techniques available at kilohertz repetition 28. C. Kan and N. H. Burnett, unpublished results. 30. L. Xu et al., Opt. Lett. 21, 2008 (1996). rates offer the potential for attosecond- 29. The electric field of a light pulse can be described in 31. We are indebted to A. J. Schmidt for his encourage- terms of a carrier of frequency and a time-varying ment and T. Brabec for useful discussions. K. Fe- resolution atomic spectroscopy and nonlin- 0 envelope of amplitude A(t ): E(t ) ϭ A(t )exp[Ϫi(0t ϩ rencz (Research Institute for Solid State Physics, ear optics in the x-ray regime. )]. This decomposition can be used to pulse dura- Budapest, Hungary) is gratefully acknowledged for tions down to the carrier oscillation cycle [T. Brabec manufacturing the silver foils. This research was sup- REFERENCES AND NOTES and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997)]. ported by the Austrian Science Foundation under ______The parameter is the relative carrier phase. It de- grants P-11109 and Y44-PHY. 1. J. C. Solem and G. C. Baldwin, Science 218, 229 termines the position of the carrier with respect to the (1982); M. Howells et al., ibid. 238, 514 (1987); J. E. envelope. 21 May 1997; accepted 9 September 1997 Trebes et al., ibid., p. 517. 2. D. Attwood, K. Halbach, K.-J. Kim, ibid. 228, 1265 (1985). 3. B. J. Macgowan et al., Phys. Rev. Lett. 65, 420 Superfluid Droplets on a Solid Surface (1990). 4. Flash x-ray sources such as those demonstrated in (3) would be ideal for the avoidance of image blur- D. Ross, J. E. Rutledge, P. Taborek* ring due to, for example, object motion during ex- posure [R. A. London et al., Appl. Opt. 28, 3397 (1989)]; however, the spatial coherence of the Photographs are presented of isolated superfluid helium-4 droplets prepared on a sources demonstrated in the water window so far cesium surface, the only material known that is not wetted by superfluid helium. Although are far from being sufficient for single-shot biologi- cal holography. thermodynamic measurements show that the cesium surface is highly uniform, the 5. A. McPherson et al., J. Opt. Soc. Am. B 4, 595 contact angle of the droplets is extremely hysteretic and depends on whether the contact (1987); X. F. Li et al., Phys. Rev. A 39, 5751 (1989). line is advancing or receding. Superfluid helium-4 droplets on an inclined surface do not 6. A. L’Huillier and Ph. Balcou, Phys. Rev. Lett. 70, 774 (1993); J. J. Macklin et al., ibid., p. 766. flow downhill but rather are strongly pinned to the surface. 7. J. L. Krause et al., ibid. 68, 3535 (1992). 8. P. B. Corkum, ibid. 71, 1995 (1993). 9. M. Lewenstein et al., Phys. Rev. A 49, 2117 (1994). 10. K. C. Kulander et al.,inProceedings of the Work- shop on Super-Intense Laser Atom Physics (SILAP) Superfluid He has unusual thermal and dows that provide an edge-on view of the III, P. Piraux, Ed. (Plenum, New York, 1993). mechanical properties (1) and is well substrate as well as a view from above at 11. K. Miyazaki and H. Takada, Phys. Rev. A 52, 3007 known for its ability to spread over surfac- an angle of 60° from the normal. The (1995). 12. I. P. Christov et al., Phys. Rev. Lett. 77, 1743 (1996); es and to flow without dissipation through substrate is a quartz microbalance with K. J. Schafer and K. C. Kulander, ibid. 78, 638 even microscopic holes. Virtually all of gold electrodes similar to those used in our (1997). the walls and surfaces used in earlier dis- earlier thermodynamic studies (5, 6). Fifty 13. J. Zhou et al., ibid. 76, 752 (1996). 14. Z. Chang et al.,inApplications of High Field and sipationless flow experiments were ob- atomic layers of Cs were vapor-deposited Short Wavelength Sources VII (OSA Tech. Digest served to be wetted by superfluid He. This onto the quartz and gold surfaces of the Ser., vol. 7, Optical Society of America, Washington, effect means that droplets on these sub- microbalance at a rate of 0.01 layer per DC, 1997), p. 187. 15. R. Haight and P. F. Seidler, Appl. Phys. Lett. 65, 517 strates are unstable and immediately second. During the evaporation, the tem- (1994). spread to form a smooth continuous film perature of the substrate and the walls of 16. S. Sartania et al., Opt. Lett. 22, 1562 (1997). over the entire surface so that vapor and the container were maintained below 6 K 17. M. Nisoli et al., ibid., p. 522. substrate are never in contact. Recent to maintain ultrahigh vacuum conditions. 