Contains research summary and reports on six research projects.Joint Services Electronics Program (Contract DAAG29-78-C-0020

Birgeneau, Robert J.

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

DSpace@MIT

X-Ray Diffuse Scattering9. X-Ray Diffuse ScatteringAcademic and Research StaffProf. R.J. Birgeneau, Dr. J.W. Chung, Dr. C. Peters, Dr. S.G.J. MochrieGraduate StudentsK. Evans-Lutterodt, H. Hong, A. Mak, L.J. Martinez-Miranda, D.Y. Noh,E. Specht, T. ThurstonJoint 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 two high-resolution computer controlled x-ray spectrometers using ahigh intensity rotating anode x-ray generator. Two more spectrometers are currently underdevelopment. The angular resolution can be made as fine as 1.8 seconds of arc; this enables oneto probe the development of order from distances of the order of the x-ray wavelength, -1 A , upto 30,000 A . The sample temperature may be varied between 2 K and 500 K with a relativeaccuracy of 2 x 10- 3 K. We also have, in collaboration with IBM, a two spectrometer system at theNational Synchrotron Light Source at Brookhaven National Laboratory. This makes possible highresolution scattering experiments with a flux more than three orders of magnitude larger than thatfrom a rotating anode x-ray generator; this in turn has opened up a new generation ofexperiments. This facility is under continuous development to improve the optics andspectrometers. Synchrotron x-ray scattering experiments are also carried out on a wiggler beamline 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 transitionsoccuring 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 metal and semiconductor surfaces and surface overlayers.9.1 Intercalation Compound Structures and TransitionsIntercalation compounds represent a family of materials in which a foreign species (e.g., Ir3) isinserted between the layers of a larnellar material such as graphite. If the intercalant enters everynth layer then the resultant material is referred to as a stage-n intercalation compound. In thisRLE P.R. No. 128X-Ray Diffuse Scatteringprogram we study both the intercalation process itself and the structure and transitions of theintercalation compound as a function of temperature, concentration, and stage index. Ourcurrent work is concentrated on the system bromine-intercalated graphite ('n Br .1Bromine-intercalated graphite has turned out to be an interesting model two dimensionalsystem. Above 69.30 C the bromine has a novel structure in which it is in-registry with thegraphite in one direction and out of registry or incommensurate in the other. This is referred to asa stripe-domain structure. One of the unusual features of such a structure, which we havecharacterized thoroughly,' is that in a diffraction pattern there are no true Bragg peaks. Rather-2 + Ithe diffraction is characterized by power law singularities, (Q-Q,) n, where the exponent -qndepends on the order (n) of the harmonic. Here the qn are predicted exactly by theory. One ofthe interesting questions which had not been addressed quantitatively to date is how such a solidmelts. Qualitatively, it is expected that one could have a continuous melting transition in whichthe bromine melts while the graphite stays crystalline. Further, on universality grounds it isexpected that such a transition, if continuous, would be isomorphous to the superfluid transitionin two-dimensional helium which is well described by a theory due to Kosterlitz and Thouless - adramatic theoretical prediction. We have used high resolution x-ray synchrotron techniques tostudy this melting transition. A high quality single crystal of stage-8 bromine intercalated graphitewas grown in situ on the x-ray spectrometer. The data from this experiment are still beinganalyzed. We find strong evidence for a sharp but continuous melting transition for the bromine.However, the liquid structure-factor in the well-correlated fluid phase is anomalous. Specifically,it does not seem to fit into the Kosterlitz-Thouless picture. We are continuing our analysis in anattempt to determine the appropriate description of this novel melting phenomenon.9.2 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 and 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 II,JG, and I. These have well-developedin-plane triangular order. If the order is truly long range then the phase is a plastic crystal.Otherwise, 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 phase transitions in a numberof materials. One of the important issues in this field has been the critical behavior