Contains summary of resarch and reports on three research projects.Joint Services Electronics Program (Contract DAALO03-86-K-0002

Birgeneau, Robert J.

Contains research summary and reports on three research projects.Joint Services Electronics Program (Contract DAALO3-86-K-0002

DSpace@MIT

X-Ray Diffuse Scattering9.0 X-Ray Diffuse ScatteringAcademic and Research StaffProf. R.J. Birgeneau, Dr. J.W. Chung, Dr. C.J. PetersGraduate StudentsK. Evans-Lutterodt, J. Hill, H. Hong, B. Keimer, A. Mak, D.Y. Noh, E. Specht, T.ThurstonJoint Services Electronics Program (Contract DAALO3-86-K-0002)Robert J. BirgeneauIn this research program, modern x-ray scattering techniques are used to studystructures and phase transitions in thin films and on surfaces. We have two principalexperimental facilities. At MIT we have four high-resolution computer-controlled x-rayspectrometers using high intensity rotating anode x-ray generators. The angular resol-ution can be made as fine as 1.8 seconds of arc; this enables one to probe the devel-opment of order from distances of the order of the x-ray wavelength, ~ 1A, up to30,000A. The sample temperature may be varied between 2K and 500K with a relativeaccuracy of 2X10-3 K. We also have, in collaboration with IBM, a two spectrometersystem at the National Synchrotron Light Source at Brookhaven National Laboratory.A third beam line designed to operate at short wave lengths is currently being imple-mented. These make possible high resolution scattering experiments with a flux morethan three orders of magnitude larger than that from a rotating anode x-ray generator;this, in turn, has opened up a new generation of experiments.As part of this JSEP program we have built an x-ray compatible high vacuum singlecrystal apparatus. This enables us to use synchrotron radiation to study the structureand transitions occurring at a single surface; the first generation of such experimentshas now been performed. Our current experiments in this program are concentrated intwo areas: 1) the phases and phase transitions of metal and semiconductor surfaces andsurface overlayers; and 2) the structure and phase transitions of rare gas multilayers onsimple substrates.9.1 Metal Surface StudiesFor our first detailed studies of metal surface reconstruction we have chosen tungsten,both pure and coated with hydrogen or oxygen. The tungsten system has been exhaus-tively studied with all of the standard surface techniques including LEED, STM, atombeam scattering, and Rutherford back scattering. In spite of this effort, there are still majorcontroversies concerning the nature of the structures and surface transitions. Our mostsuccessful experiments were for W (100) with sub-monolayer coverages of H.The system of atomic hydrogen chemisorbed onto the surface of tungsten has longbeen considered a model system for the study of chemisorption. Extensive experimentalX-Ray Diffuse Scatteringstudies have shown that the W(100) surface goes through an elaborate sequence ofphases and phase transitions as a function of increasing hydrogen coverage; however,the microscopic nature of these successive states remains problematic. We carried outa synchrotron x-ray glancing-angle diffraction study of W(1 00) at room temperature fora range of hydrogen coverages. The experiments illustrate clearly the utility of x-raysin obtaining quantitative information about the structures and the nature of the disorderin such chemisorbed surface systems.Our data suggest a simple picture in which at very low coverages there is a tradeoffwith increasing coverage, analogous to that in a two-phase coexistence region, be-tween h drogen-poor and hydrogen-rich regions until a uniform but still disordered( 2 x 2 )R45' -H phase is attained. This disagrees with the currently accepted modelwhich assumes that the hydrogen atoms are always uniformly distributed on thetungsten surface. With further increase in coverage the surface layer exhibits acommensurate-incommensurate transition (CIT) which, rather than being a solid-solidtransition as previously assumed, is actually a lattice-gas melting transition into adomain-wall fluid phase. Such surface domain-wall fluid phases should occur com-monly in chemisorbed systems.We find that the line-shape in the (,2-x,2-)R450 -H phase is well-described as aLorentzian raised to the 3/2 power. This line-shape is indicative of random field effectsin two dimensions. Specifically, in surface lattice-gas systems, impurities and defectswhich fix the sublattice locally act as random fields which round the freezing transitionand prevent the achievement of true long range order. Such random field effects havenot been seen in previous surface diffraction experiments; only x-rays provide the re-solution and simple kinematical interaction to allow such quantitative line-shape anal-ysis.9.2 Rare Gases on GraphiteIn the last year, we completed two major experiments on monolayer rare gas films.First we carried out an encyclopaedic high resolution x-ray diffraction study of thestructures and phase transitions of monolayer krypton, adsorbed on both powder andsingle crystal graphite substrates. A comprehensive series of powder diffraction profileswas