Contains summary of research and reports on three research projects.Joint Services Electronics Program (Contract DAAG29-83-K-0003

Birgeneau, Robert J.

DSpace@MIT

X-Ray Diffuse Scattering5. X-Ray Diffuse ScatteringAcademic and Research StaffProf. R.J. Birgeneau, Dr. A.R. Kortan, Dr. M. SuttonGraduate StudentsK. Evans-Lutterodt, H. -long, L.J. Marti'nez-Miranda, S.G.J. Mochrie, B.M. Ocko, E. SpechtJoint Services Electronics Program (Contract DAAG29-83-K-0003)Robert J. BirgeneauIn this research program, modern x-ray scattering techniques are used to study the structures andphase transitions in novel states of condensed matter. We have two principal experimental facilities.At M.I.T. we have three high-resolution computer controlled x-ray spectrometers using either aconventional or high intensity rotating anode x-ray generator. The angular resolution can be madeas fine as 1.8 seconds of arc; this enables one to probe the development of order from distances ofthe order of the x-ray wavelength, ~1 A, up to 30,000 A. The sample temperature may be variedbetween 2 K and 500 K with a relative accuracy of 2 x 10-3K. We are currently installing a twospectrometer system at the National Synchrotron Light Source at Brookhaven National Laboratory.This makes possible high resolution scattering experiments with a flux more than three orders ofmagnitude larger than that from a rotating anode x-ray generator. This opens up a new generation ofexperiments. Synchrotron x-ray scattering experiments are also carried out on a wiggler beam line atthe Stanford Synchrotron Radiation Laboratory.As part of the JSEP program we have built an x-ray compatible high vacuum single crystalapparatus. This enables us to use synchrotron radiation to study the structure and transitionsoccurring at single surfaces; such experiments are now being initiated. Our current experiments inthis program are concentrated in three areas: (i) the growth, structure, and phase transitions ofintercalant materials, most especially bromine-intercalated graphite, (ii) the structure and phasetransitions of smectic liquid crystals, (iii) the evolution from thin film to bulk structures of modelsystems.5.1 Intercalation Compound Structures and TransitionsIntercalation compounds represent a family of materials in which a foreign species (e.g., Br2 ) isinserted between the layers of a lamellar material such as graphite. If the intercalant enters every nthlayer then the resultant material is referred to as a stage-n intercalation compound. In this programwe study both the intercalation process itself and the structure and transitions of the intercalationcompound as a function of temperature, concentration, and stage index. Our work to date hasRLE P.R. No. 126X-Ray Diffuse Scatteringconcentrated on the systems bromine-intercalated graphite C7 Br 1-3 and potassium-mercuryintercalated graphite.The intercalate plane is found to have three sublattices and each sublattice has a centered ( 3 x 7)rectangular structure with four Br2 molecules per 2D unit cell in the commensurate phase. Thecoherently ordered in-plane bromine regions exceed 10,000 A in size. In the stage-4 material acommensurate-incommensurate (CIT) transition is observed at 342.20 ± 0.05 0K. In theincommensurate phase, a stripe domain pattern becomes established in a single domain of asublattice along the 7-fold direction. The incommensurability as a function of reduced temperatureexhibits power law behavior with an exponent of 0.50 ± 0.02 confirming existing theories. Therelative shifts observed for the various harmonics are accurately predicted by a sharp domain wallwith 4,/7 phase shifts. The intercalate layer exhibits a continuous melting transition from atwo-dimensional solid phase to a smectic liquid crystal phase, occurring at 373.41 ± 0.10 0K for astage-4 compound. In the incommensurate phase it is predicted that the superlattic peaks should bepower law singularities of the form (Q - Q ) - 2 + xn where x n = and n is the order of theharmonic. To probe these line-shape effects we have carried out a high resolution synchrotron studyof a sample of C28Br 2 grown "in situ". Dramatic changes are indeed seen in the intensities andshapes of the successive harmonic peaks. Quantitative analysis is currently underway to comparethe data critically with the theory.We have synthesized and studied stage 1 KH - GIC. 2 From in situ x-ray