of theRLE P.R. No. 128X-Ray Diffuse Scatteringnematic-smectic A transition. This might be viewed as the simplest melting transition in nature.In nearly all cases in studies of phase transitions one finds that the critical behavior isindependent of the details of the system. For the N-problem, however, the exponentscharacterizing the transition vary from system to system. In order to elucidate this unusualphenomenon we have carried out a systematic study of the N-A transition 2 in two series ofcompounds: alkylbenzoate (nCB) and thiosulphate (nS5). Here the aliphatic chain length/(Cll),,+) may be varied continuously by making appropriate mixtures. We find that as oneincreases n in both series the exponents evolve continuously from T = 1.5, vlj 2 0.80 and L -0.67 to T = 1.1, P11 = 0.6 and v = 0.5; the latter are attained at the point where the transitionchanges from being second order to first order; as such, this point is a tricritical point and indeedthe measured exponents are close to the predicted theoretical values for a tricritical point. Weconclude therefore that the varied exponents reported in the literature for other systems simplyreflect a crossover from critical to tricritical behavior.As noted above, one of the most novel phases of matter occuring in the liquid crystal family isthe "stacked hexatic." We have initiated synchrotron x-ray studies of free standing films of thematerial methylbutylphenyloctyloxybiphenylcarboxylate (80SI) which is believed to exhibit astacked hexatic phase in which the molecules are tilted with respect to the layer normal; this islabeled smectic I; at -78" C with increasing temperature the S, exhibits a transition into an ,SCphase. Our initial measurements are very promising. We find that by applying a small field viaSinuCo magnets one can orient the molecules and this, in turn, fixes the hexatic axes in the S,phase. Thus we have produced the first single-domain sample in a liquid crystal hexatic; thismakes quantitative studies of the relevant order parameters and densities possible. Currently weare studying the thermal evolution of the orientational and positional order throughout the C and Iphases. Once these measurements are concluded we will begin studies in very thin films - 2 to 10molecules thick.9.3 Structures and Transitions in Two Dimensional SolidsAs is now well-recognized, surface systems provide interesting examples of two dimensionalphases and phase transitions. There are many different categories including pristine surfacereconstruction, chemically absorbed surface overlayers and physically adsorbed layers. Raregases on graphite provide the best studied examples of this third category. Much of our surfacescience research program in the past several years has concentrated on the physics of monolayerkrypton and xenon on graphite. The principal advantages of the rare gas-graphite systems arethat, first, the interactions are simple and well-known so that first principle's calculations arepossible and second, a broad range of sophisticated experiments, carried out in thermalequilibrium, are feasible.3 In the past year we have used synchrotron radiation to probe thefreezing of submonolayer films of xenon on single crystal graphite.4The single crystal substrate experiment allows one to study the evolution of the fluid correlationRLE P.R. No. 128X-Ray Diffuse Scatteringlength up to distances approaching a micron. This is unprecedented in surface structural studies.Our experiments were carried out for a coverage of 0.92 xenon monolayers at freezing. We findthat the fluid correlation length evolves continuously up to at least 2000 A before the solid phaseis entered.4 We find that the angular width of the fluid diffraction spots scales linearly with theradial width. This is the behavior expected for a "hexatic" fluid as predicted by Halperin andNelson. Unfortunately, because of our lack of knowledge of the substrate orienting field wecannot make a definitive statement about the existence of a hexatic phase in the absence of asubstrate.We are continuing to develop our "chemically-active" single crystal apparatus. We expect toinitiate synchrotron radiation studies of molybednum surfaces in the spring of 1986.References1. S.G.J. Mochrie, A.R. Kortan, R.J. Birgeneau, and P.M. Horn, Z. Phyz. B 62, 79 (1985).2. B.M. Ocko, R.J. Birgeneau, and J.D. Litster, Z. Phyz. B 62, (1986).3. R.J. Birgeneau and P.M Horn, Science (in press).4. E.D. Specht, R.J. Birgeneau, K.L. D'Amico, D.E. Moncton, S.E. Nagler, and P.M. Horn,J. Physique Lett. 46, L-561 (1985).RLE P.R. No. 128