used to construct the two-dimensional phase diagram. The melting of thecommensurate solid was shown to be strongly first order throughout the region wheretricritical behavior was previously thought to occur; fluid-solid coexistence extends upto the termination of the commensurate phase at 130 K. A disordered weaklyincommensurate phase with lattice constant smaller than that of the 3 x 3 phasewas shown to be reentrant fluid, a system which may be described as a disorderednetwork of domain walls and which evolves continuously into a more conventional 2Dfluid. This evolution is marked by the disappearance of satellite peaks which are causedby the modulation of the overlayer by the substrate. The freezing of the reentrant fluidinto the commensurate phase was shown to be consistent with a chiral Potts transition,its freezing into the incommensurate solid consistent with a dislocation binding transi-tion. Single crystal experiments revealed the orientation of the weakly incommensuratephase. The reentrant fluid was found to have no visible orientational fluctuations,manifesting isotropic diffraction peaks. This is attributed to the strong epitaxy of do-main walls. The incommensurate solid was shown to undergo an aligned-rotatedtransition which is well described by zero-temperature calculations.76 RLE Progress Report Number 130X-Ray Diffuse ScatteringSecond, we carried out an extensive synchrotron x-ray study of monolayer xenonon single crystal graphite. A monolayer of xenon freezes at -~135K into anincommensurate solid. The incommensurate solid undergoes the sequence of phaseswith decreasing temperatures aligned -+ rotated -+ reentrant aligned, before transform-ing at -70K into a commensurate -x,3-R45 0 solid. The current theory oforientational epitaxy correctly predicts only the point at which the rotated -+ reentrantaligned transition occurs. None of the current theories can explain the entire sequence.The reentrant aligned phase at intermediate temperatures is an incommensurate solidwith a network of superlight domain walls. The observed phase transition into thecommensurate phase is first order consistent with domain wall theories. Theincommensurability decreases asST - To 1/3until the first order C-IC transition point is encountered. This 1/3 power law is appar-ently a universal behavior shared with Kr on graphite.We have estimated the potential corrugation of the surface adsorbtion from the in-tensity ratios between the main and satellite peaks in the domain wall incommensuratephsae. The corrugation of the potential estimated is close to that predicted by Steele.Along with this estimation from the onset of the rotated phase, we are able to set thelimits for the dimensionless wall width, 36 < 10 < 42. Also we estimated the wallcrossing energy which turned out to be +60K. However, the striped phase, predictedby Halpin-Healy using a similar value was not observed.9.3 Surface Roughening of AgDirect evidence of the thermal roughening of Ag (110) surface has been observedin a high resolution x-ray scattering experiment at the National Synchrotron LightSource of the Brookhaven National Laboratory. Information about the surfaceroughness, as manifested in the height-height correlation function, is obtained from thescattering intensity profile of the bulk forbidden (110) surface peak. The results indi-cate that surface roughening occurs at T, = 450 + 25 0 C. Below Tr , the Ag (110) sur-face is smooth, as characterized by delta function Bragg scattering, whereas above T,,the scattering intensity obeys a power law lineshape, indicating a rough surface withlogarithmically divergent height fluctuations. Since the transition is reversible withtemperature, it is indeed an equilibrium phase transition. Furthermore, the fact that theintegrated intensity of the bulk Ag (111) peak undergoes little change during the tran-sition, apart from the Debye-Waller factor, demonstrates that the observed changes inbulk forbidden (110) peak are due exclusively to changes in the surface morphology.In contrast to atom scattering and LEED experiments which have significant multiplescattering and inelastic scattering, x-ray experiments allow relatively simple data anal-ysis. Coupled with the high resolution of our experiment, we have demonstrated a verypowerful technique for studying surface roughening.X-Ray Diffuse ScatteringPublicationsMochrie, S.G.J., A.R. Kortan, P.M. Horn, and R.J. Birgeneau, "Novel Melting Transi-tion in a Two-Dimensional Stripe-Domain System," Phys. Rev. Lett. 58:690 (1987).Chung, J.W., K. Evans-Lutterodt, E.D. Specht, R.J. Birgeneau, P.J. Estrup, and A.R.Kortan, "Grazing-Incidence X-Ray Study of the Structures and Phase Transitions ofHydrogen on Tungsten (100)," Phys. Rev. Lett. 59:2192 (1987).Specht, E.D., A. Mak, C. Peters, M. Sutton, R.J. Birgeneau, K.L. D'Amico, D.E.Moncton, S.E. Nagler, and P.M. Horn, "Phase Diagram and Phase Transitions ofKrypton on Graphite in the Extended Monolayer Regime," Z. Phys. B 69:347 (1987).Held, G.A., J.L. Jordan-Sweet, P.M. Horn, A. Mak, and R.J. Birgeneau. "X-Ray Scat-tering Study of the Thermal Roughening of Ag(110)," Phys. Rev. Lett. 59:2075(1987).78 RLE Progress Report Number 130

