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due to their short coherence length , long penetration depth and high anisotropy , the high - t@xmath4 superconductors ( hts ) , show very unusual behaviour . apart from a proposed vortex - glass phase @xcite , which has probably been observed in the highly anisotropic bi@xmath0sr@xmath0cacu@xmath0o@xmath5 ( bscco ) at high fields @xcite , there is also the exciting phenomenon of vortex - lattice melting in these compounds . unlike in bscco , the vortex lattice melting transition in yba@xmath0cu@xmath1o@xmath2 ( ybco ) takes place at sufficiently high fields to be studied using thermal measurements such as differential thermal analysis ( dta ) @xcite and specific heat @xcite . this is mainly due to the much lower anisotropy of ybco ( @xmath6 5 ) . apart from this phenomenological difference , there are however also more fundamental differences between ybco and bscco in the crystallographic symmetry , which is orthorhombic in the former , while it is tetragonal in the latter . this leads to a fundamental difference in the growth of the samples , in that untreated ybco samples are usually heavily twinned ( having domains of interchanged @xmath7 and @xmath8 axes ) . the boundaries between these domains ( twin - planes ) act as very strong pinning sites to the vortices @xcite , which may change some of the properties of the vortex lattice in the sample . it has for instance been argued that such strong pinning may change the ( intrinsically ) first order transition to a second order transition @xcite . this was also supported by the fact that the transitions observed ( for instance by muon - spin rotation ( @xmath9sr ) @xcite and neutron small - angle scattering ( sans ) @xcite ) in bscco were generally very sharp , not inconsistent with a first order transition , whereas twinned ybco samples gave a more gradual transition . with the advent of sufficiently sized untwinned and high purity twinned samples , it became possible to study these effects in more detail using dta@xcite and specific heat@xcite to determine the true thermodynamic properties of the phase transition . in untwinned samples , dta measurements have clearly shown the existence of a first order transition@xcite , even though the sample was nt pure but had some au impurities due to the growth process . in extremely pure samples , specific heat measurements have also shown a first order transition even though the sample was heavily twinned@xcite . however , the twinned case is in general much more complicated than the untwinned one in that the order of the transition may also depend on the applied field@xcite . the order of the transition is thus probably influenced by both kinds of defects ( impurities and twin planes ) , where an excess of pinning sites of any kind drives the transition to second order . of further interest is the dependence of the melting transition on the angle of the field with respect to the @xmath3-axis @xcite . there are detailed predictions on the field dependence of the melting temperature ( melting line ) on the angle from anisotropic london theory @xcite . the nature of the transition , especially the change in entropy at melting has however only recently been investigated @xcite . we have now performed @xmath9sr and sans measurements of the vortex lattice in a large untwinned crystal of ybco with the field at different angles to the crystallographic @xmath3-axis . as is the case in the dta and specific heat measurements , we probe the _ equilibrium state _ of the vortex lattice . from sans , we obtain a microscopic measurement of the global ( long range ) arrangement of the flux lines . appropriately scaled , the sans intensity presents a phenomenological order parameter of the flux lattice ( see below ) . this allows investigations similar to those of specific heat or dta , clarifying the order of the transitions . it should however be noted that the samples used in sans are very much bigger than those used for thermal measurements . thus a possibly present first order transition may already be smeared by slight inhomogeneities over the big sample volume . in contrast , with @xmath9sr we observe the local magnetic field structure averaged over the sample . therefore smearing effects may still be present , however a sharp change of the local equilibrium structure in itself may not be regarded as a sign of a first order transition . due to the different time scales available to neutrons and muons one would expect to observe a difference in the melting line determined by the two methods if the transition is of a more glassy nature . for a ( first order ) phase transition , one would expect both methods of measurement to agree .    