studies we have learnedthat the compound forms by successive intercalation of K and then, after several hours, furtherintercalation of K and Hg to yield the final KH g - GIC compound. We find a 2 x 2RO hexagonalnetwork for the KH .5.2 Smectic Liquid CrystalsLiquid crystals are made up of rod-like molecules. In the nematic phase the axes of the moleculesalign parallel to each other but the center of mass of the molecules are still randomly distributed sothat one has a pure fluid structure factor. In the smectic A and C phases a one-dimensionalsinusoidal density wave is set up either along (A) or at an angle (C) to the molecular axis. Thus, thesesmectics are like solids in one direction and fluids in the other two. These systems exhibit particularlyinteresting phase transitions which present an important challenge to modern theories of criticalphenomena. At lower temperatures many liquid crystal materials exhibit more ordered phases suchas smectic B, F, and G. These have well-developed in-plane triangular order. If the order is truly longrange then the phase is a plastic crystal. Otherwise, the smectic may be a realization of a novel phaseof matter labelled a "stacked hexatic" with long range order in the crystalline axes but only shortrange order in the positions of the molecules. We have recently studied in some detail the smecticphases and phase transitions in a number of materials. 4 -6 Special emphasis has been given tomulticritical behavior associated with the nematic-smectic A transition.RLE P.R. No. 126X-Ray Diffuse ScatteringThe nematic-smectic A transition was once thought to be always first order. However, a series ofhigh resolution experiments, including our own, have shown that the opposite is the case and indeedthe transition is usually continuous. However, thermodynamic data have suggested that if thetemperature range over which the nematic phase is stable is sufficiently small then thenematic-smectic A transition is first order.By studying the N-A transition in appropriate mixtures it is possible to monitor continuously thiscrossover from second to first order behavior. The crossover is believed to occur at a special pointknown as a "tricritical point". At the tricritical point, mean field theory should properly describe thecritical behavior. We find that for concentrations near the tricritical point in the seriesalkoxycyanobiphenyl (NCB) and pentylbenzenethioalkoxybenzoate (n55) new critical behavior isindeed observed with exponents which are at least close to the mean field values; there are somesubtle, but real, discrepancies which require an extension of the theory.We have carried out an extensive high resolution x-ray scattering study of the nematic-smecticA(N-SA) and reentrant nematic-smectic A(RN-SA) phase transition behavior in mixtures ofoctyloxycyanobiphenyl (80CB) and hexyloxycyanobiphenyl (60CB). The smectic A phase boundary isfound to be parabolic in the temperature-concentration plane with a median temperatureTM = 38.060C and a critical concentration yo = 0.427; here y is the 60CB:80CB molecular ratio.Detailed studies of the smectic fluctuations in the nematic phase are reported for y = 0.33, 0.413,0.420, 0.429, 0.440 and 0.443. The first three concentrations exhibit N-SA and RN-SA transitionswhereas in the latter three samples with decreasing temperature the smectic correlation lengths andsusceptibility exhibit maxima at TM and then decrease with a further decrease in temperature.The data are analysed using an extension of the Pershan-Prost optimal density theory. All of thedata are well-described by the phenomenological theory; the critical exponents so-obtained are vii =0.76 ± 0.03, v L = 0.62 ± 0.05 and y = 1.49 ± 0.07. These agree quantitatively with values obtainedin single layer materials with comparable nematic ranges; thus the N-SA and RN-SA transitions areidentical in character to conventional N-SA transitions provided that one includes the crossovereffects inherent in the parabolic phase boundary. Studies of the in-plane fluid structure factor in theN, SA and RN phases show that the mean molecular spacings and positional correlations are closelysimilar to those in single layer materials; in each phase the structure factor is well described by acircularly-averaged Lorentzian with a correlation length of 6.9 A . These results argue stronglyagainst pairing models for the reentrant behavior. Our