Supersolidity, disorder and grain boundaries

1. Supersolidity, disorder and grain boundaries S. Sasaki, R. Ishiguro, F. Caupin, H.J. Maris and S. Balibar Laboratoire de Physique Statistique (ENS-Paris) now at North Western Univ. (USA) now at Tokyo University (Japan) Brown University, Providence (RI, USA) • - S. Sasaki et al. , Science 313, 1098 (2006) • - S. Sasaki , F. Caupin and S. Balibar, Phys. Rev. Lett. 99, 205302 (2007) • S. Balibar and F. Caupin « topical review » J. Phys. Cond. Mat. 20, 173201 (2008) • S. Sasaki , F. Caupin and S. Balibar, to appear in J. Low Temp. Phys. (Nov. 2008)  de la Physique, Saclay, 23 oct. 2008

2. a « supersolid » is a solid which is also superfluid a paradoxical idea solid : transverse elasticity, i.e. non-zero shear modulus a consequence of the localization of atoms crystals - glasses superfluid : a quantum fluid with zero viscosity a property of interacting Bose particles, which are indistinguishable and delocalized

3. rigid axis ( Be-Cu) solid He in a box excitation detection superfluid fraction (NCRIF) Temperature (K) could solid helium 4 flow like a superfluid ? E. Kim and M. Chan (Penn. State U. 2004): a « torsional oscillator » (~1 kHz) a change in the resonance period below ~100 mK 1 % of the solid mass decouples from the oscillating walls ? no effect in helium 3 (fermions)

4. E0 Andreev and Lifshitz 1969: delocalized vacancies could exist at T = 0 ( the crystal would be « incommensurate ») BEC => superplasticity at low velocity and long times coexistence of non-zero shear modulus and mass superflow ! zh early theoretical ideas Among others, off diagonal order (Penrose et Onsager 1956): no supersolidity symmetrization and overlap of wave functions (Reatto 1969, Chester 1969, Leggett 1970, Imry et Schwartz 1975), the rotation of a quantum solid (Leggett 1970) ...

5. more recent ideas (a selection...) Prokofev , Svistunov, Boninsegni, Pollet, Troyer 2005-7 (MC calc.): no supersolidity without free vacancies ; the probability for a real quantum crystal to be commensurate and supersolid is zero 4He crystals are commensurate (Evac = 13K) => not supersolid BUT BEC is possible in a 4He glass (Boninsegni et al. PRL 2006, see also AF Andreev JETP Lett. 2007) Galli and Reatto 2006 : variational calculation with particular trial wave functions (« SWF ») which describe the properties of solid 4He => supersolidity in a commensurate crystal ! Clark and Ceperley (2006) : supersolidity depends on trial wave functions no supersolidity in « exact » calculations ( quantum path Integral Monte Carlo); crystals are commensurate, no vacancies at T = 0, no supersolidity in perfect crystals other models of quantum crystals : Cazorla and Boronat (PRB 2006) Josserand, Rica and Pomeau (PRL 2007) supersolidity but are these models realistic ?

6. other theoretical ideas Anderson Brinkman and Huse (Science 2005): new analysis of the lattice parameter a/a (T) and the specific heat Cv(T): a small density of zero-point vacancies (< 10-3 ?); TBEC~ a few mK ; s ? not confirmed by neutron scattering (Blackburn et al. PRB 2007) critics by H.J. Maris and S. Balibar (J. Low Temp. Phys. 147, 539, 2007) two transitions ? a vortex liquid ? could supersolidity be due to the presence of defects in crystals ? Dash and Wetlaufer 2005: the He-wall interface could be superfluid PG de Gennes (Comptes Rendus - Physique 7, 561, 2006): the mobility of dislocations could depend on T; frequency dependence ? (see Kojima et al. 2007) Pollet et al. (Monte Carlo): grain boundaries should be supersolid Boninsegni et al. 2007: dislocation cores should be supersolid Biroli and Bouchaud (2008): dislocations fluctuate and favor atom exchange

7. the role of disorder:annealing, quench-cooling, grain boundaries Rittner and Reppy (Cornell, 2006-7): supersolidity disappears after annealing s up to 20 % if the samples are grown by quench-cooling the liquid from its normal state Sasaki, Ishiguro, Caupin, Maris et Balibar (ENS, Science 2006) : a dc-flow experiment with solid helium 4 superfluid mass transport in the presence of grain boundaries

8. the role of disorderS. Sasaki et al. Science 313, 1098, 2006 hélium liquide fenêtre a glass tube (1 cm ) cristallization from superfluid liquid at 1.3 K cool down to 50 mK a height difference between inside and outside any relaxation ? hélium solide any variation of the inside level requires a mass current through the solid because C = 1.1 L

