Monodisperse distributions of 1.01 mu m and 2.88 mu m polystyrene microspheres in monolayers on the surface of water were used in a study of isothermal-expansion melting in two dimensions. The equation of state, defect structures, and the translational and orientational correlation functions were obtained from digitised particle positions as the particle-number density ranged from the ordered solid to the liquid phase. The 2.88 mu m system showed evidence of defect mediated melting and of an intermediate hexatic phase, in partial accord with theoretical results of other studies. Melting in the 1.01 mu m system appeared to proceed by a weak first-order transition. If so, the difference in melting behaviour of the two samples may reflect differences in defect core creation energies which can be traced to sphere size.

We have measured the resistive and reactive mutual friction coefficients B and B' in rotating superfluid 'He-B at pressures of 1.6, 10, 20, and 29.3 bars. Near T, , Bp"/p diverges as (T, -T)", with a = -0.7, and B'p"/p -2 tends to zero. Coefficients d~~a nd d, that relate the force to v"vc, the relative velocity of normal Quid and vortex lines show relaxation-dissipation behavior tending slightly towards resonant dissipation. Within our experimental error there is no clear indication of the expected vortex core transition in our data at 20 and 29.3 bars.PACS numbers: 67.57. De, 67.57.Fg In a rotating superAuid in the interaction of quantized vortices with the normal fluid (or thermal excitations) manifests itself as a force of mutual friction between the two fluids. In equilibrium at angular velocity 0, the force F", on unit volume of normal Quid isthe suffix J denotes a component perpendicular to A. In a type II superconductor there is a similar mutual friction force mediated by quantized fiux lines; in this case the resistive and reactive forces represented by the dimensionless coefficients B and B' contribute to the longitudinal resistivity and Hall effect, respectively, in the fIux Row state. There has recently been considerable interest in the change of sign of the Hall effect for high-T;, superconductors, observed on cooling through T, in an applied field [1]. Mutual friction gives a contribution to the Hall effect of the appropriate sign to explain this if B'p"/p -2 ) 0; we show below that the opposite ineqUality holds in He-B, as predicted by Kopnin, Ivlev, and Kalatsky [2] for superconductors with an isotropic Fermi surface. Mutual friction has been extensively studied in He [3], but so far there are only limited measurements of B in superguid He [4,5]. The present experiments are the first in He designed to measure B' as well, and thus obtain complete information. We report here the results of an extensive series of measurements on the B-phase; measurements so far in the A phase are markedly less reproducible, presumably because of textural problems. Theory [6] predicts that for singular vortices the friction should be dominated by the interaction between excitations bound to the vortex core and free excitations. Consequently, the mutual friction is expected to provide valuable information on vortex core structures. Bur experimental cell, which is mounted on the nuclear refrigeration stage of a rotating cryostat [7], is shown very schematically in Fig. 1. A circular Kapton diaphragm separated two disk-shaped regions of liquid, each nominally 100 p, m thick. The roof of the cell has six electrodes set into it by means of which the modes of the diaphragm may be driven and detected electrostatically.The modes that are of interest are those with a single nodal line along the diameter. Motion of the diaphragm then displaces superAuid as indicated in the figure, while the normal fIuid is held at rest by its viscosity to a very good approximation.The frequency of these modes is of order 50 Hz at T = 0 and v...