X-Ray Diffuse Scattering

VII. X-RAY DIFFUSE SCATTERINGAcademic and Research StaffProf. R.J. BirgeneauProf. P.S. Pershan*Dr. P.W. StephensGraduate StudentsG. Aeppli E.M. Hammonds B.M. OckoJ.A. Collett P.A. Heiney C.R. SafinyaM.C. KaplanJoint Services Electronics Program (Contract DAAG29-78-C-0020)Robert J. BirgeneauThis research program centers around a two-spectrometer x-ray diffuse-scatter-ing system based on a Rigaku 12-kW rotating-anode x-ray generator. The apparatusis designed in such a way that one may easily tailor the instrumental resolutionfunction to optimize studies of structure and fluctuations in a vast range of phys-ical systems. Angular resolution of 1.8 seconds of arc and sample temperature con-trol of 2 mK between 10 K and 500 K are available. We are currently implementinga position-sensitive detection system to allow rapid scans over a wide range ofscattering angles, again with continuously variable resolution. Our current re-search program emphasizes structure and melting transitions both for monolayerphysiadsorbed films on graphite and for layered liquid crystals. The surface ex-periments involve in situ high-precision vapor-pressure and surface-coverage mea-surements. Experiments are also performed using the x-ray synchrotron facilitiesat D.E.S.Y. (Hamburg, Germany) and S.L.A.C. (Stanford). We are currently designinga two-spectrometer high-resolution x-ray system to be permanently located at theNational Synchrotron Light Source under construction at Brookhaven National Labo-ratory.Visiting Professor from Harvard University; now returned.PR No. 122(VII. X-RAY DIFFUSE SCATTERING)1. COMMENSURATE-INCOMMENSURATE TRANSITION OF MONOLAYER KRYPTONON GRAPHITEWe have carried out an x-ray scattering of the commensurate-incommensuratetransitions (C.-I.T.) of monolayer krypton on the surface of ZXY exfoliated graph-ite at temperatures of 80.0 K and 89,3 K. At submonolayer densities the krypton hasa /v x v R 300 structure, commensurate with the graphite (0001) plane. As a func-tion of chemical potential, and hence coverage, the krypton atoms move out of theV x 4 R 30' positions, forming a triangular lattice which is incommensurate withthe substrate. We find1 that (a) the transition appears to be second order withthe simple power-law behavior e(p- c 1/3 , (b) the transition occurs via the for-mation of a superlattice of domain walls, and (c) interesting and complicated line-shape phenomena occur near the transition. Current theories of the C.-I.T. are notadequate to describe these results.2. STRUCTURE, PHASE DIAGRAM AND MELTING OF XENON ON GRAPHITEThe spacing of the xenon atoms in bulk xenon is intermediate between the 2 x 2and v3 x v3 structures on graphite. This suggests that xenon might form an incom-mensurate lattice on graphite. We do indeed find that xenon forms a triangularlattice which is incommensurate except at low temperatures (T < 65 K) and highcoverages. At higher temperatures where interesting thermodynamic phenomena occur,the system thence functions as a model 2D continuous-symmetry solid. In our x-raystudies we find evidence for (i) the existence of a well-defined triple point as in3D materials, (ii) a sharp nearly second-order melting transition, and (iii) novelcoexistence phenomena at low coverages which indicate the importance of finite-sizeeffects. Our analysis of the triple-point and coexistence experiments is completeand has been submitted for publication.2 We are currently carrying out a detailedanalysis of the melting data in order to make a quantitative comparison with currenttheories such as that proposed by Kosterlitz and Thouless.PR No. 122(VII. X-RAY DIFFUSE SCATTERING)3. STRUCTURE, PHASE DIAGRAM AND TRANSITIONS OF MONOLAYER ANDBILAYER MOLECULAR OXYGEN ON GRAPHITEOxygen adsorbs onto graphite in the molecular state; the oxygen molecule isunique among homonuclear diatomic species in that it is paramagnetic with spin S = 1.The interplay between the magnetic, orientational, and structural degrees of freedommake both 3d and 2d oxygen rich and quite subtle. Previously, susceptibility andneutron-scattering studies of monolayer and bilayer oxygen on graphite have beenperformed. Both experiments suggest that oxygen solidifies at about 30 K for amonolayer and 40 K for a bilayer. The neutron studies suggest that the structureis triangular with a nearest neighbor intermolecular spacing close to that in thebulk, and concomitantly, incommensurate with the graphite. The neutron studies alsosuggest that bilayer oxygen undergoes an antiferromagnetic transition at 11.9 K.We have carried out a detailed x-ray study of the structure of monolayer and bi-layer oxygen as a function of coverage from 0.5 to 2.5 monolayers and of tempera-ture from 12 K to 50 K. We find evidence for at least