as will be shown below , our results differ quite strongly from those on a heavily twinned sample @xcite . there the melting transition observed with sans is of second order , with the intensity decreasing to zero continuously at a temperature t@xmath10 t@xmath4 . in contrast our results show a sharp decrease of the sans intensity with an infinite slope at t@xmath11 . this is consistent with a first order transition considering the large size of the sample ( see below ) . the sample consisted of a large ( 1.125 g ) ybco single crystal . it was grown untwinned by application af uniaxial stress during the cooling from the melt @xcite . for the oxygenation process , the sample was treated in flowing o@xmath0 at 490@xmath12c . magnetisation measurements using a vibrating sample magnetometer ( vsm ) indicate a t@xmath4 of 93 k. the superconducting transition is estimated from these measurements to be @xmath130.5 k. this also gives a limit for the sharpness of the melting transition ( see below ) . the @xmath9sr experiments were carried out on beamline @xmath14m3 at the paul scherrer institute ( psi ) , villigen switzerland , with a maximum field of 0.6 t and a cryostat capable of cooling to 2 k. in the experiments , a magnetic field was applied perpendicular to the incoming muon spin polarisation , while at a specified angle to the crystallographic @xmath3-direction of the sample . in this case , the spin of a stopped muon precesses with the frequency @xmath15b@xmath16 , where @xmath17 135 mhz / t is the gyromagnetic ratio of the muon in the transverse local field b@xmath16 . the angular anisotropy of the muon decay , leading to a preferred emission of the decay - positron in the direction of the muon spin due to parity violation , allows the time evolution of the muon polarisation to be measured . in the mixed state of a type - ii superconductor , the magnetic field distribution is given by the structural properties of the vortex lattice ( i.e. the penetration depth @xmath18 , the coherence length @xmath19 and the lattice morphology ) . the vortex lattice spacing is much bigger than the atomic spacing of the underlying crystal structure and is incommensurate to it . therefore the muons sample the field distribution randomly , even though they are stopped at specific crystallographic sites . this allows the field probability distribution p(b ) to be measured via the fourier transform of the oscillating time signal . as the different local fields cause the muon spin to precess at different frequencies the time signal consists of a sum of oscillations at different frequencies weighted by their relative occurrence . in order to obtain the fourier transform from the observed time data , we use a maximum entropy algorithm @xcite . in this procedure aberrations of the spectra due to finite time windows or large statistical errors at long times are avoided , as the data are not subjected to a fourier transform themselves . starting from an initially flat field distribution p(b ) , the most uniform distribution compatible with the given time spectrum is obtained by maximising its constrained entropy @xmath20 here @xmath21 is the entropy of the distribution according to shannon and @xmath22 is the usual measure giving the difference of the fourier transform of p(b ) ( @xmath23 ) to the data in the time domain ( @xmath24 ) , where @xmath25 is the error in the data . the field distribution corresponding to a vortex lattice has very characteristic features arising from its two - dimensional periodicity . at extremal points in the spatial distribution the field probability distribution exhibits van hove singularities . these singularities ideally are finite jumps at the minimum and maximum fields , and furthermore a logarithmic divergence at saddle points . due to the very high fields in the vortex cores , the field distribution is highly asymmetric with a long ` tail ' at fields higher than the average . in the entangled vortex liquid state however , the core fields are smeared out over a large distance . therefore the high field tail is truncated leading to a symmetric lineshape . we quantify the asymmetry of the lineshape by the dimensionless parameter @xmath26 a symmetric distribution corresponds to a value of @xmath27 , whereas a distribution with a high field tail has a positive @xmath28 . the sans experiments were carried out on instruments d11 , d22 and d17 at the institut laue - langevin ( ill ) , grenoble france . the neutrons typically had a wavelength of @xmath29 = 1 - 1.5 nm and the beam was collimated over a distance of 2.75 m in the experiments carried out at d17 , whereas the collimation length was 10 m in those at d11 and d22 . the distance between the sample and the detector was then varied for optimal resolution . the incoming neutron beam was aligned with the applied field to an accuracy of 0.1@xmath12 by observing the diffraction pattern from a nb single crystal . the sample was mounted in a cryomagnet capable of a field of 5 t and a temperature of 1.5 k.    the neutrons are scattered from the spatial variations of the magnetic field in the sample , due to the magnetic moment of the neutron ( @xmath30 ) , with the interaction energy @xmath31 . in the case of a type - ii superconductor in the mixed state , the field variation is periodic giving rise to bragg diffraction off the scattering planes of the vortex lattice @xcite , where the angle of refraction is given by @xmath32 here @xmath33 is the lattice spacing , which depends on the applied field as @xmath34 for a hexagonal lattice ( @xmath35 = h/2e is the magnetic flux quantum ) . thus the scattering is at very small angle , as typical vortex separations of @xmath1350 nm ( corresponding to a field of @xmath131 t ) result in a bragg angle ( from eq . [ bragg ] ) of 2@xmath36 2@xmath12 . the intensity of neutrons scattered into a bragg - peak , integrated over angle as the sample is rocked through the bragg condition , is then mainly given by the square of the form factor of a flux line , which in the london approximation is given by @xmath37 where @xmath18 is the penetration depth . the london approximation is valid in the case of an extreme type - ii superconductor with @xmath38 , a condition well satisfied by the hts . therefore , for fields much greater than b@xmath39 , corresponding to @xmath40 1 , the scattered intensity depends on the penetration depth as @xmath41 . for a classical type - ii superconductor , the temperature dependence of the scattered intensity therefore is a direct measure of that of the penetration depth . in the hts however , where thermal fluctuations may have a dominant contribution this is not necessarily the case . in order to discern effects arising from the temperature dependence of @xmath18 and those of the thermal fluctuations finally leading to the melting of the lattice we divide the observed intensities by the temperature dependence of @xmath42 this was obtained from the sans intensity at a low field ( 0.2 t ) , where the effects of thermal fluctuations are negligible ( see below ) . this quantity then takes the role of an effective flux line lattice ( fll ) order parameter , which we use to observe the melting transition and its order . because the scattered intensity depends on the penetration depth as @xmath41 the intensity in the hts is rather low , due to their long penetration depths ( @xmath18 = 150 - 200 nm ) . furthermore , substantial background scattering from the cryostat and extended defects in the sample make it necessary to subtract a diffraction pattern taken above t@xmath4 to obtain a clear signal . due to thermal contractions of the sample stick and cryostat , this background is shifted by fractions of a detector pixel in order to obtain a good subtraction . thanks to the high neutron intensity at the instruments d22 and d11 , a counting time of 30 minutes for each foreground and background was enough to obtain a reasonable signal . a typical diffraction pattern can be seen in fig .  [ pattern ] for an applied field of 0.2 t. there the field is applied at an angle of 33@xmath12 to the @xmath3-axis . this is why the observed pattern is isotropic . the distortion due to the @xmath43-anisotropy ( @xmath44 = 1.16 @xcite ) is compensated by the distortion due to the @xmath45-anisotropy at an angle of 33@xmath12 . furthermore , we note that second order diffraction spots are visible in the figure , indicating the high quality of the flux lattice . the intensities measured from such a pattern are obtained from fitting a gaussian to each individual bragg - spot and taking the sum of all spots in order to reduce the statistical error . all of these measurements of scattered intensity rely on the fact that the width of the rocking curve does not change as a function of temperature . this is because the calculation relating the scattered intensity to the penetration depth is done for the total integrated intensity@xcite , which is given by the width of the rocking curve multiplied by the intensity when fulfilling the bragg condition . the rocking curve width was checked to be constant for selected temperatures over a wide range . we therefore only consider the scattered intensities at the bragg - angle .    in order to determine an effective fll order parameter we have to divide the intensity by its temperature dependence intrinsically given by the penetration depth . therefore we have measured the scattered intensity at a low field ( 0.2 t ) where the influence of thermal fluctuations should be small . the result can be seen in fig . [ tdep ] , where the intensity at 0.2 t is given divided by the expectation of the 3d xy model . as the figure shows , the approximation of the 3d xy model , with @xmath46 ( 1 - t / t@xmath4)@xmath47 is valid for temperatures well below t@xmath4 in all of the region of interest . in the determination of the order parameter , the intensity was thus divided by ( 1 - t / t@xmath4)@xmath48 for simplicity . furthermore the insert of fig . [ tdep ] shows the temperature dependence over the full range . there we have plotted the square root of the scattered intensity to present the familiar @xmath49 dependence @xcite . it can be seen that at lower temperatures the dependence is linear down to temperatures of @xmath134 k , below which it saturates . for a d - wave superconductor , as the hts are supposed to be , a linear temperature dependence would be expected down to the lowest temperatures from simple london theory . however when non - local interactions are taken into account @xcite , a saturation at very low temperatures is predicted , not inconsistent with our data . we will come back to the temperature dependence of @xmath18 below in the discussion of the melting line . however , we note that such a big range of applicability ( down to @xmath1320 k below t@xmath4 ) for the 3d xy model is surprising , as this is thought only to be valid in the region of critical fluctuations in close vicinity of t@xmath4 .    