current preference is for models based oncompeting order parameters which are required to describe the varied behavior observed in otherpolar materials.RLE P.R. No. 126X-Ray Diffuse Scattering5.3 Structures and Transitions of Ultra-Thin Rare Gas CrystalsFor a number of years we have been studying the structure and transitions of rare gas monolayerson graphite.7' 8 This has yielded new information on the nature of melting in two dimensions and ontwo dimensional commensurate-incoin mmensulrate transitions. We have now begun studying thewetting characteristics of simple atoms and molecules on surfaces. Initial experiments on C2 H4 ongraphite show distinct layering transitions up to three layers and then a continuous evolution of thethickness to macroscopic values; the latter occurs in the liquid phase near the triple point. Initialstudies of krypton on graphite indicate that in the solid phase the system grows layer by layer with thestacking of the layers in an fcc sequence even after three layers. Further, high resolution studies ofthis layer-by-layer growth are underway.References1. A. Erbil, A.R. Kortan, R.J. Birgeneau, and M.S. Dresselhaus, in M.S. Dresselhaus, G. Dresselhaus,J.E. Fisher, and M.J. Moran, (Eds.) Intercalated Gra hite, Materials Research SocietySymposia Proceedings, Vol. 20, (North-Holland Elsevier, New York 1982) p. 21.2. A. Erbil, G. Timp, A.R. Kortan, R.J. Birgeneau, and M.S. Dresselhaus, Synthetic Metals 7, 273(1983).3. A. Erbil, A.R. Kortan, R.J. Birgeneau, and M.S. Dresselhaus, Phys. Rev. B 28, 6329 (1983).4. B.M. Ocko, R.J. Birgeneau, J.D. Litster, and M.E. Neubert, Phys. Rev. Lett. 52, 208 (1984).5. B.M. Ocko, A.R. Kortan, R.J. Birgeneau, and J.W. Goodby, J. Physique 45, 113 (1984).6. A.R. Kortan, H. von Kinel, R.J. Birgeneau, and J.D. Litster, J. Physique 45 (1984).7. P.A. Heiney, P.W. Stephens, R.J. Birgeneau, P.M. Horn, and D.E. Moncton, Phys. Rev. B 28, 6416(1983).8. P.W. Stephens, P.A. Heiney, R.J. Birgeneau, P.M. Horn, D.E. Moncton, and G.S. Brown, Phys. Rev.B. 29, 3512 (1984).RLE P.R. No. 126

X-Ray Diffuse Scattering

Contains reports on two research projects.Joint Services Electronics Program (Contract DAAG29-80-C-0104)Joint Services Electronics Program (Contract DAAG29-81-K-0029

X-Ray Diffuse Scattering5. X-Ray Diffuse ScatteringAcademic and Research StaffProf. R.J. Birgeneau, Prof. J. Akimitsu, Dr. A.R. Kortan, Dr. M. SuttonGraduate StudentsP.A. Heiney, H. Hong, L.J. Marti'nez-Miranda, S.G.J. Mochrie, B.M. Ocko, E. SpechtJoint Services Electronics Program (Contracts DAAG29-80-C-0104 and DAAG29-81-K-0029)Robert J. BirgeneauIn this research program, modern x-ray scattering techniques are used to study the structures andphase transitions in novel states of condensed matter. We have two principal experimental facilities.At M.I.T. we have three high-resolution computer controlled x-ray spectrometers using either aconventional or high intensity rotating anode x-ray generator. The angular resolution can be madeas fine as 1.8 seconds of arc; this enables one to probe the development of order from distances ofthe order of the x-ray wavelength, ~1 A, up to 30,000 A. The sample temperature may be variedbetween 2 K and 500 K with a relative accuracy of 2 x 10-3K. We are currently installing a twospectrometer system at the National Synchrotron Light Source at Brookhaven National Laboratory.This makes possible high resolution scattering experiments with a flux more than three orders ofmagnitude larger than that from a rotating anode x-ray generator. This opens up a new generation ofexperiments. Synchrotron x-ray scattering experiments are also carried out on a wiggler beam line atthe Stanford Synchrotron Radiation Laboratory.As part of this JSEP program we are designing and building an x-ray compatible high vacuumsingle crystal surface apparatus. This will enable us to use synchrotron radiation to study thestructure and transitions occurring at single surfaces. The possibilities with this seem virtuallyunlimited. Our current experiments in this program are concentrated in two areas: (i) the growth,structure, and phase transitions of intercalant materials, most especially bromine-intercalatedgraphite, (ii) the structure and phase transitions of smectic liquid crystals.5.1 Intercalation Compound Structures and TransitionsIntercalation compounds represent a family of materials in which a foreign species (e.g. Br2) isinserted between the layers of a larnellar material such as graphite. If the intercalant enters every nthlayer then the resultant material is referred to as a stage-n intercalation compound. We have initiateda program to study "in-situ", using high resolution x-ray scattering techniques, both the intercalationprocess itself and the structure and transitions of the intercalation compound as a function ofRLE P.R. No. 125X-Ray Diffuse Scatteringtemperature, concentration, and stage index. Our initial work has concentrated on the systembromine-intercalated graphite C7nBr 2. '2The intercalate plane is found to have three sublattices and each sublattice has a centered(Vf3 x 7) rectangular structure with four Br2 molecules per 2D unit cell in the commensurate phase.The coherently ordered in-plane bromine regions exceed 10,000 A in size. In the stage-4 material acommensurate-incommensurate (CIT) transition is observed at 342.20 ± 0.05 0K. In theincommensurate phase, a stripe domain pattern becomes established in a single domain of asublattice along the 7-fold direction. The incommensurability as a function of reduced temperatureexhibits power law behavior with an exponent of 0.50 ± 0.02 confirming existing theories. Therelative shifts observed for the various harmonics are accurately predicted by a sharp domain wallwith 4wr/ 7 phase shifts. A power-law lineshape reflecting the lack of true long range order isobserved for the incommensurate intercalant layer, yielding values for the exponent - consistent withmodel calculations. The intercalate layer exhibits a continuous melting transition from atwo-dimensional solid phase to a smectic liquid crystal phase, occurring at 373.41 ± 0.10 0K for astage-4 compound.We are continuing these detailed studies for lower stage material; we have also carried out someinitial experiments on graphite intercalated with potassium and mercury. This system exhibitssuperconductivity at 1 K and thus is of particular interest.5.2 Smectic Liquid CrystalsLiquid crystals are made up of rod-like molecules. In the nematic phase the axes of the moleculesalign parallel to each other but the centers of mass of the molecules are still randomly distributed sothat one has a pure fluid structure factor. In the smectic A and C phases a one-dimensionalsinusoidal density wave is set up either along (A) or at an angle (C) to the molecular axis. Thus, thesesmectics are like solids in one direction and fluids in the other two. These systems exhibit particularlyinteresting phase transitions which present an important challenge to modern theories of criticalphenomena. At lower temperatures many liquid crystal materials exhibit more ordered phases suchas smectic B, F, and G. These have well-developed in-plane triangular order. If the order is truly longrange then the phase is a plastic crystal. Otherwise, the smectic may be a realization of a novel phaseof matter labelled a "stacked hexatic" with long range order in the crystalline axes but only shortrange order in the positions of the molecules. We have recently studied in some detail the smecticphases and phase transitions in two related materials, heptyloxybenzylidene-heptylaniline (70.7)3 andbutyloxybenzilidene-heptylaniline (40.7).4Our work in 70.7 has concentrated primarily on the B-phase. We have carried out an x-raydiffraction study using both rotating anode and synchrotron sources of structures and restackingtransitions within the B phases. The system evolves from a hexagonal close-packed structure,through intermediate orthorhombic and monoclinic phases, to a simple hexagonal structure. TheRLE P.R. No. 125X-Ray Diffuse Scatteringmonoclinic phase has a temperature-dependent shear which transforms the system fromorthorhombic to hexagonal. The latter three phrases exhibit a single- q sinusoidal modulation of themolecular layers. The sinusoidal modulation is believed to represent a precursor to the tilted (G)phase at lower temperatures. This behavior is much richer than anyone had previously consideredpossible within the B-phase. The experiments demonstrate most clearly that there is need for asignificant development of theories for the structures of quasi-2D molecular solids.In 40.7 we have carried out an encyclopaedic study of all of the liquid crystal phases and phasetransitions. Here we emphasize our results for the smectic A - smectic C transition. This