four distinct phases, onlytwo of which are triangular. In particular, the bilayer phase is only triangularwithin 2 K of melting, in explicit contradiction with the neutron results. We havenot yet managed to produce an unambiguous model for the structure, although thedata are consistent with incommensurate successive layers. Work on this most in-teresting system is continuing.4. STRUCTURE OF WELL-ORDERED SMECTIC PHASESSmectic liquid crystals are conventionally defined as systems consisting of aone-dimensional density wave in a three-dimensional fluid. However, in many liquidcrystals there are additional phases, conventionally labelled, SmB, D, E, F, G, andH with various degrees of order perpendicular to the density-wave direction. Further,existing x-ray evidence seems to indicate that this in-plane order often only ex-tends a limited distance along the one-dimensional axis. As discussed in last year'sreport, we have constructed a simple model based on the Halperin-Nelson-Kosterlitz-Thouless theory of melting in 2 dimensions which appears to be able to account forthe variety of phases suggested by the experiments. Most importantly, we identifyPR No. 122(VII. X-RAY DIFFUSE SCATTERING)a new 3D phase consisting of "stacked hexatics" - a system with long-range orienta-tional order, but only short-range in-plane and between-plane positional order.3 Wehave now carried out a high-resolution x-ray study of the SmB phase of 4.0.8 which,according to existing data, appeared to be describable as the stacked hexatic phase.Unfortunately, our x-ray data show clearly that the SmB phase of 4.0.8 correspondsto an extremely soft solid.4 It now appears likely that most systems labelled ashigher order smectics are, in fact, solids as we have found for 4.0.8. This israther disappointing since our "stacked hexatic" phase would have represented a gen-uinely new phase of matter.5. CRITICAL BEHAVIOR OF THE SmA-SmC TRANSITION OF 8S5We have carried out measurements of the A-C transition in 8S5 in magnetic fieldswhich are sufficiently large that the liquid-crystal director is held fixed in theSmC phase. Hence the SmA Bragg peak splits into a ring of scattering. The angularbreadth of the ring gives the magnitude of the tilt-order parameter 4 directly. Onemay also measure simultaneously the planar spacing d. We find to great precisiondA - dC % 2 and that p exhibits mean-field behavior, that is, d u (Tc-T)1/2, overthe reduced temperature range 5 x 10 > 1 - T/T > 3 x 10 . We have constructedca straightforward theory using the Ginzburg criterion which indicates that the truecritical region should be unobservably small for most A-C transitions; this enablesone to understand a large number of hitherto puzzling results in literature. Theseresults have now been published.56. OBSERVATION OF ALGEBRAIC DECAY OF POSITIONAL ORDER IN ASMECTIC LIQUID CRYSTALA smectic-A liquid crystal in three dimensions has been predicted to exhibitalgebraic decay of the layer correlations rather than true long-range order. As aconsequence, the smectic Bragg peaks are expected to be power-law singularities of-2+n -4+2nthe form q - and q , where 11(1) is along (perpendicular to) the smecticdensity-wave direction, rather than delta-function peaks. Observation of thesephenomena requires very high instrumental resolution together with a resolutionPR No. 122(VII. X-RAY DIFFUSE SCATTERING)-2 -4function with wings which drop off much more rapidly than q l (q  ) We show thatthese requirements may be met by using a three-crystal x-ray spectrometer withmultiple-reflection channel-cut crystals as monochromator and analyzer. We findthat the smectic-A Bragg peaks observed in the liquid crystals octyloxycyanobiphenylare indeed consistent with the predicted power-law singularity form. Furthermore,the explicit values of n required to describe the measured profiles are in accor-dance with calculations of p using the harmonic approximation with empirically de-termined splay and layer compressibility elastic constants. 6References1. P.W. Stephens, P. Heiney, R.J. Birgeneau, and P.M. Horn, Phys. Rev. Lett. 43,47 (1979).2. E.M. Hammonds, P. Heiney, P.W. Stephens, R.J. Birgeneau, and P. Horn, acceptedfor publication in J. Phys. C.3. R.J. Birgeneau and J.D. Litster, J. de Physique Lettres 39, L-399 (1978).4. P. Pershan, G. Aeppli, R.J. Birgeneau, and J.D. Litster, in J.L. Birman, H.Z.Cummins, and K.K. Rebane (Eds.), Light Scattering in Solids (Plenum PublishingCompany, 1979) pp. 365-375.5. C.R. Safinya, M. Kaplan, J. Als-Nielsen, R.J. Birgeneau, D. Davidov, J.D.Litster, D.L. Johnson, and M.E. Neubert, Phys. Rev. B 21 (May 1980).6. J. Als-Nielsen, J.D. Litster, R.J. Birgeneau, M. Kaplan, C.R. Safinya, A.Lindegaard-Andersen, and S. Mathiesen, Phys. Rev. B 21 (June 1980).PR No. 122