in fig . [ sansmelt ] , we present the temperature dependence of the fll order parameter in the vicinity of t@xmath4 for two different fields . at both fields , the order parameter is constant at low temperature and decreases gradually towards the melting temperature . when the order parameter finally drops to zero , the change is very sharp occurring over a temperature range of less than 1 k. the gradual decrease of the order parameter can be modeled by including a debye - waller factor into the theoretical description of the scattered intensity . the final ` jump ' however , is a sign of the transition being of first order . the width of the transition of 1 k is not much bigger than that observed at t@xmath4 , which may be due to sample inhomogeneities . such inhomogeneities leading to a distribution of t@xmath4 may also lead to a distribution of t@xmath11 which would probably be of the same order of magnitude . furthermore , the distribution of fields inside the sample is inhomogenious @xcite , as we will also see in the discussion of the @xmath9sr results below , which will also lead to a further smearing of the melting temperatures . however , as this macroscopic field distribution is very narrow compared to the applied fields , this should nt be a big factor . it is therefore not unreasonable to expect the melting transition in such a big sample to be distributed over an interval of @xmath131 k. note also that the order parameter ( the scattered intensity ) decreases to zero above the melting transition , in agreement with the expectation for an entangled vortex liquid @xcite made up of two - dimensional ` pancake ' vortices . the situation for the untwinned sample has to be compared to that in a heavily twinned sample @xcite . this is done in fig . [ comp ] , where we show the fll order parameter for both a twinned and our untwinned sample in a field of 4 t. as can be seen in the figure , the transition is much sharper in the untwinned one . the order parameter decreases more or less linearly over a range of 5 k in the twinned sample , as would be expected from mean field theory . in the untwinned sample in contrast , the transition is at most 1 k wide . takeing also into account the temperature dependence at lower temperature , where the untwinned sample varies much slower than the twinned one , the behaviour of the untwinned sample is consistent with a first order transition . the width of the observed transition is furthermore not very much bigger than those determined from magnetisation@xcite and thermal measurements@xcite , which are done on much smaller samples where inhomogeneities and possible residual twin - planes must play a much smaller role . we now turn to the discussion of the @xmath9sr results . typical field probability distributions for temperatures above and below the melting transition can be seen in fig . [ lineshape ] for a field of 0.6 t. the situation is similar to that of bscco @xcite , with a lineshape highly asymmetric towards high fields below the melting temperature . as was discussed above , the lineshape for an ideal lattice made up of straight vortex lines is expected to show such a high field tail . above the melting temperature however , the field distribution is skewed the opposite way . this has been argued to arise from a macroscopic distribution of the local fields due to the sharp edges of the sample , with fields decreasing at the edges @xcite . this kind of macroscopic distribution is also present below the melting temperature , however the large width of the field distribution due to the well formed lattice overcomes this effect , such that an almost ideal distribution is observed . above the melting temperature in contrast , the field distribution is smeared by the fast thermal fluctuations of the pancake vortices . this leads to a strongly decreases the width of the microscopic field distribution ( ` motional narrowing ' ) and hence the observed distribution follows the macroscopic one .    in fig . [ musrmelt ] , we present the temperature dependence of the @xmath9sr lineshape asymmetry parameter @xmath28 , together with that of the mean internal field . the mean field allows a direct measurement of t@xmath4 via the onset of diamagnetic behaviour . as can be seen in the figure even at the very low field of 0.3 t , we observe a sharp melting transition in the temperature dependence of @xmath28 somewhat below t@xmath4 . the change in lineshape displayed in fig . [ lineshape ] manifests itself by a change in sign of @xmath28 . the transition is still very sharp , although thermal measurements are not sensitive enough to resolve a first order transition at such low fields . there have however recently been magnetisation measurements by means of torque magnetometry , resolving a step in magnetisation and hence a first order transition at similarly low fields @xcite .    