X-Ray Diffuse Scattering

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

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

X- Ray Diffuse Scattering9.0 X-Ray Diffuse ScatteringAcademic and Research StaffProf. R.J. Birgeneau, Prof. A. Aharony, Dr. J.W. Chung, Dr. C.J. PetersGraduate StudentsK. Evans-Lutterodt, H. Hong, B. Keimer, A. Mak, D.Y. Noh, E. Specht, T. ThurstonJoint Services Electronics Program (Contract DAALO03-86-K-0002)Robert J. BirgeneauIn this research program, modern x-ray scattering techniques are used to study thestructures and phase transistions in novel states of condensed matter. We have twoprincipal experimental facilities. At M.I.T. we have four high-resolution computer-controlled x-ray spectrometers using high intensity rotating anode x-ray generators.The angular resolution can be made as fine as 1.8 seconds of arc; this enables one toprobe the development of order from distances of the order of the x-ray wavelength,1 A , up to 30,000A. The sample temperature may be varied between 2K and 500Kwith a relative accuracy of 2x10- 3K. We also have, in collaboration with IBM, a twospectrometer system at the National Synchrotron Light Source at Brookhaven NationalLaboratory. A third beam line designed to operate at short wave lengths is currentlyunder development. These make possible high resolution scattering experiments witha flux more than three orders of magnitude larger than that from a rotating anode x-raygenerator; this, in turn, has opened up a new generation of experiments.As part of the JSEP program we have built an x-ray compatible high vacuum singlecrystal apparatus. This enables us to use synchrotron radiation to study the structureand transitions occuring at a single surface; the first generation of such experiments hasnow been performed. Our current experiments in this program are concentrated in threeareas: 1) the phases and phase transitions of metal and semiconductor surfaces andsurface overlayers; 2) the structure and phase transitions of smectic liquid crystals; and3) the growth, structure and phase transitions of intercalant materials.9.1 Single Crystal Surface StudiesAs noted above, x-ray synchrotron sources provide sufficient flux that it is possibleto carry out high resolution diffraction studies of a single monolayer. In the past yearwe have studied three different systems: 1) monolayer xenon on graphite; 2) tungsten(100) with either oxygen or hydrogen adsorbed on the surface; and 3) pristine silver(110) as a function of temperature.The xenon-on-graphite experiments represented a considerable technical advanceon previous surface overlayer experiments. We used a single crystal of graphite with amosaicity of 0.010 full-width-at-half-maximum (FWHM). This corresponds to a realspace resolution of ~2 microns. The xenon coverage was accurately controlled usingX- Ray Diffuse Scatteringa vermicular graphite ballast adjacent to the single crystal sample. We find that for abroad range of coverages, - 9 to 1.2 monolayers, with decreasing temperature thexenon exhibits the sequence of structures: aligned hexagonal incommensurate -- ro-tated hexagonal incommensurate -+ aligned hexagonal incommensurate -*~ x ,-R300 commensurate. The first and third transitions are first order while the second iscontinuous. The incommensurate-commensurate transition is similar to that exhibitedby monolayer kyrpton on graphite with a 1/3 power-law behavior; however, for xenonthis power law is pre-empted by a first order transition at 1% incommensurability. Fromthe data it is possible to deduce precise information about the surface potential andthereby to assess first principle's theoretical predictions for this model surface system.From low energy electron diffraction studies it is known that tungsten (100) exhibitsa variety of interesting surface phases when either oxygen or hydrogen is adsorbed ontothe surface. We have used high resolution synchrotron radiation to study the surfaceoxygenation and hydrogenation processes. Because of the extreme reactivity of thetungsten surface, these experiments are technically quite difficult. We have, neverthe-less, managed to observe both the saturated oxygen overlayer structure, which has asimple 2 x 2 symmetry, and various other chemisorbed phases. These data are still beinganalyzed. Quite fascinating results are obtained with the absorption of hydrogen. Forabout 0.2 monolayers of hydrogen, a centered 2 x 2 structure forms; we observe intensex-ray diffraction from this phase at room temperature. This necessitates that there isconsiderable movement of the tungsten