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

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

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

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

Contains reports on four research projects.Joint Services Electronics Program (Contract DAAG29-78-C-0020

VII. X-RAY DIFFUSE SCATTERINGAcademic and Research StaffProf. Robert J. Birgeneau Dr. Dan Davidovt Dr. Paul M. Horn$Prof. Peter S. Pershan': Dr. Peter W. StephensGraduate StudentsGabriel Aeppli Paul A. Heiney Martin C. KaplanEvelyn M. Hammond Cyrus R. SafinyaJoint Services Electronics Program (Contract DAAG29-78-C-0020)Robert J. BirgeneauWe have now completed construction of a two-spectrometer x-ray diffuse-scatteringsystem based on a Rigaku 12-kW rotating-anode x-ray generator. The system is de-signed in such a way that one may easily tailor the instrumental resolution function tooptimize studies of structure and fluctuations in a vast range of physical systems.Angular resolution of 1. 8 seconds of arc and sample temperature control of 2 mKbetween 10 K and 500 K are available. We are currently implementing a position-sensitive detection system to allow rapid scans over a wide range of scattering angles,again with continuously variable resolution. Our current research program emphasizesstructure and melting transitions both for monolayer physiadsorbed films on graphiteand for layered liquid crystals. The surface experiments involve in situ high-precisionvapor-pressure and surface-coverage measurements. We now discuss our individualprojects.1. MELTING AND COMMENSURATE-INCOMMENSURATE TRANSITIONOF KRYPTON ON GRAPHITEIt has traditionally been assumed that only surface-sensitive probes such as low-energy electron diffraction (LEED) could be used to study monolayer surface films.However, for a variety of experimental reasons LEED is extremely limited in the in-formation which it can provide. Accordingly, we have initiated a study of monolayersurface overlayers using x-ray scattering techniques. Our first experiments were per-formed on krypton physiadsorbed onto exfoliated ZYX graphite. This system is partic-ularly interesting because the ideal krypton-krypton interatomic separation is quiteclose to, albeit slightly less than, a natural superlattice (- x ,X N-) spacing provided byVisiting Professor from Harvard University.IVisiting Scientist from Hebrew University, Jerusalem, now returned.TVisiting Scientist from University of Chicago.PR No. 121(VII. X-RAY DIFFUSE SCATTERING)the (0001) graphite-plane substrate. We find that for less than monolayer coverage thekrypton forms a commensurate NT3 X £,/3 structure at all temperatures. Furthermore,for coverages greater than 0.9, the melting transition is second-order with the criticalbeha : or f the 3-component Potts lattice gas model as predicted by theory. With in-creai-n~ coverage the krypton undergoes a two-step commensurate-incommensuratetrar -ion. The details of this transition are still being investigated., LUCTURE OF XENON-ON-GRAPHITE7enon provides an interesting contrast with krypton-on-graphite in that the solid- on-interatomic spacing lies intermediate between the graphite (0001) NJ- X Nf3 and2 superlattices. XWe find that xenon for nearly all coverages and temperatures forms: incommensurate, iflating solid hexagonal overlayer. We have carried out a detailedstudy of the two-dins ' lonal solid-liquid-gas coexistence near the triple point at 99 K.;ar experiments confirn that a triple point may indeed exist in two dimensions, in con-trast to much tieoretical speculation to the contrary. Ilowever, the ZD solid exhibitsanomalous ;ouirties; in particular, the solid-structure factor varies drastically ashe relativo a -iounts of 2D solid and vapor are varied. This may reflect a fundamentalinstabilit-, cf liie interfaces in two dimensions. Work on this most interesting systemis continu V! n3, NEiiTiC-SMIECTIC A TRANSMISSION IN BILAYERt> :CTIC-LIQUID CRYSTALSF, 'ennes has proposed an elegant model which establishes an isomorphism betweenthie Iratic-smectic A transition in liquid crystals and the normal metal-superconductortransition in metals. However, because the liquid-crystal interactions are short-range,one should observe true critical behavior rather than mean-field behavior as in a super-conductor. We have carried out a detailed study of the mass-density critical fluctuationsin three bilayer smectic-liquid crystals CBOOA, 8OCB, and 8CB.2 In all cases boththe smectic susceptibility and the longitudinal correlation length exhibit helium(d = 3,n = 2)-like critical behavior as predicted by de Gennes. However, the transverse cor-relation length appears to diverge more weakly, probably due to the highly anisotropicelastic forces in the liquid crystal.4. THE NATURE OF SMECTIC B LIQUID CRYSTALSSmectic B liquid crystals constitute one of the most mysterious phases of condensedmatter. These systems exhibit considerable positional order in all three dimensions,yet they have a number of liquidlike properties which distinguish them from conventionalsolids. No rigorous model for this phase has yet been proposed. However, an importantclue may have been provided by IIalperin and Nelson who show that in two dimensionsPR No. 121(VII. X-RAY DIFFUSE SCATTERING)melting may occur in two stages with the solid first losing its positional long-range orderat T 1 and its orientational order at a higher temperature T 2 . The intermediate phasehas been labelled "hexatic." We have proposed a model 3 in which the smectic B essen-tially corresponds to stacked hexatic films. We have shown that this model appears tobe consistent with all available data. High-resolution x-ray experiments are now underway to test a number of the predictions of our model.References1. P. nI. Horn, R. J. Birgeneau, P. Heiney, and E. nI. Hammonds, "Melting of Sub-monolayer Krypton on Graphite, " Phys. Rev. Lett. 41, 961 (1978).2. J. D. Litster, J. Als-Nielsen, R. J. Birgeneau, S. S. Dana, D. Davidov, F. Garcia-Golding, Al. Kaplan, C. R. Safinya, and R. Schaetzing, "High Resolution X-ray andLight Scattering Studies of Bilayer Smectic A Compounds, " Proceedings of theBordeaux Liquid Crystal Conference, 1978.3. R. J. Birgeneau and J. D. Litster, "Bond Orientational Order MIodel for Smectic BLiquid Crystals, " J. de Physique 39, L-399 (1978).PR No. 121

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

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

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

Contains research summary and reports on five research projects.Joint Services Electronics Program (Contract DAAG29-78-C-0020)Joint Services Electronics Program (Contract DAAG29-80-C-0104