the field dependence of the melting temperatures thus determined ( the melting line ) can be seen in fig . [ meltline ] . in that figure we have also included the line of onset of irreversible magnetisation ( irreversibility line , il ) as determined with a vsm . the microscopic melting line and the il are in good agreement with each other . they follow a power law dependence of the form @xmath50 a least squares fit to both sets of data simultaneously yields the values of @xmath51 = 100(10 ) t and n = 1.30(5 ) . this is in excellent agreement with many other studies @xcite on both twinned and untwinned samples . it is thus only the order of the transition , which is affected by the presence of disorder ( e.g. in the form of twin - planes ) and not the meltingline itself . the shape of the melting line has been the ground of some debate , as a dependence @xmath52 ( 1 - t / t@xmath4)@xmath48 is expected for the vortex - glass transition proposed by fisher _ this would indicate that the observed melting line is more likely to be a glass transition , which would however be in contradiction with the observation of a first order transition . the temperature dependence of a melting line is usually calculated using the lindemann criterion that melting occurs when the mean square displacements of flux lines make up a certain fraction of the intervortex separation @xmath53 . the lindemann number @xmath54 is supposed to be a universal constant in all kinds of melting processes and theoretical estimates indicate it to be 0.1 - 0.2 . using this criterion and modeling the thermal fluctuations in the vortex lattice one can then derive an expression for the melting line @xcite @xmath55 due to the mean field assumption of the temperature dependence of the penetration depth @xmath49 ( t ) @xmath56 ( 1 - t / t@xmath4)@xmath57 this expression is usually taken to result in a value of n = 2 . as we have seen however in fig . [ tdep ] , @xmath18 follows a powerlaw , such that the value of n = 1.33 is recovered over the range of temperatures where the meltingline can be determined . furthermore , this expression allows a determination of @xmath51 , where @xmath54 is the only adjustable parameter . from the intensity in the bragg peaks , we have an independent determination of @xmath18 = 138 nm @xcite and the anisotropy of our sample has been determined from the angular dependence of the @xmath9sr linewidth as well as from the distortion of the sans pattern at high angles to the @xmath3-direction . therefore our value of @xmath51 = 100(10 ) t corresponds to a lindemann number of @xmath54 = 0.173(7 ) . this is in excellent agreement with that found from the melting line in bscco using @xmath9sr @xcite . we would like to note at this point that the lindemann number determined in bscco relied on a different expression for the thermal fluctuations taking into account the electromagnetic coupling between pancake vortices . this indicates that the lindemann criterion may indeed be universally applicable . finally , we discuss the dependence of the melting transition on the angle of the applied field to the @xmath3-direction . from the anisotropic scaling theory of blatter _ @xcite , a dependence of the melting line on angle is @xmath58 in the region of angles we investigated ( @xmath59 50@xmath12 ) , the influence of @xmath60 on @xmath61 is very small such that it can not be accurately determined this way . however using the value obtained from @xmath9sr and the distortion of the pattern @xcite , we may calculate the expected melting lines at an angle from that determined parallel to @xmath3 . this has been done in fig . [ anglemelt ] , where we show the melting temperatures determined by sans at the three different angles of 0@xmath12 , 33@xmath12 and 55@xmath12 . the lines correspond to the fit to the melting line discussed above , where the dependence on the angle has been taken into account as well . as can be seen in the figure , the data are in good agreement with the expectations of the anisotropic scaling theory . this is similar to the results of dta measurements of the melting transition as a function of angle @xcite . in addition , that work also provided a determination of the entropy change at the transition as a function of angle . due to a cancellation of the angular dependencies in the melting line and the magnetisation jump , the entropy - change turns out to be independent of the angle . this is not inconsistent with the sans result displayed in fig . [ angledep ] , where the temperature dependence of the fll order parameter is shown at the melting transition for different angles . the temperatures are normalised to t@xmath11 for direct comparison and the