is a secondorder transition in which the molecular axis spontaneously tilts with respect to the density wavedirection. This transition would appear to be the simplest liquid crystal phase change; in spite of that,it has been the subject of considerable controversy in the literature.In our previous JSEP work we have argued, using a Landau theory and the Ginzburg criterion, thatA-C transitions should exhibit mean field behavior over the temperature range accessible by currentexperimental techniques. However, if interpreted naively, recent measurements in two materials,butyloxybenzylidene-heptylaniline (40.7) and azoxy-4, 4'-di-undecyl-a-methylcinnimate (AMC-11),seem to contradict this prediction. Specifically, over the reduced range 5 x 10'3 to 5 x 10'5 in bothcases the tilt follows a power law with P,=0.36; that is, these materials seem to exhibit helium-likecritical behavior. By carrying out order parameter, heat capacity and light scattering measurementswe have found that the data are uniquely described by mean field theory with an unusually large sixthorder term. The measured P = .36 thus represents a crossover from P = -1 to 1/4 regimesdemonstrating that the original Ginzburg criterion arguments are correct. We do not, however, havea plausible microscopic explanation for the large sixth order term.References1. A.R. Kortan, A. Erbil, R.J. Birgeneau, and M.S. Dresselhaus, Phys. Rev. Lett. 49, 1427 (1982).2. A. Erbil, A.R. Kortan, R.J. Birgeneau, and M.S. Dresselhaus, Phys. Rev., submitted for publication.3. J. Collett, L.B. Sorensen, P.S. Pershan, J.D. Litster, R.J. Birgeneau, and J. Als-Nielsen, Phys. Rev.Lett. 49, 553 (1982).4. R.J. Birgeneau, C.W. Garland, A.R. Kortan, J.D. Litster, M. Meichle, B.M. Ocko, C. Rosenblatt,L.Y. Yu, and J. Goodby, Phys. Rev. A 27, 1251 (1983).RLE P.R. No. 125RLE P.R. No. 125 24

X-Ray Diftuse Scattering8. X-Ray Diffuse ScatteringAcademic and Research StaffProf. R.J. Birgeneau, Dr. A.R. Kortan, Dr. M. Sutton, Dr. J.W. ChungGraduate StudentsK. Evans-Lutterodt, H. Hong, A. Mak, L.J. Martinez-Miranda, S.G.J. Mochrie,B.M. Ocko, E. SpechtJoint Services Electronics Program (Contract DAAG29-83-K-0003)Robert J. BirgeneauIn this research program, modern x-ray scattering techniques are used to study the structuresand phase transitions in novel states of condensed matter. We have two principal experimentalfacilities. At M.I.T. we have three high-resolution computer controlled x-ray spectrometers usingeither a conventional or high intensity rotating anode x-ray generator. The angular resolution canbe made as fine as 1.8 seconds of arc; this enables one to probe the development of order fromdistances of the order of the x-ray wavelength, ~1 ., up to 30,000 A. The sample temperaturemay be varied between 2 K and 500 K with a relative accuracy of 2 x 10 K. We are currentlyinstalling a two spectrometer system at the National Synchrotron Light Source at BrookhavenNational Laboratory. This makes possible high resolution scattering experiments with a flux morethan three orders of magnitude larger than that from a rotating anode x-ray generator. Thisopens up a new generation of experiments. Synchrotron x-ray scattering experiments are alsocarried out on a wiggler beam line at the Stanford Synchrotron Radiation Laboratory.As part of the JSEP program we have built an x-ray compatible high vacuum single crystalapparatus. This enables us to use synchrotron radiation to study the structure and transitionsoccurring at single surfaces; such experiments are now being initiated. Our current experimentsin this program are concentrated in three areas: (i) the growth, structure and phase transitions ofintercalant materials, (ii) the structure and phase transitions of smectic liquid crystals, (iii) thephases and phase transitions of rare gas atom monolayer and bilayer films on graphite.8.1 Intercalation Compound Structures and TransitionsIntercalation compounds represent a family of materials in which a foreign species (e.g., Br2) isinserted between the layers of a lamellar material such as graphite. If the intercalant enters everynith layer then the resultant material is referred to as a stage-n intercalation compound. In thisprogram we study both the intercalation process itself and the structure and transitions of theintercalation compound as a function of temperature, concentration, and stage index. OurRLE P.R. No. 127A-Hay