VII. X-RAY DIFFUSE SCATTERINGAcademic and Research StaffProf. R.J. BirgeneauDr. A.R. KortanDr. P.W. Stephens*Graduate StudentsG. Aeppli P.A. Heiney S.G.J. MochrieJ.A. Collett M.C. Kaplan B.M. OckoE.M. Hammonds L. Martinez-Miranda C.R. SafinyaJoint Services Electronics Program (Contracts DAAG29-78-C-0020 andDAAG29-80-C-0104)Robert J. BirgeneauThis research program centers around a two-spectrometer x-ray diffuse-scattering system based on a Rigaku 12-kW rotating-anode x-ray generator. Theapparatus is designed in such a way that one may easily tailor the instrumentalresolution function to optimize studies of structure and fluctuations in a vastrange of physical systems. Angular resolution of 1.8 seconds of arc and sampletemperature control of 2 mK between 10 K and 500 K are available. We haveimplemented a position-sensitive detection system to allow rapid scans over awide range of scattering angles, again with continuously variable resolution.Our current research program emphasizes structure and melting transitions bothfor monolayer physiadsorbed films on graphite and for layered liquid crystals.The surface experiments involve in situ high-precision vapor-pressure and surface-coverage measurements. Experiments are also performed using the x-ray synchro-tron facilities at D.E.S.Y. (Hamburg, Germany) and S.L.A.C. (Stanford). We arecurrently designing a two-spectrometer high-resolution x-ray system to be per-manently located at the National Synchrotron Light Source under construction atBrookhaven National Laboratory.Now at Department of Physics, S.U.N.Y., Stony Brook, N.Y.PR No. 123(VII. X-RAY DIFFUSE SCATTERING)1. MELTING AND THE COMMENSURATE-INCOMMENSURATE TRANSITION OFMONOLAYER KRYPTON ON GRAPHITEWe have effected an improvement by more than an order of magnitude of ourstudies of the structure and transitions of monolayer krypton on graphite by theuse of x-ray synchrotron radiation techniques. The intensity and geometry of the-4 o-1synchrotron beam allows a resolution of 3.5 x 10 A , corresponding to a par-ticle size of about 1 micron, with reasonable diffraction signals from one mono-layer. We show that for ZYX graphite as a substrate the intrinsic krypton over-layer particle size is 2300 A. We find that, at one monolayer covering, themelting transition appears to be second order at 112.9 K with an order parameterexponent 3 = 0.065 + 0.015 and a broadening of Tc, o/<Tc> %0.0006 which we at-tribute to finite size. Although the broadening is much-less than that obtainedin coarser resolution experiments, the exponent B agrees with those previousresults. Our most dramatic results are for the commensurate-incommensuratetransition. We find that in the weakly incommensurate phase, the structurefactor is that of a well-correlated liquid. This obtains for temperatures farbelow the expected melting temperature. We speculate that this is due to a melt-ing of the domain-wall lattice. Recent theories, stimulated by this research,1-3support this view. This work appears in several publications.2. MELTING OF 1.2 MONOLAYER XENON ON GRAPHITEXenon on graphite appears to provide a model example of continuous symmetrymelting in two dimensions, albeit with a directional-ordering field from thesubstrate. Our previous work has shown that the melting transition is firstorder in the submonolayer region. 3 We have carried out an exhaustive study usingx-ray diffraction techniques of the melting transition in the 1 to 1.5 monolayerregion. We find that the solid phase is well described by a sharp Lorentzianline shape indicative of a 1/q2 Landau-Peierls diffraction peak.3 In the liquidphase we again obtain a Lorentzian profile, albeit with a measurable width. Theevolution between these two profiles is continuous, as would be expected for asecond-order transition. However, because of uniqueness problems, we can onlyPR No. 123(VII. X-RAY DIFFUSE SCATTERING)assert that the melting transition is nearly second order with a minimum liquidcorrelation length at melting of 50 A. Much higher resolution measurements usingsynchrotron radiation techniques will be required to make a stronger statement.Such experiments are now scheduled at S.S.R.L.3. STRUCTURE, PHASE DIAGRAM AND TRANSITIONS OF MONOLAYER ANDBILAYER MOLECULAR OXYGEN ON GRAPHITEOxygen adsorbs onto graphite in