18. Given the finite tube wall thickness of 0.05 mm, the actual target thickness is estimated as 100 to 200 m. work (2) has shown that alkali metals are We used the microbalance to monitor the The coherence length related to the phase error intro- a special class of materials not completely deposition and to perform thermodynamic duced by the tight focusing of the fundamental (11)ison wetted by superfluid He. In particular, Cs characterizations of the surface; the wet- the order of 10 m for wavelengths shorter than 10 nm. The target thickness has been minimized in an attempt substrates can be used to prepare super- ting temperature was measured to be Tw ϭ to keep the interaction length as close as possible to this fluid samples with a distinctly different 2.04 K. A capillary tube (0.04 cm, outside “geometric” coherence length. It is this geometric co- topology consisting of a droplet with an diameter) attached to a source of room- herence length limitation that dictates the necessity of the high pressures applied. edge where substrate, superfluid, and va- temperature gas through a mass-flow con- 19. Note that this peak irradiance is reached only on the por meet at a three-phase contact line (3). troller provided a means of putting drops propagation axis in an infinitesimally small fraction of We present here direct observations of of superfluid on the surface. We main- the cross section of the Gaussian beam. The majority of the helium atoms in the interaction volume are isolated droplets of superfluid on a sub- tained the system at liquid-vapor coexist- exposed to somewhat lower irradiances. strate (4). Both the static and the dynamic ence by filling the bottom of the container 20. The pressure in the interaction region has been esti- behaviors of the droplets were unusual. with bulk liquid 4He. The drops were ob- mated as follows. The gas flow from the target region We found that the contact angle was an served with a long-focal-distance micro- into the chamber is calculated from the known pumping speed and the measured background extremely hysteretic function of the vol- scope that provided a magnification of pressure in the target chamber. Gas flow and back- ume of the drop. Perhaps most remarkable, ϳϫ30. ground pressure then determine uniquely the pres- superfluid droplets would not move across Figures 1 and 2 show a sequence of sure in the target. 21. I. P. Christov et al., Phys. Rev. Lett. 78, 1251 (1997). the surface until considerable force was photos of superfluid drops on a Cs sub- 22. C. Kan et al., ibid. 79, 2971 (1997). applied to them. This result is surprising strate at T ϭ 1.16 K. Pictures taken with 23. We used a detector quantum efficiency of 2%, an because solid surfaces are well known not the microscope looking down on the sub- electron multiplication gain of 5 ϫ 106, and a grating diffraction efficiency of 10% (data provided by the to exert transverse forces on bulk super- strate at an angle of 30° above the hori- manufacturers) for this estimation. fluid or superfluid films without edges. zontal are shown in Fig. 1. The dark bar at 24. M. Schnu¨ rer et al., unpublished results. Our apparatus consisted of a substrate the top of the pictures is the capillary 25. M. V. Ammosov et al., Zh. Eksp. Teor. Fiz. 91, 2008 that can be rotated about a horizontal axis tube, and the lower bar is its shadow. The (1986) [Sov. Phys. JETP 64, 1191 (1986)]. 26. Siegman et al., IEEE J. Quantum Electron. 27, 1098 mounted in an optical cryostat with win- tube was left in contact with the superfluid (1991). drop so that fluid could be added and 27. Measurement of the x-ray beam profile at different Department of Physics and Astronomy, University of Cal- withdrawn. This geometry is conventional positions or direct interferometric measurement of ifornia, Irvine, CA 92697, USA. its spatial coherence will obviate the need for this for contact-angle measurements and typi- assumption. *To whom correspondence should be addressed. cally yields the advancing and receding 664 SCIENCE ⅐ VOL. 278 ⅐ 24 OCTOBER 1997 ⅐ www.sciencemag.org REPORTS contact angle (7). The drops appear oval was about 32° (8) and independent of the wetting transition that we have explored because of the viewing angle. The edge of volume of the drop; Fig. 2, A and B, show in previous work (5, 6). In order to ex- the planar gold electrode can be seen in snapshots of the same drop as fluid was added plain a receding contact angle of zero, the extreme and upper left; the Cs film is (the corresponding top view of the growing standard models based on consideration of too thin to provide appreciable optical drop is shown in Fig. 1, A and B). When metastable states on a heterogeneous sub- contrast. Figure 2 shows edge-on views of fluid was withdrawn, the contact line re- strate would require that more than half of the same droplets as shown in Fig. 1 illu- mained stationary, and the receding contact the surface be covered with patches where minated from the back. The optical axis is angle approached zero (Figs. 1C and 2C). the local contact angle is zero, that is, a fraction of a degree above the horizontal, The bulk fluid could be completely removed, where the liquid wets (7, 10). This possi- so that both the free surface of the drop but apparently a thin film remained in the bility is ruled out by microbalance mea- and its reflection in the substrate are vis- region bounded by the original contact line, surements that show that the average ible. The capillary tube can be seen pro- because, when fluid was added, the drop equilibrium coverage at liquid-vapor coex- truding from the top of the drop. The immediately resumed its previous diameter istence on our substrate at temperatures focus was adjusted so that a diameter of and only slowly increased its volume and far below the wetting temperature is less the drop lies in the focal plane. contact angle. The only way to prepare a than two monolayers, which implies that One can locate the plane of the sub- smaller drop (such as Fig. 1A) in the same the fraction of the surface that was wetted strate by drawing a line between the two area was to remove the microscopic film by is less than 4%. The possibility of point- points where the profile of the drop meets briefly heating the substrate with a flash of like pinning centers also seems unlikely its mirror image. The contact angle is light. because the contact line (Fig. 1) appears the angle between the tangent to the drop Contact-angle hysteresis is a common perfectly smooth on length scales of a few profile and the substrate at the point of phenomenon in wetting measurements of micrometers. contact. Despite the superfluidity of the conventional liquids and substrates that is Although the conventional explana- drops, the value of the contact angle that typically attributed to substrate heteroge- tions of contact-angle hysteresis due to we observed depended critically on the way neity or kinetic effects associated with the surface heterogeneity do not apply to our the drop was prepared. When the volume of viscosity of the liquid, or both (7, 9, 10). experiment, there must nevertheless be the drop was increasing, the contact angle Because our experiment used superfluid some mechanism that provides metastable and the time scale of the observations was states that can trap the droplet in config- several minutes, kinetics cannot be in- urations with a continuous range of con- A voked to explain the hysteresis we ob- tact angles. The fact that the contact line served. Similarly, it is difficult to find a did not move even when the apparent plausible source of surface heterogeneity, contact angle was reduced to zero as a because the substrate exhibits the same result of the deflation of the drop allows us sharp thermodynamic signatures of the to place a lower limit on the pinning force per unit length that these metastable states can sustain. We assume, as is cus- A tomary, that the advancing contact angle is equal to the thermodynamic equilibrium B contact angle (8), which satisfies Young’s equation
B where the ij are surface tensions, and the l, s, and v subscripts denote liquid, substrate,