uirruse scatternngcurrent work is concentrated on the systems bromine-intercalated graphite C7nBr 2 1 andSbCI5-intercalated graphite.2In bromine-intercalated graphite, the intercalate plane is found to have three sublattices andeach sublattice has a centered ( 3 x7) rectangular structure with four Br2 molecules per 2D unitcell in the commensurate phase. The coherently ordered in-plane bromine regions exceed10,000 A in size. In the stage-4 material, a commensurate-incommensurate transition is observedat 342.20 + 0.050 K. In the incommensurate phase, a stripe domain pattern becomes establishedin a single domain of a sublattice along the 7-fold direction. For this phase, current theorypredicts that the superlattice peaks should be power law singularities of the form (Q-QC) n2nwhere x -2- and n is the order of the harmonic. To probe these line-shape effects we haven 49carried out a high resolution synchrotron study of a sample of C28Br 2 grown "in situ". Dramaticchanges are indeed seen in the intensities and shapes of the successive harmonic peaks.Quantitative analysis shows that the first five harmonics are indeed well-described by the aboveform; further, x, is given by 2n2/49 to an accuracy of about 20%. We also confirm that theline-shape is independent of the domain wall separation.We have also carried out a combined x-ray diffraction and electron diffraction study ofSbCi 5-intercalated graphite.2 We have examined both single crystal and microcrystalline powdersamples using the two different techniques. With x-ray diffraction we find a single phase,commensurate 7- x 7VT structure which is stable between room-temperature and 16 K. On theother hand, initial electron diffraction measuroments showed a crystal glass transition atabout 200 K for the intercalant on decreasing temperature, in agreement with earlier studies. By acareful study of the behavior as a function of electron beam current and energy, we find that theglass transition is driven by the electron beam. Below -150 K the fluence required to drive thetransition exhibits an activation energy of -0.01 eV while above 150 K the activation energyincreases dramatically to -0.1 eV. We are currently analyzing various models for this novelbehavior. A quasi-two dimensional glass with controllable disorder should be of much generalinterest.8.2 Smectic Liquid CrystalsLiquid crystals are made up of rod-like molecules. In the nematic phase the axes of themolecules align parallel to each other but the centers of mass of the molecules are still randomlydistributed so that one has a pure fluid structure factor. In the smectic A and C phases aone-dimensional sinusoidal density wave is set up either along (A) or at an angle (C) to themolecular axis. Thus, these smectics are like solids in one direction atnd fluids in the other two.These systems exhibit particularly interesting phase transitions which present an importantchallenge to modern theories of critical phenomena. At lower temperatures many liquid crystalmaterials exhibit more ordered phases such as smectic B, F, G, and I. These have well-developedin-plane triangular order. If the order is truly long range then the phase is a plastic crystal.RLE P.R. No. 127X-Ray Diffuse ScatteringOtherwise, the smectic may be a realization of a novel phase of matter labelled a "stackedhexatic" with long range order in the crystalline axes but only short range order in the positions ofthe molecules. We are continuing to study in some detail the smectic phases and phasetransitions in a number of materials. Special emphasis has been given to nematic-smecticA-smectic C multicritical behavior.The thermotropic liquid crystal material pentylbenzenethioseptyloxybenzoate (7S5) exhibits anN-Sc transition at ~400 C. However, we have found that addition of a few mole percentoctyloxycyanobiphenyl (80CB) changes the sequence of phases to A - 4, SC. with decreasingtemperature. By careful study of the transitions in a series of mixtures, we find that there is a triplepoint, labelled the NAC multicritical point, at which the three phases come together. This NACpoint has been the subject of extensive theoretical and experimental investigation; the principalmotivation for this interest is that in some models the NAC point is a Lifshitz transition; this is aspecial multicritical point at which the coefficient of the gradient term in the Landau-Ginsburgexpansion