9. liquid phase liquid LS LS  liquid liquid crystal 2 crystal 1 solid GB solid grain boundary the physics of grain boundaries mechanical equilibrium of the liquid-solid interface : GB LS cos each groove signals the existence of an emerging grain boundary dynamics of grain boundaries : large mobility + pinning on walls

10. without grain boundaries, no flowwith grain boundaries, superfluid flow time accelerated x 250 supersolidity is not an intrinsic property of the crystalline state of helium 4, a property associated with its defects annealing - quench (Rittner and Reppy 2006-2007)

11. cristal 2:relaxation at50 mK relaxation is linear, not exponential a superfluid flow at its critical velocity 2 successive regimes: 6 m/s for 0 < t < 500 s 11 m/s for 500 < t < 1000 s more defects in the lower part of crystal 2

12. crystal 1 : only one grain boundary relaxation at V = 0.6 m/s stops when the grain boundary unpins and suddenly disappears If 1 grain boundary only with a superfluid thickness e ~ 0.3 nm , width w ~ 1cm the critical velocity inside should be: vcGB= (D2/4ews)(C-L)V =1.5(a/e)(D/w)(C /s)m/s comparable with 2 m/s measured by Telschow et al. (1974) for liquid films of atomic thickness

13. Pollet et al. PRL 98, 135301, 2007 grain boundaries : ~ 3 atomic layers superfluid except in special directions Tc~ 0.2 à 1 K depending on orientation critical velocity ?

14. a 1% superfluid density is large! (Rittner and Reppy 2007: 20% in quenched samples !) • s = 1% => grain size ~ 100nm • s = 0.03% => 3 m is it possible ? may be • how does the grain size depend on the growth method ? • constant P or contant V • from the normal liquid • from the superfluid • slow or fast • cell geometry (T gradients)

15. the ENS high pressure cell 2 cells : 11 x 11 x 10 mm3 or 11 x 11 x 3 mm3 thermal contact via copper walls thickness 10 mm 2 glass windows (4 mm thickness) indium rings => leak tight stands 65 bar at 300K pressure gauge (0 to 37 bar)

16. at T < 100 mK from the superfluid, fast growth and melting of a high quality single crystal 11 mm real time, 60 mK

17. fast growth from the normal liquid at T > 1.8 K dendrites T = 1.87 K fast pressurization of the normal liquid => dendritic growth similar to Rittner et Reppy’s quenched samples ? 11 mm

18. T = 2.58 K helium snow flakes is the roughening transition reentrant ? facets at T < 1.3 K and at T > 2 K ? Balibar, Alles and Parshin, Rev. Mod. Phys. 2005 remember Burton, Cabrera and Frank 1949-51

19. slow growth from the normal liquid at constant V growth in ~ 3 hours a temperature gradient : Twalls < Tcenter the solid is transparent but polycrystalline

20. melting a crystal after growth at constant V T = 0.04 K liquid channels appear where each grain boundary meets the glass windows grains < 10 m ripening

21. ripening at the liquid-solid equilibrium(another example)T < 0.1 K minimization of surface energy mass transport through the superfluid latent heat L = 0

22. thickness 10 mm thickness 3 mm angle 2 2 crystals + 1 grain boundary the groove angle is non-zero => the grain boundary energy GBis strictly < 2 LS => microscopic thickness , in agreement with Pollet et al. (2007). a complete wetting would imply GB LS (2 liq-sol interfaces with liquid in between) the contact line of grain boundaries with each window is a liquid channel

23. angle 2 angle measurement => grain boundary energy • align the optical axis • fit with Laplace’ equation near the cusp •  = 14.5 ± 4 ° • GB= (1.93 ± 0.04) LS other crystals : •  = 11 ± 3 °  = 16 ± 3 °

24. largeur w ; épaisseur e inverst prop. à la profondeur z (w ~ 20 m à z = 1 cm) lc : longueur capillaire the width w and the thickness e are inversely proportional to the depth z lc : capillary length near a wall : wetting of grain boundaries GB grain 2 grain 1 liquid grain 1 grain 2 wall wall S. Sasaki, F. Caupin, and S. Balibar, PRL 99, 205302 (2007) The wall is favorable to the liquid. If GBis large enough, more precisely if + c < /2the liquid phase wets the contact line. an important problem in materials science (see JG Dash Rep. Prog. Phys. 58, 115, 1995) prediction: liquid channels also where grain boundaries meet each other => between 25 and 35 bars a polycrystal contains many liquid channels

25. between 3 grains stable channels if Miller and Chadwick Acta metall. ’67Raj Acta metall. mater. ’90