Fig. 1. (A through C). Microscope images of superfluid drops on a horizontal Cs substrate Fig. 2. (A through C) Microscope images show- taken at an angle of 30° above the horizontal. ing an edge-on view of superfluid drops on a The two dark bars in each of these pictures are horizontal Cs substrate. The dark bar in the up- Fig. 3. Microscope image of a superfluid drop the capillary tube used to add and remove su- per half of the image is the capillary tube. The on a Cs substrate inclined at 10° to the horizon- perfluid (top) and its shadow, respectively. The pictures show the outline of the drop as well as tal. A drop hanging off of the capillary is also capillary is in wetting contact with the drop. From its mirror image in the reflective substrate. As the seen in the upper right. The drop on the inclined (A) to (B), fluid was added; from (B) to (C), fluid volume of the drop increased from (A) to (B), the substrate is stationary. The downhill edge of the was withdrawn. The edges of the drop were contact angle remained constant. When fluid drop has the same contact angle as shown in always smooth, and the footprint of the drop did was withdraw as in (C), the contact angle de- Fig. 2B, whereas the uphill edge has a vanishing not change size when fluid was withdrawn. creased but the diameter remained constant. contact angle.
www.sciencemag.org ⅐ SCIENCE ⅐ VOL. 278 ⅐ 24 OCTOBER 1997 665 and vapor, respectively. In this case, the are remarkable because they can resist flow 3. F. Brochard-Wyart, J. Phys. (Paris) II 3, 21 (1993). against a substantial chemical potential gra 4. D. Reinelt, H. Gau, S. Herminghaus, P. Leiderer force per unit length on the contact line - [Czech. J. Phys. 46, 431 (1996)] presented surface due to surface tension when the contact dient. Both of these effects are presumably plasmon micrographs of the region of a Cs substrate covered with superfluid. These images, however, did angle was reduced to zero was lv (1 Ϫ cos) due to metastable configurations of the su- Ϸ 46 mdyne/cm. The maximum pinning perfluid contact line, which have been in- not contain information about the contact angle. 5. J. E. Rutledge and P. Taborek, Phys. Rev Lett. 69, force must be at least as large. accessible to experimental observation until 937 (1992). Another manifestation of forces on the very recently. In order to attribute the 6. P. Taborek and J. E. Rutledge, ibid. 71, 263 (1993). contact line can be seen when a superfluid metastability to extrinsic defects, a mecha- 7. R. E. Johnson and R. H. Dettre, in Wettability,J.C. drop was placed on an inclined surface. nism that would allow small defect concen- Berg, Ed. (Dekker, New York, 1993), pp. 1–73. 8. The contact angle has been measured by J. Klier, P. Figure 3 shows an edge-on view of a drop trations to cause extremely large hysteresis Stefanyi, and A. F. G. Wyatt [Phys. Rev. Lett. 75, on a Cs surface inclined at ϳ10° to the would need to be identified. 3709 (1995)]. They obtained a slightly larger value at horizontal; a pendant drop of fluid formed T ϭ 1.16 K. 9. D. Li and A. W. Neumann, Colloid Polym. Sci. 270, by forcing He down the capillary faster REFERENCES AND NOTES 498 (1992). than the superfluid film on the outer sur- ______10. L. W. Schwartz and S. Garoff, Langmuir 1, 219 face could drain it can also be seen in the 1. J. Wilks and D. S. Betts, An Introduction to Liquid (1985). upper right corner. The most remarkable Helium (Clarendon Press, Oxford, ed. 2, 1987). 11. This work was supported by NSF grant DMR 2. E. Cheng, M. W. Cole, J. Dupont-Roc, W. F. Saam, 9623976. feature of the drop on the substrate is that J. Treiner, Rev. Mod. Phys. 65, 557 (1993), and ref- it is stationary. Even vigorous shaking of erences therein. 7 July 1997; accepted 15 September 1997 the apparatus, which caused easily discern- ible waves in the drop, did not cause it to flow down the incline. The downhill edge Developmental Patterns and the Identification of the drop had the same contact angle as the advancing edge of a growing drop, of Homologies in the Avian Hand whereas the uphill edge had a vanishing contact angle. As more fluid was added to Ann C. Burke and Alan Feduccia* the drop, it eventually rolled down the incline, often with a jerky stick-slip mo- Homologies of digits in the avian hand have been debated for 150 years. Cladistic tion. Subsequent drops immediately analysis nests birds with theropod dinosaurs. Theropod hands retain only digits