the molecular state; the oxygen molecule isunique among homonuclear diatomic species in that it is paramagnetic with spinS = 1. The interplay between the magnetic, orientational, and structural degreesof freedom make both 3d and 2d oxygen rich and quite subtle. Previously, sus-ceptibility and neutron-scattering studies of monolayer and bilayer oxygen ongraphite have been performed. Both experiments suggest that oxygen solidifiesat about 30 K for a monolayer and 40 K for a bilayer. The neutron studies sug-gest that the structure is triangular with a nearest-neighbor intermolecularspacing close to that in the bulk, and concomitantly, incommensurate with thegraphite. The neutron studies also suggest that bilayer oxygen undergoes anantiferromagnetic transition at 11.9 K. We have carried out a detailed x-raystudy of the structure of monolayer and bilayer oxygen as a function of coveragefrom 0.5 to 2.5 monolayers and of temperature from 12 K to 50 K. We find evi-dence for at least four distinct phases, only one of which is triangular. Inparticular, the bilayer phase is only triangular within 2 K of melting, in ex-plicit contradiction with the neutron results. We have not yet managed to pro-duce an unambiguous model for the bilayer structure, although the data areconsistent with incommensurate successive layers. We find convincing evidencethat at monolayer coverage the oxygen molecules lie flat on the graphite surfacewith a simple centered rectangular unit cell. Work on this system is continuing.Our first set of results has been published.4PR No. 123(VII. X-RAY DIFFUSE SCATTERING)4. NEMATIC, SMECTIC A AND SMECTIC C PHASE TRANSITIONS ANDCRITICAL BEHAVIOR IN 8S5-7S5 MIXTURESWe have carried out a series of high-precision measurements of the nematic-smectic A, smectic A-smectic C, and nematic-smectic A-smectic C triple-pointcritical behavior in a mixture of 8S5 and 7S5. The triple point occurs at a con-centration of -42 mole % 7S5. The SmA-SmC transition is mean-fieldlike in pure8S5. However, near the N-A-C triple point there is a dramatic crossover from atilt-order parameter exponent of 1/2 to 1/3 indicating true critical behavior.This crossover is undoubtedly driven by the simultaneous loss of the mass-densityordering. We find that critical fluctuations in the nematic phase are welldescribed by a single Lorentzian for c 0.42 so that no unusual line-shape ef-fects occur near the N-A-C point; this explicitly contradicts our own expecta-tions and current theories. Away from the triple point we find single power-lawbehavior for the N-SmA transitions, albeit with exponents somewhat larger thanthose predicted by the superconducting analog model. However, in the vicinity ofc = 0.42, we find continuously evolving exponents as one approaches Tc(N-SmA)with asymptotic exponents close to those of the 3d xy model. We do not fullyunderstand these results. A letter and a full manuscript on this work are inpreparation.5. STRUCTURE OF WELL-ORDERED SMECTIC PHASESWe have carried out a number of diffuse x-ray scattering studies of thewell-ordered smectic phases in the liquid-crystalline materials, 40.8, 40.7,and 6.05. We find in each case that the so-called smectic B phases are, infact, extremely soft solids with three-dimensional positional long-range order.In 40.7 and 6.05 there are restacking transitions within the well-ordered phasesin which one goes from an ABAB--- to an ABCABC--- sequence. Unfortunately, wehave not yet identified unambiguously our predicted "stacked hexatic" liquidcrystal with orientational long-range order but positional short-range order.The work on 40.8 has been published.5PR No. 123(VII. X-RAY DIFFUSE SCATTERING)References1. R.J. Birgeneau, G.S. Brown, P.M. Horn, D.E. Moncton, and P.W. Stephens, J.Phys. C 14, L49 (1981).2. D.E. Moncton, P.W. Stephens, R.J. Birgeneau, P.M. Horn, and G.S. Brown, sub-mitted to Phys. Rev. Lett.3. R.J. Birgeneau, E.M. Hammonds, P. Heiney, P.W. Stephens, and P.M. Horn, inS.K. Sinha (Ed.), Ordering in Two Dimensions (Elsevier North Holland, Inc.,1980), pp. 29-38.4. P.W. Stephens, P. Heiney, R.J. Birgeneau, P.M. Horn, J. Stoltenberg, andO.E. Vilches, Phys. Rev. Lett. 45, 1959 (1980).5. P.S. Pershan, G. Aeppli, R.J. Birgeneau, and J.D. Litster, to appear in Mol.Cryst. and Liq. Cryst. (1981).PR No. 123