26. 5 µm grain boundaries in classical crystals wetting of boundaries by the liquid phase ? Besold and Mouritsen ’94 Monte-Carlo simulation colloidal crystals Alsayed et al. Science ’05 Tm=28.3C

27. short and long range S t L S Schick and Shih PRB ’87 short range forces: complete wetting the thickness t diverges at the liquid-solid equilibrium long range forces : incomplete wetting, microscopic thickness consequences : impurity diffusion (ice), mechanical rigidity

28. the channel width w ~ (P-Pm)-1 the channel width w decreases as 1/ z (the inverse of the departure from the liquid-solid equilibrium pressure Pm) agreement with new measurements of the contact angle c liquid channels should disappear around Pm + 10 bar (where 2w ~1 nm)

29. melting growing hysteresis of the contact angle copper copper advancing angle : 22 ± 6 ° (copper) 26 ± 7 ° (glass) 37 ± 6 ° (graphite) receeding angle : 55 ± 6 ° (copper) 51 ± 5 ° (glass) 53 ± 9° (graphite) perhaps more hysteresis on copper rough walls than on glass or graphite walls whose roughness is smaller. as expected from E. Rolley and C. Guthmann (ENS-Paris) PRL 98, 166105 (2007)

30. a stacking fault : low energy, no liquid channel growth shape equilibrium shape between 2 crystals with same orientation GB smaller  larger   + c > /2no liquid channel see also H. Junes et al. (Helsinki) JLTP 2008 : 2 = 155 ± 5°

31. liquid liquid solid solid 2 possible interpretations of the experiment by Sasaki et al. (Science 2006) • mass transport either • along the grain boundaries (then vc~ 1 m/s) • or along the liquid channels • (then vc~ 3 mm/s). • This would explain why flow was observed also at 1.13 K • future experiments : • change the cell geometry, • reduce the width of liquid channels with an electric field • study h(t) with more accuracy with 1 fixed grain boundary

32. Chan et al. (sept. 2007): anomalies in single crystals grown at constant T and P are grain boundaries (together with their liquid channels) responsible for everything ? NO!

33. a superfluid network of dislocations ? Boninsegni et al. PRL 2007 along one dislocation, a coherence length l ~ a (T*/T) percolation of quantum coherence in a 3D network ? May be, but Tc << 100 mK... furthermore, helium 3 impurities increase Tc !

34. shear modulus oscillator period Day and Beamish (Nature 2007): the shear modulus increases ! similar anomalies the shear modulus increases by ~ 15 % below 100 mK (depending on He3 content!) pinning of dislocations by 3He impurities ? and grain boundaries (samples grown at constant V) ? another explanation for torsional oscialltor measurements : K increases ?

35. my opinion in June 2008 ... theory: a quasi-general consensus no supersolidity in a perfect crystal (without defects) dislocations, grain boundaries and glassy helium (if it exists...) should be superfluid at low T experiments: 2 main interpretations are possible 1 - superfluidity of some fraction of the mass, associated with defects in a mysterious way  (I/K)1/2 decreases because the inertia I decreases 2 - no superfluidity a change in the dynamics of defects (dislocations ? grain boundaries ?) the elastic constant K increases

36. new experiments by Rittner and Reppy 2008 no period change in a blocked annulus there is a macroscopic mass current in a free annulus

37. Kim and Chan 2008: influence of 3He impurities the dependence on 3He concentration is consistent with a simple model of adsorption on dislocations

38. new experiments by Beamish et al. 2008 He3 hcp and He4 hcp : same elastic anomalies He3 bcc: no elastic anomalies He4 bcc: supersolidity ? supersolidity is clearly linked to quantum statistics

39. ... and my opinion at the end of August 2008 the existence of supersolidity in solid helium 4 is confirmed it is associated with the existence of defects but also to the presence of 3He impurities it is not a purely elastic effect Supersolidity appears when 3He adsorbs on defects ! WHY ?? in liquid 4He, 3He acts against superfluidity An idea by B. Svistunov (Trieste, 22 August 08): by condensing at the nodes of a dislocation network, the 3He could provide a connection between the dislocations of the 4He crystal ...

40. perspectives Measure the rotational inertia and the shear modulus in samples with well characterized disorder : single crystals (oriented ? measure the dislocation density ?), polycrystals, glassy samples ... optics, X - rays, neutrons, thermal conductivity... search for superfluidity inside grain boundaries : flow experiments in a cell with 1 stable grain boundary and reduce the effect of liquid channels (electrostriction) measure the quantum dynamics of defects theory of quantum defects (quantum metallurgy)