surface atoms in the formation of the 2 x 2structure. With increasing hydrogen coverage a commensurate-incommensurate tran-sition occurs. These data are currently being analyzed.Surface roughening is a novel phenomenon which has been extensively investigatedtheoretically and by computer simulation. However, there have been only limited ex-perimental investigations in real materials. Recent atom beam scattering experimentshave suggested that low index metal surfaces may show a reversible roughening tran-sition. We have carried out a detailed study of the Ag (110) surface. We find that atabout 400'C the Ag (110) surface indeed becomes rough and by ~6000 the surface issufficiently disordered that it no longer gives a clear diffraction signal. Remarkably, asthe sample is cooled, the surface reforms reversibly recovering its original form at roomtemperature. The data from this experiment are currently being analyzed.9.2 Structure and Phase Transitions of Smectic LiquidCrystalsThe mechanism by which crystalline order is established as a fluid freezes is still anunsolved problems. In liquid crystal materials, the freezing process may occur in severalsteps. Each step may be thought of as the freezing out of some particular type of ran-dom motion or disorder as the system cools. Choosing the orientation in space of theaxes of the crystalline lattice is one of the crucial steps necessary for the establishmentof crystalline order. In most physical systems, this choice of orientation occurs simul-taneously with the establishment of a true spatially periodic crystal lattice. However,there is no reason why the two processes must occur simultaneously. The logical pos-sibility that a phase of matter might have a well defined orientation for the crystal axeswithout having actually established the lattice has been recognized for 50 years. Thesestrange phases of matter are called Bond Orientationally (BO) ordered to indicate that58 R.L.E. P.R. No. 129X-Ray Diffuse Scatteringit is the orientation of the bonds between nearest neighbors, not the distance betweennearest neighbors, which is becoming fixed.The suggestion that several of the unusual liquid crystal phases might be physicalrealizations of BO ordered phases was made several years ago. However, samples ofhigh enough quality and x-ray scattering equipment with high enough intensity at highresolution were not readily available. The sample problems were solved by the devel-opment of freely suspended film techniques of liquid crystal at Harvard, Bell Labs andMIT. The development of high resolution x-ray scattering apparatus on synchrotronx-ray sources has solved the latter obstacle.The signature of a BO ordered phase in an x-ray scattering experiment is a periodicvariation in the scattered intensity while rotating the lattice. We therefore performed aseries of such angular scans as the sample was cooled through the putative hexaticphase transition. At high temperatures the scan is flat to within our counting statistics.As the sample is cooled, a measurable modulation develops. Further cooling causes theslight modulation to grow into definite peaks, one every 600.Taking advantage of this extremely high quality data taken at NSLS, we performeda detailed line-shape analysis. The analysis led to the empirical discovery of math-ematical scaling relations describing the growth of the BO order. Motivated by thisdiscovery, a theoretical model was developed which explains the growth of BO orderbased only on the underlying symmetry of the physical system. Since the model appliesto any physical system with the appropriate symmetry, it is applicable to a wide varietyof theoretical and experimental systems. Using our model we can describe exactly howthe orientation of the crystal lattice develops with temperature without any knowledgeof the details of the system other than its symmetry.9.3 Intercalation Compound Structures and TransitionsIntercalation compounds represent a family of materials in which a foreign species(e.g., Br2 ) is inserted between the layers of a lamellar material such as graphite. If theintercalant enters every nth layer then the resultant material is referred to as a stage-nintercalation compound. In this program we study both the intercalation process itselfand the structure and transitions of the intercalation compound as a function of tem-perature, concentration, and stage index. Our current work is concentrated on thesystem bromine-intercalated graphite C7nBr 2. 