of ~9.7 MHz at temperature 1.3 K in dependence on the magnetic field *B*; d.c. current used for excitation was 10 mA. Inset shows a schematic arrangement of the experiment.</figcaption></figure>

Applying, at a constant temperature of ~1.3 K < T<sub>c</sub> and at zero magnetic field, a slightly subcritical exciting cur-rent I ≈ 10 mA, (I<sub>c</sub> ≈ 11.1 mA), a maximal enhancement ofthe signal was observed at frequency of ~9.7 MHz. Thiseffect, which should be according to our expectations dueto the generation of a.c. Josephson's oscillations in thesample, may be consistently accounted for as follows. Thenormal current, i<sub>N</sub>, flowing through the resistance R<sub>N</sub> shunt-ing the Josephson junction in the corresponding weak linkgives rise to a voltage drop between neighbouring super-conducting grains so that an oscillating supercurrent has toappear there. Taking then into account relation (8), thenormal current necessary for the generation of Josephson'soscillations at frequency f can be evaluated using an obvi-ous formula

$i_N = \pi h f / e R_N . (9)$

Therefore, the corresponding value of the normal currentshunting the typical weak link and generating an a.c. signalof frequency ~9.7 MHz is thus i<sub>N</sub> ≈ 5.0 × 10<sup>-11</sup> A. This fig-ure may be immediately compared with the value of thesuperconducting current component as given by Larkin'sformula [20]

$i_c \approx \Delta(0)/eR_N . (10)$

For our case where R<sub>N</sub> ≈ 4 × 10<sup>2</sup> Ω, Δ(0) = 3.7 × 10<sup>-4</sup> eV, we obtain a value i<sub>c</sub> ≈ 9.2 × 10<sup>-7</sup> A which is much higherthan the value of i<sub>N</sub> above. We can thus conclude that thebranching-off of the normal current component in weaklink is almost negligible there.

The situation, however, changes noticeably if the mag-netic field is applied. By increasing magnetic field,namely, the critical supercurrent diminishes. Keeping thusthe total current through the sample constant, the normalcurrent i<sub>N</sub> through every weak link should appreciably in-crease enhancing the voltage drop between neighbouringSC grains and shifting simultaneously the Josephson oscil-lations to higher frequencies. Just such an effect can beseen in Fig. 4 where the signal amplitude observed at aconstant frequency of ~9.7 MHz decreases with increasingmagnetic field till the background level of noise signal isreached. As we are convinced, it confirms the fact that thevery nature of so-called resistive behaviour is just thebranching-off of the normal current from the total currentflowing through the weak link. The branching-off, with in-creasing total burden of the weak links, may evidently con-tinue to the situation characterized by a condition

$i_N \approx i_c, (11)$
where Josephson's frequency attains a huge value given by $f_c \approx \Delta(0)/\pi\hbar$, ($f_c \approx 1.8 \times 10^{11}$ Hz) and which cannot be evi-dently studied by means of our experimental arrangement.In such a case, however, according to Eq. (10), the poten-tial step at the weak link becomes comparable with the SC gap voltage, $\Delta(0)/e$, and consequently, due to the strongscattering a complete destruction of Cooper's hole pairsshould take place there. Therefore, relation (11) may be in-terpreted also as a new condition for the onset of SC, de-fining the upper bound of the SC transition region wherethe resistive behaviour is observed.

**8 Conclusions** In conclusion, low temperature trans-port and current-induced Josephson's noise in heavily bo-ron-doped nanocrystalline diamond (B-NCD) PE-CVD grown films have been investigated experimentally. Theresults confirm the view that at low temperatures theneighbouring grains are electrically connected only in afew spots having characteristic dimensions of ~5 nm.These spots play either the role of transport channels fornormal carriers in the ballistic regime or the role of weaklinks generating Josephson's a.c signal if the system is inthe superconducting state. Furthermore, it has been shownthat just the granular structure of B-NCD films is the con-dition sine non qua for the existence of these interestingquantum effects.

**Acknowledgements** This work was supported by theCzech Science Foundation Contract No. 202/06/0040. Further-more, the research work at the Institute of Physics was supportedby Institutional Research Plan No. AV0Z10100521.

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