Contains research summary and 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, L.J. Martinez-Miranda, S.G.J. Mochrie,B.M. Ocko, C.R. Safinya, E. SpechtJoint Services Electronics Program (Contract DAAG29-80-C-0 104 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 made asfine as 1.8 seconds of arc; this enables one to probe the development of order from distances of the0 0order of the x-ray wavelength, -1 A, up to 30,000 A. The sample temperature may be varied between2 K and 500 K with a relative accuracy of 2 x 10' 3 K. We are currently designing and building a twospectrometer system to be installed at the National Synchrotron Light Source at Brookhaven NationalLaboratory. This will enable us to do high resolution scattering experiments with a flux more thanthree orders of magnitude larger than that from our rotating anode x-ray generator. This opens up anew generation of experiments. As part of this J.S.E.P. program we are designing and building anx-ray compatible high vacuum single crystal surface apparatus. This will enable us to usesynchrotron radiation to study the structure and transitions occurring at single surfaces. Thepossibilities with this seem virtually unlimited. Our current experiments in this program areconcentrated in two areas: (i) the structure and phase transitions of monolayer films of simple atomsand molecules physiadsorbed onto the basal planes of exfoliated graphite, (ii) the structure andphase transitions of smectic liquid crystals. We have also initiated some new experiments onintercalated graphite compounds. The initial results on this latter project are particularly promisingand we anticipate that this will expand into a major effort.5.1 Structure and Transitions of Rare Gas Atoms on GraphiteWe have carried out a series of high resolution x-ray scattering experiments at the StanfordSynchrotron Radiation Laboratory on monolayer krypton on graphite. Our emphasis has been on thecommensurate-incommensurate transition in which the krypton overlayer goes from being in registrywith the underlying graphite (specifically the V3 x V53 R 300 structure) to out of registry. Our initialRLE P.R. No. 124X-Ray Diffuse Scatteringexperiments 1 showed that in the weakly incommensurate phase. the structure is highly disordered;indeed we described it as a fluid state. This was initially considered quite controversial; however, anumber of theories have now appeared which justify our assertion. In order to probe this further, wehave carried measurements with quite high counting statistics. Detailed fits to the structure factor inthe "disordered" state show that it is well described by a Lorentzian as expected in a well-correlatedtwo-dimensional fluid. Many other possible models may be ruled out. We have also used thecommensurate krypton profile to characterize the quality of the surfaces in varied forms of exfoliatedgraphite. 2 We find that Union Carbide ZYX graphite has by far the largest surface coherence length.From previous work, including our own, it is known that for temperatures between 70 K and 150 K,monolayer xenon forms a simple triangular structure which "floats" on the graphite surface barelyrecognizing the substrate. It thus provides an ideal system for studies of continuous symmetryfreezing in two dimensions. Recent theory has suggested that the freezing transition could becontinuous in two dimensions, in start contrast to solidification in three dimensions which is alwaysstrongly first order from a poorly correlated liquid to an ordered solid. We have studied the monolayerxenon on graphite freezing transition both as a function of temperature and areal density using x-raysynchrotron radiation. 3 We find that for coverages above one monolayer, the freezing indeed occurscontinuously, with fluid correlation lengths exceeding one hundred atomic spacings. Further, we findthat a number of detailed predictions of the theory, which is based on the condensation of isolateddislocations into pairs, are confirmed. This represents the first unambiguous observation of secondorder freezing in two dimensions.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. In our recent work we have emphasized studies of binary mixtures of smectic liquidcrystal materials.The material octyloxy-p'-pentylphenyl thiolbenzoate (8 S5) exhibits as a function of decreasingtemperature nematic, smectic A and smectic C phases. By changing the aliphatic chain length by oneCH2 unit, one obtains a material, 7 S5, which has only nematic and smectic C phases. Notsurprisingly, as one adds 7 S5 to 8 S5 the temperature range over which the A phase exists isdecreased until for 8 S5.58 7 S5 the A range goes to zero. This point is called the NAC multicriticalpoint. We have studied the N-A and A-C critical behavior as a function of concentration up to theNAC point. We find that the behavior along the N-A and A-C lines is remarkably simple.4 The N-ARLE P.R. No. 124X-Ray Diffuse Scatteringtrarnilihon is characterized by I orentzian fluctuations with essentially ordinary critical behavior rightup to the NAC point. The A-C tilt transition exhibits a crossover from mean field behavior for pure 8S5 to conventional critical behavior at the NAC point. Much more exotic effects were anticipated fromthe existing theories. We have not yet understood why the observed behavior is so simple.A rather novel phenomenon which has attracted a great deal of attention in the liquid crystalcommunity is that of re-entrant nematic-smectic A behavior. In a bilayer material such asoctyloxycyano-biphenyl (80CB) as a function of decreasing temperature one has successivelynematic, smectic A and re-entrant nernatic (NRe) phases. This was initially considered quitesurprising since normally with decreasing temperature, systems go from less-ordered to more-ordered structures. In this case, however, the A-NRe transition represents the opposite evolution. Inorder to probe the physics underlying this unusual phenomenon, we have again studied binarymixtures. The material hexyloxycyanobiphenyl (60CB) exhibits only a nematic phase. Hence byadding 60 CB to 80 CB the temperature range over which the A-phase exists is decreased. At amolecular concentration ratio y = 0.427 of 60CB:80CB the A phase is first eliminated. We havestudied the smectic fluctuations in the upper and lower nematic phases for a series of concentrationsaround the critical value y = 0.427. We find that the N-A and A-NRe transitions are remarkably similar.This proves that the two nematic phases are in fact identical, that is, NRe does not represent a newstate of matter. We have constructed a simple theory for this behavior based on an idea of Pershanand Prost. In this theory one assumes that there is an optimal density for smectic A formation, andthat as the temperature is lowered due to thermal contraction one passes through this optimaldensity. Further, one assumes that the smectic A interactions decrease linearly with y, the amount of60 CB in the mixture, and quadratically with temperature about on optimum temperature T . Thevarious constants in the theory are fixed by the behavior in pure 80 CB and by critical concentrationYo = 0.427. This theory turns out to be remarkably successful in describing both the overall phasediagram and the detailed behavior of the smectic A fluctuations throughout the upper and lowernematic phases including concentrations y > yo. Thus the re-entrant phenomenon which initiallyappeared to be quite exotic can, in fact, be understood on rather simple physical grounds.References1. D.E. Moncton, P.W. Stephens, R.J. Birgeneau, P.M. Horn, and G.S. Brown, Phys. Rev. Lett.46, 1533(1981).2. R.J. Birgeneau, P.A. Heiney, and J.P. Pelz, Physica 109-11OB, 1785 (1982).3. P.A. Heiney, R.J. Birgeneau, G.S. Brown, P.M. Horn, D.E. Moncton, and P.W. Stephens, Phys. Rev.Lett. 48, 104 (1982).4. C.R. Safinya, R.J. Birgeneau, J.D. Litster, and M.E. Neubert, Phys. Rev. Lett. 47, 668 (1981).5. A.R. Kortan, H.V. Kanel, R.J. Birgeneau, and J.D. Litster, Phys. Rev. Lett. 47, 1206 (1981).RLE P.R. No. 124

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