1Bromine-intercalated graphite has turned out to be an interesting model two di-mensional system. Above 69.3°C the bromine has a novel structure in which it is in-registry with the graphite in one direction and out of registry or incommensurate in theother. This is referred to as a stripe-domain structure. One of the unusual features ofsuch a structure, which we have characterized thoroughly, is that in a diffraction patternthere are no true Bragg peaks. Rather, the diffraction is characterized by power lawsingularities, (Q - Qn)- 2+ n , where the exponent vn depends on the order (n) of theharmonic. Here the vn are predicted exactly by theory. One of the interesting questionswhich had not been addressed quantitativley to date is how such a solid melts.Qualitatively, it is expected that one could have a continuous melting transition inwhich the bromine melts while the graphite stays crystalline. Further, on universalitygrounds it is expected that such a transition, if continuous, would be isomorphous toX- Ray Diffuse Scatteringthe superfluid transition in two-dimensional helium which is well-described by a theorydue to Kosterlitz and Thouless - a dramatic theoretical prediction. We have used highresolution x-ray synchrotron techniques to study this melting transition. A high qualitysingle crystal of stage-8 bromine intercalated graphite was grown "in situ" on the x-rayspectrometer.Our results show a number of striking features: (1) the transistion is indeed contin-uous, at least for length scales varying from several thousand Angstroms to fiftyAngstroms; (2) higher harmonics of the mass density wave vanish successively as thetemperature is raised. Thus, even though from the peak positions we know that thedomain walls remain microscopically sharp, the order parameter acquires a sine-wavecharacter; (3) the transition is very rapid, with the primary evolution in the structurefactor occuring within 1 0C; (4) the aspect ratio of the scattering changes through thetransition; and (5) the detailed nature of the correlations is unusual in that a power-lawdescription of S(Q) works throughout the temperature range studied; that is, the antic-ipated crossover from algebraic to exponential decay of the positional correlations at= 1/4 does not seem to occur.We have also carried out a combined electron and x-ray diffraction of SbCI,intercalated graphite. Of particular interest is the unusual commensurate( - x ,7)R1 9.1 to glass "phase change" (C-G) in the intercalate layer that has beenobserved to take place on cooling below - 180K using TEM, where the low-temperature phase is the glass phase. The C-G phase change is not observed in x-raydiffraction experiments. It was first suggested that the C-G phase change reported forstages 1-4 occured only in dilute samples, and that further the intercalate layer was di-lute in the thin samples needed for TEM, but not in the thick samples used in x-raydiffraction. In order to determine whether the discrepancy between the x-ray and TEMresults was due to differences in sample composition or to differences in the exper-imental techniques, we performed x-ray diffraction and electron microscopy studies atlow temperatures using stage-2 SbCI5-CIG samples of common origin for both typesof experiments. We investigated the dependence of the C-G phase change on hostmaterial, host crystallite size and experimental technique. We find from x-ray andelectron diffraction experiments performed on stage-2 SbCI -GIC samples that thecrystalline to glass-phase change results from electron-beam damage. Two competingannealing processes are observed with two different activation energies. Thiscrystalline-glass phase change is the result of damage attributed to atomic displace-ments indirectly induced by electron beam irradiation. We have devised a model for thedamage process that induces the C-G phase chan e_. The model is supported by acomputer image simulation of the commensurate (,/7 x ,7 ) R1 9.1o phase.PublicationsBirgeneau, R.J., and P.M. Horn, Science 232, 329 (1986).Brock, J.D., A. Aharony, R.J. Birgeneau, K.W. Evans-Lutterodt, J.D. Litster, P.M. Horn,G.B. Stephenson, and A.R. Tajbakhish, Phys. Rev. Lett. 57, 98 (1986).Mochrie, S.G.J., A.R. Kortan, P.M. Horn, and R.J. Birgeneau, Phys. Rev. Lett. 58, 690(1987).60 R.L.E. P.R. No. 129X- Ray Diffuse ScatteringOcko, B.M., R.J. Birgeneau, and J.D. Litster, Z. Phys. B 62, 487 (1986).Salamanca-Riba, L., G. Roth, J.M. Gibson, A.R. Kortan, G. Dresselhaus, and R.J.Birgeneau, Phys. Rev. B 33, 2738, (1986).62 R.L.E. P.R. No. 1 29

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X-Ray Diffuse Scattering

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DSpace@MIT

DSpace@MIT