I-II-III, spread out across the path of the previous so digits of the modern bird hand are often identified as I-II-III. Study of the developing drop and rapidly flowed downhill. It seems manus and pes in amniote embryos, including a variety of avian species, shows ste- as if the first drop, which moved across a reotyped patterns of cartilage condensations. A primary axis of cartilage condensation dry substrate, left a trailing film that “lu- is visible in all species that runs through the humerus into digit IV. Comparison to serially bricates” the motion of subsequent drops. homologous elements of the hindlimb indicates that the retained digits of the avian hand This film, which persisted for hours, may are II-III-IV. be related to the metastable thick films we have observed in earlier experiments (6). The trailing film had submicroscopic thickness and was invisible in an edge-on A long-standing disagreement persists in and thorough reviews of the arguments (1, view. It could be detected ellipsometri- the identification of the three remaining 8, 10, 11), no consensus on digit homol- cally and was superfluid because the local digits in the adult avian manus. Many ogy has emerged. We address the issue of heating of a spot with a laser beam pro- developmental biologists use conservation avian digits, using a developmental pat- duced a thermomechanically driven bump of embryonic patterning to establish ho- tern that is conserved in all amniotes ex- in the film profile. mology (1, 2), while many paleontologists amined. We examined forelimb develop- Superfluid droplets on Cs substrates use the methodology of phylogenetic sys- ment in turtle, alligator, and several avian have spreading and flow properties that tematics to define homology a posteriori embryos (12). We also compare develop- are not simple consequences of bulk super- from cladistic analysis of multiple synapo- ment of the serially homologous fore- and fluid behavior. Liquid He has exceptional morphies (3, 4). Cladistic analyses nest hindlimbs in birds. chemical purity, and the heterogeneity of birds within the theropod dinosaurs (5). The identity of digits in modern birds our Cs surface is constrained by thermo- One key synapomorphy uniting theropods as I-II-III gained acceptance because the dynamic adsorption measurements. For is a manus reduced to three digits. These phalangeal formula of Archaeopteryx,an these reasons, He on Cs would naı¨vely be digits are identified as I-II-III because of undisputed early avian (13), coincides expected to display nearly ideal reversible early theropods such as Herrerasaurus (Fig. with digits I-II-III of the generalized ar- spreading behavior, because even the 1) that show dramatic reduction of digits chosaur hand [2-3-4-5-3(14)]. Phalangeal complications due to viscosity are negligi- IV and V (6). A theropod origin of birds formulae are widely variant among many ble. In contrast, superfluid contact angles implies that the digits of the avian manus taxa, however, and individual specimens are found to be even more hysteretic than must also be I-II-III (7, 8). However, ne- of Archaeopteryx have varying phalangeal typical classical fluid drops on macroscop- ontologists have identified the digits in formulae in the pes (15). Furthermore, ically heterogeneous surfaces. The hyster- the avian hand as II-III-IV in consider- this character is developmentally plastic. esis is so extreme that the superfluid con- ation of developmental anatomy. Despite For example, bone morphogenetic protein tact line appears to move in only one several excellent descriptive studies (2, 9) 4 (BMP4) mediates apoptosis and recent direction, that is, so as to increase the studies have shown that experimental wetted area. Department of Biology, Coker Hall, Campus Box 3280, blockage of BMP4 signaling in the avian It is difficult to reconcile these observa- University of North Carolina, Chapel Hill, NC 27599–3280, limb bud can result in hands that are tions with standard models of contact-angle USA. missing only the most distal phalanxes hysteresis. Regarded as a superfluid, droplets *To whom correspondence should be addressed. (16). Regardless, the transition to modern 666 SCIENCE ⅐ VOL. 278 ⅐ 24 OCTOBER 1997 ⅐ www.sciencemag.org