applied field was 5 t. the decrease of the order parameter can be seen to be independent of the angle as it should be for a constant entropy change at the transition . in conclusion , we have presented sans and @xmath9sr measurements of the melting of the vortex lattice in a sample of untwinned ybco . the observed behaviour is consistent with dta measurements of the latent heat showing the existence of a first order transition @xcite . this is inferred from a phenomenological fll order parameter in sans , which decreases to zero sharply at the melting transition . these findings are compared to a previous sans study of melting in twinned samples @xcite . the same fll order parameter vanishes continuously in that case , consistent with a second order phase transition . we have furthermore studied the effects of anisotropy by applying the field at an angle to the @xmath3-direction . the melting temperatures at constant field are consistent with the expectations of the scaling theory of blatter _ a determination of the anisotropy @xmath60 however is not possible , as the deviations of a cos ( @xmath62 ) dependence are negligible in the range of angles studied . the nature of the transition is unchanged by having the field at an angle , consistent with the findings of schilling _ et al . _ @xcite , who studied the dependence of the entropy change on angle . the temperature dependence of the melting line is consistent with that expected from a lindemann criterion @xcite , where the temperature dependence of the penetration depth follows that of the 3d xy model . the observed melting line extends down to very low fields ( 0.2 t ) , where @xmath9sr still indicates a very sharp transition . the range of applicability of this temperature dependence is limited , as we have shown from the temperature dependence of the scattered intensity at low fields , where thermal fluctuations do not play an important role . for temperatures below 75 k the approximation becomes invalid . we would like to note that this is a rather unexpectedly big range of applicability of the critical exponent of the 3d xy model . using the independently measured penetration depth @xcite and anisotropy @xcite for our sample , we have also determined the lindemann number from the melting line , which turns out to be c@xmath63 = 0.173(7 ) . this is in very good agreement with the lindemann number previously obtained from a detailed @xmath9sr study of the melting line in bscco @xcite . we would like to thank michel bonnaud , andreas polsak , pierre george ( ill ) and alex amato ( psi ) for technical support . financial support from the epsrc of the uk and the swiss national science foundation is gratefully acknowledged . this work was funded in part by oak ridge national laboratory , which is managed by lockheed martin energy research corporation under contract no . de - ac05 - 96or22464 for the us doe . 10 present address : division of physics and astronomy , faculty of sciences , vrije universiteit , de boelelaan 1081 , 1081hv amsterdam , the netherlands . present address : laboratoire de physique des solides , btiment 510 , universit paris - sud , 91405 orsay , france . d.  s.  fisher , m.  p.  a.  fisher , and d.  a.  huse phys . rev . b * 43 * , 130 ( 1991 ) . s.  l.  lee , p.  zimmermann , h.  keller , m.  warden , i.  m.  savi , r.  schauwecker , d.  zech , r.  cubitt , e.  m.  forgan , p.  h.  kes , t.  w.  li , a.  a.  menovsky , z.  tarnawski , phys . 71 * , 3862 ( 1993 ) . a.  schilling , r.  a.  fisher , n.  e.  phillips , u.  welp , d.  dasgupta , w.  k.  kwok , g.  w.  crabtree , nature * 382 * , 791 ( 1996 ) and phys . . lett . * 78 * , 4833 ( 1997 ) . m.  roulin , a.  junod , e.  walker , science * 273 * , 1210 ( 1996 ) . g.  blatter , m.  v.  feigelman , v.  b.  geshkenbein , a.  i.  larkin , v.  m.  vinokur , rev . * 66 * , 1125 ( 1995 ) . r.  cubitt , e.  m.  forgan , g.  yang , s.  l.  lee , d.  mck . paul , h.  a.  mook , m.  yethiraj , p.  h.  kes , t.  w.  li , a.  a.  menovsky , z.  tarnawski , k.  mortensen , nature * 365 * , 407 ( 1993 ) . a.  junod , m.  roulin , j .- y . genoud , b.  revaz , a.  erb , e.  walker , physica c * 275 * , 245 ( 1997 ) . a.  schilling , r.  a.  fisher , n.  e.  phillips , u.  welp , w.  k.  kwok , and g.  w.  crabtree , phys . lett . * 78 * , 4833 ( 1997 ) . g.  blatter , v.  b.  geshkenbein , and a.  i.  larkin , phys . lett . * 68 * , 875 ( 1992 ) . m.  j.  w.  dodgson , v.  b.  geshkenbein , h.  nordborg , and g.  blatter , phys . lett . * 80 * , 837 ( 1998 ) ; 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we present a study of the vortex lattice in untwinned yba@xmath0cu@xmath1o@xmath2 crystals , using a combination of muon spin rotation and neutron small angle scattering measurements . 
 both methods show a very sharp melting temperature consistent with a first order transition . the dependence of the melting temperature on the angle of the field with respect to the crystallographic @xmath3-axis is studied . 
 the results are compared to thermal measurements . 
 -1 cm    2