is exactly zero. We have studied the nematic and smectic mass density structurefunctions in a series of mixtures around the NAC point. We find SA-like fluctuations, that isfluctuations with a positive q2 coefficient, throughout most of the nematic phase. However, nearthe N-S boundary there is indeed a line. emerging from the NAC point, along which the q2coefficient vanishes. The gradient-squared coefficient is negative between this line and the N-Scboundary. This provides a dramatic confirmation of the Lifshitz concept. However, the detailedgeometry of the phase boundaries and the Lifshitz line remain to be explained. We are currentlyanalyzing these data quantitatively.8.3 Structures and Transitions of Monolayer Rare GasCrystalsThe phases and phase transitions of monolayer films of rare gases physisorbed onto the basalplanes of graphite continue to be the subject of active research. They provide model examples oftwo dimensional freezing and of transitions driven by competing period effects - both subjects ofconsiderable controversy. The principal advantages of the rare gas-graphite systems foraddressing these issues are that, first, the interactions are simple and well known so that firstprinciple's calculations are possible and second, a broad range of sophisticated experiments,carried out in thermal equilibrium, are feasible. In the past year we have used synchrotronradiation to probe the freezing of submonolayer films of xenon on graphite and to study a noveltransition in which a krypton monolayer spontaneously rotates with respect to the graphitesubstrate.The xenon freezing experiments were carried out using both ZYX graphite,3 an azimuthalpowder, and an exfoliated single crystal4 as substrates. The latter provides orientational as wellas, positional information. Both experiments show that the incommensurate xenon freezingtransition is continuous for coverages as low as 0.9 monolayers; further, at lower coveragesRLE P.R. No. 127X-Ray Diffuse Scatteringwhere the transition appears to be first order the fluid is very well correlated. These experimentsdemonstrate, in agreement with our original studies at 1.1 layers, that the fluid correlation lengthreaches at least 200 A before the solid appears for freezing temperatures as low as 125 K. Fromthe exfoliated single crystal studies we find that the angular width of the fluid diffraction spotsscales linearly with the radial width. This is the behavior expected for a "hexatic" fluid aspredicted by Halperin and Nelson. Unfortunately, because of our lack of knowledge of thesubstrate orienting field we cannot make a definitive statement about the existence of a hexaticphase in the absence of a substrate. Certainly we see no remnant of the hexatic-isotropictransition expected for a substrate-free hexatic fluid.Several years ago, Shiba made the interesting prediction that an incommensurate overlayerwould exhibit a continuous transition from an aligned to a rotated phase as a function of latticemismatch. The transition occurs as a result of a crossover from the non-linear to the linearmodulation regimes. Further, Shiba calculated quantitatively the expected rotation angle versuslattice mismatch for a given interaction potential ratio. Krypton on graphite turns out to provide avery good illustration of this effect. In order to probe this we have used an improved sample celldeveloped by K. D'Amico to allow for single crystal studies. We find that at -82 K analigned-rotated transition does indeed occur for a lattice mismatch of -3.5%; this threshold valuecorresponds to a domain wall half-width of about three lattice constants. Shiba's theory is foundto describe our data quantitatively.5References1. S.G.J. Mochrie, A.R. Kortan, R.J. Birgeneau, and P.M. Horn, Phys. Rev. Lett. 53, 985 (1984).2. G. Roth, L. Salamanca-Riba, A.R. Kortan, G. Dresselhaus, and R.J. Birgeneau, submitted forpublication.3. P. Dimon, P.M. Horn, M. Sutton, R.F. Birgeneau, and D.E. Moncton, Phys. Rev. B31, 437 (1985).4. S.E. Nagler, P.M. Horn, T.F. Rosenbaum, R.J. Birgeneau, M. Sutton, S.G.J. Mochrie, D.E.Moncton, and R. Clarke, Phys. Rev. B., in press.5. K.L. D'Amico, D.E. Moncton, E.D. Specht, R.J. Birgeneau, S.E. Nagler, and P.M. Horn, Phys.Rev. Lett. 53, 2250 (1984).RLE P.R. No. 127

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X-Ray Diffuse Scattering

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