A two-dimensional melting transition has been observed in a freely expanding colloidal monolayer lattice formed of 1.01-jum polystyrene microspheres in an aqueous suspension between two parallel optical flats. The correlation functions computed from digitized images of the particle distribution within a fixed sampling area are consistent with a continuous two-step melting transition. However, direct observations of defect creation and evolution reveal that the system may melt via a first-order process.PACS numbers: 64.70.Dv, 61.25.Hq, 82.70.Dd Whether the melting transition in two dimensions (2D) is first order or continuous as proposed by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY) 1 " 3 has been a challenging problem for over a decade. 4 In KTHNY theory, between the solid (S) and the liquid (L) phases, there exists an intermediate hexatic (H) phase which has short-range translational order and quasi-long-range orientational order.Melting occurs in a two-state process governed by dislocation pairs unbinding at the S-H transition and by disclination pairs unbinding at the H-L transition. These two transitions are characterized by separate divergences in the translational and orientational correlation lengths, respectively. Colloidal monolayers are an especially good experimental system for studying this problem because the charged colloidal micorspheres (CCM) in aqueous suspensions are microscopically observable. In particular, a colloidal monolayer system in a small wedge geometry, first introduced by Pansu, Pieranski, and Strzelecki 5 and by Clark, Ackerson, and Hurd, 6 has been successfully employed by Murray and Van Winkle (M-VW) 7 in the study of 2D melting.In this Letter we describe the results of a study of free-expansion melting of 2D CCM solids formed in films of highly uniform thickness. Two-dimensional populations of 1.01-jum-diam polystyrene-sulphated microspheres suspended in water were established between fused-silica optical flats in a parallel-plate film cell. With this arrangement, the particle-number density gradient inherent to the wedge method could be eliminated. Most importantly the free-expansion melting is time dependent, which allows observation of the time evolution of defects as a given sample of the monolayer melts.The films are formed between a 1.6 mm x 3.2 cm diam flat which defines their lower boundary, and a 3.2 mmx 1.27 cm diam flat which is glued to a 3.2 mm x3.2 cm flat. These are fitted in an anodized aluminum cell which is sealed by tightening alignment screws in order to press the two larger flats against a Viton rubber O ring; the space -1.2 cm 3 between the O ring and the periphery of the smaller flat serves as a 3D reservoir. Interferometry reveals that the lower flat flexes slightly concave when the cell is sealed so that the gap thickness decreases -0.011 jum from the cell center out to a ra-dius of 500 /im. This distortion gives rise to an inward directed electrostatic wall-particle compressive force. A three-nested-ring stepped annular channel was plas...

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We have made simultaneous measurements of the longitudinal and transverse NMR frequencies of He-A in fields of the order of 30 G in a parallel plate geometry, defined by Mylar films 100pm apart, so that 1 is well oriented perpendicular to the static magnetic field. Comparison of our measurements with the quadratic axial-state frequency relation indicates that the A phase is axial in the pressure range 22.6 to 29.3bars. PACS numbers: 67.57.Lm, 76.60.Jx It has recently been suggested [1,2] that the conventional identification of the Cooper pair state in the A phase of superfluid 3He with the Anderson-Brinkman-Morel [3] (or axial) state might be incorrect. Experimental information on the generalized Ginzburg-Landaufourth-order free energy coefficients pl, pz, ps, p4, and p5 suggests that the axiplanar state [4] might be more stable than the axial state over at least part of the A-phase region of the phase diagram. In addition, our own measurements of the A-phase superfluid density anisotropy at 29.3 bars [5] give a value for (p,~-ps~~) /p,~o f 0.42 +0.03 as T~T~, this represents a possibly significant departure from the value of 0.5 predicted for the axial state in the direction expected for an axiplanar order parameter. At the melting pressure strong coupling corrections [6] make the predicted anisotropy for the axial state slightly larger, 0.515.Since the identification of the A phase with the axial state is the basis for much theoretical work and also for the interpretation of a substantial number of experiments, it is important that its validity should be thoroughly checked and that was the purpose of the work described in this Letter. The relationship between the longitudinal and transverse NMR frequencies, O~~a nd Ag, of the A phase provides a precise method for doing this. For t;he axial state in an applied magnetic Beld there is a simple quadratic relation between these frequencies ll 2 2 w here AL, is the Larmor frequency of the He nucleus. For the axiplanar state O~e xceeds 0& -0& by an amount which measures the cleparture of the order parameter from the axial form. Previously, Eq.(1) has been checked carefully only at the melting pressure 34.3 bars, [7] where the identification of the A phase with the axial state seems secure. The axiplanar order parameter is specified by angles 8 and P and it can conveniently be written in terms of the spin-space unit vector triad (d, e, f) and orbit-space unit vector triad (1, m, fl) [8] as proportional to We see that spin-up and spin-down states have diferent orbital anisotropy axes at angles +P to 1; the axial phase corresponds to the limit P~0 , 8~z/4. For P g 0 and 8 P z/4 expression (2) indicates a state with a coherent sum of orbital angular momentum up and down for each spin state.The axiplanar state is more stable than the axial state if p45 = p4 + ps ) 0, in which case the angles p and 8 are given in terms of the P's by [4] tan 2P13P45 P345(2PI + Ps)' cos 8= P3(2Pl + P345) 2[Ps(2P1 + P345) + P45(2P1 + P3)](3) We note that in the limit T~Tc the order parameter(2...